Defs

📁 Source: Mathlib/Algebra/Field/Defs.lean

Statistics

Metric	Count
Definitions nnqsmul, qsmul, toDiv, toDivInvMonoid, toDivisionSemiring, toInv, toNNRatCast, toRatCast, toRing, zpow, DivisionSemiring, nnqsmul, toDiv, toGroupWithZero, toInv, toNNRatCast, toSemiring, zpow, nnqsmul, qsmul, toCommRing, toDiv, toDivisionRing, toInv, toNNRatCast, toRatCast, toSemifield, zpow, castRec, smulDivisionSemiring, castRec, smulDivisionRing, nnqsmul, toCommGroupWithZero, toCommSemiring, toDiv, toDivisionSemiring, toInv, toNNRatCast, zpow	40
Theorems div_eq_mul_inv, inv_zero, mul_inv_cancel, nnqsmul_def, nnratCast_def, qsmul_def, ratCast_def, toNontrivial, zpow_neg', zpow_succ', zpow_zero', div_eq_mul_inv, inv_zero, mul_inv_cancel, nnqsmul_def, nnratCast_def, toNontrivial, zpow_neg', zpow_succ', zpow_zero', div_eq_mul_inv, inv_zero, mul_inv_cancel, nnqsmul_def, nnratCast_def, qsmul_def, ratCast_def, toNontrivial, zpow_neg', zpow_succ', zpow_zero', cast_def, smul_def, smul_one_eq_cast, cast_def, cast_mk', ofScientific_eq_ofScientific, smul_def, smul_one_eq_cast, div_eq_mul_inv, inv_zero, mul_inv_cancel, nnqsmul_def, nnratCast_def, toNontrivial, zpow_neg', zpow_succ', zpow_zero'	48
Total	88

DivisionRing

Definitions

Name	Category	Theorems
nnqsmul 📖	CompOp	1 math math: nnqsmul_def
qsmul 📖	CompOp	1 math math: qsmul_def
toDiv 📖	CompOp	3 math math: div_eq_mul_inv, ratCast_def, nnratCast_def
toDivInvMonoid 📖	CompOp	700 math math: one_le_div_iff, WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero, DifferentiableOn.zpow, Set.preimage_mul_const_Ioo_of_neg, AddCircle.coe_equivIco_mk_apply, Lagrange.eval_iterate_derivative_eq_sum, AddCircle.exists_gcd_eq_one_of_isOfFinAddOrder, div_le_div_of_nonpos_of_le, strictConvexOn_iff_slope_strict_mono_adjacent, LinearMap.IsSymmetric.inner_map_polarization, selfAdjoint.val_div, zpow_eq_zpow_iff_of_ne_zero₀, Filter.Tendsto.div_atTop, Asymptotics.IsEquivalent.zpow, SimpleGraph.lapMatrix_toLinearMap₂', TendstoLocallyUniformlyOn.div₀, CauSeq.Completion.ofRat_div, RCLike.div_re_ofReal, NormedSpace.exp_zsmul, RootPairing.coroot_eq_polarizationEquiv_apply_root, Differentiable.fun_div, Function.FactorizedRational.divisor, Polynomial.isEquivalent_atBot_div, Lagrange.eval_interpolate_not_at_node', ContDiff.div_const, HasDerivWithinAt.div_const, abs_sub_round, differentiableAt_zpow, CancelDenoms.cancel_factors_eq_div, concaveOn_iff_slope_anti_adjacent, WeierstrassCurve.Jacobian.add_of_Y_ne', arithGeom_eq', MeasureTheory.lpNorm_fun_div_natCast, hasSum_choose_mul_geometric_of_norm_lt_one, WeierstrassCurve.Jacobian.dblX_of_Z_ne_zero, one_le_pow_mul_abs_eval_div, DifferentiableAt.div, Polynomial.div_tendsto_atTop_leadingCoeff_div_of_degree_eq, toIcoMod_eq_fract_mul, HasDerivWithinAt.fun_div, tendsto_zpow_nhdsNE_zero_cobounded, AnalyticWithinAt.fun_zpow, Asymptotics.isBigOWith_mul_iff_isBigOWith_div, Int.fract_div_mul_self_mem_Ico, WeierstrassCurve.Jacobian.Point.toAffine_of_Z_ne_zero, CancelDenoms.cancel_factors_le, Polynomial.div_tendsto_atBot_leadingCoeff_div_of_degree_eq, Set.preimage_mul_const_Iio_of_neg, Int.ceil_div_ceil_inv_sub_one, div_le_iff_of_neg, geom₂_sum, WeierstrassCurve.Projective.equiv_some_of_Z_ne_zero, IsRealClosed.exists_eq_zpow_of_isSquare, StrictConcaveOn.slope_anti_adjacent, Subring.center.coe_div, sum_smul_minpolyDiv_eq_X_pow, Int.cast_div_ofNat_charZero, Submodule.starProjection_singleton, Rat.cast_mk', same_sub_div, div_sub_same, tsum_coe_mul_geometric_of_norm_lt_one, WeierstrassCurve.Jacobian.negAddY_eq, IntermediateField.mem_adjoin_iff, Finpartition.IsEquipartition.card_biUnion_offDiag_le', Set.preimage_const_mul_Ioc_of_neg, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', iteratedDeriv_div_const, div_nonneg_of_nonpos, WeierstrassCurve.Projective.Y_eq_iff', tendsto_bdd_div_atTop_nhds_zero, WeierstrassCurve.Projective.nonsingular_of_Z_ne_zero, DifferentiableAt.zpow, MeasureTheory.integral_div, iter_deriv_zpow', WeierstrassCurve.Jacobian.negY_of_Z_ne_zero, CancelDenoms.cancel_factors_lt, zpow_two_nonneg, div_two_sub_self, IsFractionRing.mk'_eq_div, Polynomial.div_tendsto_zero_iff_degree_lt, Differentiable.zpow, Asymptotics.isBigO_iff_div_isBoundedUnder, Submodule.reflection_singleton_apply, intervalIntegral.integral_div, TendstoLocallyUniformlyOn.fun_div₀, deriv_fun_inv'', Polynomial.abs_div_tendsto_atTop_of_degree_gt, NormedSpace.expSeries_apply_eq_div', zpow_neg_two_nonneg, Even.zpow_abs, WeierstrassCurve.Projective.dblU_eq, WeierstrassCurve.Projective.Point.toAffineLift_of_Z_ne_zero, le_one_div_of_neg, Height.mulHeight₁_zpow, AddCircle.isOfFinAddOrder_iff_exists_rat_eq_div, Lagrange.coeff_eq_sum, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, DifferentiableAt.fun_div, meromorphicOrderAt_ne_top_iff, Odd.neg_one_zpow, zpow_eq_neg_zpow_iff₀, affineHomeomorph_symm_apply, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop, Asymptotics.IsLittleO.tendsto_div_nhds_zero, div_neg_iff, Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt, div_le_one_iff, Derivation.leibniz_div, GenContFract.abs_sub_convergents_le', GenContFract.compExactValue_correctness_of_stream_eq_some_aux_comp, IntermediateField.div_mem, arithGeom_zero_eq_mul_div', Odd.zpow_nonpos_iff, nnnorm_div, WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, HasStrictDerivAt.div, NormedSpace.exp_eq_tsum_div, mul_sub_mul_div_mul_nonpos_iff, Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt, derivWithin_zpow, sub_half_lt_round, Meromorphic.div, GenContFract.convs'_succ, uniformContinuous_div_const', WeierstrassCurve.Projective.addY_of_Z_ne_zero, rescale_to_shell_semi_normed_zpow, Lagrange.interpolate_eq_sum, Commute.inv_sub_inv, Valuation.map_div, Int.floor_div_natCast, ConvexOn.secant_mono_aux3, Asymptotics.div_isBoundedUnder_of_isBigO, RatFunc.mk_def, Quaternion.coe_zpow, WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero, ContDiffAt.div_const, RatFunc.mk_eq_div', RatFunc.ofFractionRing_div, Subfield.mem_closure_iff, FloorSemiring.tendsto_pow_div_factorial_atTop, ValuativeRel.div_vle_one_iff, inner_eq_norm_mul_iff_div, OnePoint.smul_some_eq_ite, selfAdjoint.val_zpow, WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, Set.preimage_const_mul_Ico_of_neg, Filter.Tendsto.atTop_div_const_of_neg, WeierstrassCurve.Affine.slope_of_Y_ne, Height.logHeight₁_div_eq_logHeight, Int.cast_negOnePow, ValuativeRel.div_vle_iff, div_le_div_right_of_neg, AnalyticOn.fun_zpow, Asymptotics.IsTheta.div, div_le_one_of_ge, deriv_fun_div, Function.FactorizedRational.mulSupport, WithAbs.tendsto_one_div_one_add_pow_nhds_one, Set.preimage_mul_const_uIcc, StrictConvexOn.secant_strict_mono_aux3, WeierstrassCurve.Affine.slope_of_Y_ne', Meromorphic.zpow, Finset.centerMass_insert, RCLike.div_im, Function.FactorizedRational.meromorphicOrderAt_eq, abs_one_div, Polynomial.div_tendsto_atBot_zero_of_degree_lt, isCoveringMap_zpow, GenContFract.conv_eq_conts_a_div_conts_b, Seminorm.rescale_to_shell_zpow, abs_div, derivWithin_fun_div, Set.image_div_const_uIcc, abs_sub_round_div_natCast_eq, Asymptotics.IsBigO.eventually_mul_div_cancel, Int.floor_div_cast_of_nonneg, ConvexOn.secant_mono_aux2, Function.FactorizedRational.finprod_eq_fun, Matrix.Pivot.listTransvecCol_getElem, StrictConcaveOn.secant_strict_mono, tsum_pow_div_one_sub_eq_tsum_sigma, div_neg_self, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, derivWithin_div_const, Matrix.projVandermonde_apply_of_ne_zero, div_lt_one_of_neg, ValuativeRel.one_vle_div_iff, AddCircle.addOrderOf_div_of_gcd_eq_one, Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero, WeierstrassCurve.Projective.negY_of_Z_ne_zero, neg_div_self, ConvexOn.slope_mono_adjacent, Set.preimage_mul_const_Iic_of_neg, Derivation.leibniz_zpow, Subfield.zpow_mem, Asymptotics.isBigO_mul_iff_isBigO_div, Odd.zpow_nonpos, WeierstrassCurve.Jacobian.dblXYZ_of_Z_ne_zero, Set.preimage_const_mul_Ioi_of_neg, logDeriv_div, WeierstrassCurve.Jacobian.addX_of_Z_ne_zero, zpow_two_pos_of_ne_zero, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, WeierstrassCurve.Affine.addX_eq_addX_negY_sub, div_lt_div_right_of_neg, WeierstrassCurve.Affine.slope_of_X_ne, inner_eq_sum_norm_sq_div_four, MeromorphicOn.div, tendsto_nat_floor_mul_div_atTop, ValuativeRel.one_rel_div_iff, Rat.cast_mkRat_of_ne_zero, DifferentiableOn.div_const, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, Int.fract_div_mul_self_add_zsmul_eq, div_le_one_of_neg, RCLike.im_eq_conj_sub, arithGeom_same_eq_mul_div', div_eq_quo_add_sum_rem_div, FiniteDimensional.basisSingleton_repr_apply, IsFractionRing.mk'_num_den', autEquivZmod_symm_apply_intCast, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, tendsto_pow_div_pow_atTop_zero, iter_deriv_zpow, toIcoMod_eq_add_fract_mul, toIocMod_eq_sub_fract_mul, IsFractionRing.div_surjective, geom_sum_eq, RCLike.conj_div, RCLike.ofReal_zpow, one_div_lt_neg_one, Odd.zpow_neg, tendsto_arithGeom_nhds_of_lt_one, concaveOn_iff_div, AnalyticOn.zpow_nonneg, one_div_le_one_div_of_neg, Differential.logDeriv_div, Filter.tendsto_div_const_atTop_of_neg, one_lt_div_of_neg, WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_ne_zero, CancelDenoms.cancel_factors_ne, NormedSpace.expSeries_div_hasSum_exp_of_mem_ball, Set.preimage_const_mul_Iio_of_neg, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, Odd.neg_zpow, WeierstrassCurve.Jacobian.addY_of_Z_ne_zero, ContDiffAt.div, Asymptotics.IsBigOWith.eventually_mul_div_cancel, iteratedDerivWithin_zpow, meromorphicOrderAt_eq_int_iff, quadratic_eq_zero_iff_of_discrim_eq_zero, WeierstrassCurve.Jacobian.dblY_of_Z_ne_zero, one_div_lt_of_neg, hasStrictDerivAt_zpow, tendsto_nat_floor_div_atTop, sub_div, one_lt_div_iff, WeierstrassCurve.Jacobian.X_eq_iff, le_div_iff_of_neg', div_le_iff_of_neg', IntermediateField.mem_adjoin_iff_div, Function.FactorizedRational.meromorphicNFOn_univ, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, HasStrictDerivAt.fun_div, Asymptotics.isLittleO_iff_tendsto', div_nonpos_iff, WeierstrassCurve.Jacobian.addMap_of_Z_ne_zero, Lagrange.leadingCoeff_eq_sum, DifferentiableWithinAt.div_const, iccHomeoI_apply_coe, div_lt_iff_of_neg, sum_Ioo_inv_sq_le, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, WeierstrassCurve.Projective.addZ_eq, RatFunc.liftRingHom_apply, Nat.cast_le_pow_sub_div_sub, AnalyticAt.fun_zpow, summable_pow_div_add, NormedSpace.expSeries_div_summable, tsum_choose_mul_geometric_of_norm_lt_one, NormedSpace.expSeries_apply_eq_div, MeromorphicOn.divisor_fun_zpow, logDeriv_apply, iteratedDerivWithin_one_div, norm_inner_eq_norm_tfae, DifferentiableWithinAt.fun_div, IsRealClosed.exists_eq_zpow_of_odd, Polynomial.isEquivalent_atTop_div, Nat.cast_choose_eq_descPochhammer_div, StrictConvexOn.slope_strict_mono_adjacent, Rat.cast_div, Rat.cast_div_of_ne_zero, RatFunc.liftRingHom_apply_div', groupCohomology.exists_div_of_norm_eq_one, GenContFract.convs_succ, Nat.div_two_lt_floor, arithGeom_eq, RCLike.re_eq_add_conj, Function.FactorizedRational.analyticAt, Quaternion.coe_div, round_eq, Asymptotics.superpolynomialDecay_iff_isLittleO, MeromorphicOn.divisor_zpow, jacobiSum_eq_gaussSum_mul_gaussSum_div_gaussSum, strictConcaveOn_iff_slope_strict_anti_adjacent, Commute.div_sub_div, logDeriv_id, one_div_mul_sub_mul_one_div_eq_one_div_add_one_div, GenContFract.convs'Aux_succ_some, circleEquivGen_symm_apply, Commute.geom_sum₂_Ico, HasDerivAt.fun_div, WeierstrassCurve.Projective.negDblY_of_Z_ne_zero, Lagrange.iterate_derivative_interpolate, Commute.geom_sum₂, Finpartition.coe_energy, deriv_zpow', FractionalIdeal.spanSingleton_div_spanSingleton, ConvexOn.secant_mono, HasDerivWithinAt.div, RatFunc.liftRingHom_apply_div, Mathlib.Meta.NormNum.isInt_zpow_pos, le_div_iff_of_neg, WittVector.exists_frobenius_solution_fractionRing, Padic.valuation_zpow, WeierstrassCurve.Affine.addY_sub_negY_addY, WeierstrassCurve.Projective.negMap_of_Z_ne_zero, CancelDenoms.cancel_factors_eq, SimpleGraph.unreduced_edges_subset, TendstoLocallyUniformly.div₀, inv_sub_inv, WeierstrassCurve.Projective.neg_of_Z_ne_zero, ContDiffOn.div, Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq, arithGeom_same_eq_mul_div, slope_def_field, ContDiffOn.fun_div, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, Meromorphic.fun_zpow, WeierstrassCurve.Projective.negDblY_eq, Set.preimage_const_mul_Ici_of_neg, quadratic_eq_zero_iff, Matrix.sub_scalar_sq_eq_disc, Set.preimage_mul_const_Ici_of_neg, Set.preimage_mul_const_Ioc_of_neg, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, StrictConvexOn.secant_strict_mono_aux2, deriv_inv'', IsFractionRing.mk'_mk_eq_div, logDeriv_id', lt_div_iff_of_neg, IntermediateField.mem_adjoin_range_iff, RatFunc.liftAlgHom_apply_div, WeierstrassCurve.Projective.addX_eq, NormedSpace.norm_expSeries_div_summable_of_mem_ball, hasSum_coe_mul_geometric_of_norm_lt_one, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, WittVector.RecursionBase.solution_spec, round_eq_zero_iff, MeromorphicOn.fun_zpow, toIocDiv_eq_neg_floor, WeierstrassCurve.Projective.Y_eq_iff, Asymptotics.superpolynomialDecay_iff_isBigO, AnalyticWithinAt.div_const, Filter.Tendsto.atBot_div_const, summable_norm_pow_mul_geometric_div_one_sub, OnePoint.smul_infty_eq_ite, Odd.zpow_nonneg_iff, ValuationSubring.top_coe_div, MeromorphicOn.zpow, AnalyticOnNhd.fun_zpow, Rat.cast_def, NormedField.continuousAt_zpow, AnalyticWithinAt.fun_zpow_nonneg, Polynomial.div_eq_quo_add_rem_div, Nat.one_sub_one_div_cast_nonneg, add_sub_div_two_lt, Set.preimage_const_mul_uIcc, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, Asymptotics.IsEquivalent.div, Rat.cast_divInt, AnalyticOn.zpow, Metric.unitSphere.coe_zpow, RatFunc.liftAlgHom_apply_ofFractionRing_mk, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational, NormedSpace.expSeries_div_summable_of_mem_ball, Mathlib.Tactic.RingNF.rat_rawCast_neg, div_lt_div_of_neg_of_lt, lt_div_iff_of_neg', AnalyticAt.hasFPowerSeriesAt, Height.logHeight₁_zpow, AnalyticOnNhd.zpow, FunctionField.inftyValuation.X_zpow, div_lt_iff_of_neg', deriv_zpow, Polynomial.C_div, derivWithin_inv', Filter.tendsto_div_const_atBot_of_neg, DifferentiableWithinAt.div, Int.sub_floor_div_mul_nonneg, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, DifferentiableOn.div, WeierstrassCurve.Jacobian.add_of_X_ne, AnalyticAt.exists_eq_sum_add_pow_mul, ValuativeRel.div_rel_one_iff, norm_div, InnerProductSpace.gramSchmidt_def'', WeierstrassCurve.Jacobian.Y_eq_iff', HasDerivWithinAt.inv, WeierstrassCurve.Projective.Point.toAffine_of_Z_ne_zero, Mathlib.Meta.NormNum.isRat_zpow_neg, AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div, AbsoluteValue.tendsto_div_one_add_pow_nhds_one, tendsto_nat_ceil_div_atTop, logDeriv_inv, half_sub, WittVector.StandardOneDimIsocrystal.frobenius_apply, UniformContinuous.div_const', Module.End.eigenspace_div, abs_neg_one_zpow, Asymptotics.IsTheta.zpow, RCLike.ofReal_div, WeierstrassCurve.Projective.X_eq_iff, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, tendsto_const_mul_zpow_atTop_zero, AnalyticWithinAt.div, WeierstrassCurve.Projective.dblY_of_Z_ne_zero, Set.preimage_mul_const_Ico_of_neg, RatFunc.liftRingHom_apply_ofFractionRing_mk, RootPairing.polarizationEquiv_symm_apply_coroot, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, Nat.one_sub_one_div_cast_le_one, LinearMap.BilinForm.IsSymm.polarization, max_div_div_right_of_nonpos, Int.fract_div_natCast_eq_div_natCast_mod, iter_deriv_inv, Odd.zpow_pos_iff, WeierstrassCurve.Affine.slope_of_Y_ne_eq_evalEval, ValuativeRel.vle_div_iff, SubfieldClass.toSubgroupClass, hasDerivWithinAt_zpow, Quaternion.normSq_zpow, Mathlib.Meta.NormNum.isRat_zpow_pos, WeierstrassCurve.Projective.negAddY_eq, AnalyticOnNhd.zpow_nonneg, iter_deriv_inv', rescale_to_shell_zpow, MeasureTheory.lpNorm_div_natCast, AnalyticWithinAt.zpow_nonneg, WeierstrassCurve.Jacobian.addX_eq, ArchimedeanClass.stdPart_div, WeierstrassCurve.Projective.add_of_X_ne, AnalyticOn.div, AnalyticAt.zpow_nonneg, QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff, NumberField.Units.coe_zpow, round_le_add_half, Odd.zpow_neg_iff, lineMap_one_half, NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop, deriv_div, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, convex_iff_div, HahnSeries.single_div_single, AnalyticOnNhd.div, pow_div_pow_eventuallyEq_atTop, MeromorphicOn.extract_zeros_poles, WeierstrassCurve.Projective.add_of_Y_ne', WeierstrassCurve.Jacobian.negAddY_of_Z_ne_zero, div_pos_iff, arithGeom_zero_eq_mul_div, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, Mathlib.Meta.NormNum.isRat_div, AnalyticOn.fun_zpow_nonneg, AnalyticWithinAt.zpow, ContDiffWithinAt.div, Asymptotics.isEquivalent_iff_tendsto_one, Even.zpow_pos_iff, Finset.centerMass_pair, one_div_lt_one_div_of_neg_of_lt, div_eq_quo_add_rem_div_add_rem_div, NormedSpace.expSeries_sum_eq_div, Filter.tendsto_div_const_atTop_iff_neg, lt_one_div_of_neg, RatFunc.liftAlgHom_apply, AddCircle.addOrderOf_eq_pos_iff, NormedSpace.expSeries_div_hasSum_exp, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, Module.End.genEigenspace_div, IntermediateField.mem_adjoin_simple_iff, Set.preimage_const_mul_Ioo_of_neg, MeromorphicOn.fun_div, HasDerivAt.div_const, pow_div_pow_eventuallyEq_atBot, WeierstrassCurve.Projective.addMap_of_Z_ne_zero, AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', WeierstrassCurve.Jacobian.nonsingular_of_Z_ne_zero, ValuativeRel.div_rel_iff, RCLike.normSq_div, Asymptotics.SuperpolynomialDecay.param_zpow_mul, one_div_le_of_neg, AnalyticAt.fun_div, Function.FactorizedRational.extractFactor, Polynomial.div_tendsto_atTop_zero_of_degree_lt, Nat.cast_choose_two, strictConcaveOn_iff_div, Hyperreal.coe_div, IsRealClosed.exists_eq_zpow_of_nonneg, HasDerivAt.div, HasDerivAt.continuousAt_div, geom_sum_Ico', tendsto_const_mul_zpow_atTop_nhds_iff, Polynomial.div_tendsto_zero_of_degree_lt, Set.preimage_mul_const_Icc_of_neg, AnalyticOnNhd.div_const, norm_zpow, Differentiable.div_const, toIcoDiv_eq_floor, QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff, logDeriv_fun_zpow, Asymptotics.SuperpolynomialDecay.mul_param_zpow, tendsto_nat_ceil_mul_div_atTop, one_div_le_neg_one, div_sub_div_same, StrictConvexOn.secant_strict_mono, ContDiffOn.div_const, AddCircle.nsmul_eq_zero_iff, MeromorphicAt.zpow, AbsoluteValue.tendsto_div_one_add_pow_nhds_zero, Metric.unitSphere.coe_div, Subfield.div_mem, sub_one_div_inv_le_two, MeasureTheory.Integrable.div_const, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Filter.Tendsto.const_div_atTop, WittVector.RecursionBase.solution_pow, Filter.tendsto_div_const_atBot_iff, iter_deriv_inv_linear_sub, WittVector.exists_frobenius_solution_fractionRing_aux, DifferentiableWithinAt.zpow, Set.preimage_mul_const_Ioi_of_neg, IntermediateField.pow_mem, meromorphicOrderAt_zpow, div_nonneg_iff, RatFunc.liftAlgHom_apply_div', AnalyticAt.div_const, WeierstrassCurve.Jacobian.negDblY_of_Z_ne_zero, AddCircle.addOrderOf_period_div, MeromorphicAt.div, sub_half, one_div_lt_one_div_of_neg, Even.zpow_nonneg, round_eq_iff, derivWithin_div, Asymptotics.isLittleO_iff_tendsto, TendstoLocallyUniformly.fun_div₀, Filter.tendsto_div_const_atTop_iff, div_sub_one, Set.preimage_div_const_uIcc, Height.mulHeight₁_div_eq_mulHeight, AddValuation.map_div, Subfield.coe_div, Polynomial.leadingCoeff_div, tendsto_pow_div_pow_atTop_atTop, NormedSpace.norm_expSeries_div_summable, slope_fun_def_field, div_sub', AddCircle.addOrderOf_div_of_gcd_eq_one', WeierstrassCurve.Jacobian.Y_eq_iff, HasStrictDerivAt.div_const, HasDerivAt.fun_inv, DifferentiableAt.div_const, one_le_div_of_neg, AnalyticOnNhd.fun_zpow_nonneg, Asymptotics.IsLittleO.eventually_mul_div_cancel, Rat.cast_zpow, Affine.Triangle.prod_div_one_sub_eq_one_of_mem_line_point_lineMap, iter_deriv_inv_linear, AnalyticAt.div, MeromorphicAt.fun_zpow, Set.preimage_const_mul_Icc_of_neg, DifferentiableOn.fun_div, RatFunc.div_def, Filter.Tendsto.div_atBot, WeierstrassCurve.Jacobian.neg_of_Z_ne_zero, Mathlib.Meta.NormNum.isInt_zpow_neg, Module.Basis.traceDual_powerBasis_eq, ConcaveOn.slope_anti_adjacent, Derivation.leibniz_div_const, AddCircle.intCast_div_mul_eq_zsmul, RCLike.div_re, div_neg_of_neg_of_pos, Filter.Tendsto.const_div_atBot, WeierstrassCurve.Projective.dblX_eq, WeierstrassCurve.Projective.addX_of_Z_ne_zero, Positive.coe_zpow, MeromorphicAt.fun_div, zpow_eq_one_iff_cases₀, Int.div_two_lt_floor, differentiableWithinAt_zpow, AnalyticAt.fun_zpow_nonneg, Nat.cast_le_pow_div_sub, ArchimedeanClass.mk_div, div_sub_div, convexOn_iff_div, zpow_eq_zpow_iff_cases₀, isCoveringMapOn_zpow, AnalyticOn.div_const, Filter.tendsto_div_const_atBot_of_pos, GenContFract.sub_convs_eq, strictConvexOn_iff_div, GenContFract.squashSeq_nth_of_not_terminated, geom_sum_Ico, one_sub_div, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, geom_sum₂_Ico, mul_sub_mul_div_mul_neg_iff, WeierstrassCurve.j_of_isShortNF, div_lt_one_iff, one_div_le_one_div_of_neg_of_le, min_div_div_right_of_nonpos, WeierstrassCurve.Projective.negAddY_of_Z_ne_zero, WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero, derivWithin_fun_inv', GenContFract.conv_eq_num_div_den, Meromorphic.fun_div, hasDerivAt_zpow, convexOn_zpow, WeierstrassCurve.Jacobian.equation_of_Z_ne_zero, WeierstrassCurve.Projective.dblX_of_Z_ne_zero, sub_div', sub_self_div_two, PadicInt.unitCoeff_coe, abs_zpow, lineMap_slope_slope_sub_div_sub, Int.cast_div_charZero, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, nnnorm_zpow, Int.cast_div, Quaternion.normSq_div, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational_off_support, Asymptotics.isLittleO_mul_iff_isLittleO_div, Matrix.sub_scalar_sq_eq_discr, MeromorphicAt.meromorphicTrailingCoeffAt_zpow, logDeriv_pow, ValuativeRel.rel_div_iff, WeierstrassCurve.j_of_isCharTwoJNeZeroNF_of_char_two, Complex.sum_div_factorial_le, div_pos_of_neg_of_neg, Padic.norm_p_zpow, Rat.cast_divInt_of_ne_zero, zpow_eq_one_iff_of_ne_zero₀, starConvex_iff_div, Filter.tendsto_div_const_atBot_iff_neg, Module.End.eigenspace_aeval_polynomial_degree_1, inv_eq_of_aeval_divX_ne_zero, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, FractionRing.mk_eq_div, logDeriv_zpow, AnalyticAt.zpow, ValuativeRel.ValueGroupWithZero.mk_eq_valuation, geom_sum_Ico_le_of_lt_one, Differentiable.div, deriv_div_const, ContDiffWithinAt.div_const, homothety_one_half, Set.preimage_const_mul_Iic_of_neg, WeierstrassCurve.Jacobian.neg_of_Z_eq_zero, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, IsFractionRing.lift_mk', WeierstrassCurve.j_of_isCharThreeJNeZeroNF_of_char_three, Field.mod_eq, Int.sub_floor_div_mul_lt, HasDerivAt.inv, IntervalIntegrable.div_const, Matrix.Pivot.listTransvecRow_getElem, exists_div_btwn, Int.fract_div_intCast_eq_div_intCast_mod, GenContFract.abs_sub_convs_le, div_neg_of_pos_of_neg, differentiableOn_zpow, HasDerivWithinAt.fun_inv, inv_eq_of_root_of_coeff_zero_ne_zero, zpow_eq_neg_one_iff₀, Function.FactorizedRational.meromorphicNFOn, AddCircle.gcd_mul_addOrderOf_div_eq, RCLike.div_I, ContDiff.div, circleEquivGen_apply, Filter.tendsto_div_const_atBot_iff_pos, AddCircle.natCast_div_mul_eq_nsmul, norm_inner_div_norm_mul_norm_eq_one_iff, WeierstrassCurve.Projective.equation_of_Z_ne_zero, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, Mathlib.Meta.NormNum.IsRat.neg_to_eq, Even.zpow_pos
toDivisionSemiring 📖	CompOp	609 math math: Pi.comul_eq_adjoint, absorbent_iff_eventually_nhdsNE_zero, FixedPoints.instFiniteDimensionalSubtypeMemSubfieldSubfield, Submodule.finrank_sup_add_finrank_inf_eq, Polynomial.natDegree_mul_leadingCoeff_inv, nnnorm_inv, NormedSpace.exp_neg_of_mem_ball, rank_fun_infinite, Rat.cast_inv_of_ne_zero, Submodule.disjoint_span_singleton', hasSum_geometric_of_norm_lt_one, Module.Basis.ofVectorSpaceIndex.linearIndependent, Subfield.rank_comap, Valuation.inversion_estimate', FixedPoints.finrank_eq_card, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, Bornology.isVonNBounded_iff_tendsto_smallSets_nhds, MeasureTheory.eLpNormEssSup_const_smul, Asymptotics.isBigO_const_smul_right, linearIndependent_option, Module.End.exists_ker_pow_eq_ker_pow_succ, linearIndepOn_iff_notMem_span, CauSeq.Completion.ofRat_inv, Rat.instSMulCommClass, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, TendstoLocallyUniformlyOn.inv₀, Subspace.instModuleDualFiniteDimensional, SeparationQuotient.mkCLM_comp_outCLM, IsNoetherian.iff_rank_lt_aleph0, Module.Basis.range_ofVectorSpace, Mathlib.Meta.NormNum.isRat_inv_pos, JacobsonNoether.exists_pow_mem_center_of_inseparable', hasSum_choose_mul_geometric_of_norm_lt_one, tsum_coe_mul_geometric_of_norm_lt_one', Subfield.comap_comap, CauSeq.inv_aux, map_ratCast_smul, Filter.inv_nhdsWithin_ne_zero, DifferentiableAt.fun_inv, NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded, LinearPMap.domain_supSpanSingleton, finrank_vectorSpan_image_finset_le, Subspace.dualLift_of_subtype, DilationEquiv.smulTorsor_symm_apply, Subspace.dualRestrict_comp_dualLift, Projectivization.map_id, diam_smul₀, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, Valuation.val_le_one_or_val_inv_lt_one, IsLocalRing.instIsLocalHomRingHomOfNontrivial, Bornology.isVonNBounded_pi_iff, FixedPoints.minpoly.eval₂', tsum_coe_mul_geometric_of_norm_lt_one, Projectivization.submodule_eq, Differentiable.fun_inv, inv_intCast_smul_eq, differentiableWithinAt_inv, Subfield.relfinrank_mul_finrank_top, finrank_vectorSpan_le_iff_not_affineIndependent, Asymptotics.IsBigO.smul, Polynomial.degree_mul_leadingCoeff_inv, RingHom.mem_fieldRange_self, LinearMap.le_rank_iff_exists_linearIndependent, Subfield.relfinrank_eq_finrank_of_le, AnalyticOn.fun_inv, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, LinearMap.isUnit_iff_range_eq_top, TendstoLocallyUniformlyOn.fun_inv₀_of_disjoint, lineMap_inv_two, Subring.center.coe_inv, isConjRoot_algHom_iff, Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff, TendstoLocallyUniformly.fun_inv₀, instNontrivialLinearMapId, Filter.inv_nhdsNE_zero, finrank_zero_iff_forall_zero, inv_intCast_smul_comm, tsum_geometric_of_norm_lt_one, FixedPoints.rank_le_card, egauge_univ, OrthonormalBasis.measurePreserving_repr, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, dist_inv_inv₀, tendsto_norm_inv_nhdsNE_zero_atTop, FiniteDimensional.span_of_finite, NormedSpace.expSeries_apply_eq_div', ContinuousLinearMap.finiteDimensional, linearIndependent_fin2, collinear_iff_of_mem, egauge_zero_zero, Matrix.conjTranspose_inv_intCast_smul, HahnEmbedding.Partial.truncLT_mem_range_extendFun, AffineIndependent.finrank_vectorSpan_add_one, Projectivization.finrank_submodule, Subfield.relrank_mul_rank_top, SubfieldClass.nnqsmul_mem, Pi.counit_eq_adjoint, DualNumber.inv_eps, RingHom.ker_isMaximal_of_surjective, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, Subspace.finrank_dualCoannihilator_eq, Asymptotics.isLittleO_pow_pow, Valuation.val_lt_one_iff, Rat.coe_castHom, uniqueDiffWithinAt_iff_accPt, Valuation.val_le_one_or_val_inv_le_one, NormedSpace.exp_eq_tsum_div, MulOpposite.finrank, EuclideanSpace.volume_closedBall_fin_three, GenContFract.convs'_succ, AffineIndependent.card_le_finrank_succ, balancedCore_mem_nhds_zero, Coplanar.finrank_le_two, Polynomial.irreducible_mul_leadingCoeff_inv, HahnEmbedding.Seed.strictMono_coeff, Bornology.isVonNBounded_iff_absorbing_le, Commute.inv_sub_inv, LinearEquiv.toSpanNonzeroSingleton_homothety, FiniteDimensional.finiteDimensional_quotient, instIsArtinianRing, Valuation.one_lt_val_iff, Subfield.coe_inv, Mathlib.Meta.NormNum.isNNRat_abs_neg, Filter.inv_cobounded₀, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, finrank_vectorSpan_insert_le, ContinuousMap.spectrum_eq_preimage_range, LinearMap.isUnit_iff_ker_eq_bot, SeparationQuotient.outCLM_uniformContinuous, linearIndepOn_id_insert_iff, Valuation.val_eq_one_iff, FDRep.instFiniteDimensionalHom, ratCast_smul_eq, MeasureTheory.integral_smul, nndist_inv_inv₀, PiLp.volume_preserving_toLp, Polynomial.cauchyBound_smul, IsNoetherian.range_finsetBasis, Submodule.finiteDimensional_sup, RingHom.coe_rangeRestrictField, LinearEquiv.mem_dilatransvections_iff_rank, finite_of_algHom_finiteType_of_isJacobsonRing, NormedSpace.exp_conj, JacobsonNoether.exists_pow_mem_center_of_inseparable, Rat.cast_inv_int, Subfield.finrank_comap, FiniteDimensional.span_finset, unitSphereToUnits_apply_coe, Polynomial.natDegree_mul_leadingCoeff_self_inv, infEDist_smul₀, Filter.tendsto_inv₀_cobounded, linearIndependent_fin_cons, norm_commutator_sub_one_le, absorbs_iff_eventually_nhdsNE_zero, LinearMap.mul_eq_one_comm, FixedPoints.finrank_le_card, Submodule.disjoint_span_singleton, egauge_le_one, Projectivization.cross_mk_of_cross_ne_zero, collinear_iff_finrank_le_one, AnalyticWithinAt.inv, Asymptotics.IsLittleO.smul, fderivWithin_inv', Module.finrank_eq_card_basis', Asymptotics.isLittleO_pow_id, MeasureTheory.Measure.hausdorffMeasure_smul₀, unitSphereToUnits_injective, EuclideanSpace.volume_closedBall_fin_two, SeparationQuotient.outCLM_isUniformEmbedding, le_egauge_smul_left, DualNumber.isMaximal_span_singleton_eps, Module.Basis.isMaxChain_range_flag, geom_sum_inv, UniformContinuousOn.fun_inv₀, DifferentiableOn.inv, nhds_basis_balanced, RingEquivClass.toLinearEquivClassRat, HahnEmbedding.IsPartial.truncLT_mem_range, star_ratCast_smul, IntermediateField.toSubfield_map, Polynomial.cauchyBound_C, FormalMultilinearSeries.radius_smul_eq, atom_iff_nonzero_span, Submodule.finrank_strictMono, DilationEquiv.mulRight_symm_apply, Mathlib.Meta.NormNum.isNNRat_ratCast, Asymptotics.IsLittleO.smul_isBigO, Asymptotics.isLittleO_const_smul_left, Rat.instSMulCommClass', Projectivization.submodule_mk, linearIndepOn_pair_iff, affineIndependent_iff_not_finrank_vectorSpan_le, DilationEquiv.mulLeft_symm_apply, CauSeq.coe_inv, RingHom.map_fieldRange, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, HahnEmbedding.Partial.truncLT_mem_range_sSupFun, geom_sum_eq, DilationEquiv.mulLeft_apply, DualNumber.exists_mul_left_or_mul_right, NumberField.place_apply, FGModuleCat.FGModuleCatCoevaluation_apply_one, Projectivization.independent_iff_iSupIndep, Subspace.dualRestrict_leftInverse, nonzero_span_atom, NormedSpace.expSeries_div_hasSum_exp_of_mem_ball, Asymptotics.isLittleO_const_smul_right, SubfieldClass.coe_nnqsmul, LinearEquiv.extendOfIsometry_symm_apply, star_inv_intCast_smul, Module.card_eq_pow_finrank, IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing, Subfield.coe_comap, infEdist_smul₀, LinearEquiv.mem_dilatransvections_iff_finrank, LinearMap.finiteDimensional', Finset.centroidWeights_apply, summable_powerSeries_of_norm_lt_one, AnalyticWithinAt.fun_inv, Subfield.subtype_apply, UniformContinuousOn.inv₀, PiLp.volume_preserving_ofLp, Subfield.relfinrank_top_right, exists_linearIndependent, HahnEmbedding.Partial.eval_smul, Submodule.finiteDimensional_inf_right, SeparationQuotient.exists_out_continuousLinearMap, CategoryTheory.finrank_hom_simple_simple_eq_zero_of_not_iso, Matrix.conjTranspose_ratCast_smul, RingHomClass.toLinearMapClassRat, DifferentiableAt.inv, NormedSpace.expSeries_div_summable, DifferentiableWithinAt.inv, Projectivization.mk_eq_mk_iff, Subfield.coe_one, tsum_choose_mul_geometric_of_norm_lt_one, NormedSpace.expSeries_apply_eq_div, Polynomial.degree_mul_leadingCoeff_self_inv, HahnEmbedding.ArchimedeanStrata.nontrivial_stratum, AffineIndependent.finrank_vectorSpan_image_finset, Projectivization.submodule_injective, LinearIsometryEquiv.toSpanUnitSingleton_apply, Asymptotics.IsBigOWith.smul, Mathlib.Meta.NormNum.isInt_inv_neg_one, DilationEquiv.smulTorsor_apply, intervalIntegral.integral_smul, Polynomial.cauchyBound_one, Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub, linearIndependent_fin_succ', Subfield.continuousSMul, IsSimpleRing.exists_algEquiv_matrix_divisionRing_finite, Configuration.ofField.instNondegenerateProjectivizationForallFinOfNatNat, DilationEquiv.mulRight_apply, Module.natCard_eq_pow_finrank, LinearMap.injective_iff_surjective, analyticAt_iff_analytic_fun_smul, Submodule.exists_fun_fin_finrank_span_eq, NormedSpace.exp_conj', Module.Basis.flag_covBy, LinearEquiv.extendOfIsometry_apply, Algebra.IsAlgebraic.algHom_bijective₂, affineIndependent_iff_le_finrank_vectorSpan, Subspace.quotAnnihilatorEquiv_apply, Commute.geom_sum₂_Ico, Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, SeparationQuotient.mk_outCLM, Commute.geom_sum₂, FiniteDimensional.finiteDimensional_self, Subfield.coe_subtype, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, Matrix.l2_opNNNorm_def, Filter.tendsto_inv₀_nhdsWithin_ne_zero, continuousConstSMul_rat, norm_inv, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, Polynomial.dvd_mul_leadingCoeff_inv, LinearMap.finiteDimensional, inv_eq_self₀, FiniteDimensional.finiteDimensional_pi', infDist_smul₀, linearIndependent_fin_snoc, OnePoint.equivProjectivization_symm_apply_mk, ContinuousLinearMap.isVonNBounded_iff, Subfield.pow_mem, le_egauge_smul_right, AnalyticOn.inv, GenContFract.of_s_head, AffineBasis.coord_apply_centroid, LinearMap.toSpanSingleton_homothety, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, IntermediateField.finiteDimensional_adjoin, Real.circleAverage_fun_smul, Projectivization.exists_smul_eq_mk_rep, TendstoLocallyUniformly.fun_inv₀_of_disjoint, NormedDivisionRing.to_continuousInv₀, Subspace.finrank_add_finrank_dualCoannihilator_eq, Subfield.inv_mem, exists_linearIndependent', IsNoetherian.iff_fg, DifferentiableOn.fun_inv, Real.circleAverage_smul, NormedSpace.norm_expSeries_div_summable_of_mem_ball, LinearMap.opNorm_extendOfNorm_le, FiniteDimensional.finiteDimensional_submodule, hasSum_coe_mul_geometric_of_norm_lt_one, Metric.unitSphere.coe_inv, Module.Basis.coe_ofVectorSpace, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, SeparationQuotient.postcomp_mkCLM_surjective, EuclideanSpace.volume_ball_fin_three, linearIndepOn_id_pair, linearIndependent_fin_succ, LinearIndependent.pair_iff', TendstoLocallyUniformlyOn.inv₀_of_disjoint, NumberField.finite_of_discr_bdd, UniformContinuous.inv₀, MeasureTheory.eLpNorm'_const_smul, Subfield.relrank_dvd_rank_top_of_le, SeparationQuotient.mk_comp_outCLM, OrthonormalBasis.measurePreserving_repr_symm, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, Valuation.map_inv, analyticAt_iff_analytic_smul, Subfield.map_map, RingHom.coe_fieldRange, collinear_iff_rank_le_one, Submodule.mem_projectivization_iff_submodule_le, RingHom.rangeRestrictFieldEquiv_apply_symm_apply, TrivSqZeroExt.inv_neg, Rat.cast_smul_eq_qsmul, Rat.cast_inv, isSimpleModule_iff_finrank_eq_one, hasFPowerSeriesOnBall_inv_one_sub, LinearPMap.supSpanSingleton_apply_smul_self, InfiniteGalois.isOpen_iff_finite, FiniteDimensional.finiteDimensional_pi, NormedSpace.expSeries_div_summable_of_mem_ball, Subspace.dualAnnihilator_iInf_eq, Module.Basis.flag_wcovBy, MeasureTheory.eLpNorm_const_smul, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', Matrix.toEuclideanLin_conjTranspose_eq_adjoint, Asymptotics.IsBigO.inv_rev, Projectivization.orthogonal_mk, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, Projectivization.cross_mk, AffineIndependent.finrank_vectorSpan, Projectivization.dependent_iff, IsClosed.balancedCore, nhds_basis_closed_balanced, HahnEmbedding.ArchimedeanStrata.iSupIndep_stratum', Subfield.relrank_top_right, AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_one, balancedCoreAux_subset, Asymptotics.IsLittleO.inv_rev, EuclideanSpace.volume_ball_fin_two, GenContFract.of_s_tail, Projectivization.smul_def, Polynomial.cauchyBound_zero, Subfield.relrank_eq_rank_of_le, Subspace.dualEquivDual_def, AffineBasis.card_eq_finrank_add_one, EuclideanSpace.volume_ball, Submodule.exists_finset_span_eq_linearIndepOn, RingHom.rangeRestrictField_bijective, Polynomial.monic_mul_leadingCoeff_inv, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, inv_sub_inv', AccPt.uniqueDiffWithinAt, Subspace.dualLift_rightInverse, Subfield.closure_preimage_le, Complex.uniformContinuous_ringHom_eq_id_or_conj, egauge_eq_zero_iff, OnePoint.smul_infty_def, analyticOn_inv, NormedDivisionRing.toNormSMulClass, Polynomial.degree_add_degree_leadingCoeff_inv, Submodule.exists_isCompl, ediam_smul₀, IntermediateField.exists_lt_finrank_of_infinite_dimensional, CauSeq.inv_apply, lineMap_one_half, self_eq_inv₀, TendstoLocallyUniformlyOn.fun_inv₀, Submodule.finrank_add_le_finrank_add_finrank, NormedSpace.exp_neg, Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero, Subfield.relfinrank_dvd_finrank_top_of_le, Collinear.finrank_le_one, Matrix.toLin_finTwoProd_toContinuousLinearMap, IntermediateField.finiteDimensional_left, Matrix.finiteDimensional, Padic.isUniformInducing_cast_withVal, TendstoLocallyUniformly.inv₀_of_disjoint, DualNumber.instIsLocalRing, HahnEmbedding.ArchimedeanStrata.archimedean_stratum, FiniteGaloisIntermediateField.finiteDimensional, Submodule.complementedLattice, nnnorm_commutator_sub_one_le, summable_geometric_iff_norm_lt_one, NormedSpace.expSeries_sum_eq_div, TendstoLocallyUniformly.inv₀, AnalyticAt.fun_inv, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, AddAction.automorphize_smul_left, NormedSpace.expSeries_div_hasSum_exp, MeasureTheory.integrable_smul_iff, GenContFract.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero, Finset.centroid_pair, krullTopology_mem_nhds_one_iff, Module.Basis.ofVectorSpace_apply_self, Affine.Simplex.point_vsub_centroid_eq_smul_vsub, Projectivization.instFiniteDimensionalSubtypeMemSubmoduleSubmodule, linearIndependent_iff_notMem_span, Submodule.fg_iff_finiteDimensional, JacobsonNoether.exists_separable_and_not_isCentral', max_aleph0_card_le_rank_fun_nat, Module.finrank_eq_rank', Subspace.dualLift_injective, krullTopology_mem_nhds_one_iff_of_normal, finiteDimensional_bot, geom_sum_Ico', LinearPMap.mkSpanSingleton_apply, Module.finrank_of_infinite_dimensional, QuotientGroup.automorphize_smul_left, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, Module.Free.of_divisionRing, volume_euclideanSpace_eq_dirac, RingHom.map_field_closure, Subfield.lift_rank_comap, Mathlib.Meta.NormNum.isRat_inv_neg, Projectivization.cross_mk_of_ne, Padic.coe_withValRingEquiv_symm, finrank_span_singleton, IntermediateField.adjoin.finiteDimensional, MulOpposite.instFiniteDimensional, uniformContinuousOn_inv₀, Rat.cast_inv_nat, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, isDomain, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, absorbs_iff_eventually_nhds_zero, exists_extension_norm_eq, Subspace.dualAnnihilator_le_dualAnnihilator_iff, Module.Basis.exists_basis, SeparationQuotient.isEmbedding_outCLM, Module.length_eq_finrank, RingHom.mem_fieldRange, Module.Dual.finrank_ker_add_one_of_ne_zero, Finset.centroid_pair_fin, Polynomial.degree_leadingCoeff_inv, MulAction.automorphize_smul_left, Asymptotics.IsBigOWith.inv_rev, LinearMap.exists_extend, affineIndependent_iff_finrank_vectorSpan_eq, Finset.centroidWeights_eq_const, analyticAt_inv, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_divisionRing, QuotientAddGroup.automorphize_smul_left, LinearMap.ker_eq_bot_iff_range_eq_top, IsIntegral.inv, le_egauge_of_forall_ne_zero, Module.Basis.mem_toFlag, NormedSpace.norm_expSeries_div_summable, rank_quotient_add_rank_of_divisionRing, IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing_finite, linearIndepOn_insert, Polynomial.cauchyBound_X_add_C, collinear_iff_exists_forall_eq_smul_vadd, FiniteDimensional.instSubtypeMemSubmoduleMap, hasStrictFDerivAt_inv', RingHom.fieldRange_eq_top_iff, LinearMap.BilinForm.toLin_restrict_ker_eq_inf_orthogonal, analyticAt_inv_one_sub, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, Asymptotics.isBigO_const_smul_left, Projectivization.generalLinearGroup_smul_def, HahnEmbedding.Partial.eval_eq_truncLT, finrank_eq_one_iff_of_nonzero, Module.End.ker_pow_le_ker_pow_finrank, linearIndependent_option', linearIndepOn_id_insert, Quaternion.coe_ofComplex, LinearMap.rank_add_le, Polynomial.qsmul_eq_C_mul, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, Module.Basis.toFlag_carrier, Polynomial.cauchyBound_X_sub_C, GenContFract.IntFractPair.exists_succ_nth_stream_of_fr_zero, instIsAtomisticSubmodule, RingHom.mem_eqLocusField, Valuation.one_le_val_iff, DualNumber.ideal_trichotomy, finrank_vectorSpan_range_add_one_le, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, exists_eq_smul_of_parallel, CauSeq.const_inv, Projectivization.cross_mk_of_cross_eq_zero, analyticOnNhd_inv, Subfield.mem_map, NormedDivisionRing.to_hasContinuousInv₀, Submodule.finrank_lt, IntermediateField.finiteDimensional_map, Projectivization.mk_eq_mk_iff', OnePoint.equivProjectivization_apply_coe, Configuration.ofField.mem_iff, coplanar_iff_finrank_le_two, Filter.tendsto_inv₀_nhdsNE_zero, DifferentiableWithinAt.fun_inv, geom_sum_Ico, RingHom.rangeRestrictFieldEquiv_apply_coe, IsIntegral.inv_mem_adjoin, instNonemptySeedRatReal, LinearMap.BilinForm.finrank_add_finrank_orthogonal, Subfield.coe_map, egauge_smul_right, differentiableAt_inv, AnalyticAt.inv, Projectivization.independent_iff, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, LinearPMap.supSpanSingleton_apply_mk, hasFDerivAt_inv', RingHom.field_closure_preimage_le, Algebra.IsAlgebraic.bijective_of_isScalarTower, Subspace.map_dualCoannihilator, Polynomial.cauchyBound_X, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, HahnEmbedding.Partial.truncLT_eval_mem_range_extendFun, Subfield.subtype_injective, ContinuousLinearMap.isOpenMap_of_ne_zero, Matrix.l2_opNorm_def, Rat.cast_pow, MeasureTheory.integrable_fun_smul_iff, OrthonormalBasis.measurePreserving_measurableEquiv, Real.exists_extension_norm_eq, LinearMap.finrank_range_add_finrank_ker, algebraMap.coe_ratCast, finrank_eq_one_iff_of_nonzero', Submodule.wcovBy_span_singleton_sup, smul_inv'', enorm_inv, IsTopologicalDivisionRing.toContinuousInv₀, UniformConvergenceCLM.isVonNBounded_iff, DualNumber.instIsPrincipalIdealRing, ContinuousMap.isUnit_iff_forall_ne_zero, Differentiable.inv, linearIndepOn_insert_iff, Subspace.dualAnnihilator_inf_eq, IntermediateField.finiteDimensional_adjoin_pair, AnalyticOnNhd.fun_inv, quotient_prod_linearEquiv, egauge_zero_right, LinearMap.le_rank_iff_exists_linearIndependent_finset, Valuation.val_le_one_iff, Quaternion.normSq_ratCast, EuclideanSpace.volume_closedBall, rat_inv_continuous_lemma, Subfield.inv_mem', SubfieldClass.toInvMemClass, Padic.isDenseInducing_cast_withVal, normalClosure.is_finiteDimensional, IntermediateField.finiteDimensional_sup, IsSimpleRing.exists_algEquiv_matrix_divisionRing, Affine.Simplex.faceOppositeCentroid_eq_affineCombination, Module.length_eq_rank, balancedCore_eq_iInter, HahnEmbedding.ArchimedeanStrata.iSupIndep_stratum, LinearMap.finiteDimensional_range, GenContFract.of_s_succ, Affine.Simplex.centroid_vsub_point_eq_smul_vsub, Submodule.finiteDimensional_inf_left, NNRat.instContinuousSMulRatReal, finrank_vectorSpan_insert_le_set, differentiableOn_inv, GenContFract.IntFractPair.succ_nth_stream_eq_some_iff, finiteDimensional_finsupp, UniformContinuous.fun_inv₀, Subspace.finrank_add_finrank_dualAnnihilator_eq, Set.finrank_mono, map_inv_intCast_smul, Filter.tendsto_inv₀_cobounded', balancedCoreAux_empty, Asymptotics.IsBigO.smul_isLittleO, Balanced.smul_mono, Valuation.inversion_estimate, Affine.Simplex.centroid_vsub_eq, LinearMap.instIsSimpleModuleEndOfNontrivial, GenContFract.IntFractPair.stream_succ_of_some, Subspace.dualPairing_eq, FiniteDimensional.span_singleton, finrank_vectorSpan_range_le, SeparationQuotient.outCLM_injective, LinearMap.instIsStablyFiniteRing, Subspace.dualEquivDual_apply, Subfield.mem_comap, OnePoint.equivProjectivization_apply_infinity, balancedCore_subset_balancedCoreAux, AnalyticOnNhd.inv, AddValuation.map_inv, GenContFract.IntFractPair.stream_succ, hahnEmbedding_isOrderedModule, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, fderiv_inv', SeparationQuotient.outCLM_isUniformInducing, egauge_smul_left
toInv 📖	CompOp	4 math math: mul_inv_cancel, zpow_neg', inv_zero, div_eq_mul_inv
toNNRatCast 📖	CompOp	22 math math: Rat.cast_nnratCast, HahnSeries.single_zero_ofScientific, Mathlib.Meta.NormNum.isNNRat_ofScientific_of_true, NNRat.intCeil_cast, RCLike.nnnorm_nnratCast, instLawfulOfScientificOfCharZero, SubfieldClass.coe_nnratCast, CauSeq.Completion.ofRat_nnratCast, nnqsmul_def, Quaternion.coe_nnratCast, RCLike.norm_nnratCast, RCLike.ofReal_nnratCast, Rat.cast_ofScientific, SubfieldClass.ofScientific_mem, NNRat.Nonneg.coe_ofScientific, selfAdjoint.val_nnratCast, SubfieldClass.nnratCast_mem, nnratCast_def, NNRat.cast_mk, Mathlib.Meta.NormNum.isNat_ofScientific_of_false, NNRat.intFloor_cast, Quaternion.re_nnratCast
toRatCast 📖	CompOp	186 math math: Padic.coe_neg, exists_rat_pow_btwn, Rat.cast_nnratCast, Rat.cast_inv_of_ne_zero, Rat.intCast_lt_cast, ArchimedeanClass.FiniteResidueField.mk_ratCast, SubfieldClass.ratCast_mem, Padic.eq_padicNorm, map_ratCast_smul, Rat.cast_intCast, CauSeq.Completion.ofRat_ratCast, Padic.coe_div, Rat.cast_comm, Rat.cast_mul, Rat.cast_finsupp_sum, Rat.cast_mk', Rat.cast_fract, Padic.coe_sub, GenContFract.exists_gcf_pair_rat_eq_nth_conts, le_iff_forall_rat_lt_imp_le, Quaternion.coe_ratCast, map_ratCast, Quaternion.ratCast_re, SimpleGraph.regularityReduced_adj, GenContFract.exists_rat_eq_of_terminates, GenContFract.exists_rat_eq_nth_num, Padic.coe_zero, LinearOrderedField.lt_inducedMap_iff, exists_rat_gt, AddCircle.isOfFinAddOrder_iff_exists_rat_eq_div, padicNormE.eq_padic_norm', DirectLimit.ratCast_def, Rat.intCast_le_cast, Rat.coe_castHom, Matrix.map_mul_ratCast, Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul, Rat.cast_inj, isAlgebraic_rat, ratCast_smul_eq, Rat.preimage_cast_Ioi, Rat.cast_add_of_ne_zero, Filter.Eventually.ratCast_atBot, Rat.cast_inv_int, Rat.preimage_cast_Icc, IsIntegral.ratCast_iff, Rat.cast_min, Rat.round_cast, padicNormE.defn, Rat.cast_list_prod, NumberField.InfinitePlace.map_ratCast, LinearOrderedField.cutMap_coe, Rat.floor_cast, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq, star_ratCast_smul, Rat.cast_lt_natCast, Rat.cast_mkRat_of_ne_zero, Rat.preimage_cast_Ico, Mathlib.Meta.NormNum.isNNRat_ratCast, Rat.cast_max, Rat.cast_lt_intCast, Padic.coe_mul, GenContFract.exists_gcf_pair_rat_eq_of_nth_contsAux, Rat.natCast_le_cast, Rat.cast_lt, SimpleGraph.nonuniformWitnesses_spec, Rat.preimage_cast_uIcc, SubfieldClass.coe_ratCast, Rat.comap_cast_atBot, GenContFract.terminates_iff_rat, Rat.cast_finsuppProd, ArchimedeanClass.FiniteElement.mk_ratCast, Matrix.conjTranspose_ratCast_smul, Rat.cast_multiset_prod, LinearOrderedField.coe_mem_cutMap_iff, SimpleGraph.not_isUniform_iff, Rat.cast_div, Rat.cast_div_of_ne_zero, Rat.cast_det, exists_rat_btwn, Padic.coe_inj, Padic.coe_one, tendsto_ratCast_atBot_iff, Rat.preimage_cast_Iic, Finpartition.coe_energy, Mathlib.Meta.NormNum.isRat_ratCast, Rat.commute_cast, Mathlib.Meta.NormNum.isInt_ratCast, IsSelfAdjoint.ratCast, ArchimedeanClass.mk_ratCast, Rat.preimage_cast_Ici, Rat.castOrderEmbedding_apply, Rat.cast_list_sum, Rat.cast_mono, Padic.exi_rat_seq_conv, Rat.cast_def, Rat.preimage_cast_Iio, Rat.cast_nonneg, Rat.cast_divInt, Rat.cast_smul_eq_qsmul, Rat.cast_inv, Rat.preimage_cast_uIoc, ArchimedeanClass.mk_le_mk_iff_ratCast, Rat.cast_abs, Rat.cast_nonpos, archimedean_iff_rat_le, Rat.cast_ofNat, Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sq, Rat.cast_sum, Rat.cast_sub_of_ne_zero, Rat.cast_natCast, Padic.denseRange_ratCast, RCLike.ratCast_re, Rat.smul_one_eq_cast, ratCast_def, selfAdjoint.val_ratCast, Rat.cast_mul_of_ne_zero, le_iff_forall_lt_rat_imp_le, Padic.valuation_ratCast, Rat.cast_lt_zero, Rat.cast_strictMono, Padic.withValUniformEquiv_cast_apply, IsIntegral.exists_int_iff_exists_rat, Padic.coe_withValRingEquiv, exists_rat_mem_uIoo, Rat.cast_pos_of_pos, RCLike.ratCast_im, ArchimedeanClass.mk_ratCast_nonneg, SimpleGraph.nonuniformWitness_spec, Rat.denseRange_cast, Rat.cast_ofScientific, Rat.cast_le_intCast, Padic.norm_rat_le_one, eq_ratCast, Padic.rat_dense, Rat.cast_zero, Rat.cast_add, Rat.ceil_cast, Padic.rat_dense', Finpartition.mk_mem_sparsePairs, Rat.cast_le_natCast, archimedean_iff_rat_lt, Rat.cast_inv_nat, exists_pos_rat_lt, Rat.preimage_cast_Ioo, LinearOrderedField.coe_lt_inducedMap_iff, Rat.cast_pos, Padic.norm_rat_le_one_iff_padicValuation_le_one, Padic.coe_add, Rat.cast_zpow, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, Rat.cast_le, Polynomial.qsmul_eq_C_mul, qsmul_def, LinearOrderedField.cutMap_self, NNRat.cast_mk, Quaternion.re_ratCast, AddCircle.addOrderOf_coe_rat, Rat.cast_injective, Rat.cast_multiset_sum, Rat.cast_neg, star_ratCast, GenContFract.exists_rat_eq_nth_conv, Rat.preimage_cast_Ioc, Rat.cast_commute, Rat.cast_pow, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, Rat.natCast_lt_cast, algebraMap.coe_ratCast, Mathlib.Meta.NormNum.isNat_ratCast, padicNorm_two_harmonic, Rat.smul_def, exists_rat_lt, Rat.cast_divInt_of_ne_zero, ArchimedeanClass.stdPart_ratCast, LinearOrderedField.inducedMap_rat, Rat.comap_cast_atTop, LinearOrderedField.mem_cutMap_iff, exists_rat_near, Filter.Eventually.ratCast_atTop, Rat.cast_sub, Rat.cast_prod, Rat.cast_one, tendsto_ratCast_atTop_iff, RCLike.ofReal_ratCast, Rat.cast_eq_zero, GenContFract.exists_rat_eq_nth_den
toRing 📖	CompOp	2219 math math: IsPrimitiveRoot.subOneIntegralPowerBasis_gen_prime, Hyperreal.InfiniteNeg.neg, Field.FiniteDimensional.of_exists_primitive_element, Polynomial.mul_div_eq_iff_isRoot, ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_one, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, FixedPoints.instFiniteDimensionalSubtypeMemSubfieldSubfield, one_le_div_iff, GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_one, legendreSym.eq_neg_one_iff, NumberField.basisMatrix_eq_embeddingsMatrixReindex, WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', Lagrange.interpolate_one, Valued.continuous_extension, AddCircle.not_isOfFinAddOrder_iff_forall_rat_ne_div, rank_fun_infinite, AddCircle.coe_equivIco_mk_apply, ValuationRing.mem_integer_iff, IntermediateField.isSeparable_of_mem_isSeparable, Affine.Simplex.faceOppositeCentroid_mem_affineSpan_face, exists_affineIndependent, Algebra.charP_iff, LieAlgebra.IsKilling.iInf_ker_weight_eq_bot, Lagrange.eval_iterate_derivative_eq_sum, HahnEmbedding.IsPartial.baseEmbedding_le, Rat.num_lt_succ_floor_mul_den, Polynomial.eq_X_sub_C_of_separable_of_root_eq, Rat.intCast_lt_cast, mem_perfectClosure_iff_natSepDegree_eq_one, ordinaryHypergeometric_sum_eq, NNRat.coe_floor, discrim_le_zero_of_nonpos, IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', IntermediateField.aeval_gen_minpoly, IsUltrametricDist.isNonarchimedean_invariantExtension, strictConvexOn_iff_slope_strict_mono_adjacent, Algebra.instIsSeparableResidueFieldOfFormallyUnramified, CauSeq.lt_irrefl, ValuationSubring.coe_mem_principalUnitGroup_iff, Hyperreal.infinite_neg, ValuationSubring.valuation_lt_one_iff, Convex.intrinsicClosure, selfAdjoint.val_div, binomialSeries_eq_ordinaryHypergeometricSeries, zpow_eq_zpow_iff_of_ne_zero₀, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, IsUltrametricDist.algNormOfAlgEquiv_extends, IsPurelyInseparable.minpoly_natDegree_eq', ZMod.pow_card_sub_one, Orientation.ne_iff_eq_neg, Valuation.isEquiv_iff_val_sub_one_lt_one, SimpleGraph.lapMatrix_toLinearMap₂', CauSeq.Completion.ofRat_div, ValuationSubring.image_maximalIdeal, NormedSpace.expSeries_eq_ofScalars, Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col, RootPairing.coroot_eq_polarizationEquiv_apply_root, Ideal.exists_comap_galRestrict_eq, NumberField.canonicalEmbedding.mem_span_latticeBasis, NumberField.integralBasis_apply, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow, UniformSpace.Completion.mul_hatInv_cancel, ValuationSubring.integralClosure_algebraMap_injective, IsPurelyInseparable.minpoly_eq', Subfield.add_mem, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, CauSeq.Completion.ofRat_inv, RootPairing.instIsRootSystemSubtypeMemSubmoduleSpanRangeCoeEmbeddingRootCorootRestrictScalars', X_pow_sub_C_splits_of_isPrimitiveRoot, NumberField.prod_nonarchAbsVal_eq, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, quadraticChar_card_card, FDRep.char_tensor, Lagrange.eval_interpolate_not_at_node', Valuation.mem_maximalIdeal_iff, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, Representation.IsIrreducible.instIsSimpleModuleMonoidAlgebraAsModule, Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty, ConvexOn.monotoneOn_slope_lt, abs_sub_round, round_neg_two_inv, NumberField.IsCMField.zpowers_complexConj_eq_top, IntermediateField.coe_algebraMap_over_bot, Finset.centroid_eq_affineCombination_fintype, ValuationSubring.mem_toSubring, Subspace.instModuleDualFiniteDimensional, Algebra.normalizedTrace_eq_of_finiteDimensional, Subfield.coe_add, Subgroup.HasDetPlusMinusOne.isParabolic_iff_of_upperTriangular, NumberField.FinitePlace.mk_apply, discrim_eq_zero_iff, CauSeq.sup_inf_distrib_right, NumberField.instFreeIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, concaveOn_iff_slope_anti_adjacent, WeierstrassCurve.Jacobian.add_of_Y_ne', arithGeom_eq', NumberField.IsCMField.unitsComplexConj_torsion, Subfield.zsmul_mem, Algebra.isInvariant_of_isGalois, WeierstrassCurve.Affine.cyclic_sum_Y_mul_X_sub_X, IsPurelyInseparable.elemExponent_min', Padic.withValUniformEquiv_norm_le_one_iff, NumberField.norm_norm_le_norm_mul_house_pow, Valued.toNormedField.norm_le_one_iff, NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd, Valued.extension_extends, Subfield.mem_toSubring, one_le_pow_mul_abs_eval_div, Valued.valuedCompletion_surjective_iff, Polynomial.div_def, Real.ofCauchy_sup, affineIndependent_iff_not_collinear_set, toIcoMod_eq_fract_mul, NumberField.RingOfIntegers.instIsIntegralClosureIntWithVal, NumberField.RingOfIntegers.instSMulDistribClass, finiteDimensional_vectorSpan_range, ValuationSubring.valuation_le_iff, RootPairing.restrictScalars_coe_coroot, Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, FiniteField.isSquare_neg_one_iff, FixedPoints.isSeparable, Rat.cast_intCast, CauSeq.Completion.ofRat_ratCast, Polynomial.exists_partition_polynomial, NumberField.IsCMField.equivInfinitePlace_symm_apply, Polynomial.fiberEquivQuotient_tmul, Int.fract_div_mul_self_mem_Ico, finrank_vectorSpan_image_finset_le, LieAlgebra.IsKilling.isCompl_ker_weight_span_coroot, CancelDenoms.cancel_factors_le, traceForm_nondegenerate_tfae, Matrix.Pivot.listTransvecCol_mul_last_col, Affine.Simplex.face_centroid_eq_iff, Rat.cast_comm, LaurentSeries.LaurentSeriesRingEquiv_def, FirstOrder.Field.realize_genericMonicPolyHasRoot, Rat.cast_mul, Lagrange.leadingCoeff_basis, LieModule.traceForm_eq_sum_finrank_nsmul', RatFunc.transcendental_X, FiniteField.isSquare_two_iff, IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, CongruenceSubgroup.exists_Gamma_le_conj', Valuation.HasExtension.instIsLocalHomSubtypeMemValuationSubringValuationSubringRingHomAlgebraMap, geom₂_sum, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, AddValuation.top_iff, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, WeierstrassCurve.Projective.equiv_some_of_Z_ne_zero, Hyperreal.neg_lt_of_tendsto_zero_of_pos, Module.exists_dual_forall_apply_eq_one, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_apply, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Valuation.isEquiv_valuation_valuationSubring, ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_three, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, isSepClosure_iff, NumberField.mixedEmbedding.norm_eq_norm, LieAlgebra.IsKilling.rootSystem_coroot_apply, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, round_two_inv, X_pow_sub_C_irreducible_iff_of_odd, StrictConcaveOn.slope_anti_adjacent, Subring.center.coe_div, Valuation.val_le_one_or_val_inv_lt_one, Irreducible.natSepDegree_eq_one_iff_of_monic', finiteDimensional_direction_affineSpan_of_finite, NumberField.FinitePlace.norm_def', Rat.cast_finsupp_sum, X_pow_sub_C_irreducible_of_odd, NumberField.mixedEmbedding.mem_idealLattice, IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers, sum_smul_minpolyDiv_eq_X_pow, Int.cast_div_ofNat_charZero, FunctionField.inftyValuation.X_inv, Hyperreal.epsilon_mul_omega, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, NumberField.Units.regOfFamily_eq_det, IsPurelyInseparable.elemExponent_min, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible', Rat.cast_mk', same_sub_div, div_sub_same, NumberField.FinitePlace.embedding_apply, IsAlgClosure.of_exists_root, WeierstrassCurve.Jacobian.negAddY_eq, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, Valuation.Integers.isPrincipal_iff_exists_isGreatest, IntermediateField.isAlgebraic_tower_bot, Rat.cast_fract, ZMod.exists_sq_eq_neg_one_iff, ValuativeRel.inv_srel_one, Normal.splits', instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Finpartition.IsEquipartition.card_biUnion_offDiag_le', GenContFract.dens_recurrence, isConjRoot_iff_exists_algEquiv, NumberField.FinitePlace.prod_eq_inv_abs_norm, inv_intCast_smul_eq, IsPurelyInseparable.elemExponent_def', instIsAlgebraicResidueFieldOfIsIntegral, LaurentSeries.valuation_single_zpow, Submodule.exists_le_ker_of_lt_top, ZMod.wilsons_lemma, Cubic.disc_eq_prod_three_roots, FirstOrder.Field.charP_of_model_fieldOfChar, Normal.minpoly_eq_iff_mem_orbit, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', CauSeq.sup_idem, WeierstrassCurve.ofJ_1728_of_two_ne_zero, finrank_vectorSpan_le_iff_not_affineIndependent, Hyperreal.coe_ofNat, Affine.Simplex.point_mem_median, sbtw_midpoint_of_ne, ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl, Field.FiniteDimensional.of_finite_intermediateField, Lagrange.eval_interpolate_not_at_node, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, Hyperreal.InfinitePos.neg, Orientation.eq_or_eq_neg, Rat.ceil_intCast_div_natCast, NumberField.RingOfIntegers.instIsFractionRing, Quaternion.coe_ratCast, LinearMap.le_rank_iff_exists_linearIndependent, ValuationSubring.valuation_unit, Affine.Simplex.median_eq_line_point_centroid, Hyperreal.infinitesimal_def, Subfield.relfinrank_eq_finrank_of_le, ContFract.convs_eq_convs', minpoly_algHom_toLinearMap, ArchimedeanClass.FiniteResidueField.mk_eq_zero, Matrix.mem_spectrum_iff_isRoot_charpoly, LieAlgebra.IsKilling.corootSpace_eq_bot_iff, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, Polynomial.abc, AddCircle.homeomorphAddCircle_apply_mk, Polynomial.natSepDegree_X_sub_C_pow, GenContFract.of_partNum_eq_one_and_exists_int_partDen_eq, Affine.Simplex.medial_reindex, NNRat.floor_coe, lineMap_inv_two, Valuation.isEquiv_iff_val_lt_val, Polynomial.exists_partition_polynomial_aux, Subring.center.coe_inv, Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one, Quaternion.ratCast_re, isConjRoot_algHom_iff, quadraticChar_two, IsPrimitiveRoot.subOneIntegralPowerBasis_gen, Height.logHeight₁_sub_le, IsFractionRing.mk'_eq_one_iff_eq, sub_inv_antitoneOn_Ioi, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, IsAlgClosure.of_exist_roots, AffineMap.slope_comp, Rat.isFractionRingDen, Affine.Simplex.univ_centroid_eq, PowerSeries.derivative_inv', discrim_le_zero, Valuation.isNontrivial_iff_exists_lt_one, IsDedekindDomain.HeightOneSpectrum.instIsNontrivialWithZeroMultiplicativeIntValuation, ConjRootClass.minpoly.map_eq_prod, Valuation.Integers.valuation_irreducible_lt_one, Affine.Simplex.affineIndependent_points_update_centroid, GenContFract.first_cont_eq, NumberField.Units.pos_at_place, IntermediateField.natCast_mem, WeierstrassCurve.Jacobian.addXYZ_of_X_eq, CancelDenoms.cancel_factors_lt, Height.logHeight₁_neg, Ring.choose_eq_smul, GenContFract.succ_nth_fib_le_of_nth_den, div_two_sub_self, IntermediateField.coe_neg, ValuationSubring.mapOfLE_valuation_apply, WeierstrassCurve.Projective.add_of_Z_eq_zero, Subfield.coe_mul, IntermediateField.isScalarTower, IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, WeierstrassCurve.Jacobian.negAddY_of_X_eq, Polynomial.roots_degree_eq_one, RatFunc.eval_one, inv_intCast_smul_comm, mul_inv_cancel, IntermediateField.algebraAdjoinAdjoin.instIsAlgebraicSubtypeMemSubalgebraAdjoinAdjoin, IsAlgClosed.instIsAlgClosure, spectralAlgNorm_def, isPurelyInseparable_iff_fd_isPurelyInseparable, CauSeq.const_lt, spectrum_diagonal, LieAlgebra.IsKilling.le_chainBotCoeff_of_rootSpace_ne_top, IsUltrametricDist.invariantExtension_apply, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, PowerBasis.equivAdjoinSimple_symm_aeval, Orientation.map_eq_neg_iff_det_neg, NumberField.instFiniteDimensional, Height.logHeight₁_one, X_pow_sub_C_irreducible_iff_forall_prime_of_odd, Algebra.algebraMap_intNorm, SeparatingDual.exists_eq_one, FiniteDimensional.span_of_finite, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, finrank_algHom, ValuationSubring.toSubring_top, FiniteField.orderOf_frobeniusAlgEquivOfAlgebraic, LieAlgebra.IsKilling.apply_coroot_eq_cast', NormedSpace.expSeries_apply_eq_div', SimpleGraph.farFromTriangleFree_iff, sbtw_iff_left_ne_and_right_mem_image_Ioi, FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation, LinearMap.rank_diagonal, Real.ofCauchy_zero, NumberField.RingOfIntegers.withValEquiv_symm_apply, LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, AffineBasis.convexHull_eq_nonneg_coord, Even.zpow_abs, ContinuousLinearMap.finiteDimensional, RootPairing.restrictScalars_pairing, CauSeq.inf_comm, Cubic.discr_eq_prod_three_roots, WeierstrassCurve.Projective.dblU_eq, FGModuleCat.instFiniteHomModuleCatObjIsFG, LinearMap.span_singleton_sup_orthogonal_eq_top, le_one_div_of_neg, algebraicClosure.isAlgebraic, Collinear.mem_affineSpan_of_mem_of_ne, NumberField.Units.coe_mul, Matrix.conjTranspose_inv_intCast_smul, AddCircle.isOfFinAddOrder_iff_exists_rat_eq_div, HahnEmbedding.Seed.baseEmbedding_strictMono, ValuationSubring.subtype_injective, Lagrange.coeff_eq_sum, RatFunc.coe_X, IsUltrametricDist.invariantExtension_extends, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow', Real.of_near, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, IntermediateField.finiteDimensional_right, ValuationRing.range_algebraMap_eq, CongruenceSubgroup.exists_Gamma_le_conj, IntermediateField.isAlgebraic_iff, Affine.Simplex.centroid_weighted_vsub_eq_zero, AffineSubspace.wOppSide_iff_exists_wbtw, IntermediateField.charZero, Real.ofCauchy_mul, Algebra.FormallyUnramified.iff_map_maximalIdeal_eq, IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower', NumberField.house_intCast, FiniteField.cast_card_eq_zero, SimpleGraph.posSemidef_lapMatrix, DualNumber.inv_eps, WeierstrassCurve.Jacobian.add_of_Y_eq, Odd.neg_one_zpow, zpow_eq_neg_zpow_iff₀, SameRay.exists_eq_smul_add, affineHomeomorph_symm_apply, Valued.exists_coe_eq_v, FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop, Matrix.minpoly_dvd_charpoly, Finset.mem_convexHull', Hyperreal.infinite_abs_iff, List.SortedLE.wbtw, LinearMap.BilinForm.apply_dualBasis_left, NumberField.FinitePlace.norm_embedding_eq, div_le_one_iff, IsNormalClosure.adjoin_rootSet, NumberField.RingOfIntegers.instIsDedekindDomainWithVal, GenContFract.abs_sub_convergents_le', IntermediateField.LinearDisjoint.trace_algebraMap, Polynomial.separable_X_pow_sub_C, NormedSpace.exp_eq_tsum, NumberField.IsCMField.isQuadraticExtension, Polynomial.valuation_of_mk, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, Rat.intCast_le_cast, Subspace.finrank_dualCoannihilator_eq, GenContFract.compExactValue_correctness_of_stream_eq_some_aux_comp, Polynomial.Gal.restrictDvd_def, Matrix.Pivot.mul_listTransvecRow_last_col, Polynomial.X_pow_sub_one_splits, arithGeom_zero_eq_mul_div', Valuation.val_lt_one_iff, OrderIso.smulRightDual_apply, Valuation.val_le_one_or_val_inv_le_one, Quaternion.inv_def, Subspace.finiteDimensional_quot_dualCoannihilator_iff, CauSeq.not_limZero_of_pos, NormedSpace.exp_eq_tsum_div, mul_sub_mul_div_mul_nonpos_iff, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, discrim_eq_zero_of_existsUnique, IntermediateField.minpoly_gen, sub_half_lt_round, ValuationSubring.eq_top_iff, LaurentSeries.inducing_coe, isSplittingField_X_pow_sub_C_of_root_adjoin_eq_top, Polynomial.exists_finset_of_splits, GenContFract.convs'_succ, Real.cauchy_sub, Rat.isNat_intCeil_ofIsNNRat, LaurentSeries.continuous_coe, SameRay.exists_eq_smul, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, ZMod.exists_sq_eq_two_iff, Coplanar.finrank_le_two, WeierstrassCurve.Projective.negAddY_of_X_eq, NumberField.IsCMField.orderOf_complexConj, Real.mk_one, gal_X_pow_sub_C_isSolvable, Lagrange.interpolate_eq_sum, IsIdempotentElem.spectrum_subset, normalClosure_eq_iSup_adjoin', ConcaveOn.antitoneOn_slope_gt, IsPrimitiveRoot.adjoinEquivRingOfIntegers_symm_apply, AffineSubspace.wOppSide_self_iff, Matrix.map_mul_ratCast, RootPairing.Base.exists_mem_span_pairingIn_ne_zero_and_pairwise_ne, CauSeq.coe_sup, FiniteDimensional.finiteDimensional_quotient, Hyperreal.archimdeanClassMk_coe, FiniteField.roots_X_pow_card_sub_X, Valuation.map_div, Int.floor_div_natCast, GenContFract.first_num_eq, Rat.associated_num_den, finiteDimensional_vectorSpan_image_of_finite, Algebra.discr_powerBasis_eq_norm, ConvexOn.secant_mono_aux3, Normal.splits, Valuation.one_lt_val_iff, archimedean_iff_nat_le, IsPrimitiveRoot.norm_eq_neg_one_pow, HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, abs_inv, Valued.integer.exists_norm_lt_one, ValuationSubring.valuation_lt_one_or_eq_one, collinear_iff_not_affineIndependent_of_ne, WeierstrassCurve.Projective.addXYZ_of_X_eq, PowerSeries.intValuation_eq_of_coe, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, Valued.continuous_valuation, rank_lt_rank_dual', isSemisimpleRing_iff_pi_matrix_divisionRing, isAlgebraic_rat, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, FiniteField.instIsSplittingFieldExtensionHSubPolynomialHPowNatXCard, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, Rat.floor_natCast_div_natCast, Hyperreal.infinitePos_neg, FormalMultilinearSeries.ofScalars_series_of_subsingleton, HahnEmbedding.Partial.orderTop_eq_iff, CauSeq.mul_pos, solvableByRad.isSolvable, finrank_vectorSpan_insert_le, WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero, WeierstrassCurve.Jacobian.equiv_zero_of_Z_eq_zero, FirstOrder.Field.instModelACFOfCharPOfIsAlgClosed, Quaternion.imJ_nnratCast, divRadical_dvd_derivative, Subfield.list_prod_mem, Polynomial.leadingCoeff_mul_prod_normalizedFactors, Subfield.coe_zero, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, Real.ofCauchy_nnratCast, Polynomial.squarefree_cyclotomic, Valuation.val_eq_one_iff, FDRep.instFiniteDimensionalHom, NormedSpace.expSeries_sum_eq, IsTopologicalDivisionRing.toIsTopologicalRing, Hyperreal.isSt_iff_abs_sub_lt_delta, FiniteField.instIsScalarTowerZModExtension, NumberField.RingOfIntegers.instIsTorsionFree_2, Subfield.mem_closure_iff, FloorSemiring.tendsto_pow_div_factorial_atTop, ValuationSubring.isLocalRing, ValuativeRel.div_vle_one_iff, selfAdjoint.val_zpow, Polynomial.X_pow_sub_C_separable_iff, IntermediateField.restrictRestrictAlgEquivMapHom_apply, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen_prime, Valued.extension_eq_zero_iff, Algebra.norm_eq_prod_embeddings, Field.isAlgebraic_of_finite_intermediateField, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_def, IsPurelyInseparable.minpoly_eq, IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer, IsDiscreteValuationRing.isRankOneDiscrete, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, Int.cast_neg_natCast, Submodule.finiteDimensional_sup, finiteDimensional_direction_map, minpoly.degree_le, WeierstrassCurve.Affine.slope_of_Y_ne, ValuativeRel.one_rel_inv, LinearEquiv.mem_dilatransvections_iff_rank, Algebra.FormallyUnramified.iff_isSeparable, Module.Basis.traceDual_def, iInf_valuationSubring_superset, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integers, Submodule.exists_le_ker_of_notMem, NumberField.Units.regulator_eq_det, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, SimpleGraph.isUniform_one, Real.lt_cauchy, RingHom.charP_iff_charP, Int.cast_negOnePow, FGModuleCat.FGModuleCatEvaluation_apply, finite_of_algHom_finiteType_of_isJacobsonRing, IsPurelyInseparable.natSepDegree_eq_one, TrivSqZeroExt.eq_smul_exp_of_ne_zero, Derivation.leibniz_inv, mem_perfectClosure_iff_pow_mem, Rat.cast_add_of_ne_zero, CauSeq.add_pos, NumberField.AdeleRing.algebraMap_snd_apply, Affine.Simplex.face_centroid_eq_centroid, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, convexHull_basis_eq_stdSimplex, Module.Basis.trace_traceDual_mul, coevaluation_apply_one, ValuationSubring.idealOfLE_le_of_le, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, Rat.cast_inv_int, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, div_le_one_of_ge, FiniteDimensional.span_finset, WithAbs.tendsto_one_div_one_add_pow_nhds_one, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, StrictConvexOn.secant_strict_mono_aux3, Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec, IsLocalRing.map_tensorProduct_mk_eq_top, GenContFract.conts_recurrenceAux, FunctionField.valuedFqtInfty.def, NormedDivisionRing.dist_eq, AdjoinRoot.mul_div_root_cancel, NumberField.Units.coe_coe, Valued.isClopen_valuationSubring, SimpleGraph.farFromTriangleFree.le_card_sub_card, Algebra.map_intNormAux, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', Matrix.finite_spectrum, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime, IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem, abs_one_div, Algebra.coe_norm_int, IsNormalClosure.splits, Valuation.exists_isUniformizer_of_isCyclic_of_nontrivial, DualNumber.maximalIdeal_eq_span_singleton_eps, IsIntegral.ratCast_iff, NumberField.Units.finrank_mul_regOfFamily_eq_det, FormalMultilinearSeries.ofScalars_sub, Valuation.mem_unitGroup_iff, abs_div, midpoint_le_right, GenContFract.IntFractPair.nth_stream_fr_lt_one, abs_sub_round_div_natCast_eq, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, instIsSeparableResidueFieldOfQuotientIdeal, Affine.Simplex.median_reindex, normalClosure.restrictScalars_eq, Valued.isClosed_valuationSubring, IsDedekindDomain.HeightOneSpectrum.valuation_def, Convex.mem_Ioo, Hyperreal.coe_eq_one, Int.floor_div_cast_of_nonneg, IsPrimitiveRoot.adjoinEquivRingOfIntegers_apply, NumberField.det_basisOfFractionalIdeal_eq_absNorm, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, Valuation.Integers.isIntegrallyClosed_integers, Rat.round_cast, ValuationSubring.valuation_le_one, FGModuleCat.instIsMonoidalClosedModuleCatIsFG, ArchimedeanClass.FiniteElement.mk_intCast, ConvexOn.secant_mono_aux2, Ideal.image_subset_nonunits_valuationSubring, CauSeq.Completion.ofRat_rat, HahnEmbedding.IsPartial.strictMono, Projectivization.cross_mk_of_cross_ne_zero, collinear_iff_finrank_le_one, finrank_quotient_span_eq_natDegree, Module.Basis.trace_mul_traceDual, Rep.instProjective, Matrix.Pivot.listTransvecCol_getElem, StrictConcaveOn.secant_strict_mono, gal_X_pow_sub_one_isSolvable, div_neg_self, bddAbove_slope_gt_of_mem_interior, GenContFract.zeroth_cont_eq_h_one, Rat.cast_list_prod, Finpartition.IsEquipartition.sum_nonUniforms_lt', NumberField.RingOfIntegers.coe_eq_zero_iff, spectralAlgNorm_mul, spectralNorm_eq_invariantExtension, HahnSeries.cardSuppLTSubfield_carrier, IntermediateField.LinearDisjoint.basisOfBasisLeft_apply, MvPowerSeries.coeff_inv, algebraicClosure.isIntegralClosure, sub_inv_antitoneOn_Icc_left, Polynomial.natSepDegree_C_mul_X_sub_C_pow, Algebra.normalizedTrace_intermediateField, LinearMap.finrank_genEigenspace_le, div_lt_one_of_neg, Algebra.FormallyEtale.iff_isSeparable, sub_smul_slope_vadd, Real.ofCauchy_sub, Subfield.sum_mem, DualNumber.isMaximal_span_singleton_eps, AlgebraicClosure.instCharP, Real.mk_lt, ValuativeRel.one_vle_div_iff, geom_sum_inv, NumberField.Units.norm, Affine.Simplex.centroid_notMem_affineSpan_of_ne_univ, AddCircle.addOrderOf_div_of_gcd_eq_one, FGModuleCat.instFiniteHom, finiteDimensional_vectorSpan_of_finite, NumberField.IsCMField.complexConj_apply_apply, NNRat.intCeil_cast, neg_div_self, WeierstrassCurve.Affine.addPolynomial_slope, ConvexOn.slope_mono_adjacent, AffineSubspace.wSameSide_and_wOppSide_iff, LocalSubring.eq_iInf_of_isIntegrallyClosedIn, List.exists_map_eq_of_sorted_nonempty_iff_sbtw, ordinaryHypergeometricSeries_apply_eq', spectrum.one_eq, NumberField.RingOfIntegers.instIsLocalizationAlgebraMapSubmonoidIntNonZeroDivisors, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, spectralMulAlgNorm_def, Rat.floor_cast, NumberField.mixedEmbedding.span_idealLatticeBasis, ConcaveOn.slope_anti, Valuation.HasExtension.maximalIdeal_comap_algebraMap_eq_maximalIdeal, Matrix.instFiniteSpectrum, mul_gaussSum_inv_eq_gaussSum, IntermediateField.LinearDisjoint.basisOfBasisRight_apply, Quaternion.imI_nnratCast, AlgebraicIndependent.lift_reprField, X_pow_sub_C_irreducible_iff_of_prime_pow, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, WeierstrassCurve.Jacobian.dblXYZ_of_Z_ne_zero, RingEquivClass.toLinearEquivClassRat, Finpartition.isUniform_one, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux, HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum, IsCyclotomicExtension.splits_cyclotomic, Quaternion.imK_nnratCast, FDRep.average_char_eq_finrank_invariants, Polynomial.IsRoot.mul_div_eq, Height.logHeight_one, NumberField.IsCMField.coe_ringOfIntegersComplexConj, PowerSeries.normalized_count_X_eq_of_coe, lift_rank_lt_rank_dual', ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier, WeierstrassCurve.Jacobian.negMap_of_Z_eq_zero, CongruenceSubgroup.IsArithmetic.conj, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, WeierstrassCurve.Affine.addX_eq_addX_negY_sub, Collinear.finiteDimensional_direction_affineSpan, ConjRootClass.minpoly_mk, finiteDimensional_direction_affineSpan_insert_set, HahnEmbedding.IsPartial.truncLT_mem_range, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, IsTranscendenceBasis.isAlgebraic_field, Ring.instIsFractionRingNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, isPurelyInseparable_iff_pow_mem, quadraticCharFun_one, FiniteField.norm_surjective, IsFractionRing.charP_of_isFractionRing, WeierstrassCurve.Affine.slope_of_X_ne, PowerBasis.equivAdjoinSimple_aeval, Rat.cast_lt_natCast, IntermediateField.isPurelyInseparable_tower_bot, IntermediateField.neg_mem, le_separableClosure_iff, Valuation.isEquiv_iff_val_le_one, IntermediateField.charP', Padic.comap_mulValuation_eq_padicValuation, Polynomial.preHilbertPoly_eq_choose_sub_add, tendsto_nat_floor_mul_div_atTop, Polynomial.roots_C_mul_X_add_C, IsSepClosure.isSeparable, affineHomeomorph_image_I, ConcaveOn.comp_affineMap, AddCircle.equivAddCircle_apply_mk, ValuativeRel.one_rel_div_iff, Finset.sum_centroidWeights_eq_one_of_card_eq_add_one, NumberField.FinitePlace.norm_lt_one_iff_mem, uniform_continuous_npow_on_bounded, isStronglyTranscendental_iff_of_field, Rat.cast_mkRat_of_ne_zero, Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing, IntermediateField.botContinuousSMul, NumberField.IsCMField.equivInfinitePlace_apply, Rat.valuation_le_one_iff_den, eq_separableClosure_iff, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, WeierstrassCurve.Affine.C_addPolynomial_slope, Int.fract_div_mul_self_add_zsmul_eq, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, LocalSubring.instAtPrimeSubtypeMemSubringToSubringOfPrime, Valuation.mem_valuationSubring_iff, ValuationSubring.coe_unitGroupMulEquiv_apply, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, div_le_one_of_neg, Coplanar.finiteDimensional_direction_affineSpan, PowerBasis.trace_gen_eq_nextCoeff_minpoly, mem_algebraicClosure_iff, arithGeom_same_eq_mul_div', NumberField.IsCMField.is_quadratic, sbtw_iff_right_ne_and_left_mem_image_Ioi, Valuation.isEquiv_iff_val_eq_one, inv_zero, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, Char.card_pow_card, Valuation.pow_Uniformizer_is_pow_generator, AddCircle.coe_fract, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered, affineIndependent_iff_not_finrank_vectorSpan_le, WeierstrassCurve.isGoodReduction_iff, FGModuleCat.FGModuleCatDual_obj, Finset.centerMass_smul_left, NumberField.IsCMField.complexConj_apply_eq_self, Rat.cast_lt_intCast, toIcoMod_eq_add_fract_mul, Valuation.Integers.le_iff_dvd, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, toIocMod_eq_sub_fract_mul, IsCyclotomicExtension.isSplittingField_X_pow_sub_one, IsPurelyInseparable.hasExponent_of_finiteDimensional, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, Algebra.norm_inv, LaurentSeries.exists_Polynomial_intValuation_lt, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, Valued.continuous_extensionValuation, FiniteField.algebraMap_norm_eq_pow, trace_eq_finrank_mul_minpoly_nextCoeff, ValuationSubring.valuation_le_one_iff, Valued.coe_valuation_eq_rankOne_hom_comp_valuation, geom_sum_eq, ValuationSubring.mem_unitGroup_iff, CongruenceSubgroup.isArithmetic_conj_SL2Z, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_sup, finiteDimensional_direction_affineSpan_insert, NNRat.coe_ceil, Rat.natCast_le_cast, IntermediateField.isAlgebraic_tower_top, Polynomial.separable_X_pow_sub_C', ConcaveOn.antitoneOn_slope_lt, Subfield.algebraMap_ofSubfield, GenContFract.of_convergence_epsilon, IsCyclotomicExtension.splits_X_pow_sub_one, IntermediateField.adjoin_one, transcendental_aeval_iff, Valuation.ideal_isPrincipal, toIcoDiv_zero_one, Algebra.normalizedTrace_eq_of_fininteDimensional, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, one_div_le_one_div_of_neg, ValuationSubring.pointwise_smul_toSubring, Subfield.zero_mem, eq_pos_convex_span_of_mem_convexHull, FiniteField.isSquare_neg_two_iff, NumberField.mixedEmbedding.covolume_idealLattice, Representation.isSemisimpleRepresentation_iff_isSemisimpleModule_asModule, Differential.logDeriv_div, Nat.Ioc_filter_modEq_card, Hyperreal.archimedeanClassMk_pos_of_tendsto, DualNumber.exists_mul_left_or_mul_right, ArchimedeanClass.FiniteElement.val_sub, Rat.ceil_natCast_div_natCast, FGModuleCat.FGModuleCatCoevaluation_apply_one, ValuationSubring.mem_carrier, Int.Ioc_filter_modEq_card, one_lt_div_of_neg, FiniteField.algebraMap_norm_eq_prod_pow, CancelDenoms.cancel_factors_ne, Real.mk_mul, Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_det, trace_eq_trace_adjoin, IntermediateField.coe_isIntegral_iff, Valuation.zero_iff, Odd.neg_zpow, instIsAlgebraicQuotientIdealResidueField, MonomialOrder.span_leadingTerm_eq_span_monomial', finiteDimensional_direction_affineSpan_range, star_inv_intCast_smul, List.exists_map_eq_of_sorted_nonempty_iff_wbtw, Polynomial.SplittingField.instExpChar, Submodule.traceDual_le_span_map_traceDual, IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, StrictConvexOn.secant_strict_mono_aux1, Valuation.instNonemptyUniformizer, LieAlgebra.IsKilling.coroot_mem_corootSpace, ArchimedeanClass.stdPart_one, one_div_lt_of_neg, NormedSpace.expSeries_apply_eq, AddCircle.card_addOrderOf_eq_totient, LocalSubring.map_maximalIdeal_eq_top_of_isMax, NumberField.IsCMField.complexEmbedding_complexConj, sum_embeddings_eq_finrank_mul, mem_perfectClosure_iff, tendsto_nat_floor_div_atTop, Real.cauchy_inv, ZMod.pow_card_sub_one_eq_one, Subfield.sub_mem, sub_div, WeierstrassCurve.Affine.derivative_addPolynomial_slope, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, one_lt_div_iff, PowerBasis.equivAdjoinSimple_gen, Ideal.ResidueField.exists_smul_eq_tmul_one, LinearEquiv.mem_dilatransvections_iff_finrank, ValuedRing.separated, NumberField.Units.mem_torsion, GenContFract.IntFractPair.stream_succ_of_int, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, Finset.centroidWeights_apply, separableClosure.eq_top_iff, finiteDimensional_vectorSpan_insert_set, Valued.integer.norm_le_one, LieAlgebra.IsKilling.apply_coroot_eq_cast, slope_pos_iff, Real.cauchy_nnratCast, NumberField.to_finiteDimensional, Hyperreal.infinitesimal_sub_st, AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', Representation.isSimpleModule_iff_irreducible_ofModule, Polynomial.natSepDegree_X_pow_char_pow_sub_C, WeierstrassCurve.Jacobian.addMap_of_Z_ne_zero, Lagrange.leadingCoeff_eq_sum, Real.mk_add, Hyperreal.infinitePos_abs_iff_infinite_abs, PowerBasis.equivAdjoinSimple_symm_gen, FiniteField.isSplittingField_of_nat_card_eq, finiteDimensional_vectorSpan_singleton, legendreSym.eq_one_iff, Algebra.isUnramifiedAt_iff_map_eq, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, ArchimedeanClass.stdPart_intCast, Submodule.finiteDimensional_inf_right, groupCohomology.norm_ofAlgebraAutOnUnits_eq, iccHomeoI_apply_coe, Valued.isOpen_valuationSubring, ModP.preVal_mk, midpoint_le_left, RatFunc.valuation_eq_LaurentSeries_valuation, ModP.v_p_lt_preVal, sum_Ioo_inv_sq_le, NumberField.Units.coe_neg_one, Valuation.IsRankOneDiscrete.generator_zpowers_eq_range, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, RingHomClass.toLinearMapClassRat, WeierstrassCurve.Projective.addZ_eq, isPurelyInseparable_iff_natSepDegree_eq_one, Irreducible.natSepDegree_eq_one_iff_of_monic, Nat.Ico_filter_modEq_card, FiniteField.two_pow_card, PadicInt.coe_adicCompletionIntegersEquiv_apply, Subfield.coe_one, ordinaryHypergeometric_eq_tsum, quadraticChar_neg_two, NormedSpace.expSeries_apply_eq_div, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, NumberField.mixedEmbedding.logMap_eq_logEmbedding, Subfield.subring_closure_le, centroid_mem_affineSpan_of_nonempty, ValuationSubring.neg_mem, NumberField.isFinitePlace_iff, IsSemisimpleRing.exists_ringEquiv_pi_matrix_divisionRing, Nat.cast_choose_eq_descPochhammer_div, AbsoluteValue.exists_one_lt_lt_one_pi_of_not_isEquiv, FGModuleCat.ihom_obj, StrictConvexOn.slope_strict_mono_adjacent, SimpleGraph.not_isUniform_iff, Rat.natFloor_natCast_div_natCast, GenContFract.convs_succ, Polynomial.sub_mod, List.exists_map_eq_of_sorted_iff_sbtw, Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub, Finset.sum_centroidWeights_eq_one_of_card_ne_zero, Ring.instIsSeparableFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Valued.toNormedField.norm_le_iff, Polynomial.bernoulli_eq_sub_sum, FDRep.char_linHom, Sbtw.of_lt_of_lt, IsGaloisGroup.finiteDimensional, Submodule.restrictScalars_traceDual, LinearMap.BilinForm.dualBasis_eq_iff, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, mul_sub_mul_div_mul_neg, Height.mulHeight₁_sub_le, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_essFiniteType, Differential.logDeriv_one, arithGeom_eq, NumberField.integralBasis_repr_apply, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, Polynomial.separable_prod_X_sub_C_iff', WithAbs.instFiniteDimensional, ValuationSubring.instIsDomainSubtypeMem, ConjRootClass.mk_neg, FiniteField.splits_X_pow_nat_card_sub_X, LaurentSeries.coe_X_compare, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, AffineMap.image_uIcc, GaussianInt.div_def, Matrix.val_planeConformalMatrix, Subfield.continuousSMul, Valuation.isNontrivial_iff_exists_unit, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder, Valuation.Integers.dvdNotUnit_iff_lt, FractionalIdeal.mem_dual, Polynomial.rootOfSplits'_eq_rootOfSplits, Height.fun_logHeight_one, Valuation.Integers.valuation_unit, Polynomial.natDegree_hilbertPoly_of_ne_zero, round_eq, Polynomial.Chebyshev.iterate_derivative_U_eval_one_dvd, Configuration.ofField.instNondegenerateProjectivizationForallFinOfNatNat, Algebra.normalizedTrace_self, Polynomial.Chebyshev.iterate_derivative_T_eval_one_dvd, Int.Ico_filter_dvd_card, RootPairing.GeckConstruction.instIsIrreducible, IntermediateField.algebraMap_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, GenContFract.of_s_head_aux, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, PowerSeries.invOfUnit_eq', one_div_mul_sub_mul_one_div_eq_one_div_add_one_div, GenContFract.convs'Aux_succ_some, Algebra.norm_eq_norm_adjoin, Real.ofCauchy_natCast, NumberField.FinitePlace.coe_apply, affineIndependent_iff_le_finrank_vectorSpan, Subfield.neg_mem, Subspace.quotAnnihilatorEquiv_apply, circleEquivGen_symm_apply, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, PadicAlgCl.isAlgebraic, Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, IntermediateField.LinearDisjoint.norm_algebraMap, Valued.closure_coe_completion_v_lt, functionField_iff, ValuationSubring.instIsFractionRingSubtypeMem, Valued.valuation_isClosedMap, Lagrange.iterate_derivative_interpolate, Finset.mem_convexHull, PowerBasis.toMatrix_isIntegral, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, rank_dual_eq_card_dual_of_aleph0_le_rank', div_eq_mul_inv, Finpartition.coe_energy, ValuativeRel.inv_rel_one, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, Valued.closure_coe_completion_v_mul_v_lt, Valuation.HasExtension.instIsScalarTower_valuationSubring', NumberField.RingOfIntegers.mk_zero, FiniteDimensional.finiteDimensional_self, GenContFract.convs'_of_int, ConvexOn.secant_mono, Valued.valuedCompletion_apply, ValuationSubring.algebraMap_apply, Subfield.multiset_sum_mem, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, Rat.fract_inv_num_lt_num_of_pos, Normal.isIntegral, Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder, Rat.commute_cast, AffineBasis.exists_affineBasis, sbtw_pointReflection_of_ne, LinearOrderedField.inducedMap_one, Wbtw.of_le_of_le, ValuationSubring.valuation_eq_iff, ordinaryHypergeometricSeries_apply_eq, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, ConvexOn.secant_mono_aux1, WeierstrassCurve.Affine.addY_sub_negY_addY, IntermediateField.list_prod_mem, GenContFract.first_contAux_eq_h_one, WeierstrassCurve.Projective.negMap_of_Z_ne_zero, Polynomial.Chebyshev.derivative_U_eval_one_dvd, Field.isAlgebraic_of_adjoin_eq_adjoin, GenContFract.IntFractPair.succ_nth_stream_eq_none_iff, inv_eq_self₀, ConvexOn.slope_mono, Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, Valued.norm_def, CancelDenoms.cancel_factors_eq, SimpleGraph.unreduced_edges_subset, OnePoint.equivProjectivization_symm_apply_mk, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, Rat.den_le_and_le_num_le_of_sub_lt_one_div_den_sq, NumberField.FinitePlace.norm_def_int, spectralNorm_one, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Polynomial.Monic.natSepDegree_eq_one_iff, Valuation.valuationSubring_isPrincipalIdealRing, vectorSpan_segment, inv_sub_inv, IntermediateField.coe_zero, X_pow_sub_C_irreducible_of_prime, CauSeq.le_sup_left, Finset.convexHull_eq, WeierstrassCurve.Projective.neg_of_Z_ne_zero, GenContFract.of_s_of_int, IsSelfAdjoint.ratCast, Real.cauchy_natCast, IsLocalRing.exists_factor_valuationRing, arithGeom_same_eq_mul_div, GenContFract.nums_recurrence, slope_def_field, ArchimedeanClass.stdPart_neg, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, Collinear.finiteDimensional_vectorSpan, Polynomial.separable_prod_X_sub_C_iff, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, ArchimedeanClass.mk_ratCast, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, centroid_mem_affineSpan_of_cast_card_ne_zero, Rat.isFractionRing, NumberField.RingOfIntegers.withValEquiv_apply, Hyperreal.IsSt.sub, ZMod.gauss_lemma, GenContFract.of_s_head, GenContFract.of_partNum_eq_one, AffineBasis.coord_apply_centroid, zpow_zero', Real.ofCauchy_ratCast, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, ValuationSubring.isIntegral_of_mem_ringOfIntegers', WeierstrassCurve.Projective.negDblY_eq, left_le_lineMap_iff_le, Algebra.norm_eq_prod_automorphisms, slope_fun_def, CongruenceSubgroup.finiteIndex_conjGL, Matrix.sub_scalar_sq_eq_disc, Polynomial.exists_approx_polynomial, Subfield.one_mem, Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField, natDegree_radical_le, IsUltrametricDist.algNormOfAlgEquiv_apply, affineIndependent_of_ne, Subfield.coe_inf, Subfield.sInf_toSubring, StrictConvexOn.secant_strict_mono_aux2, selfAdjoint.val_inv, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, LieAlgebra.IsKilling.biSup_corootSpace_eq_top, IsPRadical.isPurelyInseparable, Finset.sum_centroidWeightsIndicator, Algebra.IsUnramifiedAt.not_minpoly_sq_dvd, Nat.coprime_sub_mul_floor_rat_div_of_coprime, Subspace.finrank_add_finrank_dualCoannihilator_eq, Algebra.instIsSeparableResidueFieldOfIsUnramifiedAt, Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one, Polynomial.X_pow_sub_one_separable_iff, NumberField.RingOfIntegers.coe_injective, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, LieAlgebra.IsKilling.disjoint_ker_weight_corootSpace, List.Sorted.sbtw, Matrix.Pivot.mul_listTransvecRow_last_row, LocalSubring.le_ofPrime, wbtw_iff_right_eq_or_left_mem_image_Ici, CauSeq.const_le, IsPrimitiveRoot.exists_neg_pow_of_isOfFinOrder, one_mem_inv_coe_ideal, Rat.cast_list_sum, archimedean_iff_nat_lt, Valued.integer.coe_span_singleton_eq_closedBall, FDRep.instHasKernels, WeierstrassCurve.Projective.addX_eq, FiniteDimensional.finiteDimensional_submodule, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, wbtw_iff_left_eq_or_right_mem_image_Ici, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, IsSeparable.tower_bot, ValuativeRel.one_vlt_inv, WeierstrassCurve.Projective.addMap_of_Y_eq, SimpleGraph.FarFromTriangleFree.lt_half, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, round_eq_zero_iff, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, ArchimedeanClass.stdPart_natCast, ValuationSubring.coe_mem_nonunits_iff, NormedSpace.expSeries_apply_eq', Subfield.list_sum_mem, gal_X_sub_C_isSolvable, Polynomial.hilbertPoly_mul_one_sub_succ, toIocDiv_eq_neg_floor, Field.exists_primitive_element_iff_finite_intermediateField, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Valued.toNormedField.one_lt_norm_iff, GenContFract.exists_int_eq_of_partDen, FiniteField.isSplittingField_of_card_eq, LieModule.traceForm_eq_sum_finrank_nsmul, NNRat.ceil_coe, NumberField.RingOfIntegers.isIntegral_coe, Polynomial.dickson_one_one_zmod_p, ValuationSubring.mem_nonunits_iff_exists_mem_maximalIdeal, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, IsDedekindDomain.HeightOneSpectrum.coe_mem_adicCompletionIntegers, Valuation.IsNontrivial_iff_exists_one_lt, NumberField.Units.complexEmbedding_apply, IsStronglyTranscendental.iff_of_isFractionRing, IntermediateField.AdjoinPair.algebraMap_gen₁, NumberField.fractionalIdeal_rank, instIsSimpleModule, PowerSeries.invOfUnit_eq, Polynomial.IsSplittingField.IsScalarTower.isAlgebraic, doublyStochastic_eq_convexHull_permMatrix, LaurentSeries.valuation_LaurentSeries_equal_extension, IntermediateField.sub_mem, IsPrimitiveRoot.norm_eq_one_of_linearly_ordered, CauSeq.sup_comm, NumberField.finite_of_discr_bdd, affineIndependent_iff_affineIndependent_collinear_ne, FixedPoints.toAlgAut_surjective, IsPurelyInseparable.minpoly_natDegree_eq, Rat.cast_def, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_apply, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, Real.ofCauchy_intCast, affineIndependent_iff_not_collinear_of_ne, RatFunc.v_def, RingOfIntegers.coe_norm, minpoly.add_algebraMap, RatFunc.instCharZero, divRadical_dvd_wronskian_right, ArchimedeanClass.FiniteResidueField.mk_ne_zero, LieAlgebra.IsKilling.chainTopCoeff_add_chainBotCoeff, Nat.one_sub_one_div_cast_nonneg, add_sub_div_two_lt, NumberField.Units.coe_pow, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, LaurentSeries.LaurentSeries_coe, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, Valuation.map_inv, root_X_pow_sub_C_pow, AlgebraicIndependent.liftAlgHom_comp_reprField, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, Subalgebra.finiteDimensional_toSubmodule, legendreSym.eq_zero_iff, NumberField.RingOfIntegers.mk_one, FixedPoints.isIntegral, bddBelow_slope_lt_of_mem_interior, Rat.isFractionRingNum, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_adjoin_eq_top, collinear_iff_rank_le_one, NumberField.IsCMField.unitsMulComplexConjInv_apply, LaurentSeries.powerSeries_ext_subring, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, Set.unit_valuation_eq_one, Lagrange.eval_basisDivisor_left_of_ne, PowerSeries.instIsDiscreteValuationRing, NumberField.Units.abs_det_eq_abs_det, Affine.Simplex.span_eq_top, RingHom.rangeRestrictFieldEquiv_apply_symm_apply, Rat.cast_divInt, TrivSqZeroExt.inv_neg, FDRep.instInjectiveOfNeZeroCastCard, stdSimplex.barycenter_apply, Valuation.isNontrivial_valuation_valuationSubring_iff, Hyperreal.lt_neg_of_pos_of_infinitesimal, Quaternion.imK_ratCast, Algebra.FormallyUnramified.isSeparable, Subfield.mem_toAddSubgroup, ArchimedeanClass.mk_le_mk_iff_ratCast, Algebra.discr_powerBasis_eq_prod, FDRep.char_one, isSimpleModule_iff_finrank_eq_one, IntermediateField.charP, Algebra.IsAlgebraic.isNormalClosure_iff, Matrix.Pivot.listTransvecCol_mul_last_row_drop, IntermediateField.intCast_mem, jacobiSum_nontrivial_inv, InfiniteGalois.isOpen_iff_finite, FiniteDimensional.finiteDimensional_pi, RootPairing.restrictScalars_coe_root, Real.ofCauchy_div, IsPurelyInseparable.trans, Real.rank_rat_real, Mathlib.Tactic.RingNF.rat_rawCast_neg, IsFractionRing.ringHom_fieldRange_eq_of_comp_eq, Polynomial.leadingCoeff_preHilbertPoly, ValuationSubring.isIntegral_of_mem_ringOfIntegers, spectralAlgNorm_one, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, Valued.integer.isDiscreteValuationRing_of_compactSpace, Mathlib.Meta.NormNum.isNNRat_abs_nonneg, NumberField.inverse_basisMatrix_mulVec_eq_repr, Affine.Simplex.faceOppositeCentroid_reindex, NumberField.RingOfIntegers.instIsIntegralClosureInt, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, Rat.cast_abs, isSimpleRing, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, CauSeq.inf_le_right, NumberField.Units.coe_injective, ValuationSubring.mem_or_inv_mem', FunctionField.inftyValuation.X_zpow, RatFunc.rank_ratFunc_ratFunc, Height.mulHeight₁_eq_mulHeight, Finset.centroidWeightsIndicator_def, Coplanar.finiteDimensional_vectorSpan, Polynomial.cyclotomic_eq_minpoly_rat, NumberField.Units.coe_one, spectralAlgNorm_extends, Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row, Valued.integer.norm_unit, LaurentSeries.powerSeriesRingEquiv_coe_apply, Valuation.leIdeal_zero, IsRealClosed.toIsSemireal, ValuationSubring.prime_idealOfLE, Affine.Simplex.eq_centroid_iff_sum_vsub_eq_zero, CauSeq.Completion.ofRat_nnratCast, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, minpoly.ofSubring, nnqsmul_def, Filter.tendsto_cocompact_mul_left₀, exists_isTranscendenceBasis_and_isSeparable_of_perfectField, normal_iff, Int.sub_floor_div_mul_nonneg, Rat.isLocalizationIsInteger_iff, AlgHom.card, Hyperreal.not_infinite_neg, IntermediateField.adjoin_intCast, slope_pos_iff_gt, Quaternion.im_nnratCast, NormedDivisionRing.norm_mul, instIsDiscreteValuationRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, selfAdjoint.val_qsmul, LaurentSeries.powerSeriesEquivSubring_apply, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff, NumberField.mixedEmbedding.unitSMul_smul, ArchimedeanClass.FiniteElement.val_one, Valuation.IsNontrivial.exists_one_lt, Finpartition.IsEquipartition.sum_nonUniforms_lt, WeierstrassCurve.Jacobian.add_of_X_ne, LinearMap.det_eq_one_of_finrank_eq_zero, FDRep.simple_iff_end_is_rank_one, Rat.cast_sum, ValuativeRel.div_rel_one_iff, SimpleGraph.le_card_nonuniformWitness, Rat.instIsScalarTowerRight, FunctionField.inftyValuation.X, Rat.cast_sub_of_ne_zero, Field.primitive_element_iff_minpoly_degree_eq, IsPurelyInseparable.tower_bot, CauSeq.exists_lt, Projectivization.orthogonal_mk, Projectivization.cross_mk, LieAlgebra.IsKilling.root_apply_coroot, AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div, ValuationSubring.ofPrime_scalar_tower, AffineSubspace.finiteDimensional_sup, CauSeq.Completion.cau_seq_zero_ne_one, Rat.floor_def', Quaternion.imJ_ratCast, separableClosure.isAlgebraic, IsAlgClosure.ofAlgebraic, tendsto_nat_ceil_div_atTop, Real.cauchy_neg, FiniteField.X_pow_card_sub_X_natDegree_eq, Rat.cast_natCast, IntermediateField.expChar, Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull, FiniteField.pow_dichotomy, isGalois_iff, gaussSum_mul_gaussSum_pow_orderOf_sub_one, isPurelyInseparable_iff_perfectClosure_eq_top, Int.map_round, lineMap_le_lineMap_iff_of_lt, AlgHom.card_le, CauSeq.Completion.inv_zero, FiniteField.splits_X_pow_card_sub_X, half_sub, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, Mathlib.Meta.NormNum.IsRat.of_raw, Algebra.isSeparable_tower_bot_of_isSeparable, IsGaloisGroup.intermediateField, List.exists_map_eq_of_sorted_iff_wbtw, GenContFract.of_h_eq_intFractPair_seq1_fst_b, Rat.smul_one_eq_cast, ValuationSubring.principalUnitGroupEquiv_apply, Rat.uniformSpace_eq, abs_neg_one_zpow, Polynomial.SplittingField.instCharZero, Hyperreal.coe_one, Real.mk_const, FunctionField.inftyValuedFqt.def, mul_sub_mul_div_mul_nonpos, NumberField.Embeddings.coeff_bdd_of_norm_le, Polynomial.divByMonic_eq_div, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul, ValuationSubring.instSubringClass, Ring.instFiniteDimensionalFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin, spectralNorm.eq_of_normalClosure', SimpContFract.of_isContFract, ZMod.Ico_map_valMinAbs_natAbs_eq_Ico_map_id, GenContFract.zeroth_contAux_eq_one_zero, algebraicClosure.eq_top_iff, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, CauSeq.Completion.mul_inv_cancel, Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow, ValuationSubring.one_mem, GenContFract.of_one_le_get?_partDen, spectralNorm.spectralNorm_eq_norm_coeff_zero_rpow, Quaternion.ratCast_im, Affine.Simplex.medial_points, Valued.integer.exists_nnnorm_lt_one, GenContFract.of_s_tail, Subfield.coe_toSubring, Affine.Simplex.affineSpan_range_medial, Rat.isNat_intFloor_ofIsNNRat, Algebra.normalizedTrace_minpoly, IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_divisionRing, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, separatingDual_iff_injective, minpoly.eq_X_sub_C', Valued.integer.properSpace_iff_compactSpace_integer, isVisible_iff_lineMap, Differential.logDeriv_pow, Field.primitive_element_iff_minpoly_natDegree_eq, Rat.ringOfIntegersEquiv_apply_coe, Submodule.traceDual_eq_span_map_traceDual_of_linearDisjoint, extremePoints_doublyStochastic, Valuation.Integers.valuation_pos_iff_ne_zero, ratCast_def, Real.cauchy_intCast, Finset.sum_centroidWeights_eq_one_of_nonempty, Subfield.relrank_eq_rank_of_le, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', legendreSym.eq_one_iff', List.Sorted.wbtw, Affine.Simplex.collinear_point_centroid_faceOppositeCentroid, FixedBy.intermediateField_mem_iff, IsAlgClosure.isAlgebraic, GenContFract.fib_le_of_contsAux_b, RootPairing.polarizationEquiv_symm_apply_coroot, IntermediateField.isScalarTower_over_bot, IntermediateField.isSeparable_tower_bot, FiniteField.isSquare_iff, IntermediateField.minpoly_eq, RatFunc.instExpChar, Filter.tendsto_cocompact_mul_right₀, Nat.one_sub_one_div_cast_le_one, LinearMap.BilinForm.IsSymm.polarization, Real.mk_zero, Quaternion.ratCast_imI, Matrix.Pivot.mul_listTransvecRow_last_col_take, Int.fract_div_natCast_eq_div_natCast_mod, Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero, IsAlgClosure.separable, CauSeq.Completion.inv_mul_cancel, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, legendreSym.eq_pow, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_surjective, PowerSeries.coeff_inv, inv_sub_inv', exists_integral_multiples, Real.cauchy_add, WeierstrassCurve.Affine.slope_of_Y_ne_eq_evalEval, NumberField.RingOfIntegers.coe_eq_algebraMap, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, IsPurelyInseparable.pow_mem, Valuation.valuationSubring_not_isField, Real.ofCauchy_add, isPurelyInseparable_iff_finSepDegree_eq_one, CauSeq.le_total, ValuationSubring.mem_principalUnitGroup_iff, NumberField.mem_span_integralBasis, quadraticCharFun_eq_pow_of_char_ne_two, WeierstrassCurve.Projective.add_of_Y_eq, Ideal.coe_smul_primesOver_eq_map_galRestrict, IntermediateField.adjoin_eq_range_algebraMap_adjoin, Quaternion.normSq_zpow, Polynomial.resultant_eq_prod_roots_sub, Quaternion.coe_nnratCast, Finset.centerMass_ite_eq, ValuationSubring.toSubring_injective, spectralAlgNorm_of_finiteDimensional_normal_def, HahnEmbedding.Partial.mem_domain, isPurelyInseparable_of_finSepDegree_eq_one, WeierstrassCurve.Projective.negAddY_eq, FirstOrder.Field.instModelField, OnePoint.smul_infty_def, Height.fun_mulHeight_one, MonoidAlgebra.Submodule.instIsSemisimpleRingAddMonoidAlgebra, Hyperreal.infinite_iff_abs_lt_abs, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, WeierstrassCurve.Jacobian.addX_eq, WeierstrassCurve.Projective.add_of_X_ne, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, selfAdjoint.val_ratCast, iccHomeoI_symm_apply_coe, HahnEmbedding.Seed.mem_domain_baseEmbedding, FixedPoints.toAlgHom_bijective, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, mem_bot_iff_intCast, FiniteField.isSquare_odd_prime_iff, Algebra.normalizedTrace_def, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, IntermediateField.adjoin_natCast, finiteDimensional_direction_affineSpan_image_of_finite, QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff, NumberField.Units.coe_zpow, NumberField.mem_span_basisOfFractionalIdeal, Real.ofCauchy_inv, Polynomial.IsSplittingField.instFiniteDimensionalSplittingField, FiniteField.minpoly_frobeniusAlgHom, Rat.cast_mul_of_ne_zero, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, Real.cauchy_zero, mem_convexHull_iff_exists_fintype, Affine.Simplex.centroid_eq_iff, IntermediateField.AdjoinSimple.isIntegral_gen, RatFunc.instCharP, IsGaloisGroup.fixedPoints, Matrix.Pivot.listTransvecCol_mul_last_row, perfectField_iff_isSeparable_algebraicClosure, LieAlgebra.IsKilling.rootSystem_pairing_apply, LieAlgebra.IsKilling.chainTopCoeff_zero_right, quadraticChar_odd_prime, Valued.extensionValuation_apply_coe, round_le_add_half, Matrix.num_one, Subfield.toSubring_subtype_eq_subtype, IsDedekindDomain.HeightOneSpectrum.valuation_surjective, Quaternion.ratCast_imK, Real.ofCauchy_neg, Algebra.FormallyEtale.iff_exists_algEquiv_prod, lineMap_one_half, self_eq_inv₀, IntermediateField.isPurelyInseparable_bot, mem_algebraicClosure_iff', Polynomial.mem_normalizedFactors_iff, SimpleGraph.right_nonuniformWitnesses_card, FiniteField.sum_pow_units, List.SortedLT.sbtw, Affine.Simplex.faceOppositeCentroid_mem_median, LaurentSeries.valuation_coe_ratFunc, Quaternion.ratCast_imJ, Hyperreal.archimedeanClassMk_omega_neg, ValuationSubring.coe_unitGroupMulEquiv_symm_apply, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, WeierstrassCurve.Projective.add_of_Y_ne', Hyperreal.archimedeanClassMk_coe_nonneg, Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable, Normal.toIsAlgebraic, AlgebraicIndependent.aevalEquivField_apply_coe, LieAlgebra.IsKilling.orthogonal_span_coroot_eq_ker, Affine.Simplex.centroid_eq_affineCombination, Height.logHeight₁_eq_logHeight, HahnSeries.inv_def, Int.Ico_filter_modEq_card, Valuation.Integer.not_isUnit_iff_valuation_lt_one, CauSeq.le_sup_right, Ideal.factors_span_eq, minpoly_algEquiv_toLinearMap, Int.Ioc_filter_dvd_eq, minpoly.natSepDegree_eq_one_iff_pow_mem, Collinear.finrank_le_one, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, arithGeom_zero_eq_mul_div, FormalMultilinearSeries.ofScalars_smul, Subfield.mul_mem, Polynomial.mod_X_sub_C_eq_C_eval, NumberField.FinitePlace.norm_eq_one_iff_notMem, Valuation.exists_pow_Uniformizer, Submodule.mem_traceDual, IntermediateField.finiteDimensional_left, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, legendreSym.card_sqrts, minpoly.one, ZMod.gauss_lemma_aux, Matrix.finiteDimensional, LaurentSeries.valuation_compare, ArchimedeanClass.mk_ratCast_nonneg, isConjRoot_iff_orbitRel, AlgebraicClosure.instIsScalarTower, Hyperreal.tendsto_atBot_iff, le_perfectClosure_iff, perfectClosure.isAlgebraic, DualNumber.instIsLocalRing, IsPreconnected.eq_or_eq_neg_of_sq_eq, Polynomial.SplittingField.instCharP, NumberField.IsCMField.complexConj_eq_self_iff, PadicInt.zmod_congr_of_sub_mem_max_ideal, IntermediateField.isSeparable_sup, lineMap_le_left_iff_le, one_div_lt_one_div_of_neg_of_lt, FiniteGaloisIntermediateField.finiteDimensional, minpoly.neg, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, Polynomial.natSepDegree_X_sub_C, Convex.mem_Icc, NormedSpace.expSeries_sum_eq_div, IsSepClosure.isAlgClosure_of_perfectField_top, Real.mk_inf, GenContFract.second_contAux_eq, ZMod.nonsquare_iff_jacobiSym_eq_neg_one, lt_one_div_of_neg, GenContFract.zeroth_den_eq_one, Subfield.mem_toSubmonoid, Rat.cast_le_intCast, Polynomial.roots_C_mul_X_sub_C, ValuativeRel.one_vle_inv, AddCircle.addOrderOf_eq_pos_iff, slope_sub_smul, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, LaurentSeries.tendsto_valuation, IsGaloisGroup.subgroup, normalClosure_eq_iSup_adjoin, left_le_midpoint, isSepClosed_iff_isPurelyInseparable_algebraicClosure, WeierstrassCurve.Projective.negMap_of_Z_eq_zero, affineIndependent_iff_not_collinear, AlgebraicClosure.isAlgebraic, RatFunc.transcendental, IsGalois.finiteDimensional_of_finite, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, Rat.cast_zero, Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField, GenContFract.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero, Rat.cast_add, Finset.centroid_pair, krullTopology_mem_nhds_one_iff, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, FormalMultilinearSeries.ofScalars_comp_neg_id, Affine.Simplex.point_vsub_centroid_eq_smul_vsub, FiniteField.unitsMap_norm_surjective, gaussSum_pow_eq_prod_jacobiSum, IntermediateField.one_mem, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, MonoidAlgebra.Submodule.instIsSemisimpleModule, Affine.Simplex.centroid_mem_median, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, Rat.ceil_cast, Matrix.posDef_inv_iff, Projectivization.instFiniteDimensionalSubtypeMemSubmoduleSubmodule, Valued.integer.mem_iff, FirstOrder.Field.model_hasChar_of_charP, WeierstrassCurve.Projective.addMap_of_Z_ne_zero, X_pow_sub_C_irreducible_of_prime_pow, WeierstrassCurve.Projective.equiv_zero_of_Z_eq_zero, ValuationSubring.nonunits_le, AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', RatFunc.finrank_ratFunc_ratFunc, SimpleGraph.FarFromTriangleFree.lt_one, SimpleGraph.left_nonuniformWitnesses_card, NumberField.hermiteTheorem.natDegree_le_rankOfDiscrBdd, Submodule.fg_iff_finiteDimensional, JacobsonNoether.exists_separable_and_not_isCentral', PowerSeries.intValuation_X, AlgebraicGeometry.Proj.valuativeCriterion_existence_aux, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal, one_div_le_of_neg, sub_smul_slope, Valued.completable, max_aleph0_card_le_rank_fun_nat, LocalSubring.instIsScalarTowerSubtypeMemSubringToSubringOfPrime, toIcoMod_zero_one, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', Nat.cast_choose_two, Polynomial.Monic.eq_X_pow_char_pow_sub_C_of_natSepDegree_eq_one_of_irreducible, Real.mk_eq, krullTopology_mem_nhds_one_iff_of_normal, finiteDimensional_bot, IsGalois.integral, Rat.cast_le_natCast, archimedean_iff_int_lt, geom_sum_Ico', LinearPMap.mkSpanSingleton_apply, IsPurelyInseparable.elemExponent_le_exponent, stdSimplex.barycenter_eq_centerMass, collinear_iff_not_affineIndependent_set, IsSimpleRing.exists_ringEquiv_matrix_divisionRing, Real.ofCauchy_one, ConjRootClass.mk_def, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, selfAdjoint.val_nnratCast, NumberField.to_charZero, instCharPLinearMapSubtypeMemSubringCenterId, AffineSubspace.direction_smul, Valuation.leAddSubgroup_zero, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, toIcoDiv_eq_floor, FGModuleCat.FGModuleCatDual_coe, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv, QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff, Projectivization.cross_mk_of_ne, Algebra.isSeparable_self, tendsto_nat_ceil_mul_div_atTop, NumberField.house_nat_mul, div_sub_div_same, StrictConvexOn.secant_strict_mono, separableClosure.isSeparable, minpoly.natDegree_le, LieAlgebra.IsKilling.chainBotCoeff_le_chainLength, FractionalIdeal.abs_det_basis_change, AddCircle.nsmul_eq_zero_iff, Real.mk_sup, wbtw_or_wbtw_smul_vadd_of_nonneg, IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen, IsCyclotomicExtension.splitting_field_cyclotomic, Valued.integer.isUnit_iff_norm_eq_one, trace_eq_sum_embeddings, ValuationSubring.mem_nonunits_iff, ArchimedeanClass.FiniteElement.mk_one, le_algebraicClosure_iff, Valued.toNormedField.norm_lt_iff, Valued.integer.isPrincipalIdealRing_of_compactSpace, FDRep.char_orthonormal, NumberField.RingOfIntegers.instIsScalarTower, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Hyperreal.infiniteNeg_neg, Hyperreal.coe_abs, FormalMultilinearSeries.ofScalars_series_eq_zero, Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec, Rat.cast_inv_nat, Polynomial.bernoulli_one, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, Field.finSepDegree_eq_finrank_iff, IsFractionRing.isAlgebraic_iff', Valuation.Integers.valuation_irreducible_pos, RootPairing.restrictScalars_toLinearMap_apply_apply, NumberField.RingOfIntegers.instIsScalarTower_1, LaurentSeries.comparePkg_eq_extension, NumberField.toNNReal_valued_eq_adicAbv, FiniteDimensional.exists_is_basis_integral, IntermediateField.coe_pow, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, Normal.out, Representation.irreducible_iff_isSimpleModule_asModule, WeierstrassCurve.Jacobian.Point.toAffine_zero, FixedPoints.minpoly_eq_minpoly, algebraicClosure.isAlgClosure, IsAlgebraic.inv_iff, IsPurelyInseparable.of_injective_comp_algebraMap, Quaternion.im_ratCast, legendreSym.eq_neg_one_iff', ModP.v_p_lt_val, jacobiSum_mul_jacobiSum_inv, RatFunc.single_zpow, LaurentSeries.valuation_def, FiniteField.X_pow_card_pow_sub_X_natDegree_eq, FiniteField.bijective_frobeniusAlgEquivOfAlgebraic_pow, ConvexOn.comp_affineMap, sum_Ioc_inv_sq_le_sub, Module.length_eq_finrank, AddCircle.addOrderOf_period_div, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, ConvexOn.monotoneOn_slope_gt, NumberField.isAlgebraic, Algebra.discr_powerBasis_eq_prod'', IsRealClosed.isSquare_or_isSquare_neg, MvPowerSeries.invOfUnit_eq', IsPrimitiveRoot.coe_toInteger, sub_half, sub_inv_antitoneOn_Icc_right, FunctionField.inftyValuation.C, Valued.instFaithfulSMulCompletionOfUniformContinuousConstSMul, Finset.centroid_pair_fin, one_div_lt_one_div_of_neg, Valuation.IsNontrivial.exists_lt_one, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, Polynomial.coeff_eq_esymm_roots_of_splits, NumberField.Embeddings.finite_of_norm_le, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one, centroid_mem_affineSpan_of_card_eq_add_one, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, Valuation.Integers.isUnit_iff_valuation_eq_one, ZMod.isSquare_of_jacobiSym_eq_one, hasRankNullity, round_eq_iff, isAlgClosure_iff, affineIndependent_iff_finrank_vectorSpan_eq, LieAlgebra.IsKilling.traceForm_coroot, Finset.centroidWeights_eq_const, ValuativeRel.inv_vle_one, Cubic.eq_sum_three_roots, IntermediateField.expChar', FDRep.char_dual, FormalMultilinearSeries.ofScalars_comp_neg, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow, FiniteField.card', FGModuleCat.FGModuleCatEvaluation_apply', LieModule.traceForm_eq_sum_finrank_nsmul_mul, discrim_lt_zero, convexHull_eq_union, div_sub_one, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, ValuationRing.instValuationRingInteger, quadraticChar_eq_pow_of_char_ne_two, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, GenContFract.IntFractPair.exists_succ_get?_stream_of_gcf_of_get?_eq_some, convexHull_eq, AddValuation.map_div, NumberField.basisOfFractionalIdeal_apply, GenContFract.conts_recurrence, LieAlgebra.IsKilling.chainBotCoeff_zero_right, zpow_succ', rank_quotient_add_rank_of_divisionRing, slope_fun_def_field, GenContFract.get?_of_eq_some_of_succ_get?_intFractPair_stream, mem_separableClosure_iff, div_sub', discrim_lt_zero_of_neg, AddCircle.addOrderOf_div_of_gcd_eq_one', quadraticChar_eq_pow_of_char_ne_two', Real.cauchy_one, RingOfIntegers.algebraMap_norm_algebraMap, bijective_rangeRestrict_comp_of_valuationRing, FiniteDimensional.instSubtypeMemSubmoduleMap, isSeparable_iff_finInsepDegree_eq_one, Set.integer_valuation_le_one, Polynomial.separable_cyclotomic, Subfield.coe_toAddSubgroup, OrderIso.smulRightDual_symm_apply, one_le_div_of_neg, CyclotomicField.instCharZero, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, ValuativeRel.inv_vlt_one, GenContFract.zeroth_conv'Aux_eq_zero, PowerSeries.inv_eq_inv_aux, Algebra.discr_powerBasis_eq_prod', Polynomial.X_sub_C_mul_removeFactor, wbtw_total_of_sameRay_vsub_left, LieAlgebra.IsKilling.chainBotCoeff_add_chainTopCoeff, NumberField.FinitePlace.isFinitePlace, wbtw_or_wbtw_smul_vadd_of_nonpos, LinearMap.isCompl_span_singleton_orthogonal, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, FixedPoints.toAlgAut_bijective, Cubic.eq_prod_three_roots, right_le_midpoint, FiniteField.isSplittingField_sub, NumberField.InfinitePlace.map_intCast, Projectivization.generalLinearGroup_smul_def, GenContFract.of_h_eq_floor, MvPowerSeries.invOfUnit_eq, CauSeq.lt_total, IsUltrametricDist.isNonarchimedean_algNormOfAlgEquiv, Hyperreal.abs_omega, FDRep.instHasFiniteLimits, Valued.integer.totallyBounded_iff_finite_residueField, divRadical_dvd_wronskian_left, instIsPrincipalIdealRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, LieAlgebra.IsKilling.rootSpace_two_smul, NumberField.instFiniteIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, nnratCast_def, convexHull_rangle_single_eq_stdSimplex, AffineSubspace.SOppSide.exists_sbtw, IsUltrametricDist.isPowMul_algNormOfAlgEquiv, LaurentSeries.ratfuncAdicComplRingEquiv_apply, instIsLocalizationIntPosRat, IsIdempotentElem.quasispectrum_subset, separableClosure_le_iff, solvableByRad.isIntegral, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, LinearMap.rank_add_le, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, Valuation.Uniformizer.is_generator, instExpCharLinearMapSubtypeMemSubringCenterId, Real.cauchy_ratCast, WeierstrassCurve.Projective.Point.toAffine_zero, Nat.count_modEq_card_eq_ceil, WeierstrassCurve.Jacobian.neg_of_Z_ne_zero, Representation.is_simple_module_iff_irreducible_ofModule, Polynomial.qsmul_eq_C_mul, qsmul_def, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, quadraticChar_neg_one, Matrix.den_one, gauge_smul_left, Hyperreal.infinitesimal_neg, ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdeal, NumberField.IsCMField.infinitePlace_complexConj, Hyperreal.coe_neg, IntermediateField.isAlgebraic_adjoin_iff_bot, Module.Basis.traceDual_powerBasis_eq, ConcaveOn.slope_anti_adjacent, AddCircle.intCast_div_mul_eq_zsmul, ValuationSubring.subtype_apply, isAlgebraic_of_mem_rootSet, Rat.isNNRat_intFract_of_isNNRat, Module.End.genEigenspace_restrict_eq_top, FixedPoints.smulCommClass', Valuation.one_le_val_iff, Subring.eq_iInf_of_isIntegrallyClosedIn, DualNumber.ideal_trichotomy, IsFractionRing.lift_fieldRange, finrank_vectorSpan_range_add_one_le, Quaternion.re_ratCast, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, FixedPoints.coe_algebraMap, IsInvariantSubfield.smul_mem, ValuationSubring.valuation_eq_one_iff, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, WeierstrassCurve.Projective.dblX_eq, CauSeq.exists_gt, Real.cauchy_mul, FiniteDimensional.subalgebra_toSubmodule, Cubic.d_eq_three_roots, Set.integer_eq, Valuation.isEquiv_tfae, zpow_eq_one_iff_cases₀, Valuation.valuationSubring_eq_top_iff, Hyperreal.abs_lt_real_iff_infinitesimal, CauSeq.const_inv, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, Projectivization.cross_mk_of_cross_eq_zero, Finset.centerMass_neg_left, LieAlgebra.IsKilling.chainTopCoeff_le_chainLength, AddCircle.addOrderOf_coe_rat, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly, ValuationSubring.ofPrime_localization, ArchimedeanClass.mk_div, div_sub_div, Real.ringEquivCauchy_apply, zpow_eq_zpow_iff_cases₀, Valuation.HasExtension.instIsScalarTower_valuationSubring, FDRep.instProjectiveOfNeZeroCastCard, MvPolynomial.comp_C_integral_of_surjective_of_isJacobsonRing, GenContFract.sub_convs_eq, ZMod.prod_Ico_one_prime, LinearMap.finrank_maxGenEigenspace_eq, Real.mk_neg, spectralAlgNorm_isPowMul, Rat.cast_multiset_sum, Polynomial.hilbertPoly_mul_one_sub_pow_add, homothety_inv_two, IntermediateField.finiteDimensional_map, CauSeq.trichotomy, OnePoint.equivProjectivization_apply_coe, NumberField.Units.finrank_mul_regulator_eq_det, Configuration.ofField.mem_iff, Affine.Simplex.centroid_reindex, ValuativeRel.one_srel_inv, NumberField.InfinitePlace.prod_eq_abs_norm, IsSepClosure.isAlgClosure_of_perfectField, LieAlgebra.IsKilling.span_weight_eq_top, coplanar_iff_finrank_le_two, Valuation.isEquiv_iff_val_lt_one, GenContFract.squashSeq_nth_of_not_terminated, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, ValuationRing.coe_equivInteger_apply, Algebra.IsSeparable.of_algHom, Rat.cast_neg, IsAdjoinRoot.primitive_element_root, geom_sum_Ico, RingHom.rangeRestrictFieldEquiv_apply_coe, wbtw_pointReflection, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, one_sub_div, NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype, Algebra.isSeparable_residueField_iff, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, NumberField.FinitePlace.norm_le_one, geom_sum₂_Ico, mul_sub_mul_div_mul_neg_iff, NumberField.InfinitePlace.map_natCast, NumberField.Units.sum_mult_mul_log, WeierstrassCurve.Projective.add_of_Y_ne, Valuation.leSubmodule_zero, Collinear.wbtw_or_wbtw_or_wbtw, NumberField.Embeddings.range_eval_eq_rootSet_minpoly, star_ratCast, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton, Valued.integer.norm_coe_unit, WeierstrassCurve.j_of_isShortNF, WithAbs.instIsSeparable, Lagrange.eval_basis_self, IntermediateField.forall_mem_adjoin_smul_eq_self_iff, HahnEmbedding.Partial.exists_domain_eq_top, LaurentSeries.mem_integers_of_powerSeries, div_lt_one_iff, one_div_le_one_div_of_neg_of_le, FirstOrder.Field.model_fieldOfChar_of_charP, WeierstrassCurve.IsGoodReduction.goodReduction, RingOfIntegers.coe_algebraMap_norm, Subfield.intCast_mem, centroid_mem_affineSpan_of_card_ne_zero, IsPrimitiveRoot.minpoly_dvd_cyclotomic, Algebra.IsAlgebraic.tower_bot, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, SubfieldClass.toSubringClass, LieModule.Weight.toLinear_neg, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero, IntermediateField.isPurelyInseparable_tower_top, Algebra.Etale.iff_exists_algEquiv_prod, NumberField.RingOfIntegers.minpoly_coe, Polynomial.bernoulli_comp_one_sub_X, Mathlib.Meta.NormNum.isNat_ofScientific_of_false, ZMod.fieldRange_castHom_eq_bot, CongruenceSubgroup.IsCongruenceSubgroup.conjGL, Subspace.map_dualCoannihilator, lineMap_slope_lineMap_slope_lineMap, FDRep.scalar_product_char_eq_finrank_equivariant, WeierstrassCurve.Jacobian.dblXYZ_of_Y_eq, Rat.cast_commute, Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, ValuationSubring.algebraMap_injective, NNRat.intFloor_cast, autAdjoinRootXPowSubC_root, Hyperreal.infinitePos_abs_iff_infinite, AddCircle.equivAddCircle_symm_apply_mk, Polynomial.cyclotomic_eq_minpoly, IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers, ZMod.euler_criterion, ValuationSubring.valuation_surjective, Cubic.b_eq_three_roots, Valuation.pos_iff, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, Valued.norm_pos_iff_valuation_pos, wbtw_midpoint, sub_div', sub_self_div_two, Hyperreal.IsSt.neg, Valuation.HasExtension.instLiesOverSubtypeMemValuationSubringValuationSubringMaximalIdeal, Subfield.coe_sub, Rat.natCast_lt_cast, perfectClosure.perfectRing, MvPolynomial.isAlgebraic_of_mem_vars_of_forall_totalDegree_le, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, NumberField.Units.dirichletUnitTheorem.exists_unit, ZMod.exists_sq_eq_neg_two_iff, FixedPoints.mem_intermediateField_iff, LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZero, CauSeq.sup_inf_distrib_left, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible, abs_zpow, ArchimedeanClass.FiniteElement.mk_natCast, lineMap_slope_slope_sub_div_sub, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, Int.cast_div_charZero, smul_inv'', tendsto_pow_atTop_nhds_zero_iff, IsTopologicalDivisionRing.toContinuousInv₀, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Rat.den_intFract, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int, Valued.toNormedField.norm_lt_one_iff, CauSeq.inf_idem, Polynomial.bernoulli_comp_neg_X, two_mul_le_add_mul_sq, WeierstrassCurve.Jacobian.add_of_Z_eq_zero, Int.cast_div, gaussSum_mul_gaussSum_eq_card, IsGalois.splits, Quaternion.normSq_div, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, NumberField.RingOfIntegers.instIsIntegralClosure, Polynomial.mod_def, Int.mod_nat_eq_sub_mul_floor_rat_div, Submodule.finiteDimensional_of_le, GenContFract.of_isSimpContFract, DualNumber.instIsPrincipalIdealRing, Polynomial.pairwise_coprime_X_sub_C, Matrix.sub_scalar_sq_eq_discr, archimedean_iff_int_le, RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_u, IsUltrametricDist.isPowMul_invariantExtension, ZMod.eisenstein_lemma_aux, HahnEmbedding.Partial.exists_isMax, NumberField.mixedEmbedding.norm_unit, Algebra.prod_embeddings_eq_finrank_pow, IsSepClosure.separable, Set.Finite.convexHull_eq, FiniteField.card_algHom_of_finrank_dvd, wbtw_iff_of_le, minpoly.eq_X_sub_C, finiteDimensional_direction_affineSpan_singleton, WeierstrassCurve.j_of_isCharTwoJNeZeroNF_of_char_two, AlgebraicClosure.instCharZero, Complex.sum_div_factorial_le, Lagrange.nodal_erase_eq_nodal_div, Rat.smul_def, Collinear.affineSpan_eq_of_ne, FunctionField.inftyValuation_apply, IsGalois.separable, FiniteField.algebraMap_norm_eq_pow_sum, WeierstrassCurve.Jacobian.addMap_of_Y_eq, NumberField.instIsAlgebraicSubtypeMemSubfield, Hyperreal.st_neg, JacobsonNoether.exists_separable_and_not_isCentral, ValuationSubring.integer_valuation, Rat.cast_divInt_of_ne_zero, Finset.centroid_def, ValuationSubring.primeSpectrumEquiv_apply, Height.mulHeight₁_neg, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, zpow_eq_one_iff_of_ne_zero₀, NumberField.IsCMField.complexConj_torsion, quotient_prod_linearEquiv, Int.Ico_filter_dvd_eq, ValuationSubring.mapOfLE_comp_valuation, Real.mk_le, LieModule.range_traceForm_le_span_weight, sub_inv_antitoneOn_Iio, LinearMap.le_rank_iff_exists_linearIndependent_finset, Valuation.val_le_one_iff, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, collinear_iff_not_affineIndependent, IsGalois.to_isSeparable, Quaternion.normSq_ratCast, FDRep.dualTensorIsoLinHom_hom_hom, LinearMap.rank_finset_sum_le, instIsIntegrallyClosedSubtypeMemSubring, Subfield.mem_carrier, Valued.isTopologicalDivisionRing, LieAlgebra.IsKilling.corootSpace_zero_eq_bot, LaurentSeries.exists_ratFunc_eq_v, Real.ringEquivCauchy_symm_apply_cauchy, FixedPoints.minpoly.eval₂, IntermediateField.zsmul_mem, Valued.toNormedField.one_le_norm_iff, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, rat_inv_continuous_lemma, WeierstrassCurve.Projective.dblXYZ_of_Y_eq, gaussSum_sq, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, IntermediateField.isSeparable_tower_top, slope_def_module, LinearMap.finrank_eigenspace_le, Module.End.eigenspace_aeval_polynomial_degree_1, inv_eq_of_aeval_divX_ne_zero, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, exists_eq_sum_perm_of_mem_doublyStochastic, ValuationSubring.coe_subtype, Rat.floor_intCast_div_natCast, Real.isCauSeq_iff_lift, Ideal.Fiber.exists_smul_eq_one_tmul, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, normalClosure.is_finiteDimensional, HahnEmbedding.Seed.domain_baseEmbedding, Algebra.IsSeparable.trans, IntermediateField.finiteDimensional_sup, Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin, separableClosure.eq_bot_iff, Algebra.normalizedTrace_self_apply, ConjRootClass.mk_eq_mk, Polynomial.normalizedFactors_cyclotomic_card, Subfield.coe_neg, Affine.Simplex.faceOppositeCentroid_eq_affineCombination, Valuation.coeff_zero_minpoly, Module.length_eq_rank, Subgroup.IsArithmetic.conj, Polynomial.coeff_preHilbertPoly_self, exists_rat_near, CauSeq.const_pos, IntermediateField.AdjoinPair.algebraMap_gen₂, AffineBasis.exists_affineBasis_of_finiteDimensional, Valuation.IsRankOneDiscrete.generator_mem_range, Height.mulHeight₁_one, irreducible_X_pow_sub_C_of_root_adjoin_eq_top, NumberField.house.basis_repr_norm_le_const_mul_house, Affine.Simplex.centroid_mem_affineSpan, Valued.integer.exists_norm_coe_lt_one, Submodule.mem_traceDual_iff_isIntegral, LieAlgebra.IsKilling.rootSystem_root_apply, Hyperreal.coe_sub, NumberField.IsCMField.Units.complexConj_eq_self_iff, IntermediateField.isIntegral_iff, LinearMap.finiteDimensional_range, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, homothety_one_half, Subfield.coe_toSubmonoid, GenContFract.of_s_succ, WeierstrassCurve.Jacobian.neg_of_Z_eq_zero, Algebra.IsAlgebraic.isSeparable_of_perfectField, ArchimedeanClass.mk_inv, Affine.Simplex.centroid_vsub_point_eq_smul_vsub, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, Submodule.finiteDimensional_inf_left, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, NNRat.instContinuousSMulRatReal, finrank_vectorSpan_insert_le_set, convexHull_range_eq_exists_affineCombination, WeierstrassCurve.j_of_isCharThreeJNeZeroNF_of_char_three, wbtw_iff_sameRay_vsub, Field.mod_eq, IsRealClosed.isSquare_neg_of_not_isSquare, Int.sub_floor_div_mul_lt, IsCyclotomicExtension.isSeparable, Complex.nonempty_linearEquiv_real, IntermediateField.AdjoinSimple.algebraMap_gen, Valuation.Integers.dvd_iff_le, LieModule.Weight.coe_neg, IntermediateField.isPurelyInseparable_sup, Matrix.Pivot.listTransvecRow_getElem, map_inv_intCast_smul, NumberField.FinitePlace.norm_def, CauSeq.coe_inf, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, Rat.ringOfIntegersWithValEquiv_apply, Rat.cast_sub, GenContFract.convs'Aux_succ_none, Int.fract_div_intCast_eq_div_intCast_mod, Int.Ioc_filter_dvd_card, Rat.ceil_def', Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModule, GenContFract.abs_sub_convs_le, Affine.Simplex.centroid_vsub_eq, Valuation.isNontrivial_iff_not_a_field, FirstOrder.Field.charP_iff_model_fieldOfChar, finiteDimensional_vectorSpan_insert, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, ValuationSubring.principalUnitGroup_symm_apply, Convex.mem_Ioc, Quaternion.re_nnratCast, FDRep.simple_iff_char_is_norm_one, Valuation.HasExtension.algebraMap_injective, ValuationRing.instIsFractionRingInteger, X_pow_sub_C_irreducible_iff_of_prime, selfAdjoint.val_nnqsmul, CauSeq.inf_le_left, Subspace.dualPairing_eq, inv_eq_of_root_of_coeff_zero_ne_zero, zpow_eq_neg_one_iff₀, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, FiniteDimensional.span_singleton, Height.mulHeight_one, finrank_vectorSpan_range_le, Real.ofCauchy_inf, AddCircle.homeomorphAddCircle_symm_apply_mk, AddCircle.gcd_mul_addOrderOf_div_eq, IsPurelyInseparable.elemExponent_def, WeierstrassCurve.Jacobian.add_of_Y_ne, separableClosure.isPurelyInseparable, WeierstrassCurve.Projective.negDblY_of_Y_eq, Rat.cast_one, LinearMap.instIsStablyFiniteRing, IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers, OnePoint.equivProjectivization_apply_infinity, Convex.mem_Ico, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, LinearMap.BilinForm.apply_dualBasis_right, FixedBy.subfield_mem_iff, Hyperreal.archimedeanClassMk_epsilon_pos, GenContFract.contsAux_recurrence, circleEquivGen_apply, Rat.cast_eq_zero, isCyclic_tfae, Polynomial.IsSplittingField.finiteDimensional, AddValuation.map_inv, Hyperreal.IsSt.infinitesimal_sub, Hyperreal.tendsto_atTop_iff, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, Valuation.HasExtension.algebraMap_mem_maximalIdeal_iff, RatFunc.num_denom_neg, IsIntegral.tower_bot_of_field, Finpartition.IsEquipartition.card_interedges_sparsePairs_le', IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, degree_radical_le, perfectClosure.isPurelyInseparable, GenContFract.IntFractPair.stream_succ, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Polynomial.valuation_X_eq_neg_one, IntermediateField.isSeparable_adjoin_iff_isSeparable, AddCircle.natCast_div_mul_eq_nsmul, Lagrange.eval_basis_not_at_node, Hyperreal.Infinitesimal.neg, FDRep.finrank_hom_simple_simple, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, prod_galRestrict_eq_norm, Module.Basis.traceDual_eq_iff, IsGaloisGroup.fixedPoints_eq_bot, ZMod.pow_div_two_eq_neg_one_or_one, Quaternion.imI_ratCast, GaloisField.splits_zmod_X_pow_sub_X, Polynomial.comp_C_integral_of_surjective_of_isJacobsonRing, Valuation.isEquiv_iff_valuationSubring, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, Polynomial.Monic.eq_X_sub_C_pow_of_natSepDegree_eq_one_of_splits, Rep.instInjective, NormedSpace.exp_eq_ofScalarsSum, IntermediateField.coe_one, Polynomial.modByMonic_eq_mod, instIsInvariantSubringOfIsInvariantSubfield, IsFractionRing.charZero_of_isFractionRing, HahnEmbedding.Partial.toOrderAddMonoidHom_injective, IsPurelyInseparable.tower_top
zpow 📖	CompOp	3 math math: zpow_neg', zpow_zero', zpow_succ'

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
div_eq_mul_inv 📖	mathematical	—	toDiv NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring toRing toInv	—	—
inv_zero 📖	mathematical	—	toInv AddMonoid.toZero AddCommMonoid.toAddMonoid NonUnitalNonAssocSemiring.toAddCommMonoid NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring toRing	—	—
mul_inv_cancel 📖	mathematical	—	NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring toRing toInv Semiring.toOne	—	—
nnqsmul_def 📖	mathematical	—	nnqsmul NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring toRing NNRat.cast toNNRatCast	—	—
nnratCast_def 📖	mathematical	—	NNRat.cast toNNRatCast toDiv Semiring.toNatCast Ring.toSemiring toRing NNRat.num NNRat.den	—	—
qsmul_def 📖	mathematical	—	qsmul NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring toRing toRatCast	—	—
ratCast_def 📖	mathematical	—	toRatCast toDiv Ring.toIntCast toRing Semiring.toNatCast Ring.toSemiring	—	—
toNontrivial 📖	mathematical	—	Nontrivial	—	—
zpow_neg' 📖	mathematical	—	zpow toInv	—	—
zpow_succ' 📖	mathematical	—	zpow NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring toRing	—	—
zpow_zero' 📖	mathematical	—	zpow Semiring.toOne Ring.toSemiring toRing	—	—

DivisionSemiring

Definitions

Name	Category	Theorems
nnqsmul 📖	CompOp	1 math math: nnqsmul_def
toDiv 📖	CompOp	2 math math: div_eq_mul_inv, nnratCast_def
toGroupWithZero 📖	CompOp	477 math math: Polynomial.natDegree_mul_leadingCoeff_inv, nnnorm_inv, half_lt_self, NormedSpace.exp_neg_of_mem_ball, Rat.cast_inv_of_ne_zero, LieAlgebra.IsKilling.iInf_ker_weight_eq_bot, hasSum_geometric_of_norm_lt_one, exists_nat_one_div_lt, Mathlib.Tactic.RingNF.nnrat_rawCast, Valuation.inversion_estimate', Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, max_div_div_right, hasSum_div_const_iff, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal, RCLike.tendsto_inverse_atTop_nhds_zero_nat, CauSeq.Completion.ofRat_inv, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, Nat.cast_choose_eq_ascPochhammer_div, tendsto_const_div_atTop_nhds_zero_nat, TendstoLocallyUniformlyOn.inv₀, Mathlib.Meta.NormNum.isRat_inv_pos, div_lt_self, CauSeq.inv_aux, IsAbsoluteValue.abv_div, one_div_add_one_div, Filter.inv_nhdsWithin_ne_zero, Function.Antiperiodic.mul_const', DifferentiableAt.fun_inv, NumberField.RingOfIntegers.instSMulDistribClass, LinearMap.IsSymmetric.diagonalization_apply_self_apply, LieAlgebra.IsKilling.isCompl_ker_weight_span_coroot, Function.Antiperiodic.const_mul, cfc_map_div, one_div_pow_strictAnti, DilationEquiv.smulTorsor_symm_apply, LieModule.traceForm_eq_sum_finrank_nsmul', Nonneg.mk_div_mk, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, Valuation.val_le_one_or_val_inv_lt_one, sum_div_card_sq_le_sum_sq_div_card, TrivSqZeroExt.inv_inl, Nat.floor_div_natCast, IsAlgClosure.of_exists_root, Differentiable.fun_inv, Set.unitEquivUnitsInteger_symm_apply_coe, inv_intCast_smul_eq, TrivSqZeroExt.inv_one, Normal.minpoly_eq_iff_mem_orbit, differentiableWithinAt_inv, NNRat.cast_def, Mathlib.Meta.NormNum.isNat_inv_zero, Polynomial.degree_mul_leadingCoeff_inv, ZSpan.smul, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, AnalyticOn.fun_inv, Filter.tendsto_div_const_atTop_iff_pos, TendstoLocallyUniformlyOn.fun_inv₀_of_disjoint, lineMap_inv_two, Subring.center.coe_inv, inv_natCast_smul_eq, FractionalIdeal.count_finsuppProd, IsAlgClosure.of_exist_roots, ENNReal.orderIsoRpow_symm_apply, TendstoLocallyUniformly.fun_inv₀, AntivaryOn.div_right₀, add_halves, Nat.one_div_le_one_div, Filter.inv_nhdsNE_zero, inv_intCast_smul_comm, ValuationSubring.mem_inv_pointwise_smul_iff, tsum_geometric_of_norm_lt_one, Filter.tendsto_div_const_atTop_of_pos, IsAlgClosed.instIsAlgClosure, LieAlgebra.IsKilling.le_chainBotCoeff_of_rootSpace_ne_top, Function.Antiperiodic.div_inv, Nonneg.mk_zpow, dist_inv_inv₀, tendsto_norm_inv_nhdsNE_zero_atTop, half_pos, Function.Periodic.mul_const', lt_one_div, LieAlgebra.IsKilling.apply_coroot_eq_cast', LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, Mathlib.Tactic.LinearCombination.div_lt_const, Matrix.conjTranspose_inv_intCast_smul, Mathlib.Meta.NormNum.isNat_inv_one, Int.self_le_zpow_clog, DualNumber.inv_eps, Finset.card_div_choose_le_card_shadow_div_choose, NNRat.cast_div, MonovaryOn.div_right₀, Nonneg.inv_mk, one_div_strictAntiOn, tendsto_zpow_atTop_zero, Valuation.val_lt_one_iff, Finset.local_lubell_yamamoto_meshalkin_inequality_div, OrderIso.smulRightDual_apply, Valuation.val_le_one_or_val_inv_le_one, GenContFract.convs'_succ, Polynomial.irreducible_mul_leadingCoeff_inv, Bornology.isVonNBounded_iff_absorbing_le, Nat.floor_div_ofNat, Commute.inv_sub_inv, LinearEquiv.toSpanNonzeroSingleton_homothety, Valuation.one_lt_val_iff, Subfield.coe_inv, Filter.inv_cobounded₀, Nat.cast_div_charZero, FractionalIdeal.count_finprod_coprime, ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem, Valuation.val_eq_one_iff, tendsto_one_div_add_atTop_nhds_zero_nat, summable_const_div_iff, nndist_inv_inv₀, one_lt_div, ValuationSubring.smul_mem_pointwise_smul_iff, Int.zpow_le_iff_le_log, Monovary.div_right₀, FractionalIdeal.finprod_heightOneSpectrum_factorization, Finset.sq_sum_div_le_sum_sq_div, inv_add_inv', NormedSpace.exp_conj, Rat.cast_inv_int, Polynomial.natDegree_mul_leadingCoeff_self_inv, Matrix.conjTranspose_inv_natCast_smul, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', Filter.tendsto_inv₀_cobounded, Submodule.mem_smul_iff_inv_mul_mem, IsGaloisGroup.mulEquivCongr_apply_smul, Mathlib.Meta.NormNum.isNat_zpow_pos, isCoveringMap_zpow, div_add', norm_commutator_sub_one_le, FractionalIdeal.count_finprod, AnalyticWithinAt.inv, Function.Periodic.div_const, Filter.tendsto_zpow_atTop_atTop, fderivWithin_inv', Int.lt_zpow_iff_log_lt, AlgebraicClosure.instIsAlgClosureOfIsAlgebraic, LinearMap.IsSymmetric.diagonalization_symm_apply, geom_sum_inv, div_nat_lt_self_of_pos_of_two_le, UniformContinuousOn.fun_inv₀, one_div_mul_add_mul_one_div_eq_one_div_add_one_div, StrictMono.div_const, DifferentiableOn.inv, Mathlib.Meta.NormNum.isNNRat_zpow_pos, AddCommGroup.mul_modEq_mul_left, Nat.one_div_cast_pos, one_div_lt, Nat.cast_add_choose, add_thirds, div_two_lt_of_pos, hasSum_const_div_iff, DilationEquiv.mulRight_symm_apply, le_div_self, sup_eq_half_smul_add_add_abs_sub', Nat.floor_div_eq_div, tendsto_natCast_div_add_atTop, Int.zpow_pred_clog_lt_self, Commute.div_add_div, AddCommGroup.div_modEq_div, one_half_lt_one, DilationEquiv.mulLeft_symm_apply, Units.continuousOn_zpow₀_spectrum, CauSeq.coe_inv, instSMulDistribClassAlgEquiv, Matrix.conjTranspose_inv_ofNat_smul, RCLike.tendsto_add_mul_div_add_mul_atTop_nhds, DilationEquiv.mulLeft_apply, Polynomial.eval_homogenize, star_inv_intCast_smul, summable_div_const_iff, Nonneg.val_inv_unitsHomeomorphPos_symm_apply_coe, div_pos_iff_of_pos_right, TrivSqZeroExt.mul_inv_cancel, TrivSqZeroExt.inv_mul_cancel, HasSum.div_const, Finset.centroidWeights_apply, LieAlgebra.IsKilling.apply_coroot_eq_cast, inv_natCast_smul_comm, AnalyticWithinAt.fun_inv, Function.Antiperiodic.const_inv_mul, UniformContinuousOn.inv₀, TrivSqZeroExt.invOf_eq_inv, tsum_div_const, div_le_self, div_add_div_same, Mathlib.Meta.NormNum.IsNNRat.to_eq, Mathlib.Meta.NormNum.isNNRat_inv_pos, NNRat.cast_zpow, DifferentiableAt.inv, AlgebraicClosure.instIsAlgClosure, DifferentiableWithinAt.inv, Polynomial.degree_mul_leadingCoeff_self_inv, Nat.choose_lt_pow_div, map_inv_natCast_smul, Mathlib.Meta.NormNum.isInt_inv_neg_one, Bound.div_lt_one_of_pos_of_lt, geom_sum_of_lt_one, Nat.cast_div_div_div_cancel_right, one_div_pow_lt_one_div_pow_of_lt, DilationEquiv.mulRight_apply, NormedSpace.exp_conj', add_div', Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, Filter.tendsto_inv₀_nhdsWithin_ne_zero, exists_mem_Ico_zpow, norm_inv, TrivSqZeroExt.inv_inv, Polynomial.dvd_mul_leadingCoeff_inv, Finset.le_card_falling_div_choose, inv_eq_self₀, one_div_le_one_div, OnePoint.equivProjectivization_symm_apply_mk, AntivaryOn.div_left₀, algebraMap.coe_div, cfc_zpow, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, AnalyticOn.inv, AddCommGroup.mul_modEq_mul_right, GenContFract.of_s_head, AffineBasis.coord_apply_centroid, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, half_lt_self_iff, div_nat_le_self_of_nonnneg, star_inv_natCast_smul, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, Finset.sum_div, Nat.cast_div, TendstoLocallyUniformly.fun_inv₀_of_disjoint, NormedDivisionRing.to_continuousInv₀, Function.Periodic.const_smul₀, Int.zpow_log_le_self, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, Subfield.inv_mem, LieAlgebra.IsKilling.disjoint_ker_weight_corootSpace, Finset.sum_card_slice_div_choose_le_one, one_div_le_one_div_of_le, tendsto_pow_neg_atTop, DifferentiableOn.fun_inv, tendsto_add_mul_div_add_mul_atTop_nhds, Metric.unitSphere.coe_inv, tendsto_one_div_atTop_nhds_zero_nat, div_le_one, Multiset.sum_map_div, LieModule.traceForm_eq_sum_finrank_nsmul, Int.lt_zpow_succ_log_self, Ideal.finite_mulSupport_coe, PowerSeries.invOfUnit_eq, exists_mem_Ioc_zpow, TendstoLocallyUniformlyOn.inv₀_of_disjoint, UniformContinuous.inv₀, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, TrivSqZeroExt.isUnit_inv_iff, LieAlgebra.IsKilling.chainTopCoeff_add_chainBotCoeff, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, Valuation.map_inv, HasDerivAt.hasFDerivAt_equiv, TrivSqZeroExt.inv_neg, div_add_one, Rat.cast_inv, MonovaryOn.div_left₀, hasFPowerSeriesOnBall_inv_one_sub, FractionalIdeal.count_zpow_self, Finset.cast_subConst, Finset.nnratCast_dens, one_div_le, Complex.isOpenQuotientMap_zpow_compl_zero, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff, Asymptotics.IsBigO.inv_rev, one_half_pos, FractionalIdeal.count_neg_zpow, Function.Periodic.const_inv_mul, IsAlgClosure.ofAlgebraic, half_le_self, div_add_div, Finset.cast_mulConst, Int.clog_zpow, div_lt_one, NNRat.cast_zpow_of_ne_zero, Function.Antiperiodic.mul_const, Asymptotics.IsLittleO.inv_rev, GenContFract.of_s_tail, Nat.one_div_cast_nonneg, min_div_div_right, Algebra.IsIntegral.inv_mem, Polynomial.monic_mul_leadingCoeff_inv, Nat.cast_div_le, inv_sub_inv', Function.Periodic.mul_const_inv, Nat.one_div_pos_of_nat, analyticOn_inv, NNReal.orderIsoRpow_symm_eq, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, IsAbsoluteValue.abv_inv, ValuationSubring.coe_pointwise_smul, Polynomial.degree_add_degree_leadingCoeff_inv, Monovary.div_left₀, LieAlgebra.IsKilling.chainTopCoeff_zero_right, CauSeq.inv_apply, self_eq_inv₀, TendstoLocallyUniformlyOn.fun_inv₀, LinearEquiv.smulOfNeZero_symm_apply, NormedSpace.exp_neg, Int.le_zpow_iff_clog_le, Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero, LieAlgebra.IsKilling.orthogonal_span_coroot_eq_ker, monotone_div_right_of_nonneg, div_add_same, NNReal.tendsto_inverse_atTop_nhds_zero_nat, mem_segment_iff_div, NNRat.cast_inv, TendstoLocallyUniformly.inv₀_of_disjoint, one_div_lt_one_div, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, NNRat.cast_div_of_ne_zero, nnnorm_commutator_sub_one_le, IsSepClosure.isAlgClosure_of_perfectField_top, IsIntegral.inv_mem, TendstoLocallyUniformly.inv₀, AnalyticAt.fun_inv, Filter.EventuallyEq.div_mul_cancel_atTop, Filter.Tendsto.atTop_div_const, Int.log_zpow, GenContFract.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero, Mathlib.Tactic.LinearCombination.div_le_const, Finset.centroid_pair, same_add_div, Nat.choose_le_pow_div, LieAlgebra.IsKilling.chainBotCoeff_of_eq_zsmul_add, geom₂_sum_of_lt, Antivary.div_right₀, Monotone.div_const, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, ValuationSubring.mem_smul_pointwise_iff_exists, Mathlib.Meta.NormNum.isRat_inv_neg, NNRat.cast_divNat_of_ne_zero, FractionalIdeal.count_zpow, LieAlgebra.IsKilling.chainBotCoeff_le_chainLength, ArithmeticFunction.pdiv_zeta, uniformContinuousOn_inv₀, one_div_lt_one_div_of_lt, Int.zpow_lt_iff_lt_clog, Rat.cast_inv_nat, strictMono_div_right_of_pos, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, Nonneg.coe_div, Finset.cast_divConst, algebraicClosure.isAlgClosure, inf_eq_half_smul_add_sub_abs_sub', one_add_div, Nat.pow_le_choose, Finset.centroid_pair_fin, LieAlgebra.IsKilling.coe_invtSubmoduleToLieIdeal_eq_iSup, Polynomial.degree_leadingCoeff_inv, Asymptotics.IsBigOWith.inv_rev, isAlgClosure_iff, LieAlgebra.IsKilling.traceForm_coroot, Finset.centroidWeights_eq_const, analyticAt_inv, geom_sum_of_one_lt, Ideal.finprod_heightOneSpectrum_factorization_coe, LieModule.traceForm_eq_sum_finrank_nsmul_mul, Function.Antiperiodic.mul_const_inv, IsIntegral.inv, Mathlib.Meta.Positivity.zpow_zero_pos, Bound.one_lt_div_of_pos_of_lt, LieAlgebra.IsKilling.chainBotCoeff_zero_right, IsLocalRing.ResidueField.residue_smul, OrderIso.smulRightDual_symm_apply, LieAlgebra.IsKilling.chainTopCoeff_of_eq_zsmul_add, hasStrictFDerivAt_inv', Filter.map_div_atTop_eq, LieAlgebra.IsKilling.chainBotCoeff_add_chainTopCoeff, analyticAt_inv_one_sub, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, mem_openSegment_iff_div, MvPowerSeries.invOfUnit_eq, exists_zpow_btwn_of_lt_mul, Finset.expect_div, tendsto_inverse_atTop_nhds_zero_nat, one_div_pow_le_one_div_pow_of_le, one_div_pow_anti, GenContFract.IntFractPair.exists_succ_nth_stream_of_fr_zero, Antivary.div_left₀, Valuation.one_le_val_iff, IsSelfAdjoint.div, TrivSqZeroExt.inv_zero, Nat.cast_choose, CauSeq.const_inv, birkhoffAverage_apply_sub_birkhoffAverage, LieAlgebra.IsKilling.chainTopCoeff_le_chainLength, Nonneg.coe_zpow, Mathlib.Tactic.Ring.div_pf, analyticOnNhd_inv, NNRat.cast_divNat, ProbabilityTheory.gaussianPDFReal_mul, Circle.toUnits_apply, NormedDivisionRing.to_hasContinuousInv₀, one_le_div, one_lt_one_div, ValuationSubring.smul_mem_pointwise_smul, IsSepClosure.isAlgClosure_of_perfectField, LieAlgebra.IsKilling.span_weight_eq_top, Filter.tendsto_inv₀_nhdsNE_zero, DifferentiableWithinAt.fun_inv, Nonneg.val_inv_unitsEquivPos_symm_apply_coe, IsIntegral.inv_mem_adjoin, tsub_div, differentiableAt_inv, AnalyticAt.inv, NNRat.cast_inv_of_ne_zero, algebraMap.coe_inv, pow_sum_div_card_le_sum_pow, LieModule.Weight.toLinear_neg, Function.Periodic.mul_const, HasStrictDerivAt.hasStrictFDerivAt_equiv, hasFDerivAt_inv', Finset.expect_eq_sum_div_card, OpenPartialHomeomorph.unitBallBall_symm_apply, TrivSqZeroExt.mul_inv_rev, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction, add_div_two_lt_right, smul_inv'', enorm_inv, IsTopologicalDivisionRing.toContinuousInv₀, Summable.div_const, Commute.inv_add_inv, NNReal.tendsto_const_div_atTop_nhds_zero_nat, Differentiable.inv, Mathlib.Tactic.LinearCombination.div_lt_const_weak, OpenPartialHomeomorph.unitBallBall_apply, half_le_self_iff, Ideal.finite_mulSupport_inv, Commute.one_div_add_one_div, AnalyticOnNhd.fun_inv, Function.Periodic.const_mul, geom₂_sum_of_gt, Valuation.val_le_one_iff, rat_inv_continuous_lemma, algebraMap.coe_zpow, Subfield.inv_mem', one_le_one_div, SubfieldClass.toInvMemClass, Nat.one_div_lt_one_div, tendsto_inv_atTop_nhds_zero_nat, Affine.Simplex.faceOppositeCentroid_eq_affineCombination, Finset.cast_addConst, Function.Periodic.const_inv_smul₀, le_one_div, LieAlgebra.IsKilling.rootSystem_root_apply, left_lt_add_div_two, GenContFract.of_s_succ, differentiableOn_inv, GenContFract.IntFractPair.succ_nth_stream_eq_some_iff, TrivSqZeroExt.inv_inr, UniformContinuous.fun_inv₀, map_inv_intCast_smul, Filter.tendsto_inv₀_cobounded', Valuation.inversion_estimate, Affine.Simplex.centroid_vsub_eq, GenContFract.IntFractPair.stream_succ_of_some, FractionalIdeal.finprod_heightOneSpectrum_factorization', inv_add_inv, AnalyticOnNhd.inv, cfcUnits_zpow, add_div_eq_mul_add_div, add_div, AddValuation.map_inv, div_pos_iff_of_pos_left, GenContFract.IntFractPair.stream_succ, add_self_div_two, fderiv_inv', Fintype.expect_eq_sum_div_card
toInv 📖	CompOp	4 math math: div_eq_mul_inv, mul_inv_cancel, inv_zero, zpow_neg'
toNNRatCast 📖	CompOp	97 math math: NNRat.cast_strictMono, Finset.card_mul_cast_addConst, NNRat.not_cast_lt_zero, NNRat.cast_eq_zero, Polynomial.nnqsmul_eq_C_mul, NNRat.cast_one, NNRat.cast_commute, NNRat.cast_listProd, NNRat.cast_def, NNRat.cast_add_of_ne_zero, NNRat.cast_le, NNRat.cast_add, Nonneg.mk_nnratCast, NNRat.cast_mono, NNRat.cast_div, NNRat.cast_inj, NNRat.floor_cast, Finset.cast_subConst_mul_card, NNRat.cast_multisetProd, NNRat.one_le_cast, Nonneg.coe_nnratCast, nnqsmul_def, Finset.card_mul_cast_subConst, NNRat.cast_nonneg, NNRat.cast_prod, NNRat.coe_castHom, map_nnratCast, NNRat.preimage_cast_Iic, NNRat.natCast_le_cast, NNRat.preimage_cast_Ioi, NNRat.natCast_lt_cast, NNRat.cast_le_one, NNRat.cast_sum, NNRat.preimage_cast_uIcc, NNRat.cast_zpow, NNRat.preimage_cast_Icc, NNRat.cast_injective, nnratCast_def, Finset.cast_mulConst_mul_card, NNRat.cast_pow, NNRat.cast_multisetSum, NNRat.preimage_cast_Ici, NNRat.cast_min, NNRat.one_lt_cast, Finset.cast_subConst, star_nnratCast, Finset.nnratCast_dens, NNRat.cast_max, Finset.cast_mulConst, NNRat.cast_pos, NNRat.cast_zpow_of_ne_zero, Finset.card_mul_cast_mulConst, NNRat.ofNat_le_cast, NNRat.cast_mul, NNRat.ceil_cast, NNRat.cast_smul_eq_nnqsmul, NNRat.preimage_cast_Ico, NNRat.cast_nonpos, Finset.natCast_card_mul_nnratCast_dens, Finset.cast_addConst_mul_card, NNRat.cast_inv, NNRat.cast_div_of_ne_zero, NNRat.smul_one_eq_cast, Finset.cast_divConst_mul_card, NNRat.cast_ofNat, NNRat.cast_divNat_of_ne_zero, NNRat.preimage_cast_Ioo, Finset.cast_divConst, NNRat.cast_lt_one, map_nnratCast_smul, eq_nnratCast, NNRat.preimage_cast_Ioc, NNRat.cast_comm, NNRat.cast_lt, IsSelfAdjoint.nnratCast, NNRat.cast_zero, NNRat.commute_cast, NNRat.cast_le_natCast, DirectLimit.nnratCast_def, NNRat.cast_divNat, NNRat.cast_lt_natCast, NNRat.cast_natCast, NNRat.cast_inv_of_ne_zero, NNRat.smul_def, nnratCast_smul_eq, NNRat.cast_le_ofNat, Finset.nnratCast_dens_mul_natCast_card, NNRat.cast_lt_ofNat, Finset.card_mul_cast_divConst, Finset.cast_addConst, NNRat.preimage_cast_Iio, NNRat.ofNat_lt_cast, NNRat.cast_mul_of_ne_zero, NNRat.castOrderEmbedding_apply, NNRat.preimage_cast_uIoc, NNRat.cast_lt_zero, NNRat.cast_listSum
toSemiring 📖	CompOp	7793 math math: withSeminorms_iff_mem_nhds_isVonNBounded, Field.FiniteDimensional.of_exists_primitive_element, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, IsLocalMaxOn.fderivWithin_nonpos, Polynomial.mul_div_eq_iff_isRoot, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, FiniteField.Extension.frob_apply, LinearMap.det_toContinuousLinearMap, RatFunc.instFaithfulSMulPolynomialLaurentSeries, mfderiv_sumSwap, TangentBundle.continuousLinearMapAt_model_space, hasFDerivAt_iff_hasDerivAt, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, absorbent_iff_eventually_nhdsNE_zero, ContinuousLinearEquiv.antilipschitz, FixedPoints.instFiniteDimensionalSubtypeMemSubfieldSubfield, VectorBundleCore.toFiberBundleCore_coordChange, ContMDiffAt.coordChangeL, iteratedDeriv_scomp_two, TensorProduct.mapInclIsometry_apply, Finset.expect_ite_mem, ContinuousLinearMap.rayleigh_smul, Polynomial.Gal.galActionHom_restrict, Submodule.finrank_sup_add_finrank_inf_eq, mfderiv_prod_eq_add, Real.hasDerivAt_arccos, Real.hasDerivAt_fourier, InnerProductSpace.Core.inner_smul_right, AffineSpace.asymptoticNhds_smul, NumberField.basisMatrix_eq_embeddingsMatrixReindex, LinearIsometryEquiv.strictConvex_preimage, WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero, Polynomial.degree_normalize, TemperedDistribution.lineDerivOpCLM_eq, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', PiTensorProduct.mapL_id, Algebra.IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, Polynomial.natDegree_mul_leadingCoeff_inv, ContinuousLinearMap.instT2Space, Submodule.starProjection_apply_eq_isComplProjection, Lagrange.interpolate_one, DiffContOnCl.smul, nhds_hasBasis_absConvex_open, fderiv_iteratedFDeriv, Polynomial.differentiableWithinAt, MeasureTheory.convolution_flip, Trivialization.pullback_linear, Algebra.normalizedTrace_map, FormalMultilinearSeries.comp_rightInv_aux1, ContinuousLinearMap.hasFPowerSeriesOnBall, MDifferentiable.coordChangeL, AlgEquiv.restrictNormal_trans, RatFunc.laurent_injective, rank_fun_infinite, IsAlgClosed.roots_eq_zero_iff_degree_nonpos, IntermediateField.extendScalars_toSubfield, exists_rat_pow_btwn, ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, AddCircle.coe_equivIco_mk_apply, hasStrictFDerivAt_apply, differentiableWithinAt_finCons', NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, Orthonormal.linearIndependent, fderiv_snd, LinearIsometryEquiv.hasStrictFDerivAt, Bundle.Trivial.continuousLinearEquivAt_trivialization, ContinuousLinearMap.derivWithin_of_bilinear, HasStrictFDerivAt.isLittleOTVS, ValuationRing.mem_integer_iff, Finset.dens_union_of_disjoint, SchwartzMap.lineDerivOpCLM_eq, NumberField.InfinitePlace.isNontrivial, Algebra.normalizedTrace_algebraMap_eq_id, AddChar.card_addChar_le, NumberField.InfinitePlace.eq_iff_isEquiv, IntermediateField.finInsepDegree_top, InfiniteGalois.normal_iff_isGalois, LinearMap.BilinForm.dualSubmoduleParing_spec, Height.logHeight₁_pow, continuous_cfcₙHomSuperset_left, SpectrumRestricts.nnreal_of_nonneg, hasDerivWithinAt_Iio_iff_Iic, HasStrictFDerivAt.fun_mul', fderivWithin_ofNat, Submodule.disjoint_span_singleton', AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, hasSum_mul_left_iff, HasMFDerivAt.mul, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, LinearIsometryEquiv.comp_fderiv, Polynomial.natSepDegree_le_natDegree, MeasureTheory.condExpL1_smul, Seminorm.absorbent_closedBall_zero, ContinuousLinearMap.isBigO_comp, Lagrange.interpolate_eq_of_values_eq_on, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, ContinuousAlternatingMap.opNorm_prod, LinearMap.ortho_smul_right, Orthonormal.inner_left_finsupp, ordinaryHypergeometric_sum_eq, ArchimedeanClass.FiniteResidueField.mk_ratCast, hasSum_geometric_of_norm_lt_one, Polynomial.coe_normUnit_of_ne_zero, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, NNRat.coe_floor, norm_cfcₙHom, IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', IntermediateField.aeval_gen_minpoly, Module.Basis.ofVectorSpaceIndex.linearIndependent, OrthonormalBasis.orthogonalProjection_eq_sum, IntermediateField.adjoin_eq_top_iff_of_isAlgebraic, hasDerivWithinAt_ofNat, ContinuousLinearMap.analyticWithinAt_bilinear, ValuationSubring.mem_comap, IsIntegralClosure.rank, strictConvexOn_iff_slope_strict_mono_adjacent, HasCompactSupport.convolution_integrand_bound_left, Subfield.rank_comap, ContinuousLinearMap.compSL_apply, Mathlib.Tactic.RingNF.nnrat_rawCast, ContinuousLinearMap.continuous₂, LinearMap.IsSymmetric.inner_map_polarization, RCLike.geometric_hahn_banach_point_open, Polynomial.IsSplittingField.mul, ValuationSubring.coe_mem_principalUnitGroup_iff, fderivWithin_comp_derivWithin_of_eq, ContinuousLinearEquiv.differentiable, ContinuousLinearMap.opNorm_prod, hasDerivWithinAt_add_const_iff, IsLocalRing.ResidueField.algebraMap_residue, LinearMap.coe_toSeminorm, ContinuousLinearMap.integral_compLp, FormalMultilinearSeries.comp_partialSum, Real.sSup_smul_of_nonpos, IntermediateField.fieldRange_le, LinearMap.adjoint_adjoint, DoubleCentralizer.star_snd, ContinuousLinearMap.norm_inr_le_one, quadraticChar_card_sqrts, IntermediateField.LinearDisjoint.iff_inf_eq_bot, LinearMap.BilinForm.symmCompOfNondegenerate_left_apply, IntermediateField.normal_inf, FixedPoints.finrank_eq_card, binomialSeries_eq_ordinaryHypergeometricSeries, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, Matrix.IsHermitian.isClosedEmbedding_cfcAux, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, StarAddMonoid.toStarModuleNNRat, InnerProductSpace.toLinearIsometry_toDual, IsUltrametricDist.algNormOfAlgEquiv_extends, RCLike.normSq_to_real, ZMod.pow_card_sub_one, Polynomial.cardPowDegree_zero, Seminorm.continuous_of_continuous_comp, HasMFDerivAt.add, tendsto_inv_atTop_zero, Bornology.isVonNBounded_iff_tendsto_smallSets_nhds, galRestrict_symm_algebraMap_apply, NumberField.InfinitePlace.norm_embedding_of_isReal, hasSum_div_const_iff, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, Filter.IsBoundedUnder.smul_tendsto_zero, tendsto_const_mul_pow_nhds_iff', RatFunc.num_div, Real.hasFDerivAt_fourierChar_neg_bilinear_left, InnerProductSpace.span_gramSchmidtNormed, LinearIsometryEquiv.analyticOnNhd, hasStrictDerivAt_intCast, ContinuousAlternatingMap.uniformContinuous_eval_const, cfcₙ_norm_nonneg, ContinuousWithinAt.cfcₙ, IsGalois.tower_top_intermediateField, LeftInvariantDerivation.leibniz, MeasureTheory.convolution_eq_right', hasStrictFDerivAt_exp_of_mem_ball, quasispectrum.algebraMap_mem, hasFDerivAt_iff_hasGradientAt, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, MeasureTheory.eLpNormEssSup_const_smul, FixedPoints.minpoly.monic, Asymptotics.isBigO_const_smul_right, cfcₙHom_apply_mem_elemental, ContinuousMultilinearMap.cpolynomialOn, LinearIsometry.norm_compContinuousAlternatingMap, ClassGroup.mk0_integralRep, linearIndependent_option, IsHilbertSum.surjective_isometry, SimpleGraph.lapMatrix_toLinearMap₂', curveIntegral_smul, FormalMultilinearSeries.ofScalars_apply_eq', div_eq_mul_inv, ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, Submodule.reflection_trans_reflection, NumberField.InfinitePlace.sum_mult_eq, FixedPoints.minpoly.irreducible, extDeriv_constOfIsEmpty, RCLike.separate_convex_open_set, RootPairing.coroot_eq_polarizationEquiv_apply_root, Bundle.Trivial.symmL_trivialization, Ideal.exists_comap_galRestrict_eq, RCLike.tendsto_inverse_atTop_nhds_zero_nat, NumberField.canonicalEmbedding.mem_span_latticeBasis, Real.fderiv_fourierIntegral, Submodule.orthogonalDecomposition_symm_apply, hasStrictFDerivAt_list_prod_finRange', RatFunc.coe_mapAlgHom_eq_coe_map, Module.End.exists_ker_pow_eq_ker_pow_succ, OrthogonalFamily.linearIsometry_apply_single, NumberField.integralBasis_apply, AbsoluteValue.isEquiv_trivial_iff_eq_trivial, ContinuousLinearMapWOT.neg_apply, LinearIsometry.nnnorm_toContinuousLinearMap, ContinuousLinearMap.isStarProjection_iff_isSymmetricProjection, InnerProductSpace.rankOne_one_left_eq_innerSL, ContDiff.fderiv_succ, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow, Submodule.IsOrtho.starProjection_comp_starProjection, FormalMultilinearSeries.ofScalars_eq_zero_of_scalar_zero, convexHull_insert, fderiv_intCast, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, IntermediateField.adjoin.finrank, IsPurelyInseparable.minpoly_eq', IntermediateField.algebraMap_mem, NonUnitalCStarAlgebra.toStarModule, Finset.card_mul_cast_addConst, NormedSpace.expSeries_summable_of_mem_ball, hasDerivAt_sqrt_mul_log, Filter.EventuallyEq.fderivWithin, IsLocalRing.finrank_CotangentSpace_eq_one_iff, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, LinearMap.IsSymmetric.restrictScalars, bddBelow_smul_iff_of_neg, Matrix.GeneralLinearGroup.val_mkOfDetNeZero, linearIndepOn_iff_notMem_span, PrimeSpectrum.residueField_specComap, fderivWithin_one, ContinuousLinearMap.continuous_det, HasFiniteFPowerSeriesAt.neg, Polynomial.isEquivalent_atBot_div, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, NumberField.mixedEmbedding.convexBodyLT'_mem, NumberField.InfinitePlace.comap_mk, PiTensorProduct.mapLMonoidHom_apply, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv, ClosedSubmodule.toSubmodule_orthogonal_eq, RootPairing.instIsRootSystemSubtypeMemSubmoduleSpanRangeCoeEmbeddingRootCorootRestrictScalars', ContinuousLinearMap.map_add_add, NumberField.prod_nonarchAbsVal_eq, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, ContinuousAlternatingMap.isEmbedding_restrictScalars, ContinuousAlternatingMap.norm_constOfIsEmpty, HasFDerivWithinAt.pow, ContinuousLinearMap.sSup_unit_ball_eq_norm, Lagrange.eval_interpolate_not_at_node', ContinuousAlternatingMap.norm_ofSubsingleton_id_le, convex_iff_ordConnected, hasFDerivWithinAt_const, MeromorphicOn.divisor_fun_smul, ContinuousAlternatingMap.isClosedEmbedding_toContinuousMultilinearMap, Rat.instSMulCommClass, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, hasFDerivAt_one, Representation.IsIrreducible.instIsSimpleModuleMonoidAlgebraAsModule, Real.hasDerivAt_sigmoid, taylorWithinEval_hasDerivAt_Ioo, Manifold.IsImmersionAtOfComplement.target_subset_preimage_target, convexHull_multiset_sum, WeierstrassCurve.Jacobian.baseChange_add, IsGalois.card_aut_eq_finrank, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, NormedSpace.Dual.isClosed_image_polar_of_mem_nhds, ContinuousLinearMap.analyticWithinAt, AdjoinRoot.minpoly_root, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, HasFDerivWithinAt.add, IntermediateField.extendScalars_sup, NumberField.IsCMField.zpowers_complexConj_eq_top, IntermediateField.coe_algebraMap_over_bot, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, Matrix.IsHermitian.det_abs, MDifferentiableAt.mfderiv_prod, Nat.cast_choose_eq_ascPochhammer_div, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, tendsto_const_div_atTop_nhds_zero_nat, Algebra.normalizedTrace_surjective, LinearMap.IsPositive.ne_zero_iff, Submodule.iUnion_ssubset_of_forall_ne_top_of_card_lt, hasFDerivAtFilter_pi, ContinuousLinearMap.toLinearMap₁₂_injective, Height.mulHeight₁_eq, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, Subspace.instModuleDualFiniteDimensional, Finset.dens_cons, curveIntegrable_segment, Algebra.normalizedTrace_eq_of_finiteDimensional, hasFDerivAt_multiset_prod, IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot, SeparationQuotient.mkCLM_comp_outCLM, NumberField.FinitePlace.mk_apply, IsNoetherian.iff_rank_lt_aleph0, LinearMap.isPositive_adjoint_comp_self, Matrix.GeneralLinearGroup.IsParabolic.parabolicFixedPoint_pow, Manifold.IsImmersionAt.map_target_subset_target, Submodule.toLinearEquiv_orthogonalDecomposition_symm, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, OrthonormalBasis.repr_injective, spectrumRestricts_iff, ContinuousLinearMap.continuousSMul, hasFTaylorSeriesUpToOn_top_iff_right, NNRat.not_cast_lt_zero, ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Module.Basis.range_ofVectorSpace, concaveOn_iff_slope_anti_adjacent, arithGeom_eq', IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable', expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, HasFPowerSeriesWithinOnBall.hasSum_sub, AffineSubspace.setOf_sSameSide_eq_image2, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, intervalIntegral.integral_hasDerivWithinAt_right, Matrix.spectrum_toEuclideanLin, ContDiff.iteratedFDeriv_right, Bornology.isVonNBounded_add_of_nonempty, NumberField.canonicalEmbedding.latticeBasis_apply, IsLocalRing.ker_residue, FormalMultilinearSeries.radius_pi_eq_iInf, ContinuousLinearMap.norm_inl_le_one, MeasureTheory.norm_condExpL2_le, RatFunc.num_div_dvd, JacobsonNoether.exists_pow_mem_center_of_inseparable', ContinuousLinearEquiv.contDiff_comp_iff, Ideal.exists_mem_span_singleton_map_residueField_eq, mem_subalgebraEquivIntermediateField, SchwartzMap.pairing_apply_apply, Submodule.instStrictConvexSpace, InnerProductSpace.isIdempotentElem_rankOne_self, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, minpoly.algEquiv_apply, Algebra.isInvariant_of_isGalois, ContinuousMultilinearMap.norm_map_snoc_le, MonoidAlgebra.Submodule.exists_isCompl, NumberField.InfinitePlace.le_iff_le, LineDifferentiableWithinAt.smul, MeasureTheory.Measure.MapLinearEquiv.isAddHaarMeasure, IsPurelyInseparable.elemExponent_min', ImplicitFunctionData.isInvertible_fderiv_prodFun, Trivialization.continuousLinearMapAt_apply, hasSum_choose_mul_geometric_of_norm_lt_one, iteratedFDerivWithin_eventually_congr_set, ApproximatesLinearOn.lipschitz, NumberField.norm_norm_le_norm_mul_house_pow, IntermediateField.isScalarTower_mid', Real.hasStrictDerivAt_rpow_const_of_ne, FractionalIdeal.map_one_div, tsum_coe_mul_geometric_of_norm_lt_one', Subfield.comap_comap, ConjRootClass.aeval_minpoly_iff, Polynomial.Gal.restrict_smul, ContinuousAlternatingMap.isUniformEmbedding_toContinuousMultilinearMap, StrongDual.polarSubmodule_eq_setOf, ContinuousLinearMap.continuous_integral_comp_L1, ContinuousLinearMap.isBigOWith_sub, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd, one_le_pow_mul_abs_eval_div, ContinuousLinearMap.isUniformEmbedding_restrictScalars, ConvexCone.canLift, hasDerivWithinAt_taylorWithinEval, map_ratCast_smul, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, Polynomial.div_def, one_div_add_one_div, NNRat.cast_eq_zero, HasFTaylorSeriesUpTo.cont, ImplicitFunctionData.isCompl_ker, CategoryTheory.finrank_hom_simple_simple_le_one, ContinuousLinearMap.hasDerivAtFilter, finrank_quotient_span_eq_natDegree_norm, fderivWithin_csinh, DoubleCentralizer.intCast_snd, FractionRing.instIsScalarTower, toIcoMod_eq_fract_mul, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, DoubleCentralizer.range_toProdMulOpposite, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, ContinuousLinearMapWOT.withSeminorms, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, NumberField.InfinitePlace.nat_card_stabilizer_eq_one_or_two, Submodule.re_inner_starProjection_eq_normSq, HasFPowerSeriesOnBall.add, differentiableWithinAt_pi'', Ideal.ker_algebraMap_residueField, RatFunc.laurent_X, Lagrange.degree_basisDivisor_self, VectorField.fderiv_apply_lieBracket, NumberField.RingOfIntegers.instSMulDistribClass, MeasureTheory.inner_condExpL2_left_eq_right, Polynomial.idealX_span, QuadraticForm.posDef_toMatrix', RootPairing.restrictScalars_coe_coroot, Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, NumberField.isInfinitePlace_iff, AnalyticOnNhd.compContinuousLinearMap, AffineIsometryEquiv.linear_eq_linear_isometry, ClassGroup.Quot_mk_eq_mk, IsGaloisGroup.iff_isFractionRing, NumberField.InfinitePlace.isUnramified_iff_card_stabilizer_eq_one, Bornology.isVonNBounded_add_self, Polynomial.exists_partition_polynomial, fderiv_id, ZLattice.covolume_eq_det_inv, RCLike.algebraMap_eq_ofReal, NumberField.IsCMField.equivInfinitePlace_symm_apply, Module.Basis.constrL_basis, Polynomial.nnqsmul_eq_C_mul, IsPrimitiveRoot.minpoly_dvd_pow_mod, Submodule.reflection_orthogonal_apply, NumberField.InfinitePlace.IsUnramified.comap_algHom, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, convex_iff_sum_mem, Polynomial.fiberEquivQuotient_tmul, ContinuousLinearMap.comp_memLp, NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded, ZMod.units_pow_card_sub_one_eq_one, OrderRingHom.eq_id, MeasureTheory.integral_fintype_prod_volume_eq_pow, Real.fderiv_fourierChar_neg_bilinear_right_apply, NumberField.InfinitePlace.isometry_embedding, LinearMap.IsSymmetric.diagonalization_apply_self_apply, Matrix.isParabolic_iff_exists, Module.rankAtStalk_eq, LinearPMap.domain_supSpanSingleton, finrank_vectorSpan_image_finset_le, IntermediateField.coe_bot, Subspace.dualLift_of_subtype, LinearMap.IsPositive.re_inner_nonneg_right, ContinuousAlternatingMap.instIsUniformAddGroup, WeierstrassCurve.Projective.comp_equiv_comp, Real.fourier_continuousLinearMap_apply, Ideal.ramificationIdx_le_finrank, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, LieAlgebra.IsKilling.isCompl_ker_weight_span_coroot, norm_iteratedFDeriv_mul_le, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, Padic.complete', intervalIntegral.fderiv_integral_of_tendsto_ae, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplex, ContDiffAt.fderiv_right_succ, flip_innerSL_real, WeierstrassCurve.Jacobian.Point.toAffine_of_Z_ne_zero, Submodule.starProjection_orthogonal', RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, NormedSpace.isBounded_iff_subset_smul_ball, AffineIsometryEquiv.ofTop_apply, LieAlgebra.finrank_engel, DoubleCentralizer.natCast_fst, hasFPowerSeriesOnBall_pi_iff, LinearMap.IsSymmetric.im_inner_self_apply, RatFunc.num_one, DifferentiableAt.prodMap, ContinuousLinearMap.IsPositive.toLinearMap, AnalyticOnNhd.iteratedFDeriv_of_isOpen, Polynomial.natSepDegree_pow, ZMod.charpoly_pow_card, ContinuousLinearMap.norm_compLp_le, Submodule.toLinearEquiv_orthogonalDecomposition, Continuous.convolution_integrand_fst, PadicComplex.coe_eq, MDifferentiableOn.smul_const_section, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, ContinuousLinearEquiv.symm_toDiffeomorph, DilationEquiv.smulTorsor_symm_apply, ContDiffMapSupportedIn.structureMapCLM_apply, OrthonormalBasis.toBasis_tensorProduct, TensorProduct.congrIsometry_refl_refl, eventually_enorm_mfderivWithin_symm_extChartAt_lt, ContinuousAlternatingMap.opNNNorm_pi, NumberField.mem_maximalRealSubfield_iff, HasFPowerSeriesWithinAt.const_smul, norm_smul_inv_norm', MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, tangentMap_snd, LaurentSeries.LaurentSeriesRingEquiv_def, Field.Emb.Cardinal.directed_filtration, SchwartzMap.lineDerivOp_fourier_eq, FirstOrder.Field.realize_genericMonicPolyHasRoot, Subspace.dualRestrict_comp_dualLift, Projectivization.map_id, AddChar.expect_ne_zero_iff_eq_zero, diam_smul₀, isClosedEmbedding_cfcₙAux, Lagrange.leadingCoeff_basis, AddChar.wInner_cWeight_self, LieModule.traceForm_eq_sum_finrank_nsmul', IntermediateField.lift_insepDegree_bot', Ring.ordFrac_eq_div, innerSL_apply_apply, ContinuousLinearMapWOT.instIsUniformAddGroup, Submodule.isOrtho_sup_right, RCLike.norm_expect_le, fderiv_multiset_prod, Polynomial.eventually_atBot_not_isRoot, HasFPowerSeriesWithinOnBall.restrictScalars, NormedSpace.isVonNBounded_iff, CFC.abs_eq_cfcₙ_coe_norm, ContinuousLinearEquiv.subsingleton_or_norm_symm_pos, Finset.dens_inter_add_dens_sdiff, aemeasurable_smul_const, LinearIsometry.rTensor_def, LinearMap.adjoint_innerₛₗ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, VectorField.fderiv_apply_lieBracket_of_isSymmSndFDerivAt, HasFTaylorSeriesUpTo.hasFDerivAt, HasFDerivAtFilter.fun_sum, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, LinearMap.continuousLinearMapClassOfFiniteDimensional, hasDerivAt_neg', ContMDiffWithinAt.mfderivWithin_const, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, HasFDerivAtFilter.sub, Finset.mulConst_mul_card, Unitization.splitMul_apply, geom₂_sum, inner_eq_norm_mul_iff, ContinuousLinearMap.toBilinForm_apply, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, DoubleCentralizer.nnnorm_def', ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, LinearMap.adjoint_eq_toCLM_adjoint, HasFDerivAt.fun_mul, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, ClosedSubmodule.orthogonal_gc, LinearMap.isPositive_id, IsCyclotomicExtension.discr_odd_prime, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Seminorm.bddAbove_range_iff, fderivWithin_zero_of_not_accPt, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Finset.card_mul_divConst, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, NormedSpace.image_isVonNBounded_iff, VectorField.mpullbackWithin_smul, nnnorm_cfcₙ_lt_iff, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_apply, eqOn_dslope_sub_smul, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Submodule.orthogonalProjection_mem_subspace_eq_self, IsPurelyInseparable.insepDegree_eq, Finset.card_mul_dens, ContinuousLinearMap.nnnorm_def, ContinuousLinearMap.IsPositive.inner_nonneg_right, gauge_smul_of_nonneg, DoubleCentralizer.zero_snd, LeftInvariantDerivation.left_invariant', Field.insepDegree_le_rank, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, hasDerivAt_bernoulliFun, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, FormalMultilinearSeries.le_changeOriginSeries_radius, algebraMap.coe_logDeriv, ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff, derivWithin_fderivWithin, HasFDerivWithinAt.prodMap, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Field.Emb.Cardinal.filtration_succ, RatFunc.denom_one, Set.unit_eq, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, NumberField.mixedEmbedding.norm_eq_norm, IntermediateField.relfinrank_mul_finrank_top, Polynomial.map_div, LieAlgebra.IsKilling.rootSystem_coroot_apply, instLiesOverFiberOfIsPrime, PowerSeries.eq_divided_by_X_pow_order_Iff_Unit, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, mfderiv_comp, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, X_pow_sub_C_irreducible_iff_of_odd, IsLocalRing.finrank_cotangentSpace_eq_zero, WittVector.RecursionMain.succNthVal_spec', InnerProductSpace.span_gramSchmidtNormed_range, HasFDerivWithinAt.hasLineDerivWithinAt, ContinuousLinearMap.opNorm_comp_linearIsometryEquiv, Submodule.orthogonal_disjoint, algebraicClosure.algebraicClosure_eq_bot, ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverse, ContDiffPointwiseHolderAt.isBigO, Finset.card_mul_subConst, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, NumberField.FinitePlace.norm_def', SchwartzMap.decay', Module.Basis.ofZLatticeBasis_apply, Seminorm.smul_inf, ContinuousAlternatingMap.map_insertNth, PowerSeries.Inv_divided_by_X_pow_order_leftInv, FormalMultilinearSeries.derivSeries_coeff_one, instIsTorsionFreeCyclotomicFieldOfIsDomainOfIsFractionRing, Polynomial.isCoveringMapOn_eval, IsLocalRing.instIsLocalHomRingHomOfNontrivial, Submodule.starProjection_add_starProjection_orthogonal, Matrix.spectrum_toLpLin, HasDerivAt.comp_ofReal, OrderedFinpartition.norm_compAlongOrderedFinpartition_le, tangentConeAt_nonempty_of_properSpace, instIsZLatticeComap, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_right, ContinuousOn.cfcₙ', mdifferentiableOn_symm_coordChangeL, X_pow_sub_C_irreducible_of_odd, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, sum_div_card_sq_le_sum_sq_div_card, Continuous.integral_hasStrictDerivAt, Polynomial.mod_eq_self_iff, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Submodule.mem_orthogonal_singleton_iff_inner_right, NumberField.mixedEmbedding.mem_idealLattice, RatFunc.denom_mul_dvd, IsFractionRing.fieldEquivOfAlgEquivHom_apply, Complex.re_balance, mdifferentiableWithinAt_smul_const_section, InnerProductSpace.Core.inner_smul_left, SchwartzMap.bilinLeftCLM_apply, ContinuousMap.setOfIdeal_ofSet_eq_interior, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, Bornology.isVonNBounded_pi_iff, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, NumberField.Units.regOfFamily_eq_det, Submodule.IsLattice.rank', Filter.tendsto_const_mul_atTop_iff_pos, FiniteField.frobeniusAlgEquivOfAlgebraic_apply, ContinuousLinearMap.nhds_zero_eq_of_basis, HasGradientAt.hasDerivAt', IsHilbertSum.linearIsometryEquiv_symm_apply, SmoothBumpCovering.exists_immersion_euclidean, Fintype.expect_dite_eq, PowerSeries.Unit_of_divided_by_X_pow_order_zero, OrderedFinpartition.norm_applyOrderedFinpartition_le, iteratedDeriv_pow, ContinuousLinearMap.cpolynomialAt, HasMFDerivWithinAt.prodMk, differentiableOn_pi, InfiniteGalois.normalAutEquivQuotient_apply, IsPurelyInseparable.elemExponent_min, AffineMap.hasDerivWithinAt, Submodule.starProjection_singleton, TrivSqZeroExt.inv_inl, IsGaloisGroup.fixingSubgroup_top, HasFPowerSeriesAt.eventually_hasSum, LeftInvariantDerivation.left_invariant, mfderiv_comp_apply_of_eq, Nat.floor_div_natCast, PowerSeries.degree_weierstrassMod_lt, PowerSeries.maximalIdeal_eq_span_X, FixedPoints.minpoly.eval₂', ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, hasStrictFDerivAt_snd, tsum_coe_mul_geometric_of_norm_lt_one, WeierstrassCurve.Projective.dblU_smul, IsGreatest.nnnorm_cfcₙ, NumberField.FinitePlace.embedding_apply, NormedSpace.toIsBoundedSMul, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, WeierstrassCurve.Jacobian.negAddY_eq, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, ContinuousAlternatingMap.isClosed_range_toContinuousMultilinearMap, CategoryTheory.finrank_hom_simple_simple_eq_one_iff, Projectivization.submodule_eq, NNRat.cast_one, Valuation.Integers.isPrincipal_iff_exists_isGreatest, curveIntegralFun_smul, addInvariantVectorField_smul, IntermediateField.isAlgebraic_tower_bot, hasDerivAt_exp_zero_of_radius_pos, Module.Basis.exists_opNorm_le, ClosedSubmodule.mem_orthogonal', Finset.one_le_mulConst_self, egauge_ball_le_of_one_lt_norm, MeasureTheory.charFun_toDual_symm_eq_charFunDual, IsGaloisGroup.fixedPoints_top, inv_atTop₀, hasDerivWithinAt_iff_isLittleO, hasStrictFDerivAt_iff_isLittleOTVS, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, Normal.splits', IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply, RatFunc.laurent_algebraMap, derivWithin_fun_const_smul_field, isConjRoot_iff_exists_algEquiv, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, IsStrictOrderedRing.toContinuousInv₀, OrthogonalFamily.orthonormal_sigma_orthonormal, Set.unitEquivUnitsInteger_symm_apply_coe, IsPurelyInseparable.finInsepDegree_eq, Field.isDomain, ContinuousAlternatingMap.piLIE_apply_apply, PreInnerProductSpace.Core.smul_left, inv_intCast_smul_eq, Matrix.PosSemidef.sqrt_eq_zero_iff, IntermediateField.mem_carrier, IsPurelyInseparable.elemExponent_def', Differentiable.fderiv_norm_rpow, UniqueMDiffOn.uniqueDiffOn, FDerivMeasurableAux.le_of_mem_A, lintegral_fderiv_lineMap_eq_edist, NumberField.InfiniteAdeleRing.algebraMap_apply, RCLike.normSq_neg, ContinuousLinearMap.isBigOWith_id, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, curveIntegrable_fun_neg_iff, hasDerivWithinAt_zero, NNRat.cast_commute, IntermediateField.botEquiv_symm, ContDiffAt.hasStrictDerivAt, NNRat.cast_listProd, ContinuousLinearEquiv.coe_toDiffeomorph_symm, TrivSqZeroExt.inv_one, Submodule.reflection_symm, Normal.minpoly_eq_iff_mem_orbit, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', Subfield.relfinrank_mul_finrank_top, padicNormE.nonarchimedean', CurveIntegrable.zero, NNRat.cast_def, fderiv_comp_deriv, ContinuousMultilinearMap.contDiffAt, finrank_vectorSpan_le_iff_not_affineIndependent, Field.finSepDegree_eq_of_isAlgClosed, hasDerivAtFilter_ofNat, Asymptotics.IsBigO.smul, iteratedDeriv_comp_const_mul, Polynomial.degree_mul_leadingCoeff_inv, sbtw_midpoint_of_ne, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, curveIntegrable_smul_iff, RingHom.mem_fieldRange_self, TensorProduct.toLinearEquiv_lidIsometry, HasFPowerSeriesOnBall.restrictScalars, contractLeft_assoc_coevaluation, Field.FiniteDimensional.of_finite_intermediateField, LinearMap.BilinForm.restrict_nondegenerate_iff_isCompl_orthogonal, Complex.im_expect, Lagrange.eval_interpolate_not_at_node, ContinuousLinearMap.opNNNorm_le_iff, ContinuousLinearMap.isometry_mul_flip, OrthonormalBasis.toBasis_singleton, ZSpan.smul, AnalyticOnNhd.eval_linearMap', HasStrictFDerivAt.mul', isPowMul_spectralNorm_of_finiteDimensional_normal, fderiv_fun_pow, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, LinearMap.le_rank_iff_exists_linearIndependent, Module.Basis.ofZLatticeComap_apply, IntermediateField.relrank_mul_rank_top, IsGalois.card_fixingSubgroup_eq_finrank, NNRat.cast_add_of_ne_zero, Subfield.relfinrank_eq_finrank_of_le, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, InnerProductSpace.smul_left, ClosedSubmodule.inf_orthogonal, HasFDerivAtFilter.const_sub, LinearMap.coe_toContinuousLinearMap', balanced_ball_zero, HasFDerivWithinAt.linear_multilinear_comp, Polynomial.SplittingFieldAux.algebraMap_succ, iteratedFDerivWithin_succ_eq_comp_left, ContinuousLinearMap.isPositive_natCast, isGalois_iff_isGalois_top, minpoly_algHom_toLinearMap, ContinuousMultilinearMap.opNorm_zero_iff, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, Polynomial.hilbertPoly_smul, LinearMap.linearIndependent_of_isOrthoᵢ, hasStrictFDerivAt_exp_smul_const_of_mem_ball', ArchimedeanClass.FiniteResidueField.mk_eq_zero, NumberField.abs_discr_ge', hasFDerivWithinAt_comp_smul_iff_smul, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, convexJoin_segments, Submodule.starProjection_comp_starProjection_eq_zero_iff, FDerivMeasurableAux.differentiable_set_subset_D, Submodule.one_le_traceDual_one, Ideal.algebraMap_quotient_residueField_mk, SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, MeromorphicOn.fun_smul, monomial_has_deriv_aux, Field.finSepDegree_mul_finInsepDegree, continuous_equivFun_basis, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, LinearEquiv.toLinearEquiv_toContinuousLinearEquiv_symm, LinearIsometryEquiv.conjStarAlgEquiv_apply, MeasureTheory.smul_convolution, LinearMap.BilinForm.restrict_nondegenerate_orthogonal_spanSingleton, IsLocalRing.ResidueField.map_comp, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, IsPurelyInseparable.finrank_eq_pow, VectorField.mlieBracketWithin_const_smul_right, starConvex_iff_ordConnected, FractionalIdeal.coe_extendedHomₐ_eq_span, HasFDerivAt.le_of_lipschitzOn, Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, mem_principal_ideals_iff, LinearMap.toMatrixOrthonormal_reindex, contDiff_one_iff_fderiv, MeasureTheory.ConvolutionExistsAt.integrable, HasStrictFDerivAt.pow, InfiniteGalois.mem_bot_iff_fixed, Real.hasDerivAt_mul_log, exists_pos_right_iff_sameRay, NNRat.instSMulCommClass', Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, Filter.tendsto_div_const_atTop_iff_pos, Polynomial.natSepDegree_X_sub_C_pow, Asymptotics.isLittleOTVS_prodMk_left, inner_smul_left_eq_star_smul, fderivWithin_sinh, RCLike.mul_conj, ValueDistribution.logCounting_pow_top, NNRat.floor_coe, OnePoint.smul_infty_eq_self_iff, LinearMap.isUnit_iff_range_eq_top, WithSeminorms.continuousSMul, LinearMap.ortho_smul_left, hasLineDerivAt_iff_isLittleO_nhds_zero, deriv.scomp_of_eq, HasFDerivWithinAt.comp_of_tendsto, smul_unitClosedBall, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, Finset.subConst_le_addConst_sq, Real.hasStrictDerivAt_sinh, TestFunction.continuous_iff_continuous_comp, Polynomial.exists_partition_polynomial_aux, HasFiniteFPowerSeriesOnBall.sum, HasStrictFDerivAt.const_mul, Algebra.normalizedTrace_comp_algHom, Finset.dens_sdiff_add_dens_inter, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, inv_natCast_smul_eq, LinearMap.IsSymmetricProjection.ext_iff, ConvexOn.univ_sSup_of_countable_affine_eq, isConjRoot_algHom_iff, ContinuousLinearMap.ebound, RatFunc.laurent_div, Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff, InnerProductSpace.inner_left_rankOne_apply, Polynomial.IsSplittingField.splits_iff, cfcₙHom_nnreal_eq_restrict, TestFunction.toBoundedContinuousFunctionCLM_apply, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, RCLike.continuous_normSq, two_inv_lt_one, IsLocalFrameOn.coeff_apply_of_mem, ClosedSubmodule.orthogonal_injective, ContinuousAlternatingMap.norm_def, HasFDerivAt.finset_prod, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, IntermediateField.normal_iff_forall_map_eq, ContinuousLinearMap.smul_compLp, PowerSeries.derivative_inv', hasDerivWithinAt_abs_pos, Submodule.norm_starProjection_apply_le, instIsLocalRingTensorProductResidueFieldOfIsLocalHomRingHomAlgebraMap, ContinuousLinearMap.norm_extendTo𝕜, IsLocalMax.fderiv_eq_zero, ContinuousLinearMap.contMDiff, ContinuousLinearMap.mdifferentiable, NumberField.InfinitePlace.IsUnramified.stabilizer_eq_bot, HasStrictFDerivAt.fun_sum, LieModule.exists_nontrivial_weightSpace_of_lieIdeal, HasSum.hasSum_at_zero, Pretrivialization.continuousLinearMap_symm_apply', HasFPowerSeriesAt.add, WeierstrassCurve.Jacobian.negY_of_Z_ne_zero, HasFDerivAt.norm_sq, VectorBundleCore.coordChange_self, lineDifferentiableAt_smul_iff, differentiable_fst, ContinuousAlternatingMap.curryLeft_smul, derivWithin.scomp_of_eq, fderiv_const_smul_field, IntermediateField.extendScalars_injective, HasFTaylorSeriesUpToOn.comp_continuousAffineMap, LinearIsometry.map_starProjection', instNontrivialLinearMapId, ContinuousLinearMap.hasBasis_nhds_zero, HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, DifferentiableAt.fderiv_prodMk, ConjRootClass.minpoly.map_eq_prod, NumberField.mixedEmbedding.commMap_apply_of_isComplex, Valuation.Integers.valuation_irreducible_lt_one, innerₛₗ_apply_apply, hasFDerivWithinAt_inv, eventually_nhds_norm_smul_sub_lt, LinearIsometryEquiv.coe_toAffineIsometryEquiv, NumberField.Units.pos_at_place, DoubleCentralizer.pow_snd, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, finite_of_finite_type_of_isJacobsonRing, OrthonormalBasis.repr_self, NumberField.InfinitePlace.Completion.norm_coe, RCLike.ofReal_balance, Submodule.symmetric_isOrtho, SpectrumRestricts.nnreal_iff, iteratedDeriv_scomp_three, padicNormE.image', ContDiffAt.continuousAt_fderiv, fderiv_fun_pow', Polynomial.hilbertPoly_eq_zero_of_le_rootMultiplicity_one, hasDerivWithinAt_pi, IsometryEquiv.midpoint_fixed, NNRat.cast_add, Real.integrable_prod_sub, NormedSpace.isVonNBounded_ball, OrthogonalFamily.norm_sq_diff_sum, MDifferentiable.smul, IsAlgClosed.card_roots_eq_natDegree, Nonneg.mk_nnratCast, Ring.choose_eq_smul, norm_smul_inv_norm, ContinuousLinearEquiv.comp_hasFDerivAt_iff, ContinuousLinearMap.eq_adjoint_iff, hasMFDerivAt_sumSwap, ContinuousLinearMap.hasFDerivAt, fderivWithin_intCast, IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable, NumberField.InfinitePlace.comap_apply, ContDiffAt.fderiv_succ, ContMDiffVectorBundle.pullback, toMatrix_rotation, ContinuousLinearMap.topologicalAddGroup, tangentConeAt_univ, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, add_halves, IsFractionRing.mk'_eq_div, SchwartzMap.toLpCLM_apply, Polynomial.Separable.natSepDegree_eq_natDegree, Polynomial.div_tendsto_zero_iff_degree_lt, LinearMap.IsSymmetric.directSum_decompose_apply, derivWithin.scomp, IntermediateField.LinearDisjoint.map', ZMod.trace_pow_card, gal_X_pow_isSolvable, Subfield.splits_bot, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, HasFPowerSeriesAt.comp, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, ContinuousLinearMap.IsPositive.smul_of_nonneg, Finset.divConst_mul_card, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, InnerProductSpace.rankOne_apply, Algebra.instFiniteResidueFieldOfQuasiFiniteAt, Unitary.coe_linearIsometryEquiv_apply, segment_eq_uIcc, MeromorphicOn.divisor_pow, WeierstrassCurve.Projective.add_of_Z_eq_zero, MeasureTheory.convolution_tendsto_right, Nat.one_div_le_one_div, NumberField.InfinitePlace.card_stabilizer, ContinuousLinearMap.coe_toContinuousLinearEquivOfDetNeZero, IntermediateField.restrictScalars_normal, Submodule.reflection_singleton_apply, RCLike.nonUnitalContinuousFunctionalCalculus, IntermediateField.isScalarTower, HasFDerivAt.of_notMem_tsupport, HasFTaylorSeriesUpToOn.zero_eq', IsFractionRing.fieldEquivOfAlgEquiv_trans, fderiv_sum, Fintype.expect_ite_eq, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, AffineIsometryEquiv.pointReflection_midpoint_left, HarmonicAt.analyticAt_complex_partial, FormalMultilinearSeries.ofScalars_apply_eq, finrank_zero_iff_forall_zero, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, MvPolynomial.schwartz_zippel_totalDegree, Nat.ceil_le_two_mul, Polynomial.splits_map_iff, Ring.ordFrac_eq_ord, NormedSpace.Dual.toWeakDual_continuous, inv_intCast_smul_comm, PowerSeries.inv_eq_iff_mul_eq_one, HasFiniteFPowerSeriesAt.finite, HasFDerivWithinAt.const_mul, IsGalois.mem_range_algebraMap_iff_fixed, deriv_fun_inv'', fderiv_ofNat, Algebra.FormallySmooth.adjoin_of_algebraicIndependent, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ValuationSubring.mem_inv_pointwise_smul_iff, FormalMultilinearSeries.id_apply_one', ContinuousMultilinearMap.norm_smulRightL_le, tensorIteratedFDerivTwo_eq_iteratedFDeriv, tsum_geometric_of_norm_lt_one, AnalyticOnNhd.iteratedFDeriv, ContinuousLinearEquiv.contDiffAt_comp_iff, IntermediateField.algebraAdjoinAdjoin.instIsAlgebraicSubtypeMemSubalgebraAdjoinAdjoin, IsAlgClosed.instIsAlgClosure, FixedPoints.rank_le_card, ContinuousLinearMap.precompL_apply, cfcₙ_integral, DoubleCentralizer.nnnorm_snd, egauge_univ, Algebra.normalizedTrace_algebraMap, ContinuousLinearEquiv.isBigO_comp, isPurelyInseparable_iff_fd_isPurelyInseparable, Algebra.WeaklyQuasiFiniteAt.finite_residueField, HasStrictFDerivAt.star, OrderRingHom.apply_eq_self, OrthonormalBasis.measurePreserving_repr, Submodule.reflection_apply, openSegment_eq_Ioo, RCLike.ofReal_comp_balance, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, curveIntegralFun_segment, DifferentiableAt.hasDerivAt, Finpartition.IsEquipartition.card_biUnion_offDiag_le, fderivWithin_zero, AlgEquiv.restrictNormalHom_surjective, RCLike.geometric_hahn_banach_closed_point, differentiable_finCons', Submodule.orthogonal_eq_bot_iff, TensorProduct.adjoint_map, IsUltrametricDist.invariantExtension_apply, spectrum.pow_mem_pow, Real.hasDerivAt_arcosh, curveIntegral_neg, exists_nonneg_left_iff_sameRay, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, ConjRootClass.minpoly_injective, cfcₙ_setIntegral, Polynomial.add_mod, Matrix.linearIndependent_rows_of_invertible, HasFDerivAt.sub, VectorBundleCore.contMDiffOn_coordChange, FormalMultilinearSeries.radius_le_smul, LinearIsometryEquiv.lTensor_apply, mfderiv_comp_of_eq, PowerBasis.equivAdjoinSimple_symm_aeval, InnerProductSpace.gramSchmidt_def, HasFDerivAt.star, NumberField.instFiniteDimensional, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right, Finset.mulConst_le_card, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, iteratedFDerivWithin_succ_const, enorm_fderiv_norm_rpow_le, ContinuousLinearMap.isPositive_self_comp_adjoint, Lagrange.basis_singleton, iteratedDeriv_scomp_eq_sum_orderedFinpartition, trivialization_linear, NNRat.toNNRat_sum_of_nonneg, formalMultilinearSeries_geometric_apply_norm_le, ContinuousLinearMap.hasFPowerSeriesAt, Bundle.Trivial.continuousLinearMapAt_trivialization, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, LinearMap.adjoint_toContinuousLinearMap, WeierstrassCurve.integralModel_Δ_eq, FunctionField.ringOfIntegers.instIsIntegralClosureSubtypeMemSubalgebraPolynomial, X_pow_sub_C_irreducible_iff_forall_prime_of_odd, hasDerivAt_iff_isLittleO, IntermediateField.lift_adjoin_simple, NumberField.InfinitePlace.smul_apply, HasDerivWithinAt.hasFDerivWithinAt, Algebra.algebraMap_intNorm, Unitary.linearIsometryEquiv_coe_apply, algebraicClosure.normalClosure_eq_self, NormedSpace.isBounded_iff_subset_smul_closedBall, LDL.lowerInv_eq_gramSchmidtBasis, SeparatingDual.exists_eq_one, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, hasFPowerSeriesAt_const, hasStrictFDerivAt_pi', IntermediateField.AdjoinDouble.normal_algebraicClosure, Polynomial.natSepDegree_eq_zero_iff, HasFDerivAtFilter.neg, fderiv_eq_deriv_mul, FiniteDimensional.span_of_finite, algebraicClosure.map_eq_of_algebraicClosure_eq_bot, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, IsPurelyInseparable.exists_pow_mem_range_tensorProduct, finrank_algHom, FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius, ContinuousMultilinearMap.curry0_apply, HasFDerivWithinAt.fun_const_smul, norm_iteratedFDerivWithin_zero, iteratedFDerivWithin_of_isOpen, HasStrictFDerivAt.const_smul, hasStrictFDerivAt_natCast, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, inTangentCoordinates_eq_mfderiv_comp, FormalMultilinearSeries.radius_compNeg, Fintype.expect_ite_zero, hasFDerivAtFilter_ofNat, FiniteField.orderOf_frobeniusAlgEquivOfAlgebraic, hasFDerivAtFilter_zero, HasFDerivAt.multilinear_comp, Polynomial.differentiableOn_aeval, NormedSpace.expSeries_apply_eq_div', IsLocalRing.residue_eq_zero_iff, Polynomial.mem_iff_eq_smul_annIdealGenerator, Real.fourierIntegral_continuousMultilinearMap_apply, NumberField.IsTotallyComplex.finrank, Finset.dens_union_add_dens_inter, LinearIsometryEquiv.adjoint_eq_symm, Polynomial.natDegree_hilbertPoly_of_ne_zero_of_rootMultiplicity_lt, extDeriv_fun_smul, RatFunc.liftMonoidWithZeroHom_apply_div', fderivWithin_ccosh, TensorProduct.mapIsometry_id_id, galRestrict'_id, ContinuousAlternatingMap.toAlternatingMap_curryLeft, inv_strictAntiOn, Matrix.toEuclideanLin_apply, inner_self_eq_norm_sq_to_K, InfiniteGalois.krullTopology_mem_nhds_one_iff_of_isGalois, IsContDiffImplicitAt.hasFDerivAt, Finset.expect_ite_zero, AffineBasis.convexHull_eq_nonneg_coord, iteratedDerivWithin_eq_iteratedFDerivWithin, ContinuousLinearMap.toLinearMap₁₂_apply, FiniteField.coe_frobeniusAlgEquivOfAlgebraic, HasFDerivWithinAt.mul, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, LinearMap.IsPositive.isPositive_smul_iff, ContinuousLinearMap.sSup_sphere_eq_nnnorm, analyticOrderAt_smul_eq_top_of_left, Polynomial.IsSplittingField.adjoin_rootSet, VectorFourier.fourierPowSMulRight_eq_comp, ContinuousLinearMap.finiteDimensional, ContinuousAlternatingMap.le_opNNNorm, LinearIsometryEquiv.trans_smul, IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable, Finset.dens_eq_sum_dens_image, Polynomial.isUnit_map, HasFPowerSeriesOnBall.tendsto_partialSum_prod, RootPairing.restrictScalars_pairing, linearIndependent_fin2, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, hasFDerivWithinAt_pi', HasFDerivWithinAt.multiset_prod, IsHilbertSum.hasSum_linearIsometryEquiv_symm, Algebra.instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced, IntermediateField.isAlgebraic_adjoin_iff_top, WeierstrassCurve.Projective.dblU_eq, ContinuousLinearMap.opNorm_mul, Algebra.isGeometricallyReduced_iff, Submodule.IsOrtho.map_iff, MeasureTheory.integral_fintype_prod_eq_pow, DoubleCentralizer.smul_toProd, mfderivWithin_projIcc_one, collinear_iff_of_mem, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, FiniteField.card_algEquiv_extension, FGModuleCat.instFiniteHomModuleCatObjIsFG, NumberField.mixedEmbedding.convexBodyLT_mem, NumberField.InfinitePlace.coe_apply, Real.sInf_smul_of_nonneg, Algebra.IsAlgebraic.algHom_bijective, InnerProductSpace.Core.inner_smul_ofReal_right, NumberField.IsTotallyReal.finrank, IntermediateField.inf_toSubalgebra, egauge_zero_zero, algebraicClosure.isAlgebraic, HasFDerivAt.arctan, NumberField.ComplexEmbedding.IsConj.coe_stabilizer_mk, PiTensorProduct.mapL_one, NumberField.Units.coe_mul, Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg, Real.hasStrictDerivAt_arccos, DoubleCentralizer.toProdMulOpposite_injective, ContinuousLinearMap.norm_fst_le, Matrix.conjTranspose_inv_intCast_smul, PowerSeries.eq_mul_inv_iff_mul_eq, HahnEmbedding.Partial.truncLT_mem_range_extendFun, PointwiseConvergenceCLM.postcomp_apply, ContMDiffAt.mfderiv_apply, hasFDerivAt_snd, Finset.card_mul_addConst, PowerSeries.isUnit_divided_by_X_pow_order, IsGalois.normalClosure, ValuationSubring.subtype_injective, DoubleCentralizer.norm_fst_eq_snd, Unitization.nnnorm_def, RatFunc.coe_X, NumberField.InfinitePlace.comp_of_comap_eq, MvPowerSeries.eq_inv_iff_mul_eq_one, IsPurelyInseparable.iterateFrobenius_algebraMap, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, ContinuousLinearMap.le_opNorm, IsUltrametricDist.invariantExtension_extends, convexHull_toCone_eq_sInf, ImplicitFunctionData.range_leftDeriv, HasFDerivAt.fun_smul, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, Orthonormal.inner_left_fintype, Height.mulHeight₁_pow, IntermediateField.finiteDimensional_right, HasLineDerivAt.tendsto_slope_zero_right, RatFunc.isCoprime_num_denom, ZLattice.comap_toAddSubgroup, ValuationRing.range_algebraMap_eq, FunctionField.inftyValuation.polynomial, Complex.hasDerivAt_GammaIntegral, NormedSpace.expSeries_eq_expSeries, NormedSpace.expSeries_summable, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, compactOperator_topologicalClosure, RCLike.wInner_cWeight_eq_expect, IsFractionRing.algHom_commutes, AffineIndependent.finrank_vectorSpan_add_one, Submodule.coe_orthogonalDecomposition_symm, IntermediateField.isAlgebraic_iff, Projectivization.finrank_submodule, NumberField.ComplexEmbedding.conjugate_comp, PiTensorProduct.mapL_smul, Subfield.relrank_mul_rank_top, MeasureTheory.aestronglyMeasurable_condExpL2, Lagrange.basisDivisor_self, Submodule.orthogonalProjection_bot, Real.fderiv_fourier, DoubleCentralizer.norm_def', ContinuousLinearMap.adjointAux_norm, IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower', differentiable_apply, NNRat.coe_indicator, Submodule.range_starProjection, Fintype.expect_dite_eq', ContinuousLinearMap.fderiv, mul_inv_cancel, fderiv_neg, RCLike.toIsStrictOrderedRing, LinearIsometryEquiv.inner_map_eq_flip, MeasureTheory.convolution_smul, hasDerivAtFilter_natCast, Matrix.PosSemidef.sq_eq_sq_iff, Int.self_le_zpow_clog, padicNormE.eq_padic_norm', Polynomial.isEquivalent_atTop_lead, LinearMap.flip_injective_iff₁, FormalMultilinearSeries.ofScalars_eq_zero, EuclideanGeometry.orthogonalProjection_apply_mem, meromorphicOrderAt_ne_top_iff, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, Mathlib.Meta.NormNum.IsNNRat.of_raw, FormalMultilinearSeries.ofScalars_apply_zero, ContinuousAlternatingMap.instContinuousSMul, LinearMap.ker_smul', DualNumber.inv_eps, LinearMap.toMatrixOrthonormal_apply_apply, Finset.card_div_choose_le_card_shadow_div_choose, HasFDerivAt.restrictScalars, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, ContinuousLinearMap.fpowerSeries_apply_zero, RingHom.ker_isMaximal_of_surjective, IntermediateField.instSMulMemClass, SameRay.exists_eq_smul_add, VectorPrebundle.mk_contMDiffCoordChange, IntermediateField.coe_inclusion, Submodule.exists_add_mem_mem_orthogonal, PadicInt.algebraMap_apply, Nonneg.segment_eq_uIcc, VectorFourier.fourierIntegral_continuousLinearMap_apply, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, AffineSubspace.coe_subtypeₐᵢ, Polynomial.contraction_degree_eq_or_insep, FractionRing.algebraMap_liftAlgebra, FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop, closedConvexHull_eq_closure_convexHull, Finset.mem_convexHull', LinearMap.IsSymmetric.coe_re_inner_self_apply, Lagrange.eq_interpolate_iff, RatFunc.coe_coe, ContinuousLinearMap.comp_memLp', HasStrictFDerivAt.list_prod', PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, FiniteField.sum_pow_lt_card_sub_one, SchwartzMap.fourier_lineDerivOp_eq, Manifold.IsImmersionAtOfComplement.map_target_subset_target, LinearMap.BilinForm.span_singleton_inf_orthogonal_eq_bot, Real.sSup_smul_of_nonneg, LinearMap.BilinForm.apply_dualBasis_left, AddChar.wInner_cWeight_eq_zero_iff_ne, ContinuousLinearMapWOT.inducingFn_apply, TemperedDistribution.instLineDerivLeftSMulReal, Basis.linearEquiv_dual_iff_finiteDimensional, ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith, NumberField.FinitePlace.norm_embedding_eq, hasStrictDerivAt_exp_smul_const, Derivation.leibniz_div, ContinuousMap.setOfIdeal_ofSet_of_isOpen, Polynomial.separable_X_pow_sub_C, isBoundedBilinearMap_comp, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, Polynomial.span_singleton_annIdealGenerator, fderivWithin_sin, uniqueDiffWithinAt_of_mem_nhds, set_smul_sphere_zero, NumberField.IsCMField.isQuadraticExtension, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, Polynomial.valuation_of_mk, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, Module.Basis.mulOpposite_is_orthonormal_iff, Subspace.finrank_dualCoannihilator_eq, ContMDiff.smul, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, one_div_strictAntiOn, FormalMultilinearSeries.nnnorm_changeOrigin_le, hasStrictDerivAt_add_const_iff, Trivialization.continuousLinearEquivAt_apply, hasLineDerivWithinAt_smul_iff, Field.Emb.Cardinal.two_le_deg, NumberField.ComplexEmbedding.Extension.not_isReal_of_not_isReal, Asymptotics.IsTheta.smul, MDifferentiable.const_smul, hasMFDerivAt_fst, MeasureTheory.condExpL2_indicator_ae_eq_smul, AbsoluteValue.isEquiv_iff_lt_one_iff, fderiv_fun_sub, mfderivWithin_comp_projIcc_one, NumberField.InfinitePlace.comap_comp, RootPairing.finrank_corootSpanIn_int, LeftInvariantDerivation.lift_smul, IsMIntegralCurveOn.hasDerivWithinAt, FormalMultilinearSeries.rightInv_removeZero, Polynomial.X_pow_sub_one_splits, arithGeom_zero_eq_mul_div', tendsto_zpow_atTop_zero, isCompactOperator_iff_isCompact_closure_image_ball, Asymptotics.isLittleO_pow_pow, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, DoubleCentralizer.norm_def, ClosedSubmodule.orthogonal_closure'', Finset.local_lubell_yamamoto_meshalkin_inequality_div, hasStrictDerivAt_exp_smul_const', InfiniteGalois.fixingSubgroup_fixedField, HasCompactSupport.fderiv, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlane, LinearIsometry.toAffineIsometry_toAffineMap, MeromorphicAt.fun_smul, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, Rat.coe_castHom, SchwartzMap.smulLeftCLM_real_smul, uniqueDiffWithinAt_iff_accPt, InnerProductSpace.toDualMap_apply_apply, WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, Submodule.le_orthogonal_orthogonal, hasFDerivWithinAt_intCast, IntermediateField.finInsepDegree_le_of_left_le, LinearMap.eq_adjoint_iff_basis_left, contDiff_succ_iff_fderiv, ContinuousLinearMap.opNNNorm_prod, ContinuousLinearEquiv.comp_differentiableOn_iff, Nat.ceil_lt_two_mul, Lagrange.basisDivisor_add_symm, MDifferentiableOn.smul, ZLattice.rank, hasDerivAtFilter_zero, Subspace.finiteDimensional_quot_dualCoannihilator_iff, HasMFDerivAt.neg, smul_closedBall', NormedSpace.exp_eq_tsum_div, ZSpan.quotientEquiv_apply_mk, Polynomial.map_mod, LinearMap.IsSymmetricProjection.isIdempotentElem, HasFDerivAt.fun_const_smul, MulOpposite.finrank, Polynomial.cardPowDegree_isEuclidean, IntermediateField.isAlgebraic_adjoin_iff, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, IntermediateField.minpoly_gen, Field.Emb.Cardinal.isLeast_leastExt, Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem, Finset.divConst_le_card, Matrix.PosSemidef.posDef_iff_isUnit, Finset.one_le_mulConst, Algebra.IsQuadraticExtension.isMulCommutative_galoisGroup, LaurentSeries.inducing_coe, SeparatingDual.exists_continuousLinearEquiv_apply_eq, Manifold.pathELength_def, PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision, WeakDual.toStrongDual_inj, TrivSqZeroExt.fst_expSeries, EuclideanSpace.volume_closedBall_fin_three, NumberField.exists_conjugate_one_le_norm, NumberField.InfinitePlace.conjugate_embedding_injective, ContinuousLinearMap.uniformContinuous_restrictScalars, Cubic.splits_iff_card_roots, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, NumberField.InfinitePlace.norm_embedding_eq, isModuleTopologyOfFiniteDimensional, LinearMap.extendTo𝕜'_apply, IntermediateField.aeval_coe, LinearIsometryEquiv.fderiv, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, PrimeSpectrum.coe_preimageOrderIsoFiber_symm_apply_coe_asIdeal, ContinuousLinearMap.holderₗ_apply_apply, Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, dslope_sub_smul, hasDerivAt_id', rescale_to_shell_semi_normed_zpow, ContinuousMultilinearMap.unit_le_opNorm, LaurentSeries.continuous_coe, AffineIndependent.card_le_finrank_succ, IsLocalRing.instIsLocalHomResidueFieldRingHomResidue, balancedCore_mem_nhds_zero, convexJoin_segment_singleton, SameRay.exists_eq_smul, ContinuousMultilinearMap.curryRight_norm, hasDerivWithinAt_Iic_of_tendsto_deriv, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, Submodule.instHasOrthogonalProjectionOfCompleteSpace, Coplanar.finrank_le_two, fderiv.log, openSegment_eq_Ioo', Polynomial.irreducible_mul_leadingCoeff_inv, FDerivMeasurableAux.norm_sub_le_of_mem_A, HasFDerivAt.add, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, IsSepClosed.roots_eq_zero_iff, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, MeasureTheory.convolution_lsmul, NumberField.IsCMField.orderOf_complexConj, ContinuousAlternatingMap.instContinuousConstSMul, IsOpen.uniqueDiffWithinAt, Normal.algHomEquivAut_symm_apply, HahnEmbedding.Seed.strictMono_coeff, abs_nnqsmul, Bornology.isVonNBounded_iff_absorbing_le, curveIntegral_fun_zero, gal_X_pow_sub_C_isSolvable, meromorphicNFOn_smul_iff_right_of_analyticOnNhd, ModelWithCorners.uniqueDiffOn_preimage, LinearMap.nonneg_iff_isPositive, Lagrange.interpolate_eq_sum, Nat.floor_div_ofNat, Bornology.isVonNBounded_covers, hasDerivAt_abs_neg, coe_innerSL_apply, MvPolynomial.rank_R, HasFDerivWithinAt.const_sub, IsAlgClosed.splits_codomain, LinearMap.IsSymmetric.inner_map_self_eq_zero, ContinuousLinearMap.isCompact_image_coe_closedBall, IntermediateField.map_map, Real.deriv_sqrt_aux, OrthonormalBasis.prod_apply, iteratedFDeriv_add_apply, deriv_fderiv, PowerSeries.normUnit_X, RegularNormedAlgebra.isometry_mul', convexJoin_singleton_segment, ContDiffWithinAt.hasFDerivWithinAt_nhds, IsPrimitiveRoot.adjoinEquivRingOfIntegers_symm_apply, FiniteDimensional.nonempty_continuousLinearEquiv_iff_finrank_eq, IntermediateField.fixingSubgroup_top, HasFDerivAt.sum, HasStrictDerivAt.real_of_complex, ContinuousLinearMap.isClosed_image_coe_closedBall, IntermediateField.coe_toSubalgebra, DoubleCentralizer.central, RootPairing.Base.exists_mem_span_pairingIn_ne_zero_and_pairwise_ne, ModelWithCorners.hasMFDerivAt, WeierstrassCurve.Projective.isUnit_dblU_of_Y_eq, FiniteDimensional.finiteDimensional_quotient, Matrix.PosSemidef.det_sqrt, Hyperreal.archimdeanClassMk_coe, MeasureTheory.integral_condExpL2_eq, FiniteField.roots_X_pow_card_sub_X, HasFPowerSeriesOnBall.coeff_zero, IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_one, integral_smul_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, quadraticCharFun_eq_zero_iff, hasFDerivAtFilter_const, VectorBundleCore.localTriv_symm_fst, range_cfcₙHom, Field.Emb.Cardinal.succEquiv_coherence, IntermediateField.bot_toSubalgebra, HasMFDerivWithinAt.prodMap, Algebra.discr_powerBasis_eq_norm, LinearMap.surjective_iff_ne_zero, DivisionRing.instIsArtinianRing, hasDerivWithinAt_abs, hasFPowerSeriesOnBall_const, NNRat.floor_cast, hasFDerivAtFilter_iff_isLittleO, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, TensorProduct.lidIsometry_apply, IsSepClosed.lift_def, ContDiffMapSupportedIn.seminorm_le_iff, eventually_norm_mfderivWithin_symm_extChartAt_lt, QuasispectrumRestricts.map_zero, NumberField.InfinitePlace.mkReal_coe, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, Normal.splits, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, NumberField.InfinitePlace.smul_eq_comap, Submodule.exists_forall_notMem_of_forall_ne_top, Trivialization.comp_continuousLinearEquivAt_eq_coord_change, Subfield.mem_bot_iff_pow_eq_self, UniqueMDiffOn.uniqueDiffOn_target_inter, Mathlib.Meta.NormNum.isNNRat_abs_neg, IsPrimitiveRoot.norm_eq_neg_one_pow, VectorFourier.hasFDerivAt_fourierIntegral, Polynomial.factor_dvd_of_natDegree_ne_zero, Finset.cast_subConst_mul_card, Finset.centerMass_id_mem_convexHull, Submodule.comap_smul, LinearMap.flip_surjective_iff₁, Seminorm.ball_norm_mul_subset, coeSubmodule_differentIdeal, coe_galRestrict_apply, WeierstrassCurve.Projective.Point.toAffineLift_zero, minpoly.sub_algebraMap, IntermediateField.sup_toSubalgebra_of_isAlgebraic_left, iteratedFDeriv_sum, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, hasFDerivAt_ringInverse, LinearMap.IsPositive.inner_nonneg_left, IntermediateField.relfinrank_top_right, norm_cfcₙ_lt, ContinuousMultilinearMap.opNorm_smul_le, contDiffAt_one_iff, Function.HasTemperateGrowth.fun_smul, Filter.HasBasis.isLittleOTVS_iff, NumberField.InfinitePlace.smul_mk, HasFDerivWithinAt.of_notMem_tsupport, ContinuousLinearMap.instCStarRingId, WeakDual.coe_toStrongDual, fermatLastTheoremWith'_polynomial, NormedSpace.eq_zero_iff_forall_dual_eq_zero, hasFDerivAt_finCons, PowerSeries.intValuation_eq_of_coe, HasMFDerivWithinAt.neg, Algebra.FormallySmooth.iff_injective_lTensor_residueField, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, AffineIsometryEquiv.map_vsub, Finset.centerMass_id_mem_convexHull_of_nonpos, hasFDerivWithinAt_finCons, coeSubmodule_differentIdeal_fractionRing, Ideal.Fiber.lift_residueField_surjective, InformationTheory.hasDerivAt_klFun, Nat.cast_div_charZero, MeasureTheory.setIntegral_condExpL2_indicator, InnerProductSpace.nnnorm_rankOne, Field.rank_mul_sepDegree_of_isSeparable, ContinuousMultilinearMap.norm_restr, WeierstrassCurve.Jacobian.comp_equiv_comp, ContinuousMultilinearMap.norm_image_sub_le, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, convexHull_add, fderiv_smul, Finset.divConst_le_mulConst_sq, stereographic_apply_neg, LinearIsometry.norm_toContinuousLinearMap, OrthonormalBasis.orthogonalProjection_apply_eq_sum, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, FiniteField.instIsSplittingFieldExtensionHSubPolynomialHPowNatXCard, hasMFDerivAt_inr, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, ContinuousLinearEquiv.arrowCongr_apply, differentiable_snd, FiniteField.algebraMap_trace_eq_sum_pow, HasFDerivWithinAt.star, hasDerivAt_of_tendstoLocallyUniformlyOn, hasDerivAtFilter_iff_tendsto_slope, ContinuousLinearMap.norm_toSpanSingleton, NumberField.ComplexEmbedding.involutive_conjugate, fderivWithin_eventually_congr_set', intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left, ContinuousLinearMap.setIntegral_compLp, LinearMap.trace_eq_sum_inner, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, ContinuousLinearMap.toUniformConvergenceCLM_apply, FormalMultilinearSeries.ofScalars_series_of_subsingleton, ContinuousAlternatingMap.curryLeft_apply_apply, NormedSpace.isVonNBounded_closedBall, ContinuousLinearMap.flip_smul, logDeriv_fun_pow, Representation.IsIrreducible.finrank_eq_one_of_isMulCommutative, solvableByRad.isSolvable, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, mfderivWithin_sumInr, exists_basis_of_pairing_ne_zero, finrank_vectorSpan_insert_le, Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos, WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero, ContinuousMap.spectrum_eq_preimage_range, LinearMap.isUnit_iff_ker_eq_bot, LinearMap.BilinForm.isCompl_orthogonal_iff_disjoint, ContinuousLinearEquiv.isBigO_sub, HasFDerivAt.isBigOTVS_sub, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, Unitization.quasispectrum_inr_eq, IntermediateField.linearDisjoint_comm, ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem, SeparationQuotient.outCLM_uniformContinuous, HasCompactSupport.hasDerivAt_convolution_right, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, InnerProductSpace.isSymmetricProjection_rankOne_self, hasDerivWithinAt_neg, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, divRadical_dvd_derivative, Polynomial.leadingCoeff_mul_prod_normalizedFactors, Module.Basis.constrL_apply, MeromorphicOn.divisor_fun_pow, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, Bundle.ContinuousRiemannianMetric.continuous, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, hasMFDerivAt_neg, HasFDerivWithinAt.const_smul, Matrix.IsHermitian.charpoly_cfc_eq, NormedSpace.norm_expSeries_summable, linearIndepOn_id_insert_iff, ContinuousLinearEquiv.hasMFDerivAt, MeasureTheory.ConvolutionExistsAt.integrable_swap, FDRep.instFiniteDimensionalHom, isPowMul_spectralNorm, NormedSpace.expSeries_sum_eq, IsGreatest.norm_cfcₙ, Ideal.eq_bot_or_top, Polynomial.deriv_aeval, VectorBundleCore.trivializationAt_coordChange_eq, hasGradientWithinAt_iff_hasFDerivWithinAt, DoubleCentralizer.nnnorm_def, norm_inner_eq_norm_iff, HasFiniteFPowerSeriesOnBall.eq_partialSum, FiniteField.instIsScalarTowerZModExtension, Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, LinearMap.BilinForm.dualSubmodule_span_of_basis, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, NumberField.RingOfIntegers.instIsTorsionFree_2, ContinuousLinearMap.measurable_apply₂, IsLocalFrameOn.coeff_congr, FormalMultilinearSeries.ofScalars_add, DifferentiableAt.fderiv_norm_self, continuousOn_tangentCoordChange, ContinuousAlternatingMap.isEmbedding_toContinuousMultilinearMap, RootPairing.finrank_rootSpanIn_int, Polynomial.monic_mapAlg_iff, RCLike.im_ofReal_pow, FloorSemiring.tendsto_pow_div_factorial_atTop, tendsto_one_div_add_atTop_nhds_zero_nat, IntermediateField.equivOfEq_symm, LinearIsometryEquiv.smul_apply, LaurentSeries.val_le_one_iff_eq_coe, Matrix.card_GL_field, inner_eq_norm_mul_iff_div, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, LinearIsometryEquiv.contDiff, OnePoint.smul_some_eq_ite, summable_const_div_iff, HasFDerivAt.comp_hasFDerivWithinAt, ContDiff.continuous_fderiv_apply, FiniteDimensional.RCLike.properSpace_submodule, AffineMap.hasDerivAt_lineMap, Polynomial.dvd_C_mul, Function.hasTemperateGrowth_iff_isBigO, range_stereographic_symm, ratCast_smul_eq, cfcₙ_comp_norm, MeasureTheory.integral_smul, Seminorm.convexOn, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, Polynomial.X_pow_sub_C_separable_iff, Submodule.traceDual_top', HasGradientAtFilter.hasDerivAtFilter', IntermediateField.restrictRestrictAlgEquivMapHom_apply, Algebra.norm_eq_prod_embeddings, DifferentiableWithinAt.prodMk, PiLp.volume_preserving_toLp, MonomialOrder.isUnit_leadingCoeff, IsPurelyInseparable.minpoly_eq, Polynomial.cauchyBound_smul, SeparatingDual.dualMap_surjective_iff, NumberField.canonicalEmbedding.integralBasis_repr_apply, Finset.pluennecke_ruzsa_inequality_nsmul_add, ValuationSubring.smul_mem_pointwise_smul_iff, IsNoetherian.range_finsetBasis, IsLocalExtr.fderiv_eq_zero, EuclideanGeometry.orthogonalProjection_apply', WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, IsGalois.intermediateFieldEquivSubgroup_apply, ContMDiffAt.smul, isOpenEmbedding_stereographic_symm, Polynomial.natSepDegree_zero, intervalIntegral.integral_hasDerivWithinAt_left, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, Polynomial.ofReal_eval, HasFPowerSeriesOnBall.fderiv_eq, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, strictConvex_closedBall, SpectrumRestricts.algebraMap_image, Continuous.cfcₙ_of_mem_nhdsSet, NormedSpace.toNormSMulClass, Ideal.algebraMap_residueField_surjective, mfderivWithin_comp_of_preimage_mem_nhdsWithin_of_eq, AlgHom.fieldRange_toSubalgebra, ContinuousMultilinearMap.nnnorm_constOfIsEmpty, ContinuousLinearMapWOT.instLocallyConvexSpace, Submodule.finiteDimensional_sup, ContinuousLinearMap.instLocallyConvexSpace, Ideal.sum_ramification_inertia, PadicAlgCl.norm_extends, FunctionField.classNumber_eq_one_iff, RingHom.coe_rangeRestrictField, Asymptotics.IsLittleOTVS.zero, ContinuousLinearMap.flip_mul, minpoly.degree_le, IsAlgClosed.card_roots_map_eq_natDegree_of_isUnit_leadingCoeff, NormedSpace.inclusionInDoubleDual_norm_eq, IsFractionRing.integerNormalization_eq_zero_iff, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, WeierstrassCurve.Projective.isUnit_Y_of_Z_eq_zero, IntermediateField.fieldRange_comp_val, VectorBundle.trivialization_linear', SchwartzMap.smulLeftCLM_sum, NNRat.den_mul_den_eq_den_mul_gcd, IsRealClosed.exists_eq_pow_of_nonneg, IntermediateField.linearDisjoint_iff, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff', FractionRing.instIsScalarTower_1, AffineMap.hasDerivWithinAt_lineMap, IntermediateField.adjoin.powerBasis_gen, WeierstrassCurve.Affine.slope_of_Y_ne, LinearEquiv.mem_dilatransvections_iff_rank, NumberField.ComplexEmbedding.IsConj.eq, mfderiv_prod_eq_add_comp, ContinuousLinearMap.fderiv_of_bilinear, IsDedekindDomain.integer_empty, Ideal.card_primesOverFinset_le_finrank, NumberField.Units.regulator_eq_det, Matrix.PosSemidef.posSemidef_sqrt, hasFDerivAt_of_subsingleton, Real.hasDerivWithinAt_arccos_Ici, unitary.linearIsometryEquiv_coe_symm_apply, PiTensorProduct.tprodL_toFun, IntermediateField.toSubalgebra_map, ContinuousLinearMap.isPositive_def, IntermediateField.equivOfEq_rfl, Seminorm.gaugeSeminorm_ball, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, Continuous.cfcₙ, ContinuousLinearMap.nnnorm_toSpanSingleton, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, IntermediateField.map_fixingSubgroup, Polynomial.abs_tendsto_atTop_iff, IsLocalRing.finrank_CotangentSpace_eq_one, ContinuousLinearEquiv.hasMFDerivWithinAt, ContinuousAlternatingMap.alternatizeUncurryFin_smul, contDiffAt_map_inverse, fderiv_mul_const', LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, FGModuleCat.FGModuleCatEvaluation_apply, Complex.hasDerivAt_Gammaℝ_one, SchwartzMap.toBoundedContinuousFunctionCLM_apply, curveIntegral_segment, finite_of_algHom_finiteType_of_isJacobsonRing, Asymptotics.isLittleOTVS_fun_neg_left, TestFunction.postcompCLM_apply, Module.End.map_genEigenrange_le, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, IntermediateField.normal_iff_normalClosure_le, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, IsLocalRing.finrank_cotangentSpace_eq_zero_iff, TrivSqZeroExt.eq_smul_exp_of_ne_zero, Asymptotics.isBigOTVS_iff_smallSets, Derivation.leibniz_inv, ContinuousAlternatingMap.norm_restrictScalars, Real.fourierIntegral_continuousLinearMap_apply, OrthonormalBasis.coe_ofRepr, Submodule.starProjection_top', ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, MvPowerSeries.inv_eq_iff_mul_eq_one, mem_perfectClosure_iff_pow_mem, inv_add_inv', OrthonormalBasis.toBasis_mulOpposite, Submodule.adjoint_subtypeL, LinearMap.BilinForm.orthogonal_eq_bot_iff, MeasureTheory.convolutionExistsAt_flip, ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, hasStrictFDerivAt_exp, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, convexHull_basis_eq_stdSimplex, Module.Basis.trace_traceDual_mul, IntermediateField.relrank_top_right, IsCoercive.range_eq_top, coevaluation_apply_one, Field.Emb.Cardinal.noMaxOrder_rank_toType, LinearMap.isSymmetric_adjoint_mul_self, InnerProductSpace.Core.cauchy_schwarz_aux, ContinuousLinearMap.opNorm_mul_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, JacobsonNoether.exists_pow_mem_center_of_inseparable, ContinuousLinearMap.norm_smulRightL, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, NumberField.InfinitePlace.card_filter_mk_eq, RatFunc.num_denom_add, Convex.radon_partition, Submodule.le_traceDual_traceDual, Subfield.finrank_comap, mfderiv_comp_mfderivWithin, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1, Algebra.instFiniteResidueFieldOfFormallyUnramified, FiniteDimensional.span_finset, IsPurelyInseparable.bijective_comp_algebraMap, unitSphereToUnits_apply_coe, NNRat.one_le_cast, Submodule.reflection_orthogonalComplement_singleton_eq_neg, deriv_fun_div, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, ContinuousLinearEquiv.comp_fderiv, PosSMulMono.nnrat_of_rat, IsLocalRing.map_tensorProduct_mk_eq_top, HasFDerivWithinAt.fun_smul, Polynomial.natDegree_mul_leadingCoeff_self_inv, Complex.orthonormalBasisOneI_repr_apply, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, ContinuousLinearMap.isBigO_id, GaloisField.finrank, IsLocalRing.residue_def, RCLike.conj_mul, ContDiffAt.fderiv_right, AnalyticOn.compContinuousLinearMap, hasStrictFDerivAt_iff_isLittleO, MeasureTheory.convolution_def, WeierstrassCurve.Affine.slope_of_Y_ne', Affine.Triangle.dist_circumcenter_reflection_orthocenter, HasStrictFDerivAt.prodMk, MeasureTheory.norm_condExpL2_coe_le, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousMultilinearMap.curryLeft_norm, HasStrictFDerivAt.of_notMem_tsupport, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, HasDerivAt.hasFDerivAt, MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable, InnerProductSpace.trace_rankOne, coe_toPrincipalIdeal, AdjoinRoot.mul_div_root_cancel, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, IntermediateField.continuousSMul, NumberField.Units.coe_coe, ContinuousMultilinearMap.uncurry0_norm, hasMFDerivWithinAt_inr, FunctionField.algebraMap_injective, HasFPowerSeriesWithinOnBall.prod, Nonneg.coe_nnratCast, NormedSpace.eq_iff_forall_dual_eq, Set.coe_unit, ContinuousLinearEquiv.integral_comp_comm, Algebra.IsCentral.baseField_essentially_unique, Algebra.map_intNormAux, Matrix.conjTranspose_inv_natCast_smul, ContinuousMultilinearMap.le_opNorm, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, ContDiffOn.fderiv_of_isOpen, Bundle.Trivial.linearMapAt_trivialization, Matrix.PosDef.isUnit, continuousOn_cfcₙ, infEDist_smul₀, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', ContinuousLinearMap.continuous_restrictScalars, HasFDerivWithinAt.neg, hasStrictDerivAt_const_add_iff, iteratedFDeriv_const_smul_apply, Finset.centerMass_insert, isBoundedBilinearMap_compMultilinear, ContinuousLinearEquiv.comp_right_fderiv, hasLineDerivAt_smul_iff, Submodule.isIdempotentElem_starProjection, differentiableOn_finCons', VectorField.lieBracket_const_smul_left, RCLike.div_im, SimpContFract.determinant, hasFDerivAt_norm_rpow, Complex.re_comp_balance, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers, Submodule.mem_smul_iff_inv_mul_mem, IsGaloisGroup.mulEquivCongr_apply_smul, Algebra.ringChar_eq, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, ZSpan.repr_ceil_apply, Asymptotics.isEquivalent_nat_ceil, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime, IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem, Ideal.ResidueField.ringHom_ext_iff, HasFPowerSeriesOnBall.uniform_geometric_approx, LinearIsometry.inner_map_map, DoubleCentralizer.neg_snd, IsNormalClosure.splits, FiniteField.forall_pow_eq_one_iff, top_fixedByFinite, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ZLattice.comap_equiv_apply, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, ContinuousAlternatingMap.instIsTopologicalAddGroup, ContinuousLinearMap.analyticAt, iteratedFDeriv_succ_const, LaurentSeries.algebraMap_apply, IntermediateField.relfinrank_dvd_finrank_bot, Asymptotics.isBigOTVS_fun_neg_left, WeierstrassCurve.Projective.isUnit_addU_of_Y_ne, IsGalois.sup_right, ContDiffAt.iteratedFDeriv_right, NumberField.Units.finrank_mul_regOfFamily_eq_det, ContDiffBump.convolution_tendsto_right, Matrix.linfty_opNNNorm_toMatrix, HasFTaylorSeriesUpToOn.cont, RatFunc.laurent_at_zero, Asymptotics.isBigOTVS_fun_neg_right, Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm, IsLocalRing.ResidueField.map_comp_residue, div_add', AnalyticOnNhd.fderiv_of_isOpen, Module.Basis.coe_constrL, ContinuousAlternatingMap.le_opNorm, MvPowerSeries.constantCoeff_inv, Seminorm.rescale_to_shell_zpow, IsDedekindDomain.selmerGroup.monotone, FormalMultilinearSeries.ofScalars_sub, Valuation.mem_unitGroup_iff, Asymptotics.IsEquivalent.smul, differentiableAt_apply, ConjRootClass.monic_minpoly, NormedSpace.expSeries_hasSum_exp, midpoint_le_right, ContinuousMultilinearMap.range_toUniformOnFun, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, derivWithin_fun_div, tangentMapWithin_snd, algebraMap_galRestrict_apply, Matrix.toEuclideanCLM_toLp, Seminorm.smul_closedBall_zero, WeakDual.CharacterSpace.homeoEval_naturality, minpoly.map_eq_of_isSeparable_of_isPurelyInseparable, DifferentiableWithinAt.hasDerivWithinAt, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, CPolynomialOn.iteratedFDeriv, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, linearIndependent_fin_cons, LinearMap.BilinForm.dualSubmodule_dualSubmodule_flip_of_basis, ContinuousLinearMap.isPositive_id, IntermediateField.adjoin_simple_adjoin_simple, FormalMultilinearSeries.coeff_eq_zero, analyticOrderAt_centeredMonomial, IntermediateField.adjoin_simple_toSubalgebra_of_integral, normalClosure.restrictScalars_eq, differentiableAt_pi'', RCLike.conjCLE_coe, Height.mulHeight_pow, HasFPowerSeriesOnBall.sum, Module.End.hasUnifEigenvalue_iff_mem_spectrum, contDiffOn_stereoToFun, Real.hasFDerivAt_fourier, absorbs_iff_eventually_nhdsNE_zero, LinearMap.mul_eq_one_comm, ContinuousLinearMap.isUniformAddGroup, LeftInvariantDerivation.evalAt_coe, Unitary.coe_symm_linearIsometryEquiv_apply, mfderivWithin_sumInl, fderiv_inverse, smul_sphere', hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, FractionalIdeal.count_ne_zero, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_right, IsRealClosed.exists_eq_pow_of_odd, IsPrimitiveRoot.adjoinEquivRingOfIntegers_apply, HasFPowerSeriesOnBall.fderiv, range_cfcₙ, LinearMap.adjoint_rTensor, NumberField.det_basisOfFractionalIdeal_eq_absNorm, dist_midpoint_midpoint_le, RCLike.normSq_inv, Matrix.PosSemidef.sqrt_eq_one_iff, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, LinearMap.IsPositive.add, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, NumberField.InfinitePlace.isUnramified_smul_iff, ImplicitFunctionData.leftDeriv_fderiv_implicitFunction, Field.Emb.cardinal_eq_of_isSeparable, IntermediateField.AdjoinSimple.norm_gen_eq_one, FixedPoints.finrank_le_card, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, NumberField.InfinitePlace.orbitRelEquiv_apply_mk'', LinearMap.adjoint_inner_right, padicNormE.defn, MeasureTheory.mem_lpMeas_indicatorConstLp, iteratedFDeriv_const_smul_apply', IsAbelianGalois.toIsMulCommutative, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, map_nnrat_smul, PiLp.hasFDerivAt_toLp, stereoInvFun_apply, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, IntermediateField.range_val, PiTensorProduct.mapL_coe, Finset.dens_le_one, IntermediateField.instFiniteSubtypeMemBot, ArchimedeanClass.FiniteElement.mk_intCast, NumberField.InfinitePlace.Completion.locallyCompactSpace, IntermediateField.isCyclotomicExtension_lcm_sup, Filter.EventuallyEq.hasDerivAt_iff, Submodule.disjoint_span_singleton, Manifold.IsImmersionAt.writtenInCharts, fderiv_pow, InnerProductSpace.rankOne_eq_zero, ContinuousLinearMap.lipschitz, Polynomial.differentiable_aeval, DoubleCentralizer.range_toProd, zpow_zero', map_mem_perfectClosure_iff, egauge_le_one, fderiv_one, AlgEquiv.card_le, Projectivization.cross_mk_of_cross_ne_zero, collinear_iff_finrank_le_one, Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, finrank_quotient_span_eq_natDegree, RCLike.mul_wInner_left, padicNormE.add_eq_max_of_ne', Polynomial.natSepDegree_eq_natDegree_of_separable, Module.Basis.trace_mul_traceDual, Submodule.isOrtho_sSup_right, LinearIsometry.lTensor_apply, ClosedSubmodule.bot_orthogonal_eq_top, LinearIsometry.norm_compContinuousMultilinearMap, ContinuousAlternatingMap.norm_curryLeft, hasDerivAtFilter_neg, RatFunc.numDenom_div, Complex.ofReal_balance, tsum_pow_div_one_sub_eq_tsum_sigma, IntermediateField.linearDisjoint_iff', Real.hasDerivAt_binEntropy, Submodule.norm_sq_eq_add_norm_sq_starProjection, hasDerivAt_gronwallBound_shift, AffineIsometry.linear_eq_linearIsometry, Algebra.IsGeometricallyReduced.isReduced_algebraicClosure_tensorProduct, UniqueDiffOn.of_real, ContMDiffOn.coordChangeL, IsGaloisGroup.fixedPoints_fixingSubgroup, gal_X_pow_sub_one_isSolvable, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, HasFDerivAt.pow, ContinuousLinearMapWOT.smul_apply, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, Asymptotics.isBigOTVS_iff_isBigO, ContinuousMultilinearMap.isLeast_opNorm, Polynomial.existsUnique_hilbertPoly, fderivWithin_comp_derivWithin, Asymptotics.IsLittleO.smul, ContDiff.continuous_fderiv, ContinuousAlternatingMap.apply_apply, Finpartition.IsEquipartition.sum_nonUniforms_lt', hasFDerivAt_id, Bornology.isVonNBounded_sub_of_nonempty, Real.hasDerivAt_qaryEntropy, NumberField.RingOfIntegers.coe_eq_zero_iff, innerSL_inj, AffineIsometryEquiv.coe_ofEq_apply, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, MeasureTheory.condExpIndSMul_smul, Module.finrank_eq_card_basis', hasDerivAt_add_const_iff, IntermediateField.extendScalars.orderIso_apply, hasDerivWithinAt_pow, Ideal.instFinite, Submodule.closed_of_finiteDimensional, hasDerivWithinAt_iff_hasFDerivWithinAt, Asymptotics.isLittleO_pow_id, MeasureTheory.Measure.hausdorffMeasure_smul₀, Polynomial.natDegree_removeFactor, RatFunc.instIsScalarTowerOfPolynomial_1, Padic.norm_p_pow, MeasureTheory.ae_ae_add_linearMap_mem_iff, NumberField.InfinitePlace.IsRamified.comap_embedding_conjugate, MeasureTheory.lintegral_nnnorm_condExpL2_le, MvPowerSeries.coeff_inv, Monotone.ae_hasDerivAt, IsPurelyInseparable.injective_comp_algebraMap, StrongDual.toLp_of_not_memLp, AffineSubspace.isometryEquivMap.toAffineMap_eq, Ideal.surjectiveOnStalks_residueField, DoubleCentralizer.add_fst, Quaternion.expSeries_odd_of_imaginary, deriv_pi, LinearMap.IsSymmetric.coe_toSelfAdjoint, Polynomial.natSepDegree_C_mul_X_sub_C_pow, unitSphereToUnits_injective, Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_map, AlgebraicClosure.instIsAlgClosureOfIsAlgebraic, HasFPowerSeriesWithinAt.coeff_zero, Algebra.normalizedTrace_intermediateField, NumberField.InfinitePlace.even_card_aut_of_not_isUnramified, EuclideanSpace.volume_closedBall_fin_two, OrthonormalBasis.toBasis_map, ContDiffMapSupportedIn.uniformSpace_eq_iInf, hasFDerivAt_apply, SeparationQuotient.outCLM_isUniformEmbedding, RatFunc.num_C, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, Matrix.piLp_ofLp_toEuclideanLin, LinearMap.finrank_genEigenspace_le, cfcₙAux_id, Nonneg.val_unitsEquivPos_symm_apply_coe, LinearMap.IsSymmetric.diagonalization_symm_apply, PiTensorProduct.liftIsometry_tprodL, HasStrictFDerivAt.cexp, WeierstrassCurve.Jacobian.map_add, maximal_orthonormal_iff_basis_of_finiteDimensional, Matrix.projVandermonde_apply_of_ne_zero, VectorField.mpullback_smul_apply, DualNumber.isNilpotent_iff_eps_dvd, OnePoint.map_smul, contDiffWithinAt_iff_of_ne_infty, NormedSpace.inclusionInDoubleDual_norm_le, mfderiv_sumInl, ValuationSubring.principalUnitGroup_le_principalUnitGroup, RatFunc.smul_eq_C_mul, SeparatingDual.instNontrivialContinuousLinearMapIdOfContinuousSMul, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, AnalyticOnNhd.eval_linearMap, LinearEquiv.coe_toContinuousLinearEquiv_symm, hasFTaylorSeriesUpToOn_pi', curveIntegral_segment_const, IsFractionRing.fieldEquivOfAlgEquiv_refl, hasDerivWithinAt_one, mfderiv_sub, le_egauge_smul_left, sub_smul_slope_vadd, tendsto_inv_nhdsGT_zero, galLift_algebraMap_apply, VectorBundleCore.localTriv_symm_apply, DualNumber.isMaximal_span_singleton_eps, Module.Basis.isMaxChain_range_flag, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, WeakDual.isCompact_closedBall, ArchimedeanClass.stdPart_eq_sInf, geom_sum_inv, AffineSubspace.setOf_wOppSide_eq_image2, ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv, NumberField.Units.norm, ContinuousLinearMap.isPositive_toLinearMap_iff, instPolynormableSpaceProd, TangentBundle.trivializationAt_apply, ConvexOn.sSup_of_countable_affine_eq, isNormalClosure_normalClosure, VectorFourier.iteratedFDeriv_fourierIntegral, TestFunction.coe_ofSupportedInCLM, Real.differentiableAt_rpow_of_ne, PointedContMDiffMap.smul_def, Hyperreal.stdPart_coe, Polynomial.natSepDegree_X, FGModuleCat.instFiniteHom, ContDiffBump.normed_convolution_eq_right, IsScalarTower.AlgEquiv.restrictNormalHom_comp, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, Finset.card_mul_mulConst, ContinuousLinearMap.uniformContinuousConstSMul, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContDiffMapSupportedIn.continuous_iff_comp_withOrder, HasLineDerivAt.tendsto_slope_zero, IntermediateField.mem_fixedField_iff, NumberField.IsCMField.complexConj_apply_apply, ContinuousAlternatingMap.instUniformContinuousConstSMul, IntermediateField.finrank_eq_one_iff, ContinuousLinearMap.holder_smul_left, RatFunc.laurent_laurent, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, IntermediateField.lift_top, ContinuousLinearMap.precompR_apply, HarmonicAt.differentiableAt_complex_partial, LaurentSeries.exists_ratFunc_val_lt, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, WeierstrassCurve.Affine.addPolynomial_slope, IsGaloisGroup.fixingSubgroup_le_of_le, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, one_div_mul_add_mul_one_div_eq_one_div_add_one_div, Field.instIsLocalRing, isSymmSndFDerivAt_iff_iteratedFDeriv, RatFunc.num_algebraMap, IntermediateField.sInf_toSubalgebra, HasFDerivWithinAt.mul_const, absorbent_nhds_zero, ContMDiffAt.const_smul_section, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, Polynomial.natSepDegree_map, Matrix.GeneralLinearGroup.IsParabolic.pow, Derivation.leibniz_zpow, ordinaryHypergeometricSeries_apply_eq', MeasureTheory.hasFDerivAt_convolution_right_with_param, ContinuousLinearEquiv.differentiableAt, fderiv_pow', ContMDiffAt.mfderiv_const, AnalyticOn.domDomCongr_iteratedFDeriv, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, ContMDiffSection.coe_smul, fderiv_mul, IntermediateField.adjoin_map, Finset.addConst_le_subConst_sq, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, Asymptotics.IsLittleO.isLittleOTVS, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, hasDerivAt_ofNat, LinearIsometry.isConformalMap, LinearIsometryEquiv.reflections_generate, ContinuousLinearMap.ratio_le_opNorm, IntermediateField.finrank_lt_of_gt, Submodule.map_orthogonal_equiv, mfderiv_prodMap, iteratedFDerivWithin_eq_equiv_comp, Algebra.WeaklyQuasiFiniteAt.finite_locoalization, DifferentiableAt.isBigOTVS_sub, Matrix.l2_opNNNorm_mulVec, AddCommGroup.mul_modEq_mul_left, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, hasFDerivAt_prodMk_left, nhds_basis_balanced, Lagrange.degree_interpolate_erase_lt, NumberField.ComplexEmbedding.IsConj.symm, map_mem_separableClosure_iff, HasStrictFDerivAt.isLittleO, IntermediateField.insepDegree_bot', HasCompactSupport.hasFDerivAt_convolution_right, Set.coe_integer, instOrderedSMulProd, IntermediateField.fixedField_antitone, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, ClosedSubmodule.top_orthogonal_eq_bot, PrimeSpectrum.mem_image_comap_basicOpen, ZMod.card_units, ArchimedeanClass.FiniteResidueField.ofArchimedean_inj, differentialIdeal_le_iff, nnqsmul_def, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, SchwartzMap.norm_iteratedFDeriv_le_seminorm, Submodule.norm_orthogonalProjection_apply_le, Filter.tendsto_neg_const_mul_pow_atTop, instPolynormableSpaceSubtypeMemSubmodule, LinearMap.deriv, VectorPrebundle.linear_trivializationOfMemPretrivializationAtlas, AlgebraicIndependent.lift_reprField, uniqueDiffWithinAt_convex_of_isRCLikeNormedField, cfcₙHom_eq_cfcₙHom_of_cfcHom, Continuous.fderiv, Polynomial.hilbertPoly_succ, X_pow_sub_C_irreducible_iff_of_prime_pow, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, HasFDerivWithinAt.inner, RingEquivClass.toLinearEquivClassRat, NormedSpace.polar_ball_subset_closedBall_div, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, IntermediateField.isAlgebraic_adjoin, galLift_comp, SameRay.exists_pos_right, DoubleCentralizer.smul_fst, Finset.card_mul_cast_subConst, iteratedDerivWithin_const_smul_field, norm_fderiv_le_of_lipschitz, IsCyclotomicExtension.splits_cyclotomic, IsLocalRing.ResidueField.instIsScalarTower_1, mem_subalgebraEquivIntermediateField_symm, InnerProductSpace.toDualMap_apply, FDRep.average_char_eq_finrank_invariants, TotallyBounded.isVonNBounded, instIsLiouvilleSubtypeMemIntermediateField, Polynomial.factor_dvd_of_degree_ne_zero, RCLike.normSq_nonneg, Nat.one_div_cast_pos, CategoryTheory.finrank_endomorphism_eq_one, hasFDerivWithinAt_finCons', IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two, NumberField.InfinitePlace.instMonoidWithZeroHomClassReal, NumberField.IsCMField.coe_ringOfIntegersComplexConj, Subalgebra.LinearDisjoint.exists_field_of_isDomain_of_injective, AffineIsometryEquiv.ofTop_symm_apply_coe, InfiniteGalois.mulEquivToLimit_symm_continuous, TangentBundle.coordChange_model_space, ZMod.pow_card, ContinuousLinearMap.adjoint_inner_left, PowerSeries.normalized_count_X_eq_of_coe, fderivWithin_cos, WeierstrassCurve.Jacobian.addX_of_Z_ne_zero, PointwiseConvergenceCLM.isInducing_inducingFn, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, TensorProduct.inner_mapIncl_mapIncl, Nonneg.val_unitsHomeomorphPos_symm_apply_coe, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, WeierstrassCurve.Affine.addX_eq_addX_negY_sub, Field.DirectLimit.nontrivial, ContinuousLinearEquiv.arrowCongr_symm, ContinuousLinearMap.isBoundedBilinearMap, ArchimedeanClass.stdPart_map_real, fdifferential_apply, ContinuousMultilinearMap.opNorm_nonneg, ContinuousMultilinearMap.hasBasis_nhds_zero, ContinuousMultilinearMap.instIsUniformAddGroup, ball_normSeminorm, HasFPowerSeriesWithinOnBall.sum, instTotallySeparatedSpaceAlgEquivOfIsIntegral, InnerProductSpace.AlgebraOfCoalgebra.mul_def, Real.hasStrictDerivAt_arcosh, Field.toIsField, LinearMap.extendTo𝕜_apply, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq, Filter.EventuallyEq.iteratedFDerivWithin, HahnEmbedding.IsPartial.truncLT_mem_range, RatFunc.liftMonoidWithZeroHom_apply_div, MeromorphicAt.fun_pow, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, NNRat.cast_nonneg, compContinuousLinearMap_zero, HasLineDerivWithinAt.smul, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, LinearMap.range_dualMap_eq_dualAnnihilator_ker, mdifferentiable_smul_const_section, Finset.expect_eq_single_of_mem, FormalMultilinearSeries.apply_eq_pow_smul_coeff, RatFunc.num_dvd, hasDerivAtFilter_id, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Ideal.ResidueField.liftₐ_comp_toAlgHom, Filter.Tendsto.atTop_smul_nhds_tendsto_asymptoticNhds, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, minpoly.isIntegrallyClosed_eq_field_fractions, ContinuousLinearEquiv.integrable_comp_iff, Asymptotics.isBigOTVS_congr, ContinuousLinearMap.instContinuousEvalConst, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, star_ratCast_smul, fderivWithin_ccos, Nat.cast_add_choose, Asymptotics.isBigOTVS_neg_right, MDifferentiableOn.coordChangeL, hasDerivAt_update, quadraticCharFun_one, VectorField.mlieBracketWithin_const_smul_left, Lagrange.degree_interpolate_lt, ContinuousLinearMap.IsPositive.isSymmetric, ContinuousAlternatingMap.ofSubsingletonLIE_apply, add_thirds, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, nnnorm_apply_le_nnnorm_cfcₙ, fderiv_fun_add, MeromorphicOn.fun_pow, FormalMultilinearSeries.compAlongComposition_bound, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_fst, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, NNRat.coe_castHom, IntermediateField.toSubfield_map, FractionalIdeal.canonicalEquiv_mk0, ContinuousLinearMap.lipschitz_apply, PowerBasis.equivAdjoinSimple_aeval, Trivialization.prod.isLinear, inner_eq_sum_norm_sq_div_four, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, IntermediateField.extendScalars_adjoin, NumberField.InfinitePlace.isInfinitePlace, IsAlgClosed.exists_pow_nat_eq, fderiv_pow_ring, constFormalMultilinearSeries_apply_zero, IntermediateField.isPurelyInseparable_tower_bot, Polynomial.cauchyBound_C, le_separableClosure_iff, DifferentiableAt.fderiv_restrictScalars, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, Normal.algHomEquivAut_apply, inTangentCoordinates_eq, LinearIsometryEquiv.conjStarAlgEquiv_trans, IsCyclotomicExtension.finrank, FormalMultilinearSeries.radius_smul_eq, Polynomial.preHilbertPoly_eq_choose_sub_add, DifferentiableAt.comp_ringHom, AffineIsometryEquiv.ofEq_symm, RatFunc.laurentAux_div, Polynomial.abs_tendsto_atBot_iff, ContinuousLinearMap.bilinearComp_zero_right, FractionalIdeal.coe_dual_one, RootPairing.finrank_corootSpanIn, tendsto_nat_floor_mul_div_atTop, Polynomial.roots_C_mul_X_add_C, ZMod.instIsDomain, DivisibleHull.instIsStrictOrderedModuleNNRat, LinearMap.IsSymmetric.continuous, IsContMDiffRiemannianBundle.exists_contMDiff, Filter.tendsto_const_mul_pow_atTop_iff, Module.End.IsSemisimple.pow, ContinuousMap.ideal_isMaximal_iff, PrimeSpectrum.iInf_localization_eq_bot, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, BaireSpace.instBarrelledSpace, hasDerivAtFilter_add_const_iff, LinearIsometry.extend_apply, NumberField.FinitePlace.norm_lt_one_iff_mem, IntermediateField.extendScalars_inf, Polynomial.Gal.instIsScalarTowerSplittingField, hasDerivAt_jacobiTheta₂_fst, AdjoinRoot.span_maximal_of_irreducible, hasSum_const_div_iff, IsGaloisGroup.of_isGalois, uniform_continuous_npow_on_bounded, InnerProductSpace.rank_rankOne, LinearMap.isSymmetric_sum, FiniteField.pow_finrank_eq_natCard, MDifferentiableAt.const_smul, LinearMap.toSeminorm_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, Submodule.isOrtho_top_left, atom_iff_nonzero_span, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_inner, IntermediateField.botContinuousSMul, NumberField.IsCMField.equivInfinitePlace_apply, IsometricContinuousFunctionalCalculus.toNonUnital, Finset.dens_eq_card_div_card, Submodule.finrank_strictMono, RatFunc.mk_eq_div, contMDiffAt_coordChangeL, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isReal, HasFDerivWithinAt.fun_sub, LinearMap.flip_bijective_iff₁, InnerProductSpace.toDual_apply_apply, LinearMap.flip_bijective_iff₂, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, ContinuousLinearMap.nonneg_iff_isPositive, Real.hasDerivAt_arcsin, RCLike.real_smul_eq_coe_smul, Mathlib.Meta.NormNum.isNNRat_ratCast, eq_separableClosure_iff, Int.log_one_right, WeierstrassCurve.Affine.C_addPolynomial_slope, LinearMap.BilinForm.mem_dualSubmodule, coe_lpBCFₗᵢ, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, Submodule.linearEquiv_det_reflection, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, LinearMap.isSymmetric_linearIsometryEquiv_conj_iff, sup_eq_half_smul_add_add_abs_sub', Trivialization.symmL_continuousLinearMapAt, Nat.floor_div_eq_div, ValuationSubring.coe_unitGroupMulEquiv_apply, ProperCone.innerDual_singleton, quadraticCharFun_mul, Finset.dens_disjiUnion, Submodule.IsOrtho.map, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, LinearIsometryEquiv.comp_differentiableOn_iff, RingOfIntegers.norm_algebraMap, LinearIsometryEquiv.comp_differentiableAt_iff, differentiable_inner, tendsto_natCast_div_add_atTop, Asymptotics.IsLittleO.smul_isBigO, HasFPowerSeriesWithinOnBall.sub, HasLineDerivAt.tendsto_slope_zero_left, Submodule.mk_mem_projectivization_iff, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, ContDiffWithinAt.continuousLinearMap_comp, NumberField.InfinitePlace.smul_coe_apply, LinearMap.minpoly_dvd_charpoly, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, spectrum.pow_image_subset, derivWithin_const_smul_field, ValuationRing.isFractionRing_iff, HasFDerivWithinAt.prodMk, tsum_mul_left, ContinuousAlternatingMap.norm_ofSubsingleton, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_list_prod', segment_eq_Icc', Submodule.toLinearMap_starProjection_eq_isComplProjection, Asymptotics.isLittleO_const_smul_left, Rat.instSMulCommClass', Matrix.cRank_diagonal, FunctionField.ringOfIntegers.instIsDomainSubtypeMemSubalgebraPolynomial, hasStrictFDerivAt_finCons, InnerProductSpace.rankOne_def, MDifferentiableWithinAt.coordChangeL, minpoly.degree_le_of_ne_zero, Diffeomorph.mfderivToContinuousLinearEquiv_coe, TensorProduct.nnnorm_map, Module.Basis.ofZLatticeBasis_span, arithGeom_same_eq_mul_div', MvPowerSeries.inv_mul_cancel, ContinuousLinearMap.coe_flipₗᵢ', HasMFDerivAt.prodMap, ValuationSubring.unitGroup_injective, Projectivization.submodule_mk, AddCommGroup.div_modEq_div, NumberField.IsCMField.is_quadratic, div_eq_quo_add_sum_rem_div, star_nnrat_smul, PiTensorProduct.norm_eval_le_injectiveSeminorm, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, IsFractionRing.mk'_num_den', deriv_inv, IntermediateField.normal_iff_forall_fieldRange_le, Submodule.sub_starProjection_mem_orthogonal, ContinuousLinearMap.fpowerSeriesBilinear_apply_add_three, contDiffOn_succ_iff_fderiv_of_isOpen, PointwiseConvergenceCLM.equivWeakDual_apply, Polynomial.fderiv_aeval, one_half_lt_one, fderivWithin_fderivWithin_eq_of_mem_nhds, linearIndepOn_pair_iff, Char.card_pow_card, ContinuousLinearMap.norm_smulRight_apply, Valuation.pow_Uniformizer_is_pow_generator, Real.hasStrictDerivAt_cosh, Module.End.maxUnifEigenspaceIndex_le_finrank, contDiff_iff_continuous_differentiable, tendsto_pow_div_pow_atTop_zero, hasDerivAt_const, dslope_sub_smul_of_ne, affineIndependent_iff_not_finrank_vectorSpan_le, FiniteField.finrank_zmod_extension, FGModuleCat.FGModuleCatDual_obj, Finset.centerMass_smul_left, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Module.Basis.equivFunL_symm_apply_repr, ArchimedeanClass.FiniteResidueField.ofArchimedean_injective, PrincipalIdeals.normal, IsometryEquiv.map_midpoint, fderiv_mul', LinearIsometryEquiv.conjStarAlgEquiv_ext_iff, OrthonormalBasis.repr_apply_apply, IsGalois.normalAutEquivQuotient_apply, IsGalois.normalBasis_apply, UniformSpace.Completion.norm_toComplL, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, NumberField.IsCMField.complexConj_apply_eq_self, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, instSMulDistribClassAlgEquiv, Complex.hasDerivAt_Gammaℂ_one, VectorField.lieBracket_fmul_left, integrable_cfcₙ, iteratedDerivWithin_fun_const_smul_field, RingHom.map_fieldRange, HasFDerivAtFilter.sum, RatFunc.num_zero, ContinuousFunctionalCalculus.toNonUnital, toIcoMod_eq_add_fract_mul, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right, ContinuousMultilinearMap.analyticAt, hasMFDerivAt_id, ClosedSubmodule.orthogonal_eq_inter, Valuation.Integers.le_iff_dvd, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, IntermediateField.adjoin_simple_eq_top_iff_of_isAlgebraic, ContinuousMultilinearMap.prodL_apply, toIocMod_eq_sub_fract_mul, FormalMultilinearSeries.radius_inv_eq_limsup, Real.hasStrictDerivAt_log, Polynomial.hilbertPoly_zero_left, HasFDerivWithinAt.cexp, IsCyclotomicExtension.isSplittingField_X_pow_sub_one, Matrix.conjTranspose_inv_ofNat_smul, hasFDerivWithinAt_iff_hasDerivWithinAt, IsAlgClosed.card_roots_map_eq_natDegree_from_simpleRing, IsFractionRing.div_surjective, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet, hasFTaylorSeriesUpToOn_succ_iff_right, ContinuousLinearMap.coe_flipMultilinearEquiv, Seminorm.bddAbove_iff, LaurentSeries.exists_Polynomial_intValuation_lt, NonUnitalAlgHom.coe_Lmul, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, QuadraticForm.equivalent_weightedSumSquares, ContinuousMultilinearMap.norm_map_init_le, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, hasMFDerivWithinAt_id, LeftInvariantDerivation.left_invariant'', ordinaryHypergeometricSeries_apply_zero, Lagrange.basis_empty, SchwartzMap.compCLMOfAntilipschitz_apply, Polynomial.SplittingFieldAux.scalar_tower', ContinuousAlternatingMap.hasStrictFDerivAt, FiniteField.algebraMap_norm_eq_pow, SchwartzMap.fourierInv_apply_eq, trace_eq_finrank_mul_minpoly_nextCoeff, SchwartzMap.smulRightCLM_apply_apply, LinearOrderedField.inducedOrderRingHom_toFun, NormedSpace.norm_expSeries_summable_of_mem_ball, gal_prod_isSolvable, LinearIsometryEquiv.conjStarAlgEquiv_refl, CurveIntegrable.fun_zero, Field.Emb.Cardinal.strictMono_leastExt, IntermediateField.rank_adjoin_eq_one_iff, InnerProductSpace.laplacian_smul, NNRat.natCast_le_cast, HahnEmbedding.Partial.truncLT_mem_range_sSupFun, hasStrictFDerivAt_iff_hasStrictDerivAt, geom_sum_eq, RCLike.tendsto_add_mul_div_add_mul_atTop_nhds, ValuationSubring.mem_unitGroup_iff, mem_segment_iff_sameRay, NNRat.instContinuousInv₀, binomialSeries_apply, eventually_singleton_add_smul_subset, VectorField.mpullback_apply, LinearMap.IsSymmetric.toSelfAdjoint_apply, RatFunc.liftOn_div, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure_1, ContinuousLinearMapWOT.instIsTopologicalAddGroup, fderiv_mem_iff, galLiftEquiv_apply, iteratedFDeriv_neg_apply, Submodule.coe_orthogonalDecomposition, VectorField.lieBracket_eq, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, hasMFDerivWithinAt_fst, ContinuousLinearMap.coe_restrict_scalarsL', differentiableAt_fst, ContinuousLinearMapWOT.isInducing_inducingFn, fderivWithin_fderivWithin_eq_of_eventuallyEq, NumberField.InfinitePlace.LiesOver.comap_eq, DoubleCentralizer.star_fst, NNRat.coe_ceil, differentiableOn_pi'', InnerProductSpace.laplacianWithin_smul, StrongDual.polarSubmodule_eq_polar, Polynomial.separable_X_pow_sub_C', StrictConvex.affinity, NumberField.InfinitePlace.even_finrank_of_not_isUnramifiedIn, Submodule.finrank_orthogonal_span_singleton, summable_prod_mul_pow, IsAlgClosed.factors, instIsScalarTowerAtPrimeFractionRing, PiTensorProduct.liftEquiv_symm_apply, Finset.nonneg_addConst, IsLocalRing.ResidueField.lift_comp_residue, Subfield.algebraMap_ofSubfield, Polynomial.fact_irreducible_factor, RCLike.geometric_hahn_banach_point_point, IsCyclotomicExtension.splits_X_pow_sub_one, norm_cfcₙ_lt_iff, Algebra.TensorProduct.isField_of_isAlgebraic, ContinuousLinearMap.fpowerSeries_apply_add_two, TestFunction.coe_ofSupportedInLM, IntermediateField.rank_top, mfderivWithin_eventually_congr_set', transcendental_aeval_iff, toIcoDiv_zero_one, LinearMap.span_singleton_sup_ker_eq_top, LinearMap.dualMap_injective_iff, concaveOn_iff_div, LinearMap.isPositive_natCast, inner_smul_real_right, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Algebra.normalizedTrace_eq_of_fininteDimensional, TensorProduct.toLinearEquiv_congrIsometry, Asymptotics.isLittleOTVS_fun_neg_right, ContinuousMultilinearMap.opNorm_zero, hasFDerivAt_exp_smul_const', Finset.mulConst_empty_left, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, PowerSeries.IsWeierstrassFactorization.natDegree_eq_toNat_order_map, FormalMultilinearSeries.ofScalars_norm_le, Submodule.isOrtho_iSup_left, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall, IsCoercive.bounded_below, IsLocalFrameOn.toBasisAt_coe, LinearMap.BilinForm.exists_orthogonal_basis, NumberField.mixedEmbedding.covolume_idealLattice, inv_nhdsGT_zero, Representation.isSemisimpleRepresentation_iff_isSemisimpleModule_asModule, IntermediateField.finrank_eq_fixingSubgroup_index, Commute.cfcₙHom, Hyperreal.archimedeanClassMk_pos_of_tendsto, DualNumber.exists_mul_left_or_mul_right, NumberField.place_apply, Submodule.norm_subtypeL, RatFunc.num_inv_dvd, ContinuousLinearMapWOT.hasBasis_seminorms, Submodule.mem_orthogonal', ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, FGModuleCat.FGModuleCatCoevaluation_apply_one, Projectivization.independent_iff_iSupIndep, MvPolynomial.finrank_R, hasFDerivAt_finCons', LinearMap.toMatrixOrthonormal_symm_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, contDiffPointwiseHolderAt_iff, ContinuousLinearMap.IsStarNormal.orthogonal_range, segment_eq_Icc, ContinuousLinearMap.aestronglyMeasurable_comp₂, Subspace.dualRestrict_leftInverse, FiniteField.algebraMap_norm_eq_prod_pow, Matrix.posDef_gram_iff_linearIndependent, instPolynormableSpaceForall, WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_ne_zero, SchwartzMap.smulLeftCLM_const, hasStrictFDerivAt_piLp, NumberField.house_pow_le, nonzero_span_atom, Finset.dens_eq_one, MDifferentiableAt.smul_section, Subfield.bot_eq_of_zMod_algebra, Lagrange.eval_basisDivisor_right, trace_eq_trace_adjoin, IntermediateField.coe_isIntegral_iff, LinearMap.toMatrix_innerₛₗ_apply, NormedSpace.expSeries_div_hasSum_exp_of_mem_ball, strictConvexSpace_iff, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub, PointwiseConvergenceCLM.equivWeakDual_symm_apply, hasDerivAt_of_tendstoUniformlyOn, Asymptotics.isLittleO_const_smul_right, TensorProduct.toLinearEquiv_commIsometry, PadicInt.Coe.ringHom_apply, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, WeierstrassCurve.Jacobian.addY_of_Z_ne_zero, PowerSeries.X_inv, fderiv_fun_sum, AffineMap.hasDerivAt, hasDerivWithinAt_congr_set, Submodule.norm_sq_eq_add_norm_sq_projection, smul_sphere, LinearMap.extendTo𝕜'_apply_re, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, tangentCoordChange_comp, star_inv_intCast_smul, HasFDerivWithinAt.fun_neg, LinearIsometry.norm_iteratedFDeriv_comp_left, NNRat.num_mul_num_eq_num_mul_gcd, LinearMap.range_toContinuousLinearMap, summable_div_const_iff, Submodule.orthogonal_gc, Nonneg.val_inv_unitsHomeomorphPos_symm_apply_coe, NumberField.Embeddings.card, fderiv_const_smul_of_invertible, ContinuousLinearEquiv.dimH_image, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, hasFDerivWithinAt_pow', ContDiffMapSupportedIn.structureMapLM_apply_withOrder, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_right, IsGaloisGroup.fixingSubgroup_fixedPoints, HasFTaylorSeriesUpToOn.continuousLinearMap_comp, IsGaloisGroup.mulEquivAlgEquiv_apply_apply, Module.card_eq_pow_finrank, IsFractionRing.stabilizerHom_surjective, hasStrictDerivAt_finCons', InfiniteGalois.proj_adjoin_singleton_val, normalClosure_def, Finset.dens_sdiff_add_dens, Polynomial.Splits.def, hasDerivWithinAt_taylorWithinEval_at_Icc, LinearMap.BilinForm.toDual_def, dist_iteratedFDerivWithin_zero, curveIntegral_restrictScalars, ContinuousLinearMap.hasFDerivAtFilter, IntermediateField.lift_inf, HasFPowerSeriesOnBall.hasSum, ContinuousLinearMap.isBoundedLinearMap_comp_right, Algebra.QuasiFinite.finite_fiber, quadraticChar_exists_neg_one', Matrix.PosSemidef.toLinearMap₂'_zero_iff, Submodule.starProjection_isSymmetric, IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing, HasFDerivAt.iterate, Polynomial.rootSet_C_mul_X_pow, Submodule.starProjection_apply, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, Algebra.QuasiFinite.instFiniteResidueField, NumberField.Embeddings.instNonemptyRingHomOfIsAlgebraicRatOfIsAlgClosed, HasFPowerSeriesWithinAt.pi, Matrix.eRank_diagonal, NormedSpace.isVonNBounded_iff', IsLocalRing.ResidueField.mapEquiv_apply, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv', RCLike.inv_im, WeakDual.isSeqCompact_closedBall, LinearMap.BilinForm.dualBasis_repr_apply, hasStrictDerivAt_finCons, IsFractional.div_of_nonzero, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, PiTensorProduct.liftEquiv_apply, HasFDerivAt.cexp, DoubleCentralizer.add_snd, Lagrange.degree_basisDivisor_of_ne, has_antideriv_at_fourier_neg, NumberField.InfinitePlace.isRamified_iff, hasFTaylorSeriesUpTo_top_iff', NumberField.InfinitePlace.card_isUnramified, hasStrictDerivAt_zpow, NormedSpace.expSeries_apply_eq, Field.rank_mul_insepDegree_of_isPurelyInseparable, MvPowerSeries.C_inv, fderivWithin_iteratedFDerivWithin, IntermediateField.linearDisjoint_comm', rescale_to_shell, ContinuousLinearMap.rayleighQuotient_add, ContinuousMultilinearMap.contDiff, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, LinearIsometry.toSpanSingleton_apply, hasFDerivAt_iff_tendsto, IsFractionRing.fieldEquivOfAlgEquiv_algebraMap, PolynormableSpace.induced, Polynomial.natSepDegree_eq_natDegree_iff, LinearMap.isSelfAdjoint_iff', Subspace.dual_finrank_eq, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, NumberField.IsCMField.complexEmbedding_complexConj, ContinuousLinearMap.deriv_of_bilinear, sum_embeddings_eq_finrank_mul, Orientation.areaForm'_apply, Padic.padicNormE.is_norm, mem_perfectClosure_iff, VectorBundleCore.coe_coordChange, IntermediateField.smul_mem, tendsto_nat_floor_div_atTop, hasFDerivAtFilter_iff_hasDerivAtFilter, Subfield.coe_comap, NumberField.InfinitePlace.isComplex_smul_iff, AlgHom.map_fieldRange, innerSLFlip_apply_apply, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable, tendsto_inv_atTop_nhdsGT_zero, ContinuousLinearEquiv.mdifferentiableOn, ContinuousLinearMap.nnnorm_holder_apply_apply_le, TrivSqZeroExt.mul_inv_cancel, IsFractionRing.closure_range_algebraMap, Polynomial.annIdealGenerator_mem, NNRat.natCast_lt_cast, NNRat.tendsto_inv_atTop_nhds_zero_nat, Affine.Triangle.dist_orthocenter_reflection_circumcenter, OrthogonalFamily.hasSum_linearIsometry, Polynomial.hasFDerivAt, ZMod.pow_card_sub_one_eq_one, Asymptotics.isTheta_const_smul_left, FiniteField.instFiniteExtension_1, strictConvex_iff_convex, IntermediateField.extendScalars_self, Polynomial.splits_iff, upperBounds_smul_of_neg, Distribution.mapCLM_apply, WeierstrassCurve.Affine.derivative_addPolynomial_slope, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, Subalgebra.isField_of_algebraic, finrank_euclideanSpace, Polynomial.IsSplittingField.splits, FormalMultilinearSeries.norm_compContinuousLinearMap_le, PowerBasis.equivAdjoinSimple_gen, RatFunc.ofFractionRing_comp_algebraMap, LieModule.exists_nontrivial_weightSpace_of_isNilpotent, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, WeierstrassCurve.Jacobian.X_eq_iff, Ideal.ResidueField.map_algebraMap, algebraMap_mk, LinearMap.IsPositive.isSelfAdjoint, infEdist_smul₀, Field.Emb.Cardinal.equivSucc_coherence, ContinuousLinearMap.bilinear_hasTemperateGrowth, FiniteField.frobeniusAlgEquivOfAlgebraic_symm_apply, Polynomial.IsSplittingField.splits', IntermediateField.finrank_top, LinearMap.mem_span_iff_continuous_of_finite, NNRat.cast_le_one, IsContinuousRiemannianBundle.exists_continuous, Bornology.isVonNBounded_iff_smul_tendsto_zero, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, RatFunc.algebraMap_X, Module.AEval.isTorsion_of_finiteDimensional, NumberField.InfinitePlace.IsRamified.isReal, DoubleCentralizer.norm_snd, NumberField.CMExtension.equivMaximalRealSubfield_apply, Submodule.top_orthogonal_eq_bot, Lagrange.basisDivisor_eq_zero_iff, ConvexOn.sSup_of_nat_affine_eq, ContinuousLinearMap.postcomp_apply, FunctionField.ringOfIntegers.instIsIntegrallyClosedSubtypeMemSubalgebraPolynomial, convexJoin_assoc, TrivSqZeroExt.inv_mul_cancel, Ideal.ResidueField.exists_smul_eq_tmul_one, Submodule.fst_orthogonalDecomposition_apply, LinearEquiv.mem_dilatransvections_iff_finrank, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, minpoly.ker_aeval_eq_span_minpoly, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, LinearEquiv.coe_toContinuousLinearEquiv', hasFDerivWithinAt_one, Matrix.rank_eq_finrank_span_row, IsDedekindDomain.FiniteAdeleRing.instIsScalarTower, map_equiv_traceDual, NNRat.cast_sum, IntermediateField.restrictScalars_adjoin_eq_sup, Submodule.orthogonal_orthogonal_eq_closure, RatFunc.intDegree_C, ContinuousLinearEquiv.nhds, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, Submodule.smul_starProjection_singleton, NumberField.Units.mem_torsion, FiniteGaloisIntermediateField.isGalois, LinearMap.BilinForm.dualBasis_injective, ContinuousLinearMap.opNorm_comp_le, contMDiff_smul, MeasureTheory.dist_convolution_le, DoubleCentralizer.nnnorm_fst, LinearMap.finiteDimensional', ContinuousLinearMap.isUnit_iff_isUnit_toLinearMap, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, with_gaugeSeminormFamily, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, Filter.tendsto_mul_const_atTop_iff_pos, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, summable_powerSeries_of_norm_lt_one, PowerSeries.constantCoeff_inv, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, slope_pos_iff, inv_natCast_smul_comm, IntermediateField.mem_adjoin_iff_div, contMDiffOn_continuousLinearMapCoordChange, LinearEquiv.isPositive_symm_iff, NumberField.to_finiteDimensional, ContinuousLinearMap.instCompleteSpace, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, Module.Basis.exists_opNNNorm_le, aestronglyMeasurable_smul_const_iff, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, absConvexHull_add_subset, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, NNRat.instContinuousSMulOfIsScalarTowerOfRat, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, Convex.exists_forall_hasDerivWithinAt, PiTensorProduct.mapL_mul, cfcHom_real_eq_restrict, Finset.centerMass_mem_convexHull, hasDerivWithinAt_taylor_coeff_within, IntermediateField.Lifts.lt_iff, ContinuousLinearMap.toLinearMap_innerSL_apply, Polynomial.Gal.restrictComp_surjective, NumberField.ComplexEmbedding.IsConj.isReal_comp, HasFPowerSeriesAt.hasStrictDerivAt, Submodule.orthogonalFamily_self, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, IsAlgClosure.equivOfEquiv_comp_algebraMap, IntermediateField.top_toSubalgebra, hasFDerivAt_ofNat, Subfield.subtype_apply, Subfield.roots_X_pow_char_sub_X_bot, IntermediateField.extendScalars_le_iff, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Module.Basis.equivFunL_apply, Representation.isSimpleModule_iff_irreducible_ofModule, Polynomial.natSepDegree_X_pow_char_pow_sub_C, hasFDerivAt_list_prod_finRange', LinearMap.IsSymmetric.adjoint_eq, Trivialization.continuousLinearEquivAt_apply', instIsArtinianRing, LinearMap.isPositive_sum, ContinuousMultilinearMap.flipLinear_apply_apply, Submodule.starProjection_norm_le, HasStrictFDerivAt.neg, mfderiv_add, ContinuousAlternatingMap.norm_toContinuousMultilinearMap, HasGradientAt.hasFDerivAt, Lagrange.natDegree_basisDivisor_self, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, PowerSeries.mul_inv_cancel, Finset.addConst_le_card, LinearMap.hasDerivWithinAt, PiLp.volume_preserving_ofLp, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, Finset.dens_mul_card, rescale_to_shell_semi_normed, Localization.subalgebra.isLocalization_ofField, FormalMultilinearSeries.comp_id, IsSepClosed.splits_domain, ContinuousMultilinearMap.hasStrictFDerivAt, Submodule.inner_orthogonalProjection_eq_of_mem_right, Subfield.relfinrank_top_right, Submodule.reflection_reflection, fderivWithin_comp_smul_eq_fderivWithin_smul, ContinuousLinearMap.isLeast_opNNNorm, RatFunc.num_denom_mul, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_one, ContinuousMap.adjoin_id_eq_span_one_union, IsGaloisGroup.fixedPoints_bot, exists_linearIndependent, Submodule.isOrtho_iff_le, MeasureTheory.condExp_smul, Polynomial.hilbertPoly_add_left, TrivSqZeroExt.invOf_eq_inv, Finset.expect_boole_mul', hasFTaylorSeriesUpTo_succ_nat_iff_right, PowerBasis.equivAdjoinSimple_symm_gen, FiniteField.isSplittingField_of_nat_card_eq, tangentConeAt_of_mem_nhds, iteratedFDeriv_add, hasFDerivWithinAt_zero, ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun, tsum_div_const, HasFDerivWithinAt.norm_sq, hasFDerivWithinAt_piLp, IntermediateField.coe_val, NNRat.mul_den, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, ContinuousLinearMapWOT.isEmbedding_inducingFn, IsPrimitiveRoot.minpoly_dvd_mod_p, differentiableOn_piLp, Polynomial.SplittingField.splits, ClosedSubmodule.iInf_orthogonal, WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne, Asymptotics.isLittleOTVS_iff_smallSets, hasDerivAt_fourier_neg, nhds_hasBasis_absConvex, Finset.one_le_divConst, div_add_div_same, Module.End.IsSemisimple.aeval, HahnEmbedding.Partial.eval_smul, Submodule.finiteDimensional_inf_right, EuclideanGeometry.reflection_apply_of_mem, norm_fderiv_norm_rpow_le, AlgHom.fieldRange_toSubfield, SeparationQuotient.exists_out_continuousLinearMap, HasFPowerSeriesOnBall.neg, VectorFourier.fderiv_fourierIntegral, Polynomial.splits_id_iff_splits, ContinuousLinearMap.uncurryBilinear_apply, LinearMap.IsSymmetric.isSymmetric_smul_iff, Matrix.isStrictlyPositive_iff_posDef, groupCohomology.norm_ofAlgebraAutOnUnits_eq, VectorBundle.continuousOn_coordChange', CategoryTheory.finrank_hom_simple_simple_eq_zero_iff, LinearMap.isPositive_linearIsometryEquiv_conj_iff, ZSpan.coe_floor_self, HasFDerivWithinAt.smul_const, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, IntermediateField.fixingSubgroup_le, ContinuousLinearMap.mfderiv_eq, Seminorm.sSup_empty, ModP.preVal_mk, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, hasFDerivWithinAt_singleton, LinearEquiv.coe_toContinuousLinearEquiv_symm', OrthonormalBasis.equiv_self_rfl, ContinuousAlternatingMap.isLeast_opNorm, midpoint_le_left, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, RatFunc.valuation_eq_LaurentSeries_valuation, InnerProductSpace.coe_gramSchmidtBasis, CategoryTheory.finrank_hom_simple_simple_eq_zero_of_not_iso, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, NormedSpace.isVonNBounded_of_isBounded, HasStrictFDerivAt.add, IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero, iteratedFDeriv_eq_equiv_comp, Submodule.reflection_inv, sum_Ioo_inv_sq_le, NumberField.Units.coe_neg_one, Real.smul_iInf_of_nonpos, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, Matrix.conjTranspose_ratCast_smul, RingHomClass.toLinearMapClassRat, Unitization.norm_eq_sup, WeierstrassCurve.Projective.addZ_eq, Real.hasDerivAt_cos, mfderivWithin_comp_of_preimage_mem_nhdsWithin, Matrix.ofLp_toEuclideanCLM, Quaternion.expSeries_even_of_imaginary, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Nat.cast_le_pow_sub_div_sub, summable_pow_div_add, hasDerivAtFilter_iff_isLittleO, Polynomial.IsSplittingField.instIsTorsionFreeSplittingField, AlgebraicClosure.instIsAlgClosure, NormedSpace.expSeries_div_summable, PrimeSpectrum.residueField_comap, HasStrictFDerivAt.restrictScalars, NumberField.InfinitePlace.card_isUnramified_compl, FiniteField.two_pow_card, AffineIsometry.map_vsub, Projectivization.mk_eq_mk_iff, RatFunc.map_apply_div, PiTensorProduct.mapL_comp, PadicInt.coe_adicCompletionIntegersEquiv_apply, IntermediateField.finrank_eq_finrank_subalgebra, Subfield.coe_one, Submodule.norm_starProjection, isCompactOperator_iff_image_closedBall_subset_compact, IntermediateField.finrank_eq_one_iff_eq_top, fderiv_cos, Filter.Tendsto.cfcₙ, Algebra.Transcendental.rank_eq_cardinalMk, tsum_choose_mul_geometric_of_norm_lt_one, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, ordinaryHypergeometric_eq_tsum, FormalMultilinearSeries.isLittleO_one_of_lt_radius, Algebra.instFiniteResidueFieldOfIsUnramifiedAt, hasDerivAt_exp_smul_const, Finset.dens_empty, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', WeierstrassCurve.Affine.map_slope, Meromorphic.fun_smul, Unitary.linearIsometryEquiv_coe_symm_apply, Asymptotics.isBigOTVS_neg_left, isPrincipalIdealRing, NormedSpace.expSeries_apply_eq_div, Polynomial.degree_mul_leadingCoeff_self_inv, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, Polynomial.isRoot_gcd_iff_isRoot_left_right, ContDiff.comp_continuousLinearMap, HahnEmbedding.ArchimedeanStrata.nontrivial_stratum, ZMod.sq_add_sq, exists_dual_vector, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, nnratCast_def, Semifield.toIsField, NumberField.mixedEmbedding.logMap_eq_logEmbedding, AffineIndependent.finrank_vectorSpan_image_finset, hasFDerivWithinAt_comp_smul_smul_iff, IntermediateField.restrictRestrictAlgEquivMapHom_injective, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_apply, ContinuousLinearMap.rayleighQuotient_le_norm, Mathlib.Meta.NormNum.IsRat.natFloor, Projectivization.submodule_injective, IsLocalRing.ResidueField.map_map, IsSepClosed.exists_pow_nat_eq, Nat.choose_lt_pow_div, ZMod.euler_criterion_units, ProbabilityTheory.hasDerivAt_complexMGF, gauge_smul_left_of_nonneg, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff, AffineIsometryEquiv.symm_constVSub, DifferentiableWithinAt.isBigOTVS_sub, ContMDiffWithinAt.smul, LinearMap.isPositive_toContinuousLinearMap_iff, ContinuousLinearMap.norm_def, OrthogonalFamily.summable_of_lp, IsLocalRing.exists_surjective_of_not_isLocalRing, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, LinearIsometryEquiv.analyticWithinAt, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', HasFPowerSeriesAt.apply_eq_zero, Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff, LinearIsometryEquiv.toSpanUnitSingleton_apply, Asymptotics.IsBigOWith.smul, NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', fderivWithin_zero_of_notMem_closure, AddChar.wInner_cWeight_eq_one_iff_eq, map_inv_natCast_smul, PowerSeries.map_eq_zero, ContinuousLinearMap.le_opNorm_of_le, iteratedDeriv_comp_const_smul, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDual, iteratedDerivWithin_one_div, norm_inner_eq_norm_tfae, Cubic.splits_iff_roots_eq_three, ContinuousMultilinearMap.opNorm_pi, curveIntegral_fun_add, DilationEquiv.smulTorsor_apply, ContinuousLinearEquiv.lipschitz, iteratedDeriv_vcomp_three, intervalIntegral.integral_smul, Submodule.isCompl_orthogonal_of_hasOrthogonalProjection, Algebra.adjoin_eq_top_of_primitive_element, exists_nonneg_right_iff_sameRay, IsCyclotomicExtension.discr_prime_pow_ne_two, Submodule.reflection_mul_reflection, Polynomial.isEquivalent_atTop_div, Real.hasDerivWithinAt_arcsin_Ici, OpenPartialHomeomorph.MDifferentiable.comp_symm_deriv, UniqueDiffWithinAt.smul_iff, HasStrictFDerivAt.arctan, curveIntegral_fun_neg, hasMFDerivAt_inl, HasStrictDerivAt.hasStrictFDerivAt, PowerSeries.mul_inv_rev, FiniteField.coe_frobeniusAlgEquivOfAlgebraic_iterate, NumberField.isFinitePlace_iff, gal_C_isSolvable, deriv.scomp, AnalyticAt.analyticOrderAt_eq_natCast, HasFDerivAtFilter.const_smul, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, differentiableAt_finCons, InnerProductSpace.gramSchmidt_triangular, Algebra.normalizedTrace_algebraMap_apply_eq_self, ContinuousMultilinearMap.instContinuousConstSMul, NormedSpace.equicontinuous_TFAE, ContinuousLinearMap.differentiable, hasDerivAt_taylorWithinEval_succ, Submodule.starProjection_map_apply, Bornology.IsBounded.smul₀, LinearMap.dualMap_bijective_iff, NumberField.InfinitePlace.IsUnramified.eq, HasFDerivAt.multiset_prod, LinearMap.star_eq_adjoint, LinearEquiv.toLinearEquiv_toContinuousLinearEquiv, contDiffWithinAt_succ_iff_hasFDerivWithinAt', ContinuousLinearMap.range_smulRight_apply, IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two, IsLocalFrameOn.eventually_eq_sum_coeff_smul, Filter.EventuallyEq.iteratedFDerivWithin', contDiffOn_succ_iff_hasFDerivWithinAt, HasFDerivAt.mul_const, Polynomial.cauchyBound_one, Set.val_unitEquivUnitsInteger_apply_coe, Polynomial.sub_mod, Nat.div_two_lt_floor, differentiableWithinAt_euclidean, ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub, IntermediateField.finrank_adjoin_eq_one_iff, ContinuousLinearMap.opNorm_add_le, IsLocalRing.ResidueField.map_residue, ContinuousLinearMap.sSup_sphere_eq_norm, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, DoubleCentralizer.neg_toProd, FormalMultilinearSeries.radius_unshift, IsGaloisGroup.finiteDimensional, HasFPowerSeriesAt.fderiv_eq, CategoryTheory.endomorphism_simple_eq_smul_id, LinearPMap.adjointDomainMkCLM_apply, IntermediateField.normal_iff_forall_map_le', Submodule.restrictScalars_traceDual, LinearMap.BilinForm.dualBasis_eq_iff, spectrum.map_pow_of_nonempty, NumberField.RingOfIntegers.rank, hasStrictFDerivAt_zero, Matrix.isPositive_toEuclideanLin_iff, ContinuousLinearMap.coe_restrictScalarsIsometry, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, IntermediateField.normal_iff_forall_fieldRange_eq, Polynomial.aeval_conj, ContinuousLinearMap.norm_inr, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, Submodule.starProjection_bot, arithGeom_eq, RootPairing.polarizationEquiv_apply, instIsAbelianGaloisSubtypeMemIntermediateField_1, Nat.cast_div_div_div_cancel_right, NumberField.integralBasis_repr_apply, ContinuousLinearMap.differentiableWithinAt, continuousMultilinearCurryFin0_apply, linearIndependent_fin_succ', Finset.cast_mulConst_mul_card, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, Polynomial.separable_prod_X_sub_C_iff', HasFDerivWithinAt.mapsTo_tangent_cone, Field.finSepDegree_le_finrank, WithAbs.instFiniteDimensional, PiTensorProduct.dualSeminorms_bounded, RootPairing.linearIndepOn_root_baseOf, FormalMultilinearSeries.radius_neg, VectorPrebundle.pretrivialization_linear', Field.nonempty_algHom_of_range_minpoly_subset, FiniteField.splits_X_pow_nat_card_sub_X, HasFDerivWithinAt.mul_const', extDeriv_smul, PointwiseConvergenceCLM.coeLMₛₗ_apply, ContinuousLinearMap.postcompCompactConvergenceCLM_apply, HasStrictFDerivAt.iterate, LaurentSeries.coe_X_compare, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, Submodule.orthogonal_closure, LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, ContinuousMultilinearMap.curryMidEquiv_apply, Finset.dens_biUnion_le, StrictConvexSpace.strictConvex_closedBall, fderiv_const_mul, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq, instArchimedeanNNRat, ApproximatesLinearOn.lipschitz_sub, Matrix.val_planeConformalMatrix, ContinuousMultilinearMap.iteratedFDeriv_eq, Subfield.continuousSMul, FormalMultilinearSeries.le_mul_pow_of_radius_pos, ZSpan.norm_fract_le, differentialIdeal_le_fractionalIdeal_iff, HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal, IntermediateField.finrank_bot, IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zero, ConjRootClass.splits_minpoly, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, ContinuousLinearMap.reApplyInnerSelf_apply, ZSpan.fundamentalDomain_reindex, IsSimpleRing.exists_algEquiv_matrix_divisionRing_finite, inv_zero, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, fderiv_exp, Affine.Simplex.direction_mongePlane, DoubleCentralizer.algebraMap_snd, Finset.expect_dite_eq', NormedSpace.expSeries_apply_zero, ConvexCone.smul_mem_iff, IntermediateField.fixingSubgroup_antitone, ContinuousLinearMap.differentiableAt, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, Valuation.Integers.dvdNotUnit_iff_lt, AnalyticAt.analyticOrderNatAt_eq_iff, fderiv_arctan, fderivWithin_const, RatFunc.laurentAux_algebraMap, RCLike.wInner_cWeight_const_left, MeasureTheory.integrable_smul_const, hasFiniteFPowerSeriesOnBall_const, InfiniteGalois.restrict_fixedField, LinearMap.le_def, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, Finset.dens_le_dens_sdiff_add_dens, Mathlib.Tactic.Ring.inv_zero, iteratedFDerivWithin_succ_apply_left, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, HasFDerivAtFilter.fun_const_smul, hasStrictFDerivAt_norm_sq, FractionalIdeal.mem_dual, Matrix.linearIndependent_cols_iff_isUnit, Ideal.isSimpleOrder, Submodule.starProjection_unit_singleton, SchwartzMap.fourier_evalCLM_eq, RatFunc.algebraMap_eq_C, LinearIsometryEquiv.comp_differentiableWithinAt_iff, tfae_of_isNoetherianRing_of_isLocalRing_of_isDomain, LinearMap.adjoint_toSpanSingleton, DoubleCentralizer.one_snd, Valuation.Integers.valuation_unit, OrthonormalBasis.coe_toBasis, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, Polynomial.natDegree_hilbertPoly_of_ne_zero, Polynomial.div_eq_zero_iff, Polynomial.IsSplittingField.adjoin_rootSet', IsLocalRing.ResidueField.map_id, IntermediateField.sepDegree_bot, convexJoin_convexJoin_convexJoin_comm, ValuationSubring.unitGroup_strictMono, LinearMap.BilinForm.dualSubmodule_dualSubmodule_of_basis, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, Configuration.ofField.instNondegenerateProjectivizationForallFinOfNatNat, Module.natCard_eq_pow_finrank, contDiffOn_infty_iff_fderiv_of_isOpen, mem_quasispectrum_iff, hasDerivWithinAt_natCast, LinearMap.injective_iff_surjective, Algebra.normalizedTrace_self, NumberField.canonicalEmbedding.nnnorm_eq, RatFunc.algebraMap_apply_div, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, galLiftEquiv_symm_apply, convexHull_sum, ContinuousLinearEquiv.analyticOn, RatFunc.div_smul, ContinuousMultilinearMap.opNorm_add_le, fderiv_pow_ring', ContinuousLinearMap.map_sub₂, ContinuousLinearMap.bilinearComp_apply, analyticAt_iff_analytic_fun_smul, IntermediateField.algebraMap_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, ContinuousMultilinearMap.instContinuousEval, differentiableAt_piLp, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Submodule.reflection_sub, InfiniteGalois.instCompactSpaceAlgEquivOfIsGalois, IsAlgClosure.equivOfEquiv_symm_algebraMap, Submodule.exists_fun_fin_finrank_span_eq, TemperedDistribution.instLineDerivSMulReal, iteratedDeriv_comp_neg, fderiv_natCast, IsConjRoot.exists_algEquiv, IntermediateField.finInsepDegree_bot', NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, Module.Basis.flag_covBy, Nonneg.unitsHomeomorphPos_apply_coe, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_le, SchwartzMap.evalCLM_apply_apply, cfcUnits_pow, Algebra.norm_eq_norm_adjoin, Algebra.IsAlgebraic.algHom_bijective₂, LinearMap.IsSymmetric.natCast, HasFDerivAtFilter.fun_sub, OpenPartialHomeomorph.MDifferentiable.mfderiv_bijective, ClosedSubmodule.mem_orthogonal, IsSelfAdjoint.sq_spectrumRestricts, Height.mulHeight_eq, fderiv_const, AddChar.expect_eq_zero_iff_ne_zero, DiffContOnCl.smul_const, NumberField.FinitePlace.coe_apply, Matrix.posDef_iff_eq_conjTranspose_mul_self, MeasureTheory.condExpIndL1_smul', Polynomial.differentiableAt_aeval, affineIndependent_iff_le_finrank_vectorSpan, Subspace.quotAnnihilatorEquiv_apply, circleEquivGen_symm_apply, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, Commute.geom_sum₂_Ico, ContinuousLinearMap.toContinuousLinearEquivOfDetNeZero_apply, WeakDual.CharacterSpace.compContinuousMap_apply, tsum_const_smul'', Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, LinearMap.re_inner_adjoint_mul_self_nonneg, PointwiseConvergenceCLM.coeLM_apply, hasDerivAt_id, differentiable_pi, HasFTaylorSeriesUpToOn.fderivWithin, NNRat.cast_pow, Real.hasDerivAt_rpow_const, IntermediateField.restrictScalars_bot_eq_self, ContinuousLinearEquiv.hasFDerivWithinAt, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, ContinuousMultilinearMap.isLeast_opNNNorm, Complex.ofReal_comp_balance, functionField_iff, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, LinearMap.BilinForm.linearIndependent_of_iIsOrtho, SeparationQuotient.mk_outCLM, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff, RCLike.normSq_mul, LinearMap.isPositive_self_comp_adjoint, PadicInt.toZMod_eq_residueField_comp_residue, RatFunc.eval_C, Polynomial.hilbertPoly_X_pow_succ, Polynomial.isEquivalent_atBot_lead, Lagrange.iterate_derivative_interpolate, FormalMultilinearSeries.id_comp, Finset.mem_convexHull, fderivWithin.log, circleIntegral.integral_smul, ContinuousLinearMap.norm_map_tail_le, deriv_update, Field.finSepDegree_eq_finrank_of_isSeparable, HasFPowerSeriesAt.restrictScalars, AlgebraicClosure.Monics.splits_finsetProd, contMDiffOn_symm_coordChangeL, hasDerivAt_integral_of_dominated_loc_of_deriv_le, tangentBundleCore_coordChange_model_space, Nonneg.coe_nnqsmul, add_div', ContinuousLinearMap.instStarModuleId, NumberField.mixedEmbedding.mixedEmbedding_apply_isReal, Polynomial.hasFDerivAt_aeval, Finset.nonneg_addConst_self, IntermediateField.adjoin.range_algebraMap_subset, Seminorm.convex_ball, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, LinearIsometryEquiv.toLinearEquiv_lTensor, DoubleCentralizer.instIsCentralScalar, Matrix.linearIndependent_of_posDef_gram, ContDiffAt.restrictScalars_iteratedFDeriv, exists_dual_vector'', ContinuousLinearMapWOT.instContinuousSMul, Commute.geom_sum₂, Finpartition.coe_energy, PiTensorProduct.injectiveSeminorm_apply, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, ContinuousLinearMap.isBoundedLinearMap_comp_left, LinearIsometryEquiv.toLinearEquiv_smul, MeasureTheory.MemLp.continuousLinearMap_comp, Valuation.HasExtension.instIsScalarTower_valuationSubring', RingHom.SurjectiveOnStalks.residueFieldMap_bijective, NumberField.RingOfIntegers.mk_zero, norm_fderiv_iteratedFDeriv, FiniteDimensional.finiteDimensional_self, tsum_mul_right, curveIntegralFun_neg, Subfield.coe_subtype, meromorphicOrderAt_smul, Asymptotics.isLittleOTVS_map, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, conformalFactorAt_inner_eq_mul_inner', InfiniteGalois.limitToAlgEquiv_apply, hasFDerivAtFilter_snd, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, LinearIsometryEquiv.analyticOn, ValuationSubring.algebraMap_apply, LinearIsometryEquiv.analyticAt, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, IsLocalRing.ResidueField.map_id_apply, Matrix.l2_opNNNorm_def, hasMFDerivAt_const, NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConj, ContinuousLinearEquiv.strictConvex_image, ContinuousMultilinearMap.instIsBoundedSMul, IntermediateField.mem_lift, IntermediateField.isAlgebraic_adjoin_pair, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, instIsDomain, PowerSeries.inv_eq_zero, hasDerivAtFilter_sub_const_iff, CyclotomicRing.instIsScalarTowerCyclotomicField, RatFunc.faithfulSMul, IsRealClosed.exists_eq_pow_of_isSquare, spectrum.hasDerivAt_resolvent, ContinuousLinearMap.integrable_comp, ContinuousLinearMap.adjointAux_adjointAux, HasStrictFDerivAt.const_sub, RatFunc.num_X, Submodule.coe_inner, Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, fderiv_sub, LinearMap.det_map, NumberField.Embeddings.instNonemptyRingHom, hasDerivAt_exp, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, ZSpan.span_top, LinearMap.hasEigenvalue_zero_tfae, hasFDerivAt_single, DivisionRing.continuousConstSMul_rat, Ideal.finrank_quotient_map, MvPolynomial.schwartz_zippel_sup_sum, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_orthonormalBasis, MeasureTheory.condExpL2_indicator_of_measurable, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, Complex.hasDerivAt_logTaylor, Nonneg.unitsEquivPos_apply_coe, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, iteratedDeriv_vcomp_eq_sum_orderedFinpartition, LinearMap.eq_adjoint_iff, ContinuousLinearMapWOT.instContinuousAdd, WittVector.exists_frobenius_solution_fractionRing, NumberField.mixedEmbedding.norm_smul, Real.hasStrictDerivAt_arsinh, hasSum_mul_right_iff, VectorField.mpullbackWithin_smul_apply, Algebra.discr_mul_isIntegral_mem_adjoin, iter_deriv_pow', HasFDerivWithinAt.iterate, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, uniqueDiffOn_univ, hasDerivAt_iff_tendsto_slope_zero, HasMFDerivWithinAt.sum, IntermediateField.finrank_sup_le, Orthonormal.inner_right_finsupp, NumberField.InfinitePlace.IsRamified.comap_embedding, ordinaryHypergeometricSeries_apply_eq, LinearMap.norm_extendTo𝕜'_apply_sq, Asymptotics.isLittleOTVS_iff_isLittleO, WithSeminorms.equicontinuous_TFAE, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, EuclideanSpace.basisFun_repr, ImplicitFunctionData.hasStrictFDerivAt, TrivSqZeroExt.inv_inv, ContinuousLinearMap.integral_comp_id_comm', Height.AdmissibleAbsValues.mulSupport_finite, UniqueMDiffWithinAt.uniqueDiffWithinAt, NumberField.InfinitePlace.LiesOver.embedding_comp_eq_or_conjugate_embedding_comp_eq, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, Polynomial.dvd_mul_leadingCoeff_inv, ContinuousLinearMap.coprodEquivL_apply_apply, HasFTaylorSeriesUpToOn.hasFDerivAt, Finset.le_card_falling_div_choose, mfderiv_prod_right, LinearIsometry.norm_toContinuousLinearMap_comp, galRestrictHom_symm_algebraMap_apply, hasStrictFDerivAt_inv, RatFunc.algebraMap_C, ContinuousLinearMap.isBigOWith_comp, ContinuousLinearMap.flip_add, exists_pos_left_iff_sameRay, IntermediateField.adjoinRootEquivAdjoin_apply_root, LinearMap.finiteDimensional, hasFiniteFPowerSeriesAt_const, continuous_clm_apply, IntermediateField.fixingSubgroup_isClosed, FiniteDimensional.finiteDimensional_pi', AffineSubspace.isometryEquivMap.coe_apply, infDist_smul₀, ContinuousAlternatingMap.hasBasis_nhds_zero, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, LinearIsometry.coe_toSpanSingleton, Bornology.isBounded_iff_isVonNBounded, Polynomial.cardPowDegree_apply, spectrum.map_polynomial_aeval_of_nonempty, linearIndependent_fin_snoc, ContinuousLinearEquiv.isBigO_sub_rev, ContinuousLinearMap.isSelfAdjoint_iff', Submodule.sndL_comp_coe_orthogonalDecomposition, HasFDerivWithinAt.restrictScalars, DoubleCentralizer.pow_toProd, OrthonormalBasis.equiv_apply_euclideanSpace, measurable_fderiv_apply_const, OnePoint.equivProjectivization_symm_apply_mk, Submodule.le_traceDual, stereographic_neg_apply, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, IsLocalFrameOn.coeff_apply_of_notMem, isSelfAdjoint_starProjection, krullTopology_isTotallySeparated, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, InnerProductSpace.gramSchmidt_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, VectorBundleCore.localTriv_coordChange_eq, Finset.divConst_empty_left, LinearMap.BilinForm.isAdjointPair_iff_eq_of_nondegenerate, ContinuousMultilinearMap.uncurryRight_apply, IntermediateField.rank_bot, eventually_norm_symmL_trivializationAt_self_comp_lt, RCLike.ofReal_pow, ContinuousLinearMap.isVonNBounded_iff, NumberField.FinitePlace.norm_def_int, InnerProductSpace.Core.inner_smul_ofReal_left, mfderivWithin_zero_of_not_mdifferentiableWithinAt, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, fderiv_inv, FiniteField.unit_isSquare_iff, Differentiable.prodMk, Complex.orthonormalBasisOneI_repr_symm_apply, ModelWithCorners.hasMFDerivWithinAt, derivWithin_comp_mul_left, Manifold.riemannianEDist_def, HasFDerivAtFilter.prodMk, hasDerivAt_circleMap, HasFDerivAtFilter.isLittleO, convexHullAddMonoidHom_apply, curveIntegralFun_fun_zero, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Subfield.pow_mem, vectorSpan_segment, ContinuousLinearMap.bilinearComp_zero, HasFDerivAt.fun_pow', le_restrictScalars_separableClosure, ZSpan.map, algebraMap.coe_div, IsSimpleModule.finrank_eq_one_of_isMulCommutative, IntermediateField.coe_zero, NumberField.InfinitePlace.isRamified_iff_card_stabilizer_eq_two, X_pow_sub_C_irreducible_of_prime, Submodule.IsLattice.finrank_of_pi, DifferentiableAt.prodMk, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, Finset.convexHull_eq, HasMFDerivWithinAt.mul', ContinuousLinearEquiv.norm_symm_pos, MvPolynomial.aeval_toPolynomialAdjoinImageCompl_eq_zero, Submodule.sInf_orthogonal, ContinuousAlternatingMap.uniformContinuous_coe_fun, ContinuousMultilinearMap.cpolynomialAt, ContinuousLinearMap.NonlinearRightInverse.right_inv, norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, curveIntegralFun_def', PointedContMDiffMap.instIsScalarTowerSomeENatTop, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace, NumberField.RingOfIntegers.instIsTorsionFree, NumberField.discr_eq_basisMatrix_det_sq, IntermediateField.adjoin.algebraMap_mem, Submodule.isOrtho_span, contDiffOn_fderiv_coord_change, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, IsLocalRing.exists_factor_valuationRing, IntermediateField.instIsScalarTowerSubtypeMem_1, RatFunc.num_eq_zero_iff, ZSpan.exist_unique_vadd_mem_fundamentalDomain, ContinuousMultilinearMap.ratio_le_opNorm, arithGeom_same_eq_mul_div, HasFDerivAtFilter.fun_add, MvPowerSeries.map_eq_zero, ContinuousLinearEquiv.subsingleton_or_nnnorm_symm_pos, ContinuousLinearMap.norm_extendTo𝕜'_bound, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff, slope_def_field, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, HasFDerivWithinAt.hasDerivWithinAt, le_egauge_smul_right, Matrix.PosSemidef.isUnit_sqrt_iff, spectralNorm_smul, hasDerivAt_iff_hasFDerivAt, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, Complex.im_balance, Nonneg.coe_inv, Polynomial.eventually_atTop_not_isRoot, HasFiniteFPowerSeriesOnBall.neg, Complex.ofReal_expect, Padic.complete'', Algebra.IsCentral.instContinuousLinearMap, IsSemisimpleRing.exists_algEquiv_pi_matrix_of_isAlgClosed, HasFDerivAtFilter.comp, Polynomial.separable_prod_X_sub_C_iff, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, LinearMap.charpoly_constantCoeff_eq_zero_iff, norm_derivWithin_eq_norm_fderivWithin, Asymptotics.IsEquivalent.pow, lineDifferentiableWithinAt_smul_iff, NumberField.ComplexEmbedding.isConj_apply_apply, Fintype.expect_ite_mem, ArchimedeanClass.mk_ratCast, iteratedFDeriv_zero_apply, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, ContinuousLinearMap.le_def, isSolvable_of_isScalarTower, WeakDual.isClosed_closedBall, contDiff_succ_iff_fderiv_apply, WeierstrassCurve.Projective.map_dblU, hasDerivAt_fourier, AlgebraicGeometry.ValuativeCommSq.commSq, coe_lpPiLpₗᵢ, Submodule.complete_of_finiteDimensional, Subfield.bot_eq_of_charZero, VectorBundleCore.localTriv_apply, LinearIsometry.inr_apply, Finset.pluennecke_ruzsa_inequality_pow_div, AddCommGroup.mul_modEq_mul_right, fderiv_ccos, LinearMap.isPositive_zero, DoubleCentralizer.zero_fst, IntermediateField.finrank_bot_mul_relfinrank, fderiv_update, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, LinearMap.toSpanSingleton_homothety, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, FiniteField.Matrix.charpoly_pow_card, Asymptotics.superpolynomialDecay_mul_param_pow_iff, ContinuousLinearMap.hasFDerivWithinAt, fdifferential_comp, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, minpoly.dvd_map_of_isScalarTower, LinearIsometry.orthonormal_comp_iff, half_lt_self_iff, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv, WeierstrassCurve.Projective.negDblY_eq, Diffeomorph.uniqueDiffOn_image, ContinuousLinearMap.le_opNorm₂, Algebra.norm_eq_prod_automorphisms, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, slope_fun_def, Seminorm.continuous_iff, HasFDerivAt.smul_const, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, ContinuousLinearMap.norm_uncurryMid, IsLocalFrameOn.linearIndependent, Field.lift_rank_mul_lift_insepDegree_of_isPurelyInseparable, Matrix.sub_scalar_sq_eq_disc, InnerProductSpace.rankOne_def', ContDiff.fderiv_apply, EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, ContinuousLinearMap.opNorm_mul_le, ContinuousLinearMap.uncurryLeft_norm, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_right, hasFDerivAtFilter_fst, Polynomial.exists_approx_polynomial, Submodule.isClosed_orthogonal, Submodule.IsLattice.rank_of_pi, ContinuousLinearMap.opNorm_subsingleton, star_inv_natCast_smul, hasStrictDerivAt_abs_neg, ContinuousLinearMap.holder_smul_right, Filter.EventuallyEq.fderiv, HasFDerivWithinAt.multilinear_comp, HasFPowerSeriesOnBall.tendstoUniformlyOn', HasFPowerSeriesWithinOnBall.const_smul, natDegree_radical_le, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, FiniteField.trace_pow_card, fderiv_apply_one_eq_deriv, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, HasFTaylorSeriesUpToOn.compContinuousLinearMap, hasFDerivAt_zero_of_eventually_const, Finset.sum_div, OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_top, IsUltrametricDist.algNormOfAlgEquiv_apply, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, IntermediateField.bot_eq_top_iff_finrank_eq_one, ContinuousAlternatingMap.continuous_restrictScalars, HasFPowerSeriesOnBall.sub, IntermediateField.finiteDimensional_adjoin, contDiffAt_succ_iff_hasFDerivAt, ContinuousLinearMap.IsPositive.inner_nonneg_left, Real.circleAverage_fun_smul, IntermediateField.isTranscendenceBasis_adjoin_iff, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, hasFDerivAt_const, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_left, HasFDerivAt.inner, LinearMap.adjoint_lTensor, EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, LinearEquiv.smulOfNeZero_apply, LinearMap.slope_comp, IntermediateField.lift_injective, MeasureTheory.Integrable.convolution_integrand, HasFDerivAtFilter.star, RatFunc.intDegree_add, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, Projectivization.exists_smul_eq_mk_rep, OrthonormalBasis.map_apply, LinearMap.toMatrixOrthonormal_apply, DivisibleHull.qsmul_def, MeasureTheory.condExpL1CLM_lpMeas, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, fderivWithin_exp, FiniteGaloisIntermediateField.adjoin_map, NumberField.InfinitePlace.embedding_of_isReal_apply, Submodule.isSymmetricProjection_starProjection, Nat.cast_div, deriv_inv'', ContinuousLinearMap.mdifferentiableWithinAt, SeparatingDual.completeSpace_continuousLinearMap_iff, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, OrthogonalFamily.inner_sum, LinearMap.IsPositive.smul_of_nonneg, NormedSpace.vonNBornology_eq, Function.Periodic.const_smul₀, HasStrictFDerivAt.fun_sub, ClosedSubmodule.mem_orthogonal_toSubmodule_iff, iteratedDeriv_fun_const_smul_field, HasFDerivAt.lim, hasDerivWithinAt_const, FormalMultilinearSeries.compAlongComposition_norm, Polynomial.tendsto_nhds_iff, ContinuousLinearMap.isometry_mul, Subspace.finrank_add_finrank_dualCoannihilator_eq, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', ContinuousLinearMap.isOpen_injective, isCoveringMapOn_npow, NonUnitalCommCStarAlgebra.toStarModule, Submodule.le_traceDual_comm, ContDiff.continuous_iteratedFDeriv', IsFractionRing.mk'_mk_eq_div, IntermediateField.coe_extendScalars, NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding, Polynomial.X_pow_sub_one_separable_iff, NumberField.RingOfIntegers.coe_injective, OrthonormalBasis.sum_repr_symm, HasFDerivAt.const_mul, Meromorphic.pow, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, Finset.sum_card_slice_div_choose_le_one, StrongDual.toLpₗ_apply, IntermediateField.AdjoinSimple.trace_gen_eq_zero, Orthonormal.inner_left_sum, DoubleCentralizer.sub_toProd, formalMultilinearSeries_geometric_apply_norm, IntermediateField.lift_sepDegree_bot', exists_linearIndependent', ContinuousLinearMap.continuous_uncurry_of_multilinear, IsNoetherian.iff_fg, Polynomial.differentiableOn, Pi.orthonormalBasis.toBasis, LinearIsometry.map_starProjection, tendsto_pow_neg_atTop, IsLocalFrameOn.coeff_apply_zero_at, CyclotomicRing.adjoin_algebra_injective, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, egauge_ball_one_le_of_one_lt_norm, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', instLiesOverResidueFieldBotIdeal, instIsTopologicalGroupAlgEquiv, isQuotientCoveringMap_zpow, Real.circleAverage_smul, NNRat.addSubmonoid_closure_range_pow, Polynomial.natSepDegree_C_mul, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, HasFDerivAt.mul, tendsto_add_mul_div_add_mul_atTop_nhds, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, IsLocalRing.split_injective_iff_lTensor_residueField_injective, VectorField.lieBracket_const_smul_right, WeierstrassCurve.Projective.addX_eq, NormedSpace.norm_expSeries_div_summable_of_mem_ball, Asymptotics.IsBigO.hasFDerivWithinAt, LinearMap.continuous_of_nonzero_on_open, Submodule.inf_orthogonal, FiniteDimensional.finiteDimensional_submodule, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, hasSum_coe_mul_geometric_of_norm_lt_one, RatFunc.denom_X, InnerProductSpace.innerSL_norm, hasFDerivAt_exp_zero, NNRat.cast_multisetSum, LinearIsometryEquiv.strictConvex_image, Filter.tendsto_const_mul_pow_atBot_iff, fderiv_add, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, SchwartzMap.le_seminorm, Ioo_subset_openSegment, IsLocalDiffeomorph.mfderivToContinuousLinearEquiv_coe, DoubleCentralizer.nnnorm_fst_eq_snd, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, toWeakSpace_closedConvexHull_eq, tendsto_one_div_atTop_nhds_zero_nat, Unitization.norm_def, IntermediateField.relrank_dvd_rank_top_of_le, convexHull_pi, Finset.addConst_mul_card, Submodule.IsOrtho.le, Submodule.reflection_map, ContinuousAlternatingMap.instT3Space, LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpace, WittVector.RecursionBase.solution_spec, Polynomial.gcd_map, InnerProductSpace.span_gramSchmidt_Iic, MDifferentiableAt.smul, Module.Basis.coe_ofVectorSpace, Submodule.det_reflection, ClassGroup.mk_mk0, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, ContinuousLinearMap.measurable_apply, SeparationQuotient.postcomp_mkCLM_surjective, IsSepClosed.algebraMap_surjective, hasFDerivAtFilter_iff_isLittleOTVS, IntermediateField.finSepDegree_adjoin_simple_le_finrank, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, Matrix.ker_diagonal_toLin', ContinuousMultilinearMap.norm_ofSubsingleton_id_le, ContinuousAlternatingMap.curryLeft_same, ContinuousMultilinearMap.curryRight_apply, NormedSpace.expSeries_apply_eq', ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Submodule.inner_orthogonalProjection_eq_of_mem_left, ContMDiffWithinAt.mfderivWithin, gal_X_sub_C_isSolvable, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, Polynomial.hilbertPoly_mul_one_sub_succ, differentiableWithinAt_pi, star_nnqsmul, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, toIocDiv_eq_neg_floor, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Hyperreal.instIsStrictOrderedRing, Int.log_natCast, Multiset.sum_map_div, ContinuousLinearMap.extendTo𝕜_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, eventually_norm_symmL_trivializationAt_comp_self_lt, ContinuousLinearMap.IsPositive.add, EuclideanSpace.volume_ball_fin_three, Field.Emb.Cardinal.filtration_apply, FiniteField.isSplittingField_of_card_eq, Mathlib.Tactic.Ring.inv_single, Polynomial.natSepDegree_mul_eq_iff, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff', InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis, CurveIntegrable.fun_neg, linearIndepOn_id_pair, MeromorphicAt.pow, AffineSubspace.subtypeₐᵢ_linear, AlgebraicClosure.toSplittingField_coeff, LieModule.traceForm_eq_sum_finrank_nsmul, linearIndependent_fin_succ, NNRat.ceil_coe, NumberField.RingOfIntegers.isIntegral_coe, Int.lt_zpow_succ_log_self, mfderivWithin_const, IntermediateField.relrank_dvd_rank_bot, hasStrictFDerivAt_pow', Polynomial.hasStrictDerivAt_aeval, AnalyticOn.iteratedFDeriv_comp_perm, ContinuousLinearMap.norm_single, LinearMap.flip_injective_iff₂, VectorPrebundle.exists_coordChange, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, DoubleCentralizer.one_fst, ContinuousLinearMap.norm_extendTo𝕜', ValuationSubring.unitGroup_le_unitGroup, Lagrange.degree_basis, NNRat.instSMulCommClass, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, IsDedekindDomain.HeightOneSpectrum.coe_mem_adicCompletionIntegers, StrongDual.polar_univ, IsLocalRing.ResidueField.algebraMap_eq, AlgHom.liftNormal_commutes, fderivWithin_eventually_congr_set, Lagrange.eval_basis_of_ne, NumberField.Units.complexEmbedding_apply, IsStronglyTranscendental.iff_of_isFractionRing, LinearIsometry.coe_toAffineIsometry, NumberField.count_multisetInfinitePlace_eq_mult, FractionalIdeal.map_div, Polynomial.isUnit_or_eq_zero_of_isUnit_integerNormalization_primPart, linearIndependent_of_ne_zero_of_inner_eq_zero, WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne', ContDiffMapSupportedIn.postcompCLM_apply, ValuationSubring.principal_units_le_units, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ContinuousAlternatingMap.curryLeft_zero, IsContDiffImplicitAt.bijective, Polynomial.natSepDegree_smul_nonzero, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, OnePoint.smul_infty_eq_ite, ContinuousAlternatingMap.restrictScalarsLI_apply, fderivWithin_fun_const, PerfectField.splits_of_natSepDegree_eq_one, ContinuousMultilinearMap.opNNNorm_prod, IntermediateField.AdjoinPair.algebraMap_gen₁, ContinuousLinearEquiv.comp_right_differentiableOn_iff, Padic.isAbsoluteValue, OpenPartialHomeomorph.MDifferentiable.mfderiv_surjective, NumberField.fractionalIdeal_rank, ContinuousLinearMap.opENorm_comp_le, hasGradientAt_iff_hasFDerivAt, Asymptotics.IsTheta.isThetaTVS, Asymptotics.isEquivalent_nat_floor, RatFunc.denom_div, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, IsLocalRing.finrank_cotangentSpace_le_one_iff, LinearIndependent.pair_iff', curveIntegrable_neg_iff, PowerSeries.invOfUnit_eq, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, HasFPowerSeriesOnBall.tendsto_partialSum, maximal_orthonormal_iff_orthogonalComplement_eq_bot, ValuationRing.of_integers, hasMFDerivWithinAt_const, FractionalIdeal.map_inv, iteratedFDeriv_one_apply, ContinuousLinearEquiv.iteratedFDeriv_comp_left, Filter.Tendsto.zero_smul_isBoundedUnder_le, NumberField.InfinitePlace.not_isUnramified_iff, Submodule.reflection_orthogonal, quasispectrum.algebraMap_mem_iff, hasFDerivAt_exp_smul_const_of_mem_ball, fderiv_fun_mul', NumberField.InfinitePlace.isUnramified_iff, IsDiscreteValuationRing.exists_lift_of_le_one, Finset.centerMass_segment', ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, HasFPowerSeriesOnBall.factorial_smul, HasFDerivAt.const_smul, HasFDerivAt.hasLineDerivAt, WeierstrassCurve.Affine.Point.map_map, doublyStochastic_eq_convexHull_permMatrix, derivWithin_pi, ContinuousAlternatingMap.norm_image_sub_le', NormedSpace.expSeries_sum_eq_rat, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, HasFPowerSeriesWithinAt.prod, Valuation.HasExtension.algebraMap_mem_valuationSubring, Module.End.finite_spectrum, IsGalois.intermediateFieldEquivSubgroup_symm_apply, ContMDiffMap.coe_smul, iteratedFDeriv_succ_apply_right, NumberField.InfinitePlace.denseRange_algebraMap_pi, Submodule.isOrtho_top_right, FormalMultilinearSeries.leftInv_coeff_one, LinearMap.IsSymmetric.smul, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, ContinuousLinearMap.hasMFDerivAt, IsAlgClosed.exists_eval₂_eq_zero, TensorProduct.assocIsometry_apply, NumberField.finite_of_discr_bdd, Matrix.toLin_conjTranspose, mdifferentiableOn_continuousLinearMapCoordChange, hasDerivAtFilter_intCast, FixedPoints.toAlgAut_surjective, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, Orthonormal.inner_finsupp_eq_sum_left, cfcHom_nnreal_eq_restrict, QuasispectrumRestricts.algebraMap_image, fderiv_deriv, Padic.exi_rat_seq_conv, Matrix.IsHermitian.spectral_theorem, PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable, IsPurelyInseparable.minpoly_natDegree_eq, integrableOn_cfcₙ, hasFPowerSeriesAt_pi_iff, MeasureTheory.eLpNorm'_const_smul, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_apply, NumberField.RingOfIntegers.mapRingHom_apply, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, IntermediateField.LinearDisjoint.of_inf_eq_bot, RatFunc.intDegree_polynomial, norm_cfcₙ_le, toPrincipalIdeal_eq_iff, NumberField.InfinitePlace.isReal_smul_iff, AlgHom.coe_fieldRange, hasDerivWithinAt_univ, Asymptotics.isLittleOTVS_neg_right, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, LinearIsometryEquiv.hasFDerivAt, IntermediateField.adjoin_simple_toSubalgebra_of_isAlgebraic, ContinuousAlternatingMap.uniformContinuous_toContinuousMultilinearMap, TrivSqZeroExt.isUnit_inv_iff, Seminorm.ball_zero_absorbs_ball_zero, RatFunc.v_def, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm, minpoly.add_algebraMap, Subfield.relrank_dvd_rank_top_of_le, HasFDerivAtFilter.add, Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap, ContinuousLinearEquiv.contDiffWithinAt_comp_iff, PointwiseConvergenceCLM.precomp_apply, divRadical_dvd_wronskian_right, NormedSpace.exp_def, Matrix.PosSemidef.sq_sqrt, uniqueMDiffWithinAt_iff, ArchimedeanClass.FiniteResidueField.mk_ne_zero, ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff, LinearIsometryEquiv.rTensor_apply, Polynomial.div_eq_quo_add_rem_div, LinearIsometryEquiv.inner_map_map, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, NumberField.Units.coe_pow, IsPurelyInseparable.algebraMap_elemReduct_eq', InnerProductSpace.isStarProjection_rankOne_self, SeparationQuotient.mk_comp_outCLM, coord_norm', StrictConvex.smul, Trivialization.apply_eq_prod_continuousLinearEquivAt, HasFDerivWithinAt.comp, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, ContinuousLinearMapWOT.ext_dual_iff, LinearIsometry.integral_comp_comm, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, LaurentSeries.LaurentSeries_coe, contDiff_clm_apply_iff, HasFPowerSeriesAt.hasFDerivAt, OrthonormalBasis.measurePreserving_repr_symm, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, Polynomial.SplittingFieldAux.instIsSplittingFieldNatDegree, Finset.centroid_mem_convexHull, hasStrictFDerivAt_finCons', analyticAt_iff_analytic_smul, spec_cfcₙAux, norm_fderiv_norm, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, root_X_pow_sub_C_pow, ClosedSubmodule.orthogonal_eq_top_iff, fderiv_comp, eventually_enorm_mfderiv_extChartAt_lt, AlgebraicIndependent.liftAlgHom_comp_reprField, Finset.expect_boole_mul, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, EuclideanSpace.piLpCongrLeft_single, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, NumberField.RingOfIntegers.mk_one, hasFDerivAt_exp_smul_const, LinearIsometryEquiv.norm_iteratedFDeriv_comp_right, HasFPowerSeriesOnBall.eventually_hasSum, Field.Algebra.IsSeparable.finSepDegree_eq, ContinuousLinearMap.hasStrictFDerivAt, DivisibleHull.qsmul_of_nonneg, IntermediateField.finrank_top', Subfield.map_map, NumberField.conj_basisMatrix, WeierstrassCurve.Projective.baseChange_add, RingHom.coe_fieldRange, collinear_iff_rank_le_one, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, oneTangentSpaceIcc_def, smul_unitBall, LaurentSeries.powerSeries_ext_subring, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, Set.unit_valuation_eq_one, Submodule.mem_projectivization_iff_submodule_le, Lagrange.eval_basisDivisor_left_of_ne, PowerSeries.isNoetherianRing, IsSymmSndFDerivAt.iteratedFDeriv_cons, IntermediateField.inclusion_self, NumberField.Units.abs_det_eq_abs_det, RingHom.rangeRestrictFieldEquiv_apply_symm_apply, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, TrivSqZeroExt.inv_neg, Complex.im_comp_balance, IntermediateField.lift_bot, IsPurelyInseparable.algebraMap_iterateFrobenius, Lagrange.natDegree_basisDivisor_of_ne, RCLike.normSq_eq_def', Polynomial.C_mul_dvd, ContinuousLinearMap.comp_analyticOn, Polynomial.isBoundedUnder_abs_atBot_iff, analyticOrderAt_pow, hasStrictDerivAt_const, Rat.cast_smul_eq_qsmul, div_add_one, ContinuousLinearMap.continuousConstSMul, fderiv_finset_prod, ModelWithCorners.hasMFDerivWithinAt_symm, PosSMulStrictMono.nnrat_of_rat, IsGalois.fixedField_top, Bundle.Trivial.trivialization.isLinear, ContinuousLinearMap.coeFn_compLpL, hasStrictFDerivAt_list_prod_attach', stdSimplex.barycenter_apply, IsPrimitiveRoot.norm_pow_sub_one_two, deriv_single, IntermediateField.normalClosure_of_normal, StrongDual.norm_toLpₗ_le, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, hasFDerivWithinAt_euclidean, FractionalIdeal.exists_ne_zero_mem_isInteger, ClosedSubmodule.mem_orthogonal_iff, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, HasFPowerSeriesWithinAt.restrictScalars, DoubleCentralizer.sub_fst, tangentConeAt_real_subset_isRCLikeNormedField, range_deriv_subset_closure_span_image, AbsoluteValue.hasBasis_uniformity, Matrix.PosDef.isStrictlyPositive, Module.Basis.parallelepiped_eq_map, ArchimedeanClass.mk_le_mk_iff_ratCast, Algebra.discr_powerBasis_eq_prod, ContDiffMapSupportedIn.norm_apply_le_seminorm, Polynomial.mem_iff_annIdealGenerator_dvd, NNRat.one_lt_cast, contDiffOn_clm_apply, ContinuousLinearMap.le_opNNNorm, spectrum.subset_polynomial_aeval, FDRep.char_one, ContinuousLinearEquiv.det_coe_symm, NumberField.InfinitePlace.isometry_embedding_of_isReal, IsFractionRing.restrictScalars_fieldEquivOfAlgEquiv, LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range, FormalMultilinearSeries.id_apply_zero, SchwartzMap.hasDerivAt, isSimpleModule_iff_finrank_eq_one, stabilizer_isOpen_of_isIntegral, FunctionField.ringOfIntegers.instIsDedekindDomainSubtypeMemSubalgebraPolynomialOfIsSeparableRatFunc, Algebra.IsAlgebraic.isNormalClosure_iff, Submodule.starProjection_orthogonal, Seminorm.inf_apply, ClassGroup.mk_eq_mk, PiTensorProduct.mapLMultilinear_apply_apply, ContinuousLinearMap.instNonnegSpectrumClassRealId, iteratedDeriv_comp_two, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, ContinuousLinearMap.uncurryMid_apply, ContinuousMap.setOfIdeal_eq_compl_singleton, hasFDerivAt_update, Polynomial.div_C, LinearPMap.supSpanSingleton_apply_smul_self, IntermediateField.sup_toSubalgebra_of_left, spectralNorm_extends, isBoundedBilinearMap_apply, HasFPowerSeriesWithinOnBall.coeff_zero, InfiniteGalois.isOpen_iff_finite, FiniteDimensional.finiteDimensional_pi, RootPairing.restrictScalars_coe_root, FormalMultilinearSeries.analyticOnNhd, galLift_id, InfiniteGalois.mem_range_algebraMap_iff_fixed, hasDerivAtFilter_iff_tendsto, NormedSpace.expSeries_div_summable_of_mem_ball, Matrix.IsHermitian.eigenvectorUnitary_coe, Polynomial.natSepDegree_pow_of_ne_zero, Polynomial.natSepDegree_one, hasStrictFDerivAt_ringInverse, Subspace.dualAnnihilator_iInf_eq, NumberField.InfinitePlace.even_finrank_of_not_isUnramified, ContDiffOn.continuousOn_fderiv_of_isOpen, Polynomial.leadingCoeff_preHilbertPoly, ContinuousLinearMap.mul_apply', Finset.cast_subConst, LinearMap.finrank_maxGenEigenspace, Field.Emb.Cardinal.deg_lt_aleph0, WeierstrassCurve.Δ_integral_of_isIntegral, ContDiffOn.continuousLinearMap_comp, LinearMap.BilinForm.dualBasis_involutive, HasFDerivAt.fun_sum, stereographic_target, star_nnratCast, fderiv_zero_of_not_differentiableAt, Unitary.norm_map, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, tendsto_const_mul_pow_nhds_iff, NNRat.instTrivialStar, LinearMap.instStarModuleId, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, Submodule.starProjection_apply_mem, NumberField.inverse_basisMatrix_mulVec_eq_repr, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, RatFunc.denom_div_dvd, InnerProductSpace.rankOne_comp_rankOne, ContinuousLinearMap.opNorm_zero, Polynomial.separable_gcd_right, MeasureTheory.convolution_lsmul_swap, IntermediateField.relfinrank_bot_left, NNReal.coe_expect, Real.hasStrictDerivAt_arctan, HasFTaylorSeriesUpToOn.prodMk, FixedPoints.smul_polynomial, Polynomial.separable_gcd_left, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, ContinuousMultilinearMap.norm_iteratedFDeriv_le, ContDiffAt.domDomCongr_iteratedFDeriv, Module.Basis.traceDual_involutive, SpectrumRestricts.starAlgHom_apply, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, RatFunc.laurent_C, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, LinearMap.BilinForm.orthogonal_span_singleton_eq_toLin_ker, ZLattice.volume_image_eq_volume_div_covolume, hasDerivAtFilter_finCons', NumberField.InfinitePlace.card_real_embeddings, mfderivWithin_prodMap, Polynomial.Gal.splits_in_splittingField_of_comp, LinearIsometry.toLinearMap_rTensor, PiLp.hasStrictFDerivAt_apply, hasStrictFDerivAt_fst, DifferentiableAt.comp_semilinear₁, Matrix.toEuclideanLin_eq_toLin, IsAlgClosed.exists_root, NumberField.Units.coe_injective, Finset.nnratCast_dens, UniqueMDiffOn.uniqueDiffOn_inter_preimage, DoubleCentralizer.pow_fst, RatFunc.rank_ratFunc_ratFunc, IntermediateField.toSubalgebra_injective, StrongDual.toLpₗ_of_not_memLp, isConformalMap_complex_linear_conj, MeromorphicAt.meromorphicTrailingCoeffAt_smul, fderiv_smul_const, PiTensorProduct.mapL_apply, hasDerivWithinAt_finCons', Matrix.isHermitian_iff_isSymmetric, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, mfderiv_sumInr, ContinuousMultilinearMap.norm_iteratedFDeriv_le', support_iteratedFDeriv_subset, hasStrictFDerivAt_finset_prod, convex_RCLike_iff_convex_real, NumberField.Units.coe_one, Module.Basis.flag_wcovBy, spectralAlgNorm_extends, Submodule.le_orthogonal_iff_le_orthogonal, fderiv_fun_neg, Lagrange.degree_interpolate_le, curveIntegral_zero, IntermediateField.le_extendScalars_iff, Finset.subConst_le_card, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Submodule.IsOrtho.comap_iff, InnerProductSpace.rankOne_comp, LaurentSeries.powerSeriesRingEquiv_coe_apply, Ideal.eq_bot_of_prime, Polynomial.C_div, Submodule.mem_orthogonal, StrongDual.mem_polarSubmodule, exists_dual_vector', derivWithin_inv', Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Asymptotics.IsTheta.const_smul_left, Asymptotics.isLittleOTVS_comm, summable_mul_left_iff, RatFunc.instIsScalarTowerOfPolynomial, ContinuousLinearMap.hasBasis_nhds_zero_of_basis, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable', minpoly.ofSubring, hasFPowerSeriesWithinAt_pi_iff, isCompactOperator_iff_isCompact_closure_image_closedBall, MeasureTheory.eLpNorm_const_smul, NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, gal_one_isSolvable, IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace, LinearMap.continuous_of_finiteDimensional, hasDerivAt_iff_isLittleO_nhds_zero, HasFDerivAt.le_of_lip', inner_smul_right, Filter.Tendsto.atTop_smul_const_tendsto_asymptoticNhds, Polynomial.normalize_eq_self_iff_monic, SchwartzMap.tsupport_smulLeftCLM_subset, HasMFDerivAt.sub, IntermediateField.extendScalars.orderIso_symm_apply_coe, InnerProductSpace.toMatrix_rankOne, PowerSeries.Unit_of_divided_by_X_pow_order_nonzero, IsFractionRing.injective_comp_algebraMap, eventually_norm_symmL_trivializationAt_lt, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, cfcₙHom_real_eq_restrict, normal_iff, LinearMap.polar_AbsConvex, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, differentiableAt_euclidean, subsingleton_nnrat_module, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', AlgHom.card, FormalMultilinearSeries.changeOriginSeries_summable_aux₁, hasFDerivAtFilter_finCons, PiTensorProduct.liftIsometry_comp_mapL, MvPowerSeries.inv_eq_zero, iteratedFDeriv_smul_const_apply, IsAlgClosure.equivOfEquiv_symm_comp_algebraMap, Seminorm.continuous_from_bounded, OrthonormalBasis.reindex_toBasis, ContinuousLinearMap.opNorm_le_iff, slope_pos_iff_gt, RCLike.geometric_hahn_banach_open, Submodule.map_smul', InnerProductSpace.isSymmetric_rankOne_self, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, FractionalIdeal.smul_mem_dual_one, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, Padic.valuation_pow, Finset.dens_filter_add_dens_filter_not_eq_dens, Real.hasDerivAt_cosh, fderiv_const_sub, continuousMultilinearCurryLeftEquiv_apply, tsupport_fderiv_subset, HasFPowerSeriesAt.deriv, NumberField.InfinitePlace.isReal_comap_iff, fderiv_id', ArchimedeanClass.FiniteResidueField.mk_le_mk, LinearIsometryEquiv.symm_rTensor, LinearMap.isSymmetricProjection_iff, uniqueMDiffWithinAt_iff_inter_range, mfderiv_snd, HasMFDerivWithinAt.add, LaurentSeries.powerSeriesEquivSubring_apply, IntermediateField.sepDegree_bot', Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, RootPairing.polarizationEquiv_toLinearMap, HasCompactSupport.iteratedFDeriv, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, TensorProduct.commIsometry_symm, isStarProjection_starProjection, precomp_compactConvergenceCLM_apply, unitary.norm_map, Asymptotics.IsBigOTVS.rfl, Set.EqOn.iteratedFDerivWithin, NumberField.mixedEmbedding.unitSMul_smul, ContinuousLinearEquiv.fderiv, IntermediateField.inclusion_injective, Differential.instDifferentialAlgebraSubtypeMemIntermediateField, Seminorm.bddBelow_range_add, ContinuousAlternatingMap.restrictScalarsCLM_apply, ContMDiffWithinAt.mfderivWithin_apply, Asymptotics.IsLittleOTVS.bot, SchwartzMap.tsupport_fderivCLM_subset, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_left, ContinuousLinearMap.isBigOTVS_comp, Finpartition.IsEquipartition.sum_nonUniforms_lt, WeierstrassCurve.Jacobian.add_of_X_ne, ContinuousLinearEquiv.mdifferentiableWithinAt, one_half_pos, FDRep.simple_iff_end_is_rank_one, hfdifferential_apply, Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sq, IntermediateField.LinearDisjoint.bot_right, ContinuousLinearMap.NonlinearRightInverse.right_inv', ContinuousLinearEquiv.mdifferentiable, AnalyticAt.exists_eq_sum_add_pow_mul, Ideal.ResidueField.algHom_ext_iff, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, ContinuousLinearMap.integral_comp_L1_comm, curveIntegralFun_add, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, ContinuousLinearMap.opNorm_zero_iff, IsPrimitiveRoot.squarefree_minpoly_mod, LinearEquiv.isSymmetric_symm_iff, Polynomial.isSplittingField_C, InnerProductSpace.gramSchmidt_def'', Real.hasDerivAt_fourierChar, OrthonormalBasis.equiv_symm, AnalyticOnNhd.fderiv, LinearMap.range_smul', AlgebraicClosure.Monics.map_eq_prod, Field.primitive_element_iff_minpoly_degree_eq, WeierstrassCurve.Jacobian.Y_eq_iff', hasDerivAt_intCast, LinearOrderedSemifield.toPosSMulStrictMono_rat, nndist_midpoint_midpoint_le, HasFDerivWithinAt.sub, Seminorm.absorbent_ball_zero, minpoly.dvd_map_of_isScalarTower', HasFDerivAtFilter.fun_neg, LinearEquiv.coe_toContinuousLinearEquiv, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcₙHom, SchwartzMap.smulLeftCLM_neg, IntermediateField.map_fixingSubgroup_index, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, Projectivization.orthogonal_mk, AlgHom.fieldRange_eq_top, ContinuousLinearEquiv.comp_differentiableAt_iff, IntermediateField.normal_iff_forall_map_le, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, Projectivization.cross_mk, mfderiv_zero_of_not_mdifferentiableAt, Algebra.IsAlgebraic.bijective_of_isScalarTower', Asymptotics.IsTheta.pow, ValuationSubring.ofPrime_scalar_tower, Trivialization.continuousLinearEquivAt_prod, HasFPowerSeriesAt.const_smul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, Ideal.bot_isMaximal, iteratedFDeriv_succ_eq_comp_right, ContinuousOn.cfcₙ, SchwartzMap.iteratedPDeriv_eq_iteratedFDeriv, ContinuousMultilinearMap.changeOriginSeries_support, ContinuousLinearEquiv.comp_hasFDerivAt_iff', separableClosure.isAlgebraic, IntermediateField.adjoin_toSubalgebra, IsAlgClosure.ofAlgebraic, tendsto_nat_ceil_div_atTop, curveIntegralFun_sub, Asymptotics.isBigOTVS_fun_comm, FunctionField.ringOfIntegers.algebraMap_injective, ContDiffMapSupportedIn.seminorm_apply, Field.sepDegree_mul_insepDegree, FormalMultilinearSeries.isLittleO_of_lt_radius, tsupport_iteratedFDeriv_subset, OrthogonalFamily.eq_ite, AffineSubspace.sSameSide_smul_vsub_vadd_right, FiniteField.X_pow_card_sub_X_natDegree_eq, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, ContinuousMultilinearMap.hasFDerivAt, ODE.hasDerivWithinAt_picard_Icc, MeasureTheory.lpNorm_const_smul, VectorField.lieBracket_smul_left, AffineIndependent.finrank_vectorSpan, Real.iteratedFDeriv_fourier, RatFunc.denom_inv_dvd, Seminorm.smul_closedBall_subset, Projectivization.dependent_iff, LieModule.exists_nontrivial_weightSpace_of_isSolvable, instIsScalarTowerCyclotomicField, DoubleCentralizer.algebraMap_fst, NumberField.ComplexEmbedding.isConj_symm, differentiableOn_euclidean, hasDerivWithinAt_diff_singleton, ValuationSubring.surjective_unitGroupToResidueFieldUnits, fderiv_continuousLinearEquiv_comp, FiniteField.pow_dichotomy, nnnorm_fderiv_norm_rpow_le, hasFDerivWithinAt_natCast, NumberField.mixedEmbedding.indexEquiv_apply_isReal, NumberField.ComplexEmbedding.Extension.comp_eq, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, hasStrictFDerivAt_exp_zero_of_radius_pos, div_add_div, ContinuousLinearMap.toBilinForm_injective, quasispectrumRestricts_iff_spectrumRestricts_inr, Ideal.ramificationIdx_mul_inertiaDeg_of_isLocalRing, rootOfSplitsXPowSubC_pow, AlgHom.card_le, InnerProductSpace.mem_span_gramSchmidt, ContinuousLinearMap.mfderivWithin_eq, ContinuousMultilinearMap.nnnorm_ofSubsingleton, inner_smul_real_left, Ideal.ResidueField.lift_algebraMap, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, tsum_prod_pow_eq_tsum_sigma, FiniteField.splits_X_pow_card_sub_X, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, IntermediateField.rank_eq_one_iff, ContDiff.continuous_iteratedFDeriv, TangentBundle.symmL_model_space, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, IsGaloisGroup.intermediateField, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, MeasureTheory.integrable_condExpL2_indicator, Real.hasDerivAt_Gamma_one_half, IsClosed.balancedCore, ImplicitFunctionData.range_rightDeriv, tangentCoordChange_self, toSpanSingleton_derivWithin, HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub, LinearMap.finrank_range_dualMap_eq_finrank_range, fderiv_norm_smul, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, ContinuousAlternatingMap.isLeast_opNNNorm, ContinuousLinearMap.isEmbedding_restrictScalars, lowerBounds_smul_of_neg, Polynomial.natDegree_preHilbertPoly, Finset.cast_mulConst, NNRat.cast_pos, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, HasFiniteFPowerSeriesOnBall.eq_partialSum', Int.clog_zpow, VectorField.mlieBracket_const_smul_left, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, ValuationSubring.principalUnitGroupEquiv_apply, Module.End.eigenspace_div, LinearIsometry.enorm_toContinuousLinearMap, coe_lpBCFₗᵢ_symm, range_mfderiv_coe_sphere, uniqueMDiffOn_iff_uniqueDiffOn, coe_lpPiLpₗᵢ_symm, AlgEquiv.restrictNormalHom_id, Bornology.isVonNBounded_sub, differentiable_piLp, ClosedSubmodule.inf_orthogonal_eq_bot, HasFPowerSeriesOnBall.pi, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, Submodule.reflection_eq_self_iff, nhds_basis_closed_balanced, galRestrict_apply, Polynomial.span_minpoly_eq_annihilator, stereographic_source, ContinuousMultilinearMap.piₗᵢ_symm_apply, HahnEmbedding.ArchimedeanStrata.iSupIndep_stratum', Finset.subConst_mul_card, AlgHom.coe_toContinuousLinearMap, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, ContDiff.iteratedFDeriv_right', Subfield.relrank_top_right, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, NumberField.ComplexEmbedding.IsReal.comp, ContinuousLinearMap.norm_id_le, HasFDerivAt.le_of_lipschitz, AnalyticAt.analyticOrderAt_ne_top, AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_one, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, LinearEquiv.canLiftContinuousLinearEquiv, Ring.instFiniteDimensionalFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, IsDedekindDomain.selmerGroup.fromUnit_ker, Matrix.ofLp_toEuclideanLin_apply, IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin, balancedCoreAux_subset, spectralNorm.eq_of_normalClosure', ContinuousOn.cfcₙ_of_mem_nhdsSet, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm', Filter.Tendsto.isVonNBounded_range, NumberField.exists_ideal_in_class_of_norm_le, AffineIndependent.convexHull_inter', Real.hasFDerivAt_fourierIntegral, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isComplex, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left, NumberField.mixedEmbedding.normAtPlace_apply, SchwartzMap.integralCLM_apply, Finset.dens_inter_add_dens_union, Polynomial.irreducible_factor, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, NumberField.ComplexEmbedding.lift_comp_algebraMap, PolynormableSpace.withSeminorms', hasDerivAt_one, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, SameRay.exists_nonneg_left, HasStrictFDerivAt.hasStrictDerivAt, LinearMap.BilinForm.finrank_orthogonal, IsAlgClosure.equivOfEquiv_algebraMap, FormalMultilinearSeries.radius_shift, EuclideanSpace.volume_ball_fin_two, Ideal.instLiesOverBotOfIsPrime, ContinuousLinearEquiv.comp_right_differentiableAt_iff, fderivWithin_sqrt, isClosedEmbedding_cfcₙHom_of_cfcHom, fderivWithin_natCast, Finset.card_mul_cast_mulConst, ContinuousMap.spectrum_eq_range, NormedSpace.polar_ball, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, IsZLattice.span_top, IsSepClosed.splits_codomain, innerSLFlip_apply, ContinuousLinearEquiv.differentiableOn, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, ContinuousLinearEquiv.hasStrictFDerivAt, Nat.one_div_cast_nonneg, AlgHom.mem_fieldRange, IsStrictOrderedRing.toHasContinuousInv₀, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, fderivWithin_derivWithin, Submodule.ker_starProjection, WeakDual.ker_isMaximal, IntermediateField.finrank_fixedField_eq_card, ContinuousLinearEquiv.mfderiv_eq, hasDerivAt_const_mul, Trivialization.coe_continuousLinearEquivAt_eq, hasLineDerivAt_iff_tendsto_slope_zero, Algebra.normalizedTrace_minpoly, InnerProductSpace.toContinuousLinearMap_toDualMap, HasFDerivAt.list_prod', separableClosure.isSepClosure, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, IntermediateField.finrank_comap, Polynomial.coeff_inv_units, FiniteField.pow_finrank_eq_card, InfiniteGalois.toAlgEquivAux_eq_liftNormal, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, Projectivization.smul_def, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', separatingDual_iff_injective, minpoly.eq_X_sub_C', RCLike.normSq_pos, Polynomial.root_gcd_iff_root_left_right, ContinuousLinearEquiv.comp_contDiffWithinAt_iff, isNilpotent_tensor_residueField_iff, Differential.logDeriv_pow, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable', IsSelfAdjoint.commute_cfcₙHom, Field.primitive_element_iff_minpoly_natDegree_eq, ContinuousLinearMap.measurable_coe, HasFDerivAt.fun_neg, ContinuousLinearMap.analyticOn, fderiv_sinh, ContinuousLinearMap.nndist_le_opNNNorm, Polynomial.IsSeparableContraction.natSepDegree_eq, strictConvex_iff_ordConnected, norm_iteratedFDeriv_prod_le, IntermediateField.normalClosure_def'', inner_eq_ofReal_norm_sq_left_iff, contDiff_nat_iff_continuous_differentiable, QuasispectrumRestricts.nonUnitalStarAlgHom_apply, hasFDerivAt_pow', ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, NNRat.ofNat_le_cast, absorbent_ball, extremePoints_doublyStochastic, Polynomial.cauchyBound_zero, SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv, Valuation.Integers.valuation_pos_iff_ne_zero, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, OrderedFinpartition.compAlongOrderFinpartition_apply, Trivialization.continuousLinearEquivAt_symm_apply, Submodule.topologicalClosure_eq_top_iff, hasDerivAt_abs, mdifferentiableOn_coordChangeL, HasFiniteFPowerSeriesOnBall.add, RatFunc.num_mul_dvd, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, WeierstrassCurve.Projective.addU_smul, iteratedDeriv_comp_const_sub, ContDiffAt.iteratedFDeriv_comp_perm, Polynomial.hasDerivAt, HasFDerivAt.fun_add, Subfield.relrank_eq_rank_of_le, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, Subspace.dualEquivDual_def, AffineBasis.card_eq_finrank_add_one, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', VectorPrebundle.mk_coordChange, ContinuousLinearMap.opNorm_lsmul_le, PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, Field.Emb.Cardinal.strictMono_filtration, convexHull_eq_union_convexHull_finite_subsets, EuclideanSpace.volume_ball, LinearMap.IsSymmetric.zero, IntermediateField.relfinrank_eq_finrank_of_le, OrthonormalBasis.repr_symm_single, FiniteField.nonempty_algHom_extension, NumberField.canonicalEmbedding.norm_le_iff, ContinuousMultilinearMap.instUniformContinuousConstSMul, RootPairing.polarizationEquiv_symm_apply_coroot, WeakDual.CharacterSpace.norm_le_norm_one, IntermediateField.isScalarTower_over_bot, IntermediateField.isSeparable_tower_bot, Submodule.exists_finset_span_eq_linearIndepOn, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, FiniteField.isSquare_iff, Matrix.linfty_opNorm_toMatrix, IntermediateField.minpoly_eq, hasDerivAt_natCast, AdjoinRoot.powerBasis_dim, Seminorm.rescale_to_shell, RingHom.rangeRestrictField_bijective, Mathlib.Meta.NormNum.IsRat.natCeil, Submodule.reflection_bot, RootPairing.linearIndepOn_coroot_iff, ContinuousMultilinearMap.opNNNorm_pi, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, Polynomial.natSepDegree_C, NNRat.cast_mul, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.fourier_bilin_convolution_eq_integral, closedBall_normSeminorm, Real.hasStrictDerivAt_cos, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left, Polynomial.monic_mul_leadingCoeff_inv, ContinuousLinearMap.isPositive_def', HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, ContinuousLinearMap.coe_restrictScalarsL, NNRat.ceil_cast, LinearMap.adjoint_inner_left, Nat.cast_div_le, IntermediateField.mem_toSubalgebra, legendreSym.eq_pow, IntermediateField.isSplittingField_iff, iter_deriv_inv, HasMFDerivAt.comp_hasMFDerivWithinAt, PowerSeries.coeff_inv, AlgEquiv.restrictNormal_commutes, NumberField.InfinitePlace.comap_mk_lift, Matrix.star_dotProduct_gram_mulVec, exists_integral_multiples, hasStrictFDerivAt_exp_zero, ValuationSubring.coe_comap, ContinuousLinearMap.norm_compL_le, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, NumberField.mixedEmbedding_injective, Matrix.vecMul_injective_iff_isUnit, ContMDiffVectorBundle.contMDiffOn_coordChangeL, IntermediateField.bot_toSubfield, EulerSine.antideriv_cos_comp_const_mul, ZMod.orderOf_dvd_card_sub_one, Finset.dens_singleton, curveIntegral_eq_intervalIntegral_deriv, Filter.EventuallyEq.fderivWithin', ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, Field.sepDegree_eq_of_isPurelyInseparable_of_isSeparable, ContinuousLinearMap.inCoordinates_eq, meromorphicOrderAt_smul_of_ne_zero, AccPt.uniqueDiffWithinAt, NumberField.RingOfIntegers.coe_eq_algebraMap, mfderiv_prodMk, NumberField.InfinitePlace.comap_smul, Bornology.isVonNBounded_add, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, Subspace.dualLift_rightInverse, NumberField.InfinitePlace.not_isUnramified_iff_card_stabilizer_eq_two, IntermediateField.topEquiv_symm_apply_coe, HasFPowerSeriesAt.sub, RatFunc.liftOn'_div, hasMFDerivWithinAt_snd, ContDiffAt.continuousLinearMap_comp, ContinuousMultilinearMap.norm_domDomCongr, FiniteGaloisIntermediateField.adjoin_val, FractionalIdeal.spanFinset_coe, HasStrictFDerivAt.fun_neg, hasDerivWithinAt_zpow, LieAlgebra.rank_le_finrank_engel, Finset.centerMass_segment, HasFDerivWithinAt.arctan, ZSpan.quotientEquiv.symm_apply, Subfield.closure_preimage_le, OrthogonalFamily.range_linearIsometry, HasStrictFDerivAt.sum, NNRat.cast_smul_eq_nnqsmul, ValuationSubring.mem_principalUnitGroup_iff, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, HasCompactSupport.fderiv_apply, Submodule.ker_orthogonalProjection, NumberField.mem_span_integralBasis, quadraticCharFun_eq_pow_of_char_ne_two, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, innerSL_real_flip, Lagrange.interpolate_eq_add_interpolate_erase, Submodule.reflection_map_apply, Ideal.coe_smul_primesOver_eq_map_galRestrict, HasDerivAt.real_of_complex, Module.mem_support_iff_nontrivial_residueField_tensorProduct, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt', SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, IntermediateField.adjoin_eq_range_algebraMap_adjoin, AffineIsometry.map_vadd, Polynomial.mul_mod, ContinuousMultilinearMap.curry0_norm, ContinuousLinearMap.opNNNorm_mul_flip_apply, ContinuousLinearMap.compLeftContinuousBounded_apply, Submodule.sup_orthogonal_of_hasOrthogonalProjection, Nat.one_div_pos_of_nat, MeasureTheory.lpTrimToLpMeas_ae_eq, ContinuousLinearMap.norm_fst, IsFractionRing.fieldEquivOfAlgEquivHom_injective, ContinuousAlternatingMap.nnnorm_toContinuousMultilinearMap, Algebra.discr_isUnit_of_basis, OrderedFinpartition.applyOrderedFinpartition_apply, HasFPowerSeriesOnBall.hasFDerivAt, MeasureTheory.charFun_eq_charFunDual_toDualMap, IntermediateField.rank_top', IntermediateField.isAlgebraic_adjoin_simple, NormedAlgebra.Real.nonempty_algEquiv_or, egauge_eq_zero_iff, ContinuousLinearMap.opNNNorm_comp_le, RatFunc.denom_C, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_iSup_right, TensorProduct.toLinearEquiv_assocIsometry, ContinuousMultilinearMap.analyticOn, FormalMultilinearSeries.changeOriginSeries_summable_aux₂, HasMFDerivAt.prod, MeromorphicNFAt.smul_analytic, fderivWithin_csin, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, RatFunc.num_div_dvd', Module.Projective.exists_dual_eq_one, WeierstrassCurve.Projective.negAddY_eq, Submodule.IsOrtho.disjoint, ContinuousMultilinearMap.curryMid_apply, iteratedDeriv_eq_iteratedFDeriv, OnePoint.smul_infty_def, ZLattice.volume_image_eq_volume_div_covolume', inv_smul_lt_iff_of_neg, IntermediateField.AdjoinSimple.normal_algebraicClosure, PiTensorProduct.mapL_opNorm, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, FiniteGaloisIntermediateField.adjoin_simple_map_algEquiv, SchwartzMap.compCLM_apply, MonoidAlgebra.Submodule.instIsSemisimpleRingAddMonoidAlgebra, iter_deriv_inv', toMatrix_innerSL_apply, OrthonormalBasis.equiv_apply_basis, ClosedSubmodule.sInf_orthogonal, NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, intervalIntegral.fderivWithin_integral_of_tendsto_ae, hasStrictFDerivAt_one, Function.HasTemperateGrowth.smul, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, LaurentSeries.powerSeriesEquivSubring_coe_apply, IntermediateField.normal_iff_forall_map_eq', HasStrictFDerivAt.isBigOTVS_sub, Finset.nonneg_subConst_self, DoubleCentralizer.mul_fst, rescale_to_shell_zpow, Polynomial.isBoundedUnder_abs_atTop_iff, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, WeierstrassCurve.Jacobian.addX_eq, balanced_closedBall_zero, iteratedFDeriv_zero_fun, Submodule.HasOrthogonalProjection.exists_orthogonal, IntermediateField.intermediateFieldMap_apply_coe, HasFDerivAt.prodMk, IntermediateField.topEquiv_apply, ContinuousLinearEquiv.comp_contDiffOn_iff, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, MDifferentiableAt.coordChangeL, Submodule.smul_mem_iff, Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two, perfectField_iff_splits_of_natSepDegree_eq_one, Manifold.IsImmersionAt.target_subset_preimage_target, RootPairing.eq_baseOf_iff, Submodule.starProjection_top, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, EulerSine.antideriv_sin_comp_const_mul, hasFDerivAt_sub_const, FixedPoints.toAlgHom_bijective, Lagrange.interpolate_apply, affineCombination_mem_convexHull, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, Submodule.iInf_orthogonal, ContinuousLinearMap.norm_restrictScalars, ContinuousLinearMapWOT.instT3Space, coe_normSeminorm, Algebra.normalizedTrace_algebraMap_apply, IsLocalRing.ResidueField.finite_of_module_finite, ContinuousLinearEquiv.arrowCongrSL_apply, Algebra.normalizedTrace_def, Lagrange.interpolate_eq_iff_values_eq_on, crossProduct_ne_zero_iff_linearIndependent, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, uniqueDiffWithinAt_univ, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, Ideal.FinrankQuotientMap.span_eq_top, Pretrivialization.continuousLinearMap_apply, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, NumberField.Units.coe_zpow, NumberField.mem_span_basisOfFractionalIdeal, RatFunc.natDegree_num_mul_right_sub_natDegree_denom_mul_left_eq_intDegree, ContDiffBump.convolution_eq_right, Polynomial.IsSplittingField.instFiniteDimensionalSplittingField, hasFDerivWithinAt_fst, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, FiniteField.minpoly_frobeniusAlgHom, ValuationSubring.coe_pointwise_smul, ModelWithCorners.transContinuousLinearEquiv_range, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, hasFDerivAt_natCast, FormalMultilinearSeries.analyticAt_changeOrigin, mem_convexHull_iff_exists_fintype, ContinuousLinearMap.opNorm_mul_apply_le, hasFDerivAt_intCast, PiTensorProduct.tprodL_apply, CStarMatrix.normedSpaceCore, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt, IntermediateField.AdjoinSimple.isIntegral_gen, HasFPowerSeriesAt.tendsto_partialSum, Differential.logDeriv_algebraMap, Polynomial.aeval_ofReal, Diffeomorph.uniqueDiffOn_preimage, deriv_pow_field, ZSpan.repr_fract_apply, ContinuousLinearMap.orthogonal_range, NormedDivisionRing.toNormSMulClass, IsGaloisGroup.fixedPoints, contDiff_one_iff_hasFDerivAt, HasFiniteFPowerSeriesAt.add, Submodule.lipschitzWith_starProjection, HasFPowerSeriesAt.hasDerivAt, Polynomial.degree_add_degree_leadingCoeff_inv, hasDerivWithinAt_congr_set', Module.End.IsSemisimple_smul, Submodule.exists_isCompl, HasFDerivWithinAt.comp_hasFDerivAt_of_eq, LieAlgebra.IsKilling.rootSystem_pairing_apply, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply, map_mem_algebraicClosure_iff, NormedSpace.norm_smul_le, HasFPowerSeriesAt.eventually_hasSum_sub, Polynomial.mem_roots_map, meromorphicOrderAt_pow, ordinaryHypergeometricSeries_eq_zero_iff, Polynomial.hasDerivAt_aeval, ediam_smul₀, ContinuousLinearMap.comp_cpolynomialOn, HasFDerivAt.linear_multilinear_comp, Localization.subalgebra.isFractionRing_ofField, ContinuousLinearMap.opNorm_smul_le, Algebra.IsQuadraticExtension.isCyclic, InnerProductSpace.span_gramSchmidt, Asymptotics.isLittleOTVS_congr, FunctionField.ringOfIntegers.instIsFractionRingSubtypeMemSubalgebraPolynomial, hasDerivAt_gronwallBound, fderiv_zero, hasDerivWithinAt_const_add_iff, convexHull_toCone_isLeast, PerfectField.separable_iff_squarefree, NumberField.mixedEmbedding.logMap_apply, IsDedekindDomain.selmerGroup.fromUnitLift_injective, NNRat.cast_nonpos, EuclideanGeometry.hasFDerivAt_inversion, fderiv_comp', MeasureTheory.convolutionExistsAt_iff_integrable_swap, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, PiLp.hasFDerivAt_ofLp, deriv_div, torusIntegral_smul, ZLattice.comap_comp, Polynomial.Gal.restrict_surjective, WeierstrassCurve.Projective.baseChange_dblU, LinearEquiv.smulOfNeZero_symm_apply, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, norm_iteratedFDeriv_one, RatFunc.C_injective, Continuous.cfcₙ', VectorField.mpullback_smul, hasDerivAt_ofReal_cpow_const, LinearIsometryEquiv.comp_differentiable_iff, NumberField.InfinitePlace.even_nat_card_aut_of_not_isUnramified, Submodule.finrank_add_le_finrank_add_finrank, convex_iff_div, hasDerivAt_norm_rpow, hasFDerivAtFilter_id, HasStrictFDerivAt.fun_const_smul, OrthonormalBasis.span_apply, isConformalMap_id, iteratedFDerivWithin_eventually_congr_set', ContinuousMultilinearMap.analyticOnNhd, Module.End.generalized_eigenvec_disjoint_range_ker, instFiniteResidueField, IntermediateField.isPurelyInseparable_bot, NumberField.mixedEmbedding.latticeBasis_apply, ClosedSubmodule.orthogonal_toSubmodule_eq, HasFDerivAt.hasDerivAt, Polynomial.mem_normalizedFactors_iff, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, IsLocalRing.isLocalHom_residue, FiniteField.sum_pow_units, ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal, convexIndependent_iff_finset, pow_div_pow_eventuallyEq_atTop, differentiableAt_finCons', ContinuousLinearMap.isPositive_iff, LaurentSeries.valuation_coe_ratFunc, TensorProduct.mapIsometry_apply, Finset.natCast_card_mul_nnratCast_dens, gal_mul_isSolvable, ContinuousMultilinearMap.compContinuousLinearMapL_apply, Hyperreal.archimedeanClassMk_omega_neg, VectorBundleCore.inCoordinates_eq, Seminorm.smul_closedBall_preimage, HasFDerivWithinAt.unique_on, ValuationSubring.coe_unitGroupMulEquiv_symm_apply, HasStrictFDerivAt.prodMap, MeromorphicOn.extract_zeros_poles, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, VectorField.pullbackWithin_eq, Matrix.IsHermitian.cfcAux_id, cfcₙAux_mem_range_inr, Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero, ContinuousLinearMap.norm_bilinearRestrictScalars, NumberField.InfinitePlace.isUnramified_iff_stabilizer_eq_bot, ContinuousLinearMap.nhds_zero_eq, WeierstrassCurve.Jacobian.negAddY_of_Z_ne_zero, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, Hyperreal.archimedeanClassMk_coe_nonneg, ContinuousLinearMap.norm_inl, Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable, AlgebraicIndependent.aevalEquivField_apply_coe, LinearMap.IsSymmetric.sub, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, LieAlgebra.IsKilling.orthogonal_span_coroot_eq_ker, ContinuousLinearEquiv.comp_differentiable_iff, cfcₙ_norm_sq_nonneg, MvPolynomial.irreducible_toPolynomialAdjoinImageCompl, SchwartzMap.instFourierSMul, HasFPowerSeriesOnBall.prod, IsGaloisGroup.to_isFractionRing, Unitization.nnnorm_eq_sup, SchwartzMap.fourierTransformCLM_apply, AffineSubspace.signedInfDist_singleton, HasFPowerSeriesWithinOnBall.neg, norm_deriv_eq_norm_fderiv, IntermediateField.LinearDisjoint.exists_field_of_isDomain, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Trivialization.symm_continuousLinearEquivAt_eq, IsDiscreteValuationRing.TFAE, Finset.expect_univ, DoubleCentralizer.zero_toProd, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_right, Ideal.factors_span_eq, minpoly_algEquiv_toLinearMap, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, Finset.one_le_divConst_self, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, ContinuousLinearMap.bilinearComp_zero_left, ContinuousLinearMap.nnnorm_smulRight_apply, Subfield.relfinrank_dvd_finrank_top_of_le, hasFPowerSeriesWithinOnBall_pi_iff, hasDerivAt_zero, LinearIsometryEquiv.smul_trans, Ideal.injective_algebraMap_quotient_residueField, SchwartzMap.fderivCLM_fourier_eq, ContinuousMultilinearMap.instContinuousSMul, spectralNorm.eq_of_tower, withSeminorms_pi, IsAlgClosed.card_roots_map_eq_natDegree_of_leadingCoeff_ne_zero, ContinuousLinearEquiv.contDiffOn_comp_iff, Collinear.finrank_le_one, mellin_const_smul, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, FiniteField.instIsCyclicAlgEquivOfFinite, arithGeom_zero_eq_mul_div, NumberField.norm_embedding_le_house, ContMDiffOn.const_smul_section, Finset.cast_addConst_mul_card, FormalMultilinearSeries.ofScalars_smul, SchwartzMap.derivCLM_apply, ContDiffAt.fderiv, Matrix.toLin_finTwoProd_toContinuousLinearMap, HasFPowerSeriesOnBall.eventually_hasSum_sub, Polynomial.mod_X_sub_C_eq_C_eval, TensorProduct.toLinearMap_mapIsometry, ContinuousMultilinearMap.opNNNorm_le_iff, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, NumberField.FinitePlace.norm_eq_one_iff_notMem, NumberField.canonicalEmbedding_injective, Module.End.IsSemisimple_smul_iff, IntermediateField.restrictScalars_toSubalgebra, Valuation.exists_pow_Uniformizer, div_add_same, PowerSeries.eq_inv_iff_mul_eq_one, VectorBundleCore.continuousOn_coordChange, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, hasDerivWithinAt_inter', Submodule.mem_traceDual, ContinuousAlternatingMap.instCompleteSpace, IntermediateField.finiteDimensional_left, mfderiv_comp_apply, NumberField.InfinitePlace.LiesOver.mk_embedding_comp, AffineSubspace.subtypeₐᵢ_linearIsometry, Unitary.inner_map_map, legendreSym.card_sqrts, ContDiffBump.dist_normed_convolution_le, HasFDerivWithinAt.fun_sum, Algebra.normalizedTrace_trans_apply, fderiv_fun_const_smul, hasDerivAt_exp_smul_const_of_mem_ball', Real.hasDerivAt_arctan', TensorProduct.enorm_map, ZMod.gauss_lemma_aux, Matrix.finiteDimensional, deriv_comp_mul_left, hasDerivAt_neg, NNReal.tendsto_inverse_atTop_nhds_zero_nat, LinearMap.IsSymmetric.id, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, isCompactOperator_iff_image_ball_subset_compact, intervalIntegral.integral_hasDerivAt_right, tsupport_fderiv_apply_subset, hasFTaylorSeriesUpToOn_succ_iff_left, LaurentSeries.valuation_compare, mem_segment_iff_div, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Padic.isUniformInducing_cast_withVal, HasCompactSupport.hasDerivAt_convolution_left, Polynomial.hasStrictDerivAt, ArchimedeanClass.mk_ratCast_nonneg, isConjRoot_iff_orbitRel, RingHomClass.toLinearMapClassNNRat, AlgebraicClosure.instIsScalarTower, Hyperreal.tendsto_atBot_iff, IsConformalMap.comp, le_perfectClosure_iff, perfectClosure.isAlgebraic, Polynomial.isUnit_or_eq_zero_of_separable_expand, DualNumber.instIsLocalRing, ContinuousLinearEquiv.isBigO_comp_rev, smul_inv_le_iff_of_neg, Real.hasStrictDerivAt_arcsin, MvPowerSeries.X_inv, AlgHom.bijective, NumberField.IsCMField.complexConj_eq_self_iff, LinearMap.surjective, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, HahnEmbedding.ArchimedeanStrata.archimedean_stratum, HasFPowerSeriesWithinOnBall.add, LinearMap.span_singleton_inf_orthogonal_eq_bot, Commute.cfcₙ, WeierstrassCurve.Jacobian.isUnit_Y_of_Z_eq_zero, ContinuousLinearMap.add_compLp, IntermediateField.isSeparable_sup, curveIntegralFun_restrictScalars, Finset.centerMass_pair, NumberField.mixedEmbedding.commMap_apply_of_isReal, IsFractionRing.num_mul_den_eq_num_iff_eq, FiniteGaloisIntermediateField.finiteDimensional, PowerSeries.ker_coeff_eq_max_ideal, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, div_eq_quo_add_rem_div_add_rem_div, instSecondCountableTopologyContinuousLinearMapIdOfFiniteDimensional, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, meromorphicNFAt_smul_iff_right_of_analyticAt, Polynomial.natSepDegree_X_sub_C, ContinuousLinearMap.adjointAux_inner_right, hasFDerivWithinAt_ofNat, HasDerivWithinAt.Ioi_iff_Ioo, RatFunc.algebraMap_apply, MeromorphicOn.smul, MaximalSpectrum.iInf_localization_eq_bot, Submodule.complementedLattice, Finset.subConst_empty_right, HasMFDerivWithinAt.mul, OpenPartialHomeomorph.MDifferentiable.symm_comp_deriv, ContinuousLinearEquiv.isOpen, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, HilbertBasis.repr_self, TensorProduct.commIsometry_apply, ContinuousLinearEquiv.coe_toDiffeomorph, IntermediateField.coe_smul, IsGaloisGroup.fixingSubgroup_bot, summable_geometric_iff_norm_lt_one, Ring.instFaithfulSMulSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, Algebra.IsAlgebraic.algEquivEquivAlgHom_apply, continuousMultilinearCurryRightEquiv_symm_apply', MeasureTheory.condExpInd_smul', NormedSpace.expSeries_sum_eq_div, ContinuousLinearMap.isBigO_sub, IsSepClosure.isAlgClosure_of_perfectField_top, ContinuousAt.cfcₙ, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, DoubleCentralizer.norm_fst, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq, measurable_smul_const, IntermediateField.relfinrank_dvd_finrank_top_of_le, IntermediateField.set_range_subset, SchwartzMap.smul_apply, ContDiffMapSupportedIn.continuousSMul, ContinuousLinearMap.prodL_apply, Real.hasStrictDerivAt_sin, StrongDual.zero_mem_polar, RCLike.mul_self_norm, TensorProduct.congrIsometry_symm, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, Filter.EventuallyEq.div_mul_cancel_atTop, ContinuousAlternatingMap.norm_ofSubsingleton_id, LinearIsometry.contDiff, Trivialization.continuousLinearMapAt_symmL, Field.finSepDegree_dvd_finrank, LinearMap.isStarProjection_toContinuousLinearMap_iff, NNRat.smul_one_eq_cast, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, MeromorphicOn.divisor_smul, Manifold.pathELength_eq_lintegral_mfderiv_Icc, HasFDerivAtFilter.isLittleOTVS, to_moduleIsTorsionFree, LinearMap.IsSymmetric.orthogonal_range, exists_linearIndependent_algEquiv_apply, iteratedDerivWithin_eq_equiv_comp, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, Polynomial.roots_C_mul_X_sub_C, HasFDerivAt.const_sub, Polynomial.differentiableAt, LinearPMap.adjointDomainMkCLMExtend_apply, nnnorm_cfcₙ_le_iff, InfiniteGalois.restrictNormalHom_continuous, exists_pow_btwn, dimH_orthogonalProjection_le, Algebra.IsSeparable.sepDegree_eq, slope_sub_smul, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, AddAction.automorphize_smul_left, fderiv_ccosh, NormedSpace.expSeries_div_hasSum_exp, LaurentSeries.tendsto_valuation, Submodule.traceDual_bot, galRestrictHom_symm_apply, AlgHom.restrictNormal_comp, instDiscreteTopologySubtypeMemSubmoduleIntComap, Pretrivialization.continuousOn_continuousLinearMapCoordChange, IsLocalRing.ResidueField.instIsScalarTower, ContDiffMapSupportedIn.seminorm_postcompLM_le, IsGaloisGroup.subgroup, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, MeasureTheory.integrable_smul_iff, ContinuousMultilinearMap.bound, DoubleCentralizer.coe_fst, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_left, instIsScalarTowerQuotientIdealResidueField, left_le_midpoint, HasStrictFDerivAt.fun_smul, hasStrictFDerivAt_ofNat, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, NumberField.abs_discr_ge_of_isTotallyComplex, FiniteField.bijective_frobeniusAlgHom_pow, Module.End.genEigenspace_div, smul_inv_lt_iff_of_neg, ContDiffPointwiseHolderAt.fderiv, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, Int.log_zpow, fderiv_fun_mul, IsGalois.of_separable_splitting_field_aux, curveIntegral_fun_sub, HasFiniteFPowerSeriesOnBall.finite, IntermediateField.coe_equivMap_apply, Submodule.re_inner_starProjection_nonneg, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, Algebra.instIsEpiOfIsDomainOfIsFractionRing, NumberField.mixedEmbedding.latticeBasis_repr_apply, IsGalois.finiteDimensional_of_finite, LocallyConvexSpace.convex_open_basis_zero, Submodule.adjoint_orthogonalProjection, NumberField.FinitePlace.instMonoidWithZeroHomClassReal, Filter.HasBasis.isBigOTVS_iff, IntermediateField.mem_adjoin_simple_iff, Real.sInf_smul_of_nonpos, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, HasFDerivAt.pow', NumberField.canonicalEmbedding.apply_at, HasStrictFDerivAt.pow', RatFunc.mk_one, LieAlgebra.IsKilling.finrank_rootSpace_eq_one, Complex.IsConservativeOn.hasDerivAt_wedgeIntegral, hasFDerivWithinAt_iff_hasGradientWithinAt, IntermediateField.finrank_le_of_le_left, Real.fourierIntegral_continuousLinearMap_apply', CurveIntegrable.smul, Finset.mulConst_empty_right, AffineIsometryEquiv.ofEq_rfl, IntermediateField.finInsepDegree_bot, Finset.centroid_pair, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, Polynomial.isUnit_iff_degree_eq_zero, ContinuousLinearMap.hasFDerivAt_of_bilinear, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, Submodule.isOrtho_bot_right, mfderivWithin_prodMk, LinearMap.adjoint_comp, FormalMultilinearSeries.min_radius_le_radius_add, ContinuousAlternatingMap.opNorm_le_iff, krullTopology_mem_nhds_one_iff, RatFunc.algebraMap_injective, hasStrictDerivAt_one, FormalMultilinearSeries.ofScalars_comp_neg_id, Module.Basis.ofVectorSpace_apply_self, Affine.Simplex.point_vsub_centroid_eq_smul_vsub, same_add_div, FiniteField.unitsMap_norm_surjective, Nat.choose_le_pow_div, quadraticChar_sq_one', Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, MonoidAlgebra.Submodule.instIsSemisimpleModule, Field.nonempty_algEquiv_of_range_minpoly_eq, AlgEquiv.fieldRange_eq_top, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, HasStrictFDerivAt.multiset_prod, MvPowerSeries.mul_inv_cancel, Finset.dens_biUnion, OpenPartialHomeomorph.MDifferentiable.mfderiv_injective, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, LinearMap.IsPositive.inner_nonneg_right, strictConvex_iff_div, Matrix.toEuclideanLin_apply_piLp_toLp, Finset.centerMass_eq_of_sum_1, Projectivization.instFiniteDimensionalSubtypeMemSubmoduleSubmodule, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, pow_div_pow_eventuallyEq_atBot, Lagrange.interpolate_empty, LaurentSeries.coe_range_dense, X_pow_sub_C_irreducible_of_prime_pow, InnerProductSpace.span_gramSchmidt_Iio, Field.Emb.Cardinal.iSup_adjoin_eq_top, ContinuousAlternatingMap.curryLeft_add, NumberField.AdeleRing.algebraMap_fst_apply, WeierstrassCurve.Affine.Point.map_some, HasFPowerSeriesAt.pi, LinearMap.dualMap_surjective_iff, smul_ball, ZMod.expand_card, LinearIsometryEquiv.lTensor_def, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', Seminorm.smul_ball_preimage, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', ContDiff.hasStrictDerivAt, LinearIsometry.strictConvexSpace_range_iff, RatFunc.finrank_ratFunc_ratFunc, linearIndependent_iff_notMem_span, HasFDerivWithinAt.smul, skewAdjointPart_eq_I_smul_imaginaryPart, NormedSpace.expSeries_eq_expSeries_rat, WeierstrassCurve.Jacobian.nonsingular_of_Z_ne_zero, ContinuousAlternatingMap.prodLIE_apply, Submodule.mem_orthogonal_singleton_iff_inner_left, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isReal, mfderivWithin_eventually_congr_set, Submodule.fg_iff_finiteDimensional, ValueDistribution.logCounting_pow_zero, Padic.rat_dense', JacobsonNoether.exists_separable_and_not_isCentral', IntermediateField.toSubalgebra_iSup_of_directed, Manifold.IsImmersionAtOfComplement.writtenInCharts, PowerSeries.intValuation_X, Finset.addConst_empty_left, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, LinearIsometry.inl_apply, hasDerivAt_pow, SchwartzMap.decay, span_flip_eq_top_iff_linearIndependent, NumberField.ComplexEmbedding.IsUnmixed.isReal_iff_isReal, ModelWithCorners.uniqueDiffWithinAt_image, LinearIsometryEquiv.comp_hasFDerivAt_iff', Submodule.mem_adjoint_iff, ZMod.pow_card_pow, FormalMultilinearSeries.summable_nnnorm_mul_pow, RCLike.normSq_div, norm_fderiv_le_of_lipschitzOn, RCLike.im_sq_le_normSq, ContinuousLinearMap.isBoundedLinearMap, LieAlgebra.IsKilling.chainLength_smul, LinearMap.isSymmetric_iff_isSelfAdjoint, ContinuousLinearMap.opNorm_le_iff_lipschitz, sub_smul_slope, CPolynomialOn.fderiv, Finset.dens_eq_zero, IsCyclotomicExtension.Rat.finrank, max_aleph0_card_le_rank_fun_nat, Submodule.reflection_involutive, SchwartzMap.convolution_flip, toIcoMod_zero_one, ContinuousLinearMap.opNorm_flip, Module.Basis.parallelepiped_map, Hyperreal.stdPart_of_tendsto, IsLocalMaxOn.fderivWithin_eq_zero, LinearMap.BilinForm.dualSubmodule_flip_dualSubmodule_of_basis, Int.clog_natCast, Polynomial.cardPowDegree_nonzero, OrderRingHom.subsingleton, Module.finrank_eq_rank', continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, ContinuousLinearMap.precompCompactConvergenceCLM_apply, VectorPrebundle.continuousOn_coordChange, IsAlgClosed.eval_surjective, VectorField.mpullbackWithin_apply, LinearMap.isSymmetric_iff_sesqForm, FormalMultilinearSeries.radius_compContinuousLinearMap_le, hasDerivWithinAt_derivWithin_iff, hasDerivAt_sub_const_iff, Subspace.dualLift_injective, hasStrictDerivAt_exp, HasStrictFDerivAt.mul_const', ContinuousLinearMap.IsPositive.adjoint_conj, measurable_fderiv_with_param, Finset.dens_sdiff_add_dens_eq_dens, strictConcaveOn_iff_div, LinearIsometryEquiv.reflections_generate_dim, krullTopology_mem_nhds_one_iff_of_normal, geom₂_sum_of_lt, mfderiv_const, IsConformalMap.smul, iteratedFDeriv_prodMk, isCoveringMap_npow, IsAlgClosed.splits, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection, IntermediateField.finrank_bot', Finset.cast_divConst_mul_card, WeierstrassCurve.Projective.map_addU, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, Algebra.IsAlgebraic.algEquivEquivAlgHom_symm_apply, SchwartzMap.lineDerivOp_apply_eq_fderiv, Real.hasStrictDerivAt_sqrt, finiteDimensional_bot, Complex.hasDerivAt_Gamma_one, ContinuousLinearMap.exist_extension_of_finiteDimensional_range, geom_sum_Ico', ArchimedeanClass.FiniteResidueField.mk_lt_mk, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range, hasFDerivWithinAt_pi, LinearPMap.mkSpanSingleton_apply, intervalIntegral.integral_smul_const, galLiftEquiv_algebraMap_apply, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, stdSimplex.barycenter_eq_centerMass, Polynomial.deriv, InnerProductSpace.laplacianWithin_smul_nhds, ContinuousLinearMap.differentiableOn, ContinuousMultilinearMap.uncurry0_apply, LinearMap.BilinForm.apply_toDual_symm_apply, Module.finrank_of_infinite_dimensional, QuotientGroup.automorphize_smul_left, differentiableWithinAt_apply, ContinuousLinearMap.isPositive_iff', ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, LinearIsometryEquiv.comp_hasFDerivAt_iff, IsGalois.map_fixingSubgroup, Real.hasDerivAt_tan_of_mem_Ioo, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, Submodule.finrank_add_finrank_orthogonal, NumberField.mixedEmbedding.finrank, ContinuousLinearMap.star_eq_adjoint, IsUnramifiedAtInfinitePlaces.card_infinitePlace, CyclotomicRing.instIsTorsionFreeCyclotomicField, Submodule.orthogonal_eq_top_iff, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, FractionalIdeal.eq_zero_or_one, ContinuousMultilinearMap.curryLeft_apply, ContinuousAlternatingMap.hasFDerivWithinAt, ValuationSubring.mem_smul_pointwise_iff_exists, Finset.centerMass_smul, WeierstrassCurve.Jacobian.Point.toAffineLift_zero, AlgHom.toContinuousLinearMap_norm, instCharPLinearMapSubtypeMemSubringCenterId, Finset.dens_disjUnion, RatFunc.denom_algebraMap, iteratedDeriv_comp_three, IntermediateField.fixingSubgroup_isOpen, AffineSpace.asymptoticNhds_eq_smul, PiLp.hasFDerivAt_apply, Submodule.lipschitzWith_orthogonalProjection, Module.Free.of_divisionRing, AffineSubspace.direction_smul, ContMDiffWithinAt.coordChangeL, Polynomial.hasFDerivWithinAt_aeval, HasFPowerSeriesWithinAt.neg, Int.clog_one_right, continuousOn_cfcₙ_setProd, Real.hasDerivAt_exp, fderiv_sqrt, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, toIcoDiv_eq_floor, volume_euclideanSpace_eq_dirac, FGModuleCat.FGModuleCatDual_coe, RingHom.map_field_closure, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Asymptotics.isThetaTVS_comm, Subfield.lift_rank_comap, hasStrictDerivAt_inv, Polynomial.contDiff_aeval, Projectivization.cross_mk_of_ne, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, NNRat.cast_divNat_of_ne_zero, ProperCone.hyperplane_separation_of_notMem, OrderedFinpartition.applyOrderedFinpartition_update_left, FractionalIdeal.exists_eq_spanSingleton_mul, LinearMap.continuous_of_isClosed_ker, Module.ker_algebraMap_end, orthogonalFamily_iff_pairwise, ZSpan.map_fundamentalDomain, tendsto_nat_ceil_mul_div_atTop, RCLike.re_ofReal_pow, FiniteGaloisIntermediateField.adjoin_simple_map_algHom, ContinuousMultilinearMap.norm_compContinuous_linearIsometryEquiv, separableClosure.isSeparable, FormalMultilinearSeries.radius_le_radius_derivSeries, minpoly.natDegree_le, ContinuousAlternatingMap.curryLeftLI_apply, ContinuousLinearMap.norm_single_le_one, ArithmeticFunction.pdiv_zeta, Real.nonempty_algEquiv_or, ContMDiffWithinAt.const_smul_section, Padic.coe_withValRingEquiv_symm, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, LinearMap.IsSymmetric.im_inner_apply_self, Submodule.inf_orthogonal_eq_bot, FunctionField.ringOfIntegers.instIsNoetherianPolynomialSubtypeMemSubalgebraOfIsSeparableRatFunc, HasFDerivWithinAt.fun_mul', WeierstrassCurve.Affine.baseChange_slope, uniqueDiffOn_convex_of_isRCLikeNormedField, ContinuousLinearMap.norm_compSL_le, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_left, ContinuousLinearEquiv.uniqueDiffOn_preimage_iff, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, AdjoinRoot.minpoly_powerBasis_gen, RCLike.nnnorm_nnqsmul, ContDiffMapSupportedIn.withSeminorms, differentiableWithinAt_snd, PrimeSpectrum.isHomeomorph_comap_tensorProductMap_of_isPurelyInseparable, Submodule.isOrtho_sSup_left, Bundle.Trivial.trivialization.coordChangeL, MeasureTheory.withDensityᵥ_smul, wbtw_or_wbtw_smul_vadd_of_nonneg, ContDiffAt.exists_eventually_eq_hasDerivAt, DivisibleHull.qsmul_of_nonpos, ContinuousMultilinearMap.analyticWithinAt, Bornology.isVonNBounded_vadd, derivWithin_fun_const_smul', innerₛₗ_apply, hasFDerivAtFilter_iff_tendsto, finrank_span_singleton, InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis, HasFDerivWithinAt.isBigOTVS_sub, Lagrange.sum_basis, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, trace_eq_sum_embeddings, ContinuousLinearEquiv.hasFDerivAt, hasStrictFDerivAt_list_prod, iteratedDeriv_const_smul_field, IntermediateField.adjoin.finiteDimensional, IntermediateField.botEquiv_def, MulOpposite.instFiniteDimensional, InnerProductSpace.isIdempotentElem_rankOne_self_iff, le_algebraicClosure_iff, IsCauSeq.geo_series_const, Filter.EventuallyEq.iteratedFDeriv, ContinuousMultilinearMap.toUniformOnFun_toFun, ContinuousLinearMap.opNorm_nonneg, IntermediateField.adjoin_adjoin_comm, IntermediateField.adjoin_eq_top_iff, Pretrivialization.continuousLinearMap_symm_apply, Polynomial.abs_isBoundedUnder_iff, div_le_egauge_ball, hasDerivAtFilter_pi, stereographic_apply, MeasureTheory.inner_condExpL2_eq_inner_fun, StrongDual.toLp_apply, inverse_mfderiv_mul_left, OrthogonalFamily.norm_sum, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace, HasFDerivAtFilter.iterate, Submodule.inner_starProjection_left_eq_right, IntermediateField.toSubalgebra_lt_toSubalgebra, Finset.addConst_empty_right, ContinuousLinearMap.normOneClass, MeasureTheory.mem_lpMeas_self, ContinuousLinearMap.opNNNorm_subsingleton, IntermediateField.finSepDegree_bot', ContMDiffAt.mfderiv, ContinuousLinearMap.IsPositive.spectrumRestricts, Module.End.IsSemisimple.minpoly_squarefree, IntermediateField.val_mk, OrthonormalBasis.sum_repr, hasDerivAtFilter_const_add_iff, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, NumberField.InfinitePlace.embedding_injective, Real.iteratedFDeriv_fourierIntegral, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, differentiableAt_snd, ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, IsCoercive.ker_eq_bot, NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal, RatFunc.eq_C_iff, Bornology.isVonNBounded_insert, hasDerivWithinAt_abs_neg, ContinuousLinearEquiv.analyticOnNhd, NumberField.InfinitePlace.mem_stabilizer_mk_iff, RatFunc.num_mul_eq_mul_denom_iff, StieltjesFunction.ae_hasDerivAt, IsConformalMap.injective, mem_galBasis_iff, InnerProductSpaceable.innerProp, fderivWithin_const_apply, IntermediateField.rank_sup_le, IntermediateField.LinearDisjoint.self_right, LinearIsometry.strictConvexSpace_range, ContinuousLinearMap.opNorm_neg, WittVector.RecursionBase.solution_pow, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, FormalMultilinearSeries.ofScalars_series_eq_zero, IsLocalRing.CotangentSpace.span_image_eq_top_iff, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, Field.finSepDegree_eq_finrank_iff, FormalMultilinearSeries.changeOrigin_eval, krullTopology_discreteTopology_of_finiteDimensional, LinearMap.toSeminorm_ball_zero, Lagrange.eval_interpolate_at_node, Valuation.Integers.valuation_irreducible_pos, LinearIsometryEquiv.hasFDerivWithinAt, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, RootPairing.restrictScalars_toLinearMap_apply_apply, LinearMap.finrank_maxGenEigenspace_zero_eq, AlgHom.normal_bijective, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, Submodule.fstL_comp_coe_orthogonalDecomposition, quadraticChar_apply, inner_smul_left_eq_smul, NumberField.toNNReal_valued_eq_adicAbv, Finset.expect_dite_eq, iter_deriv_inv_linear_sub, MeromorphicOn.pow, RCLike.re_sq_le_normSq, FiniteDimensional.exists_is_basis_integral, Module.Basis.ofZLatticeBasis_comap, isStarProjection_iff_eq_starProjection_range, Int.log_zero_right, ContinuousLinearMap.reApplyInnerSelf_smul, ContinuousLinearMap.add_compLpL, Polynomial.isIntegrallyClosed_iff', NonUnitalCStarAlgebra.toIsScalarTower, convexJoin_left_comm, IntermediateField.coe_pow, LinearIsometryEquiv.symm_units_smul, IsGaloisGroup.mulEquivAlgEquiv_symm_apply, IsHilbertSum.linearIsometryEquiv_symm_apply_single, WittVector.exists_frobenius_solution_fractionRing_aux, DivisionRing.isDomain, AffineIsometryEquiv.map_vadd, closedAbsConvexHull_eq_closure_absConvexHull, exists_embedding_euclidean_of_compact, Complex.norm_fderiv_le_one_of_mapsTo_ball, UnitAddTorus.mFourierBasis_repr, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, HasFPowerSeriesAt.prod, Nonneg.coe_div, LinearMap.toSeminorm_apply, AlgEquiv.restrictNormalHom_apply, InfiniteGalois.mk_toAlgEquivAux, hasDerivAt_ofReal_cpow_const', Normal.out, hasStrictDerivAt_natCast, LinearIsometryEquiv.toLinearIsometry_rTensor, Complex.hasDerivAt_Gamma_one_half, VectorPrebundle.contMDiffOn_contMDiffCoordChange, Representation.irreducible_iff_isSimpleModule_asModule, Real.smul_iSup_of_nonneg, Submodule.starProjection_minimal, EuclideanGeometry.orthogonalProjection_linear, instIsAbelianGaloisSubtypeMemIntermediateField, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, ContinuousLinearMap.contMDiffWithinAt, lineDeriv_smul, ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk, PiTensorProduct.mapL_pow, Finset.cast_divConst, LinearMap.continuous_of_isClosed_graph, IntermediateField.adjoin_simple_comm, algebraicClosure.isAlgClosure, DoubleCentralizer.natCast_toProd, OrthonormalBasis.sum_rankOne_eq_id, NumberField.InfinitePlace.mkComplex_coe, ContinuousLinearMap.dslope_comp, mdifferentiableAt_coordChangeL, hasDerivAt_finCons', MeasureTheory.Lp.toTemperedDistribution_toLp_eq, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, absorbs_iff_eventually_nhds_zero, AlgEquiv.liftNormal_commutes, ModP.v_p_lt_val, AlgebraicGeometry.geometrically_iff_of_commRing_of_isClosedUnderIsomorphisms, ContinuousLinearMap.unit_le_opNorm, HasFPowerSeriesWithinAt.add, IntermediateField.inclusion_inclusion, Submodule.starProjection_mem_subspace_eq_self, NNRat.cast_lt_one, Field.Emb.Cardinal.adjoin_image_leastExt, inf_eq_half_smul_add_sub_abs_sub', ContinuousLinearMap.adjoint_inner_right, exists_extension_norm_eq, map_nnratCast_smul, HasMFDerivAt.prodMk, Subspace.dualAnnihilator_le_dualAnnihilator_iff, FiniteField.X_pow_card_pow_sub_X_natDegree_eq, ContinuousLinearMap.norm_id, FormalMultilinearSeries.id_apply_of_one_lt, Module.Basis.exists_basis, hasFDerivAt_integral_of_dominated_of_fderiv_le'', gal_zero_isSolvable, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, HasFDerivWithinAt.fun_pow', FiniteField.bijective_frobeniusAlgEquivOfAlgebraic_pow, SeparationQuotient.isEmbedding_outCLM, sum_Ioc_inv_sq_le_sub, Module.length_eq_finrank, differentiable_pi'', HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, ContDiff.contDiff_fderiv_apply, hasStrictDerivAt_exp_zero_of_radius_pos, LinearMap.isPositive_iff, PowerSeries.C_inv, ContinuousLinearMap.measurable_apply', IntermediateField.le_iff_le, IntermediateField.extendScalars_restrictScalars, FractionalIdeal.map_canonicalEquiv_mk0, NormedSpace.closedBall_inv_subset_polar_closedBall, FiniteField.nonempty_algHom_iff_finrank_dvd, ContDiffMapSupportedIn.postcompLM_apply, NNRat.floor_def, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, analyticOrderAt_smul, ContinuousLinearMap.norm_smulRightL_le, Real.smul_iSup_of_nonpos, one_add_div, DoubleCentralizer.one_toProd, MeasureTheory.withDensityᵥ_smul', spectralNorm_extends_of_finiteDimensional, IsOpen.uniqueDiffOn, Algebra.discr_powerBasis_eq_prod'', convexHull_prod, InfiniteGalois.fixedField_bot, RingHom.mem_fieldRange, differentiableAt_iff_restrictScalars, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, hasDerivAtFilter_const, smul_mem_asymptoticCone_iff, LinearIsometryEquiv.symm_smul_apply, SchwartzMap.tsupport_derivCLM_subset, Module.Dual.finrank_ker_add_one_of_ne_zero, RCLike.normSq_zero, hasDerivAt_single, deriv_fun_const_smul_field, NNRat.instIsScalarTowerRight, Nat.pow_le_choose, OrthonormalBasis.coe_toBasis_repr_apply, Algebra.adjoin_eq_top_of_intermediateField, FunctionField.inftyValuation.C, Valued.instFaithfulSMulCompletionOfUniformContinuousConstSMul, Finset.centroid_pair_fin, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, IntermediateField.adjoin_subset_adjoin_iff, inner_smul_right_eq_smul, IsAlgClosed.roots_eq_zero_iff, differentiableOn_apply, Algebra.map_intTraceAux, LinearIsometryEquiv.star_eq_symm, ContinuousLinearEquiv.dimH_preimage, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, IntermediateField.mem_extendScalars, Polynomial.degree_leadingCoeff_inv, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, MulAction.automorphize_smul_left, SchwartzMap.integral_smul_laplacian_right_eq_left, differentiableAt_pi, HasFDerivWithinAt.fun_add, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, hasStrictDerivAt_exp_of_mem_ball, FormalMultilinearSeries.radius_prod_eq_min, ContinuousLinearMapWOT.add_apply, OrthonormalBasis.coe_equiv_euclideanSpace, NumberField.mixedEmbedding.norm_real, RCLike.conjAe_coe, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, hasFDerivAt_zero, ZMod.isCyclic_units_two, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, Valuation.Integers.isUnit_iff_valuation_eq_one, LinearMap.exists_extend, NNRat.cast_comm, derivWithin_div, NonUnitalCommCStarAlgebra.toSMulCommClass, isAlgClosure_iff, HasFDerivAt.mul_const', IsSepClosed.factors_of_separable, Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, ContinuousAlternatingMap.nnnorm_ofSubsingleton, affineIndependent_iff_finrank_vectorSpan_eq, LieAlgebra.IsKilling.traceForm_coroot, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, WeierstrassCurve.Jacobian.addU_smul, InfiniteGalois.proj_of_le, HasFiniteFPowerSeriesOnBall.fderiv', Finset.expect_apply, WittVector.RecursionBase.solution_spec', Submodule.orthogonalProjectionFn_eq, Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective, ContinuousMultilinearMap.currySum_apply, Submodule.IsOrtho.ge, OpenPartialHomeomorph.MDifferentiable.ker_mfderiv_eq_bot, RootPairing.finrank_rootSpanIn, FiniteField.expand_card, Module.Basis.traceDual_repr_apply, FormalMultilinearSeries.ofScalars_comp_neg, SeminormedSpace.Core.norm_smul, Polynomial.differentiableWithinAt_aeval, Submodule.bot_orthogonal_eq_top, signedDist_apply, Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, ContinuousLinearMap.IsPositive.conj_starProjection, FGModuleCat.FGModuleCatEvaluation_apply', LieModule.traceForm_eq_sum_finrank_nsmul_mul, WeakDual.CharacterSpace.equivAlgHom_coe, HasStrictFDerivAt.fun_pow', IsSemisimpleModule.exists_end_algEquiv_pi_matrix_divisionRing, convexHull_eq_union, measurable_fderiv, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux, le_egauge_ball_one, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, toPrincipalIdeal_def, IsSelfAdjoint.nnratCast, Orthonormal.comp_linearIsometryEquiv, QuotientAddGroup.automorphize_smul_left, quadraticChar_eq_pow_of_char_ne_two, Submodule.map_orthogonal, Complex.re_expect, HasStrictFDerivAt.comp, DoubleCentralizer.natCast_snd, ContDiffMapSupportedIn.bounded_iteratedFDeriv, IntermediateField.coe_type_toSubalgebra, IntermediateField.relrank_eq_rank_of_le, CompactConvergenceCLM.continuousSMul, WeierstrassCurve.Projective.map_add, convexHull_eq, HasFiniteFPowerSeriesOnBall.hasFDerivAt, LinearMap.ker_eq_bot_iff_range_eq_top, IntermediateField.lift_adjoin, NNRat.cast_zero, convexJoin_assoc_aux, hasStrictDerivAt_zero, NumberField.basisOfFractionalIdeal_apply, VectorBundleCore.coordChange_linear_comp, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, ContinuousLinearMap.isBigOTVS_fun_comp, Module.Basis.ofZLatticeComap_repr_apply, RCLike.normSq_eq_zero, Mathlib.Meta.Positivity.zpow_zero_pos, le_egauge_of_forall_ne_zero, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, FormalMultilinearSeries.coeff_iterate_fslope, LinearMap.IsSymmetric.conj_inner_sym, HasFPowerSeriesAt.eq_zero, ContinuousLinearMap.coeFn_compLp, ContinuousLinearMap.flip_zero, FiniteField.Extension.exists_frob_pow_eq, FormalMultilinearSeries.leftInv_removeZero, IsGaloisGroup.fixedPoints_le_of_le, deriv_const_smul', tendsto_pow_div_pow_atTop_atTop, ContinuousLinearMapWOT.ext_iff, Module.Basis.mem_toFlag, hasStrictDerivAt_exp_smul_const_of_mem_ball', ContinuousAlternatingMap.instT2Space, ContinuousLinearMap.extendTo𝕜'_apply, NumberField.mem_multisetInfinitePlace, ClosedSubmodule.orthogonal_disjoint, fderivWithin_cosh, IsLocalFrameOn.coeff_eq_of_eq, MvPowerSeries.eq_mul_inv_iff_mul_eq, iteratedFDerivWithin_const_of_ne, ContinuousMultilinearMap.norm_ofSubsingleton, ContinuousLinearMap.isAdjointPair_inner, IntermediateField.extendScalars_top, NormedSpace.norm_expSeries_div_summable, TensorProduct.norm_map, analyticOrderNatAt_pow, ContinuousLinearMap.coe_le_coe_iff, AddChar.linearIndependent, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, hasFDerivAtFilter_finCons', ContinuousLinearEquiv.analyticWithinAt, rank_quotient_add_rank_of_divisionRing, IsSemisimpleRing.exists_algEquiv_pi_matrix_divisionRing_finite, slope_fun_def_field, LinearMap.BilinForm.comp_symmCompOfNondegenerate_apply, IntermediateField.algebraicIndependent_adjoin_iff, IsLocalRing.ResidueField.residue_smul, LinearIsometryEquiv.differentiableAt, linearIndepOn_insert, Real.fourier_continuousMultilinearMap_apply, NumberField.InfinitePlace.card_add_two_mul_card_eq_rank, LinearIsometryEquiv.differentiable, NumberField.InfinitePlace.mem_orbit_iff, RatFunc.isScalarTower_liftAlgebra, Unitization.splitMul_injective, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_snd, isInvertible_mfderiv_extChartAt, WeierstrassCurve.Jacobian.map_addU, Polynomial.cauchyBound_X_add_C, MDifferentiableAt.smul_const_section, NumberField.InfinitePlace.isUnramifiedIn_comap, IntermediateField.rank_eq_rank_subalgebra, Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial, FormalMultilinearSeries.ofScalars_series_injective, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Nonneg.Icc_subset_segment, collinear_iff_exists_forall_eq_smul_vadd, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousMultilinearMap.norm_map_insertNth_le, quadraticChar_eq_pow_of_char_ne_two', Asymptotics.IsTheta.const_smul_right, HasFPowerSeriesAt.coeff_zero, Submodule.orthogonal_le_orthogonal_iff, DoubleCentralizer.sub_snd, Algebra.normalizedTrace_trans, RingOfIntegers.algebraMap_norm_algebraMap, ModelWithCorners.coe_transContinuousLinearEquiv, IsSimpleRing.exists_algEquiv_matrix_of_isAlgClosed, SeparatingDual.completeSpace_continuousMultilinearMap_iff, Submodule.orthogonal_le_iff_orthogonal_le, ContMDiffOn.smul_section_of_tsupport, WeierstrassCurve.Jacobian.Y_eq_iff, ContDiffOn.comp_continuousLinearMap, Field.lift_rank_mul_lift_sepDegree_of_isSeparable, LinearMap.BilinForm.orthogonal_eq_top_iff, ContMDiffWithinAt.smul_section, Polynomial.differentiable, FiniteDimensional.instSubtypeMemSubmoduleMap, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, Polynomial.rootSet_monomial, ContinuousLinearEquiv.coord_norm', Set.integer_valuation_le_one, NumberField.InfinitePlace.eq_iff_eq, IntermediateField.fixedField_bot, HasFPowerSeriesOnBall.hasSum_sub, ContinuousLinearMap.nnnorm_id, smul_mem_asymptoticCone, Polynomial.isCoprime_map, absConvexHull_eq_convexHull_balancedHull, FractionRing.isScalarTower_liftAlgebra, Bundle.Trivial.symmₗ_trivialization, ProbabilityTheory.hasDerivAt_mgf, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, HasFPowerSeriesAt.eq_zero_of_eventually, hasMFDerivAt_snd, IntermediateField.toSubalgebra_strictMono, Polynomial.IsSeparableContraction.degree_eq, ContinuousLinearMap.isPositive_zero, div_le_egauge_closedBall, hasStrictFDerivAt_inv', IntermediateField.lift_sup, LinearMap.mem_span_iff_bound, Set.Finite.convexHull_eq_image, PowerSeries.inv_eq_inv_aux, Algebra.discr_powerBasis_eq_prod', PadicAlgCl.coe_eq, Polynomial.X_sub_C_mul_removeFactor, uniqueMDiffWithinAt_iff_uniqueDiffWithinAt, Algebra.algebraMap_intTrace, hasFDerivAt_exp_smul_const_of_mem_ball', convexJoin_right_comm, hasDerivAt_mul_const, SameRay.exists_pos_left, RingHom.fieldRange_eq_top_iff, SchwartzMap.smulLeftCLM_sub, Submodule.snd_orthogonalDecomposition_apply, NumberField.FinitePlace.isFinitePlace, hasFDerivAtFilter_natCast, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', LinearMap.BilinForm.toLin_restrict_ker_eq_inf_orthogonal, cfcₙ_apply_mem_elemental, LinearEquiv.det_coe_symm, asymptoticCone_submodule, Module.Basis.ofZLatticeBasis_repr_apply, wbtw_or_wbtw_smul_vadd_of_nonpos, HasMFDerivAt.sum, normalClosure.normal, intervalIntegral.integral_hasStrictDerivAt_right, MvPolynomial.schwartz_zippel_sum_degreeOf, quasispectrum_eq_spectrum_union_zero, Ideal.inertiaDeg_le_finrank, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, iteratedDeriv_fun_pow_zero, FixedPoints.toAlgAut_bijective, SchwartzMap.fourier_fderivCLM_eq, SpectrumRestricts.nnreal_iff_spectralRadius_le, right_le_midpoint, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, Asymptotics.isBigO_const_smul_left, PadicInt.ker_toZMod, ContinuousLinearMap.integral_comp_id_comm, FiniteField.isSplittingField_sub, hasStrictFDerivAt_exp_smul_const, IsGalois.fixingSubgroup_normal_of_isGalois, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, MDifferentiableOn.smul_section, PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply_coe, AbsoluteValue.isEquiv_iff_exists_rpow_eq, SchwartzMap.fourier_convolution_apply, Seminorm.smul_ball_zero, Filter.Tendsto.inv_tendsto_atTop, separableClosure.map_eq_of_separableClosure_eq_bot, mem_openSegment_iff_div, Polynomial.degree_div_le, Asymptotics.isBigOTVS_map, NNRat.commute_cast, Projectivization.generalLinearGroup_smul_def, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, MvPowerSeries.invOfUnit_eq, LinearIsometry.norm_toContinuousLinearMap_le, Real.hasStrictDerivAt_tan, AffineSubspace.isometryEquivMap.apply_symm_apply, Submodule.starProjection_le_starProjection_iff, iteratedFDerivWithin_zero_fun, IntermediateField.adjoin_adjoin_left, RCLike.wInner_cWeight_const_right, Finset.expect_div, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, HasStrictFDerivAt.mul, intervalIntegral.integral_hasStrictDerivAt_left, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, ContinuousLinearMap.analyticOnNhd, fderiv_fst, iter_deriv_inv_linear, HahnEmbedding.Partial.eval_eq_truncLT, finrank_eq_one_iff_of_nonzero, InfiniteGalois.algEquivToLimit_continuous, divRadical_dvd_wronskian_left, Module.End.ker_pow_le_ker_pow_finrank, NNRat.cast_le_natCast, IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C', LieAlgebra.isRegular_iff_finrank_engel_eq_rank, IntermediateField.normalClosure_mono, ContinuousAlternatingMap.differentiable, WeakDual.toStrongDual_apply, tendsto_inverse_atTop_nhds_zero_nat, ContinuousLinearEquiv.uniqueDiffOn_image_iff, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, LinearMap.eq_adjoint_iff_basis_right, IsLocalRing.subsingleton_tensorProduct, CategoryTheory.finrank_endomorphism_simple_eq_one, ContinuousLinearMap.hasMFDerivWithinAt, ContinuousLinearEquiv.nnnorm_symm_pos, InnerProductSpace.laplacian_smul_nhds, convexHull_rangle_single_eq_stdSimplex, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, MeasureTheory.lpNorm_expect_le, Submodule.instOrthogonalCompleteSpace, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, linearIndependent_option', IsSepClosed.splits_of_separable, IsUltrametricDist.isPowMul_algNormOfAlgEquiv, LaurentSeries.ratfuncAdicComplRingEquiv_apply, IsSepClosed.exists_root, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, trace_eq_sum_automorphisms, IsSelfAdjoint.commute_cfcₙ, linearIndepOn_id_insert, Fintype.expect_ite_eq', FormalMultilinearSeries.le_radius_pi, Quaternion.coe_ofComplex, Real.hasDerivAt_arctan, AffineSpace.asymptoticNhds_eq_smul_vadd, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, continuousMultilinearCurryLeftEquiv_symm_apply, Polynomial.Monic.dvd_iff_fraction_map_dvd_fraction_map, Finset.pluennecke_ruzsa_inequality_pow_mul, convexHull_union, WithLp.unitization_mul, FixedPoints.smul, hasDerivAt_exp_smul_const', DoubleCentralizer.instStarModule, quasispectrum.preimage_algebraMap, convexHull_sub, NNRat.addSubmonoid_closure_range_mul_self, IsScalarTower.AlgEquiv.restrictNormalHom_comp_apply, VectorBundleCore.localTriv.isLinear, instOrderIsoClassContinuousLinearMapIdOfNonUnitalAlgEquivClassOfStarHomClassOfContinuousMapClass, hasDerivWithinAt_id, solvableByRad.isIntegral, ContinuousMultilinearMap.smulRightL_apply, ContinuousLinearMap.contDiff, Submodule.le_traceDual_mul_iff, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, LinearMap.rank_add_le, ContinuousLinearMap.instBorelSpace, LinearMap.isStarProjection_iff_isSymmetricProjection, LinearIsometryEquiv.toLinearEquiv_rTensor, norm_apply_le_norm_cfcₙ, fderiv_mul_const, innerₛₗ_apply_coe, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, fderiv_csinh, exists_pos_left_iff_sameRay_and_ne_zero, ClassGroup.equiv_mk0, NumberField.RingOfIntegers.map_mk, HasStrictFDerivAt.fun_add, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, IsLocalMinOn.fderivWithin_nonneg, instExpCharLinearMapSubtypeMemSubringCenterId, ContinuousLinearMap.norm_snd_le, IntermediateField.sup_toSubalgebra_of_right, Submodule.orthogonalDecomposition_apply, iteratedFDeriv_succ_eq_comp_left, IntermediateField.algebraAdjoinAdjoin.instFaithfulSMulSubtypeMemSubalgebraAdjoinAdjoin, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff, Submodule.isOrtho_self, LinearIsometryEquiv.toLinearIsometry_lTensor, WeierstrassCurve.Jacobian.neg_of_Z_ne_zero, fderiv_of_notMem_tsupport, ContinuousLinearMap.smul_compLpL, AddChar.wInner_cWeight_eq_boole, DifferentiableOn.prodMk, Representation.is_simple_module_iff_irreducible_ofModule, IntermediateField.insepDegree_bot, hasStrictFDerivAt_const, FormalMultilinearSeries.summable_norm_mul_pow, ContinuousLinearMap.contMDiffOn, Polynomial.qsmul_eq_C_mul, Polynomial.Gal.restrictProd_injective, IsFractionRing.algEquiv_commutes, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv, contMDiffOn_coordChangeL, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, IntermediateField.equivOfEq_apply, SpectrumRestricts.rightInvOn, ContinuousLinearEquiv.arrowCongrSL_symm_apply, NormedSpace.ext_iff, Nat.inv_pos_of_nat, IntermediateField.rank_bot', OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_univ, krullTopology_t2, ContinuousLinearMap.nnbound, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, convexHull_list_sum, Module.Basis.toFlag_carrier, ContinuousLinearMap.opNorm_mulLeftRight_le, Polynomial.cauchyBound_X_sub_C, DoubleCentralizer.intCast_fst, NNRat.mul_num, instIsAtomisticSubmodule, gauge_smul_left, PointwiseConvergenceCLM.evalCLM_apply, Algebra.norm_algebraMap, IsPurelyInseparable.algebraMap_elemReduct_eq, ClosedSubmodule.orthogonal_closure, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, ContDiffPointwiseHolderAt.iteratedFDeriv, IntermediateField.le_sup_toSubalgebra, ContinuousLinearMap.norm_compLpL_le, ZSpan.vadd_mem_fundamentalDomain, LinearMap.toSeminormFamily_apply, perfectClosure.map_eq_of_algEquiv, Polynomial.rootSet_X_pow, algebraicClosure.map_eq_of_algEquiv, AddChar.map_neg_eq_conj, RatFunc.denom_add_dvd, Module.End.mem_spectrum_iff_isRoot_charpoly, Field.nonempty_algHom_of_minpoly_eq, mfderiv_fst, ContDiffMapSupportedIn.structureMapCLM_zero_injective, ContinuousAlternatingMap.neg_one_pow_smul_map_insertNth, Finset.pluennecke_ruzsa_inequality_nsmul_sub, RCLike.iInter_halfSpaces_eq, mfderivWithin_fst, NumberField.IsCMField.infinitePlace_complexConj, NumberField.prod_archAbsVal_eq, Polynomial.rootSet_prod, Hyperreal.stdPart_omega, IntermediateField.isAlgebraic_adjoin_iff_bot, ContinuousMultilinearMap.piₗᵢ_apply, meromorphicAt_smul_iff_of_ne_zero, Module.Basis.traceDual_powerBasis_eq, NumberField.ComplexEmbedding.isReal_comp_iff, RCLike.normSq_to_complex, Derivation.leibniz_div_const, Matrix.PosSemidef.sqrt_mul_self, ContDiffAt.continuousAt_iteratedFDeriv, Polynomial.not_irreducible_C, ZSpan.fract_apply, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, Real.deriv_arcsin_aux, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, IsLocalMin.fderiv_eq_zero, Finset.dens_eq_sum_dens_fiberwise, IntermediateField.fieldRange_val, IntermediateField.liftAlgEquiv_apply, ContinuousLinearMap.cpolynomialOn, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, LinearMap.coe_toContinuousLinearMap_symm, Matrix.range_diagonal, NumberField.ComplexEmbedding.IsConj.comp, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable, HasFDerivWithinAt.finset_prod, ContinuousAlternatingMap.nnnorm_constOfIsEmpty, hasStrictFDerivAt_list_prod', RatFunc.num_div_denom, ContinuousLinearMap.le_opENorm, continuousMultilinearCurryFin1_symm_apply, IntermediateField.insepDegree_top, ValuationSubring.subtype_apply, Quaternion.hasSum_expSeries_of_imaginary, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, Trivialization.symmL_apply, ContinuousMultilinearMap.opNorm_le_iff, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, RingHom.mem_eqLocusField, StrongDual.mem_polar_iff, separableClosure_le_separableClosure_iff, FormalMultilinearSeries.radius_pi_le, DualNumber.ideal_trichotomy, MeasureTheory.lpMeasToLpTrim_ae_eq, Submodule.orthogonal_eq_inter, ContinuousLinearMap.mdifferentiableOn, RCLike.normSq_add, AffineSubspace.sOppSide_smul_vsub_vadd_left, MeasureTheory.eLpNorm_condExpL2_le, RCLike.div_re, ContinuousLinearMap.lsmul_flip_apply, IsGaloisGroup.card_eq_finrank, finrank_vectorSpan_range_add_one_le, ContinuousAlternatingMap.alternatizeUncurryFin_curryLeft, hasDerivAt_iff_tendsto, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, HasStrictFDerivAt.smul_const, FixedPoints.coe_algebraMap, ContinuousLinearEquiv.coord_self, sub_smul_dslope, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, cardinalMk_algHom, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, ContinuousAlternatingMap.unit_le_opNorm, RCLike.geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, LinearMap.range_smulRight_apply, IsGalois.tfae, norm_iteratedFDeriv_smul_le, exists_eq_smul_of_parallel, ContDiffAt.differentiableAt_iteratedFDeriv, NNRat.floor_natCast_div_natCast, WeierstrassCurve.Projective.dblX_eq, TrivSqZeroExt.inv_zero, LinearMap.IsPositive.adjoint_eq, SMulCommClass.nnrat, Trivialization.prod_apply', fderivWithin_zero_of_not_differentiableWithinAt, IntermediateField.transcendental_adjoin_iff, ContinuousLinearMap.sSup_unitClosedBall_eq_norm, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, NumberField.InfinitePlace.isUnramified_iff_mult_le, iteratedDeriv_vcomp_two, ContinuousLinearEquiv.coord_norm, Nat.cast_choose, ContinuousAlternatingMap.opNNNorm_le_iff, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic, ContinuousOn.continuousOn_iteratedFDeriv, intervalIntegral.integral_hasDerivAt_left, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1, MeasureTheory.lpMeasToLpTrim_smul, Real.hasStrictDerivAt_const_rpow, Submodule.starProjection_orthogonal_val, VectorField.lieBracketWithin_eq, Polynomial.natSepDegree_mul, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, MDifferentiableOn.smul_section_of_tsupport, isStarProjection_iff_eq_starProjection, LinearEquiv.conjAlgEquiv_surjective, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, RCLike.geometric_hahn_banach_point_closed, LinearMap.IsSymmetricProjection.le_iff_range_le_range, ContinuousLinearMap.map_add₂, hasDerivWithinAt_intCast, Module.End.hasEigenvalue_iff_mem_spectrum, birkhoffAverage_apply_sub_birkhoffAverage, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, Polynomial.natDegree_mod_lt, IntermediateField.rank_comap, Projectivization.cross_mk_of_cross_eq_zero, VectorPrebundle.coordChange_apply, ContinuousMultilinearMap.norm_map_cons_le, LinearMap.not_hasEigenvalue_zero_tfae, NumberField.InfinitePlace.even_card_aut_of_not_isUnramifiedIn, ContinuousMultilinearMap.norm_smulRight, EuclideanGeometry.orthogonalProjection_apply, Module.Basis.extendOfIsLattice_apply, hasFDerivAt_exp_zero_of_radius_pos, LSeries_hasDerivAt, separableClosure.separableClosure_eq_bot, Polynomial.div_C_mul, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_right, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly, IntermediateField.rank_bot_mul_relrank, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, Real.hasDerivAt_fourierIntegral, IsLocalRing.instFiniteResidueField, ContinuousLinearEquiv.strictConvex_preimage, ordinaryHypergeometricSeries_eq_zero_of_neg_nat, NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex, ContinuousAlternatingMap.bound, Nat.cast_le_pow_div_sub, IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C, ContinuousLinearMap.hasDerivWithinAt, differentiableWithinAt_piLp, LinearIsometry.rTensor_apply, hasStrictFDerivAt_pow, ArchimedeanClass.mk_div, FormalMultilinearSeries.derivSeries_apply_diag, NormedSpace.polar_closedBall, Submodule.norm_orthogonalProjection, SameRay.exists_nonneg_right, AnalyticAt.fderiv, Bundle.Prod.contMDiffVectorBundle, ContinuousLinearEquiv.differentiableWithinAt, IntermediateField.sup_toSubalgebra_of_isAlgebraic_right, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, fderiv_comp_smul, Submodule.instHasOrthogonalProjectionTop, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, LinearMap.BilinForm.eq_top_of_restrict_nondegenerate_of_orthogonal_eq_bot, ContinuousLinearMap.opNorm_lsmul, LinearIsometry.toLinearMap_lTensor, Submodule.comap_smul', IntermediateField.toSubalgebra_le_toSubalgebra, convexOn_iff_div, ValuationSubring.ker_unitGroupToResidueFieldUnits, HasFPowerSeriesWithinOnBall.hasSum, Valuation.HasExtension.instIsScalarTower_valuationSubring, coe_innerₛₗ_apply, FormalMultilinearSeries.norm_changeOriginSeriesTerm, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, PiLp.hasStrictFDerivAt_ofLp, fderivWithin_arctan, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, Nonneg.coe_zpow, Module.Basis.continuous_coe_repr, ContinuousLinearMap.norm_id_of_nontrivial_seminorm, NumberField.InfinitePlace.comap_id, curveIntegral_add, IsAlgClosed.isAlgClosure_of_transcendence_basis, HasGradientAt.hasDerivAt, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, hasDerivAt_exp_zero, Subfield.mem_map, GenContFract.sub_convs_eq, HasFTaylorSeriesUpTo.zero_eq', InfiniteGalois.limitToAlgEquiv_symm_apply, AffineSubspace.setOf_sOppSide_eq_image2, NumberField.coe_discr, galRestrict'_comp, ContinuousLinearEquiv.analyticAt, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, LinearMap.finrank_maxGenEigenspace_eq, NNRat.cast_divNat, InnerProductSpace.continuousLinearMapOfBilin_apply, ContinuousMultilinearMap.norm_def, Polynomial.degree_mod_lt, NormedSpace.double_dual_bound, instFieldContMDiffRing, summable_mul_right_iff, NNRat.instIsTopologicalSemiring, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, IntermediateField.adjoin_toSubfield, spectralAlgNorm_isPowMul, inv_smul_le_iff_of_neg, MeasureTheory.convolution_eq_swap, ContinuousLinearMap.map_zero₂, isInvertible_mfderivWithin_extChartAt_symm, ModelWithCorners.coe_transContinuousLinearEquiv_symm, fderivWithin_def, UniformCauchySeqOnFilter.one_smulRight, mulInvariantVectorField_smul, differentiable_finCons, ContDiff.fderiv_right, hasDerivAt_const_add_iff, HasFDerivAt.prodMap, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, Polynomial.hilbertPoly_mul_one_sub_pow_add, VectorField.mlieBracketWithin_apply, HasFPowerSeriesWithinOnBall.tendsto_partialSum, Submodule.finrank_lt, IsTranscendenceBasis.lift_rank_eq_max_lift, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', ContinuousAlternatingMap.opNorm_pi, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, ValuationSubring.smul_mem_pointwise_smul, IntermediateField.finiteDimensional_map, FormalMultilinearSeries.id_apply_one, strictConvexOn_iff_div, ContinuousLinearEquiv.comp_contDiff_iff, minpoly.degree_dvd, Projectivization.mk_eq_mk_iff', fderiv_csin, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, OnePoint.equivProjectivization_apply_coe, ContinuousLinearMap.norm_snd, ZSpan.repr_floor_apply, IsPurelyInseparable.isPRadical, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv, MvRatFunc.rank_eq_max_lift, separableClosure.map_eq_of_algEquiv, NumberField.Units.finrank_mul_regulator_eq_det, IsPrimitiveRoot.lcm_totient_le_finrank, IsPurelyInseparable.instNonemptyAlgHomOfPerfectField, MeasureTheory.condExpIndSMul_ae_eq_smul, ContinuousAlternatingMap.uniformContinuous_restrictScalars, Configuration.ofField.mem_iff, HasFTaylorSeriesUpTo.fderiv, ContinuousLinearMap.iteratedFDeriv_comp_right, linearIndependent_pow, norm_fderiv_le_of_lip', RatFunc.aeval_X_left_eq_algebraMap, IsSepClosure.isAlgClosure_of_perfectField, LieAlgebra.IsKilling.span_weight_eq_top, coplanar_iff_finrank_le_two, ContinuousMultilinearMap.apply_zero_uncurry0, ContinuousMap.idealOf_compl_singleton_isMaximal, Polynomial.residueFieldMapCAlgEquiv_symm_X, IntermediateField.finSepDegree_top, fderiv_cosh, Polynomial.IsSplittingField.adjoin_rootSet_eq_range, IntermediateField.lift_rank_comap, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, ValuationRing.coe_equivInteger_apply, support_fderiv_subset, HasStrictFDerivAt.fun_mul, IsLocalFrameOn.generating, ContDiff.continuousLinearMap_comp, ContinuousLinearMap.precomp_apply, ContinuousLinearMap.norm_holderL_le, hasFDerivWithinAt_pow, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, PolynormableSpace.withSeminorms, Nonneg.val_inv_unitsEquivPos_symm_apply_coe, contDiff_infty_iff_fderiv, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, hasDerivWithinAt_inv, geom_sum_Ico, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Asymptotics.isBigOTVS_prodMk_left, MeasureTheory.lpMeas.ae_fin_strongly_measurable', gaugeSeminormFamily_ball, spectralNorm_eq_of_equiv, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, hasStrictDerivAt_id, Polynomial.splits_iff_splits, curveIntegral_sub, Polynomial.Monic.irreducible_iff_irreducible_map_fraction_map, AlgHom.restrictNormal_commutes, RingHom.rangeRestrictFieldEquiv_apply_coe, quadraticCharFun_zero, RCLike.sqrt_normSq_eq_norm, WeierstrassCurve.Jacobian.isUnit_X_of_Z_eq_zero, mdifferentiable_smul_section, NNRat.cast_lt_natCast, Matrix.IsHermitian.charpoly_eq, RatFunc.associated_num_inv, IsIntegral.inv_mem_adjoin, HasFDerivWithinAt.mul', IntermediateField.normalClosure_le_iff_of_normal, FiniteField.orderOf_frobeniusAlgHom, instNonemptySeedRatReal, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, HasGradientAt.fderiv_apply, SchwartzMap.instFourierInvSMul, ContinuousAlternatingMap.instContinuousEval, differentiableWithinAt_complex_iff_differentiableWithinAt_real, ContinuousLinearMap.comp_analyticOnNhd, TemperedDistribution.derivCLM_apply_apply, ValuationSubring.comap_comap, NNRat.cast_natCast, AffineSubspace.setOf_wSameSide_eq_image2, LinearIsometryEquiv.integrable_comp_iff, AlgHom.fieldRange_of_normal, range_derivWithin_subset_closure_span_image, NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, IntermediateField.Lifts.eq_iff, Module.End.genEigenspace_le_genEigenspace_finrank, norm_iteratedFDeriv_zero, algebraMap.coe_expect, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, FiniteField.even_card_iff_char_two, NumberField.FinitePlace.norm_le_one, geom_sum₂_Ico, hasDerivWithinAt_Ici_of_tendsto_deriv, NumberField.Units.sum_mult_mul_log, Polynomial.hasFDerivWithinAt, LinearMap.BilinForm.finrank_add_finrank_orthogonal, MeasureTheory.condExpIndSMul_smul', LinearMap.hasDerivAt, Subfield.coe_map, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, norm_iteratedFDeriv_eq_norm_iteratedDeriv, MDifferentiableWithinAt.smul, HasMFDerivWithinAt.comp, Complex.isometryOfOrthonormal_symm_apply, Real.hasStrictDerivAt_rpow_const, Field.Emb.Cardinal.adjoin_basis_eq_top, ContinuousLinearMap.postcompUniformConvergenceCLM_apply, egauge_smul_right, VectorField.lieBracket_smul_right, NumberField.ComplexEmbedding.IsReal.isConjGal_one, HasFDerivAtFilter.restrictScalars, RCLike.normSq_apply, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, NumberField.ComplexEmbedding.conjugate_coe_eq, NumberField.Embeddings.range_eval_eq_rootSet_minpoly, Finset.subConst_empty_left, Ideal.algebraMap_residueField_eq_zero, LinearMap.flip_surjective_iff₂, IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable', CurveIntegrable.sub, HasFiniteFPowerSeriesOnBall.fderiv_eq, smul_closedBall, ContMDiffOn.smul, NumberField.ComplexEmbedding.lift_algebraMap_apply, IntermediateField.iInf_toSubalgebra, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton, IsGaloisGroup.card_fixingSubgroup_eq_finrank, IntermediateField.normalClosure_map_eq, Complex.hasDerivAt_log_sub_logTaylor, hasStrictDerivAt_iff_hasStrictFDerivAt, UniformConvergenceCLM.instContinuousSemilinearMapClass, ContinuousLinearEquiv.comp_contDiffAt_iff, WeierstrassCurve.j_of_isShortNF, WithSeminorms.isVonNBounded_iff_seminorm_bounded, ContinuousAlternatingMap.hasFDerivAt, WithAbs.instIsSeparable, FormalMultilinearSeries.summable, HasFPowerSeriesAt.locally_zero_iff, zpow_succ', hasDerivAt_iff_tendsto_slope, TrivSqZeroExt.isUnit_or_isNilpotent, intervalIntegral.fderiv_integral, PiTensorProduct.mapL_add, Lagrange.eval_basis_self, fderiv_fun_const, ContinuousLinearMap.analyticAt_bilinear, inner_gradient_left, eventually_norm_trivializationAt_lt, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_left, TensorProduct.congrIsometry_apply, IntermediateField.relrank_bot_left, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff', ConvexOn.exists_affine_le_of_lt, HasFPowerSeriesAt.hasStrictFDerivAt, Projectivization.independent_iff, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, ModelWithCorners.uniqueDiffOn_preimage_source, MvPowerSeries.mul_inv_rev, MeasureTheory.integral_prod_smul, ContinuousLinearMap.toPointwiseConvergenceCLM_apply, LaurentSeries.mem_integers_of_powerSeries, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, Ideal.bijective_algebraMap_quotient_residueField, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, Polynomial.IsPrimitive.isUnit_iff_isUnit_map, algebraMap_galRestrict'_apply, isBoundedLinearMap_continuousMultilinearMap_comp_linear, algebraMap.coe_inv, Numbering.dens_prefixed, RingOfIntegers.coe_algebraMap_norm, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, innerSL_apply_coe, differentiableOn_finCons, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, hasDerivAt_exp_of_mem_ball, AffineSubspace.sSameSide_smul_vsub_vadd_left, ContinuousLinearMap.bound, hasStrictDerivAt_exp_smul_const_of_mem_ball, MeasureTheory.eLpNorm_le_eLpNorm_fderiv, NumberField.mixedEmbedding.convexBodySum_volume, Polynomial.IsSplittingField.IsScalarTower.splits, ContMDiff.const_smul_section, tendsto_algebraMap_inv_atTop_nhds_zero_nat, ContinuousLinearMap.isPositive_one, Finset.dens_union_le, Polynomial.monic_annIdealGenerator, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, ContinuousLinearMap.isPositive_sum, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, RatFunc.algebraMap_monomial, Real.hasDerivAt_Gamma_nat, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, Polynomial.hilbertPoly_zero_right, HasStrictFDerivAt.inner, WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero, Height.AdmissibleAbsValues.product_formula, galRestrictHom_apply, LinearPMap.supSpanSingleton_apply_mk, RatFunc.denom_dvd, Algebra.Etale.iff_exists_algEquiv_prod, ZSpan.fract_eq_fract, HasMFDerivAt.comp, hasDerivAt_pi, ContinuousLinearMap.toUniformConvergenceCLM_symm_apply, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, derivWithin_fun_inv', Lagrange.natDegree_basis, Meromorphic.fun_pow, hasFDerivAt_inv', LinearMap.toMatrix_adjoint, RingHom.field_closure_preimage_le, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Algebra.IsAlgebraic.bijective_of_isScalarTower, hasDerivWithinAt_finCons, Finset.expect_eq_sum_div_card, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, IntermediateField.le_normalClosure, CFC.abs_smul, Subspace.map_dualCoannihilator, FormalMultilinearSeries.rightInv_coeff, Meromorphic.smul, OpenPartialHomeomorph.unitBallBall_symm_apply, Polynomial.cauchyBound_X, hasDerivAt_zpow, ContinuousLinearMapWOT.instContinuousLinearMapClass, MeasureTheory.AEStronglyMeasurable.convolution_integrand', FormalMultilinearSeries.summable_norm_apply, FDRep.scalar_product_char_eq_finrank_equivariant, ContinuousMultilinearMap.norm_constOfIsEmpty, uniqueDiffOn_extChartAt_target, cfcₙHom_of_cfcHom_map_quasispectrum, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, IntermediateField.equivOfEq_trans, mfderiv_neg, VectorBundle.pullback, convexOn_zpow, hasFDerivWithinAt_of_subsingleton, WeierstrassCurve.Jacobian.equation_of_Z_ne_zero, Polynomial.annIdealGenerator_eq_zero_iff, HahnEmbedding.Partial.truncLT_eval_mem_range_extendFun, Subfield.subtype_injective, isClosedMap_smul_left, ContinuousLinearMap.isOpenMap_of_ne_zero, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, ContinuousLinearMap.integral_comp_comm, hasFDerivWithinAt_iff_tendsto, FormalMultilinearSeries.compAlongOrderedFinpartition_apply, IntermediateField.normalClosure_def', LinearMap.im_inner_adjoint_mul_self_eq_zero, Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, ValuationSubring.algebraMap_injective, fderiv_pi, ContinuousLinearMapWOT.sub_apply, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', autAdjoinRootXPowSubC_root, ContinuousLinearMap.map_neg₂, Matrix.l2_opNorm_def, IsAlgClosed.surjective_restrictDomain_of_isAlgebraic, Rat.cast_pow, EuclideanGeometry.Sphere.secondInter_map, PowerSeries.Inv_divided_by_X_pow_order_rightInv, OrthogonalFamily.linearIsometry_apply, ContinuousMultilinearMap.le_opNNNorm, HasFiniteFPowerSeriesOnBall.sub, Ideal.ResidueField.liftₐ_algebraMap, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Bornology.isVonNBounded_singleton, Matrix.toEuclideanLin_toLp, ModuleCat.isScalarTower_of_algebra_moduleCat, IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers, IntermediateField.mem_bot, nnnorm_cfcₙ_le, ZMod.euler_criterion, NumberField.hermiteTheorem.rank_le_rankOfDiscrBdd, ContinuousLinearMapWOT.continuous_dual_apply, continuous_stereoInvFun, ContinuousLinearMap.iteratedFDeriv_comp_left, Submodule.orthogonalProjection_eq_zero_iff, ContinuousLinearMap.holderL_apply_apply, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, StrongDual.mem_polar_singleton, FormalMultilinearSeries.comp_rightInv_aux2, ZSpan.coe_fract_self, TrivSqZeroExt.mul_inv_rev, IntermediateField.adjoin_algebraic_toSubalgebra, Field.sepDegree_le_rank, ContinuousMultilinearMap.opNorm_prod, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, Asymptotics.isLittleOTVS_insert, Real.hasDerivAt_sinh, isClosedEmbedding_smul_left, MeasureTheory.integrable_fun_smul_iff, MeasureTheory.condExpL1CLM_smul, isConformalMap_const_smul, add_div_two_lt_right, wbtw_midpoint, hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, Complex.norm_fderiv_le_div_of_mapsTo_ball, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1, norm_innerSL_le, MeromorphicAt.smul, NNRat.smul_def, Algebra.QuasiFinite.instIsArtinianRingFiber, AffineSubspace.subtypeₐᵢ_toAffineMap, IsFractionRing.num_mul_den_eq_num_iff_eq', IntermediateField.mem_restrict, HasStrictFDerivAt.sub, OrthonormalBasis.measurePreserving_measurableEquiv, IsDedekindDomain.integer_univ, ContinuousLinearMap.isLeast_opNorm, fderiv_const_smul_of_field, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, ContinuousLinearMap.IsPositive.isSelfAdjoint, spectrum.map_pow_of_pos, HasLineDerivAt.smul, MvPolynomial.isAlgebraic_of_mem_vars_of_forall_totalDegree_le, Real.exists_extension_norm_eq, OrthonormalBasis.sum_repr', Finset.expect_ite_eq, continuousMultilinearCurryRightEquiv_apply, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, Seminorm.convex_closedBall, hasStrictFDerivAt_intCast, LinearMap.finrank_range_add_finrank_ker, algebraMap.coe_ratCast, Submodule.coe_orthogonalProjection_apply, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, NumberField.Units.dirichletUnitTheorem.exists_unit, Submodule.starProjection_coe_eq_isCompl_projection, IsLocalDiffeomorphAt.mfderivToContinuousLinearEquiv_coe, HasFDerivAt.neg, ContDiffMapSupportedIn.structureMapLM_zero_apply, ContinuousMap.idealOfSet_ofIdeal_isClosed, RCLike.ofRealAm_coe, Matrix.linearIndependent_cols_of_invertible, RCLike.normSq_one, LinearMap.BilinForm.isAdjointPairLeftAdjointOfNondegenerate, LinearMap.injective_iff_antilipschitz, AffineIndependent.convexHull_inter, ContinuousAlternatingMap.prodLIE_symm_apply, analyticOrderAt_smul_eq_top_of_right, fderiv_comp_deriv_of_eq, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_apply, Polynomial.monic_normalize, Polynomial.map_dvd_map', DifferentiableOn.hasDerivAt, ContinuousLinearMapWOT.instContinuousNeg, Bornology.sUnion_isVonNBounded_eq_univ, finrank_eq_one_iff_of_nonzero', ArchimedeanClass.FiniteElement.mk_natCast, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, NumberField.ComplexEmbedding.isConj_one_iff, PowerSeries.smul_inv, Finset.divConst_empty_right, LinearIsometryEquiv.norm_iteratedFDeriv_comp_left, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, IntermediateField.LinearDisjoint.isDomain, Submodule.wcovBy_span_singleton_sup, PosSMulMono.toPosSMulReflectLE, tendsto_pow_atTop_nhds_zero_iff, ContDiff.fderiv, Submodule.starProjection_apply_eq_zero_iff, ContMDiffAt.smul_section, fderiv_list_prod', SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, AnalyticOnNhd.eval_continuousLinearMap', nnratCast_smul_eq, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, Module.Basis.norm_repr_le_norm, PadicInt.coe_dpow_eq, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, IntermediateField.finrank_dvd_of_le_right, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, Orthonormal.inner_right_fintype, HasMFDerivAt.mul', ContinuousLinearMap.flipₗᵢ_symm, ImplicitFunctionData.rightDeriv_fderiv_implicitFunction, Asymptotics.IsBigOTVS.refl, two_mul_le_add_mul_sq, NumberField.InfinitePlace.comap_surjective, WeierstrassCurve.Jacobian.add_of_Z_eq_zero, Asymptotics.isTheta_const_smul_right, HasFDerivAt.star_star, ContinuousLinearMap.postcomp_uniformConvergenceCLM_apply, ZMod.orderOf_units_dvd_card_sub_one, IsGalois.splits, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, hasDerivAt_of_tendsto_locally_uniformly_on', Polynomial.resultant_eq_zero_iff, NumberField.InfinitePlace.card_complex_embeddings, HasGradientWithinAt.hasFDerivWithinAt, ContinuousLinearMap.dist_le_opNorm, FormalMultilinearSeries.rightInv_coeff_one, IntermediateField.fixingSubgroup_bot, hasFDerivAt_exp, ContinuousAlternatingMap.opNNNorm_prod, IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar, IsAlgClosed.splits_domain, mfderivWithin_id, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Pi.orthonormalBasis_repr, CyclotomicRing.eq_adjoin_primitive_root, Polynomial.hasDerivWithinAt, ZSpan.mem_fundamentalDomain, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, uniqueDiffWithinAt_extChartAt_target, IntermediateField.finrank_le_of_le_right, ApproximatesLinearOn.lipschitzOnWith, Polynomial.mod_def, norm_fderiv_norm_id_rpow, ContinuousLinearMap.isBigOTVS_id, LinearMap.isAdjointPair_inner, MeasureTheory.condExpIndL1Fin_smul', LinearMap.IsPositive.adjoint_conj, ContinuousLinearMap.norm_holder_apply_apply_le, Polynomial.Gal.card_of_separable, LinearMap.isPositive_one, Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iff, Finset.Nonempty.dens_pos, mfderivWithin_sumSwap, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Affine.Simplex.affineSpan_pair_eq_altitude_iff, LinearMap.orthogonal_span_singleton_eq_to_lin_ker, UniformConvergenceCLM.isVonNBounded_iff, DualNumber.instIsPrincipalIdealRing, Polynomial.pairwise_coprime_X_sub_C, NNReal.tendsto_const_div_atTop_nhds_zero_nat, Matrix.sub_scalar_sq_eq_discr, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, absorbent_ball_zero, SMulCommClass.nnrat', ContinuousAlternatingMap.continuous_toContinuousMultilinearMap, Submodule.norm_subtypeL_le, RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_u, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, IsUltrametricDist.isPowMul_invariantExtension, isGalois_bot, hasDerivWithinAt_iff_tendsto_slope, fderiv_const_smul, hasFDerivAtFilter_pi', measurable_fderiv_apply_const_with_param, constFormalMultilinearSeries_apply_succ, IntermediateField.mem_fixingSubgroup_iff, FormalMultilinearSeries.continuousOn, Polynomial.natSepDegree_X_pow, hasFDerivAt_inv, IntermediateField.intermediateFieldMap_symm_apply_coe, mfderiv_prod_left, IntermediateField.finrank_dvd_of_le_left, Affine.Simplex.direction_altitude, LinearIsometryEquiv.symm_lTensor, ContinuousLinearMap.coe_ofIsClosedGraph, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, DoubleCentralizer.toProdHom_apply, ContinuousAlternatingMap.enorm_toContinuousMultilinearMap, NNRat.cast_le_ofNat, ContinuousMap.isUnit_iff_forall_ne_zero, Submodule.isOrtho_bot_left, ContinuousMultilinearMap.isUniformInducing_toUniformOnFun, LieAlgebra.IsKilling.mem_sl2SubalgebraOfRoot_iff, NumberField.mixedEmbedding.norm_unit, algebraMap_galRestrictHom_apply, Algebra.prod_embeddings_eq_finrank_pow, DoubleCentralizer.mul_snd, HasFDerivWithinAt.comp_hasFDerivAt, hasMFDerivWithinAt_inl, ContinuousLinearMap.fpowerSeries_apply_one, IntermediateField.map_id, fderiv_continuousLinearEquiv_comp', Finset.nnratCast_dens_mul_natCast_card, ContinuousLinearMap.smulRightL_apply_apply, continuousOn_clm_apply, logDeriv_pow, Set.Finite.convexHull_eq, Real.hasDerivAt_sqrt, ContinuousLinearMapWOT.ContinuousLinearMap.continuous_toWOT, LinearMap.range_smul, SchwartzMap.one_add_le_sup_seminorm_apply, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, HasFDerivAt.fun_mul', Seminorm.continuous_iff_continuous_comp, Hyperreal.stdPart_epsilon, minpoly.eq_X_sub_C, constFormalMultilinearSeries_zero, Polynomial.SplittingField.adjoin_rootSet, OpenPartialHomeomorph.unitBallBall_apply, isSplittingField_iff_intermediateField, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, ContinuousMultilinearMap.instIsTopologicalAddGroup, half_le_self_iff, Asymptotics.IsBigO.isBigOTVS, IsScalarTower.nnrat, LinearPMap.adjointAux_inner, HasStrictFDerivAt.mul_const, Asymptotics.isLittleOTVS_neg_left, Real.hasDerivWithinAt_arccos_Iic, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, ContDiffBump.convolution_tendsto_right_of_continuous, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, linearIndepOn_insert_iff, FractionalIdeal.den_mem_inv, NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iff, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, Lagrange.nodal_erase_eq_nodal_div, ContinuousLinearMap.opNNNorm_mul_apply, AbsoluteValue.isEquiv_iff_isHomeomorph, isGalois_iff_isGalois_bot, eventually_norm_mfderiv_extChartAt_lt, ContinuousMultilinearMap.curryFinFinset_apply, InfiniteGalois.fixingSubgroup_isClosed, IsSepClosed.surjective_restrictDomain_of_isSeparable, EuclideanGeometry.orthogonalProjection_eq_iff_mem, NormedField.nhdsWithin_isUnit_neBot, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, Submodule.le_traceDual_iff_map_le_one, Subspace.dualAnnihilator_inf_eq, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, OrderedFinpartition.applyOrderedFinpartition_update_right, ConjRootClass.irreducible_minpoly, FiniteField.algebraMap_norm_eq_pow_sum, eq_midpoint_of_dist_eq_half, Field.insepDegree_le_of_left_le, IntermediateField.finiteDimensional_adjoin_pair, IsLocalRing.instIsScalarTowerResidueField, IsLocalRing.ResidueField.lift_residue_apply, MvPowerSeries.smul_inv, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, VectorBundleCore.coordChange_comp, SchwartzMap.denseRange_toLpCLM, IntermediateField.normal_sup, IsAlgClosed.associated_iff_roots_eq_roots, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, hasFDerivAt_fst, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, Asymptotics.isLittleOTVS_sup, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, IntermediateField.coe_algebraMap_apply, mfderiv_comp_mfderivWithin_of_eq, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, LinearMap.IsSymmetric.coe_re_inner_apply_self, SchwartzMap.integrable_pow_mul_iteratedFDeriv, FormalMultilinearSeries.radius_eq_liminf, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, NumberField.IsCMField.complexConj_torsion, quotient_prod_linearEquiv, Polynomial.residueFieldMapCAlgEquiv_algebraMap, HasFTaylorSeriesUpToOn.restrictScalars, starConvex_iff_div, ContinuousLinearMap.apply_apply, ContinuousLinearEquiv.comp_differentiableWithinAt_iff, Submodule.traceDual_top, egauge_zero_right, Asymptotics.isThetaTVS_iff_isTheta, hasFDerivAt_pi', ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk, RatFunc.toFractionRingAlgEquiv_apply, OrthogonalFamily.summable_iff_norm_sq_summable, ContinuousLinearMap.norm_map_removeNth_le, Module.End.exists_isNilpotent_isSemisimple, Polynomial.isCoprime_iff_aeval_ne_zero, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, LieModule.range_traceForm_le_span_weight, iteratedFDeriv_neg, separableClosure.isGalois, Real.fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, LinearMap.le_rank_iff_exists_linearIndependent_finset, IsSymmSndFDerivWithinAt.eq, ContinuousLinearMap.map_smulₛₗ₂, CurveIntegrable.add, Asymptotics.superpolynomialDecay_param_pow_mul_iff, geom₂_sum_of_gt, PiTensorProduct.mapLMultilinear_opNorm, hasDerivWithinAt_inter, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, ContinuousMultilinearMap.norm_image_sub_le', hasFPowerSeriesAt_iff', Quaternion.normSq_ratCast, NumberField.InfinitePlace.apply, LinearMap.canLiftContinuousLinearMap, LinearIsometryEquiv.differentiableOn, RCLike.geometric_hahn_banach_closed_compact, WeierstrassCurve.Jacobian.isUnit_addZ_of_X_ne, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, inner_gradient_right, hasDerivAt_exp_smul_const_of_mem_ball, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, IntermediateField.restrictScalars_adjoin, hasStrictDerivAt_exp_zero, Transcendental.linearIndependent_sub_inv, deriv_const_smul_field, NonUnitalCStarAlgebra.toSMulCommClass, Submodule.orthogonalProjection_norm_le, HasFDerivAt.mul', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, DoubleCentralizer.intCast_toProd, Matrix.PosDef.posDef_sqrt, IntermediateField.finrank_adjoin_simple_eq_one_iff, Function.HasTemperateGrowth.isBigO_uniform, differentiableOn_snd, norm_cfcₙ_le_iff, iteratedFDerivWithin_zero_apply, EuclideanSpace.volume_closedBall, FiniteField.natCard_algEquiv_extension, FractionalIdeal.coe_mk0, ClassGroup.mk_def, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, fderiv_single, IsSepClosed.exists_aeval_eq_zero, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, Submodule.orthogonalProjection_orthogonal, Set.Finite.isVonNBounded, slope_def_module, Real.hasStrictDerivAt_exp, openSegment_subset_union, Nat.cast_inv_le_one, LinearMap.finrank_eigenspace_le, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_symm_apply, Algebra.finite_of_essFiniteType_of_isAlgebraic, algebraMap.coe_zpow, inv_eq_of_aeval_divX_ne_zero, Height.logHeight_pow, le_egauge_closedBall_one, hasFDerivAt_list_prod_attach', Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mul, instSubsingletonAlgHomOfIsPurelyInseparable, Polynomial.IsSplittingField.map, MonoidWithZeroHomClass.ext_nnrat_iff, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, LinearIsometryEquiv.rTensor_def, MeasureTheory.norm_condExpL2_le_one, ContinuousLinearEquiv.mdifferentiableAt, HasCompactSupport.convolution_integrand_bound_right, ValuationSubring.coe_subtype, MeromorphicAt.meromorphicTrailingCoeffAt_pow, bddAbove_smul_iff_of_neg, LinearMap.mem_span_iff_continuous, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, fderivWithin_mem_iff, Padic.isDenseInducing_cast_withVal, Ideal.Fiber.exists_smul_eq_one_tmul, UniqueMDiffOn.uniqueDiffWithinAt_range_inter, AddChar.inv_apply_eq_conj, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, Asymptotics.isBigOTVS_comm, DifferentiableAt.lineDeriv_eq_fderiv, OrthonormalBasis.repr_reindex, Ideal.ResidueField.mapₐ_apply, normalClosure.is_finiteDimensional, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, NNRat.cast_lt_ofNat, Nat.one_div_lt_one_div, MeasureTheory.condExpL2_comp_continuousLinearMap, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, FormalMultilinearSeries.ofScalars_norm_eq_mul, isBoundedBilinearMap_smulRight, inCoordinates_tangent_bundle_core_model_space, isOpen_setOf_linearIndependent, NormedSpace.expSeries_hasSum_exp_of_mem_ball, LinearIsometryEquiv.differentiableWithinAt, Polynomial.separable_map, IntermediateField.finiteDimensional_sup, IsSimpleRing.exists_algEquiv_matrix_divisionRing, tendsto_inv_atTop_nhds_zero_nat, IntermediateField.Lifts.le_iff, VectorBundle.prod, Algebra.normalizedTrace_self_apply, AnalyticOnNhd.eval_continuousLinearMap, Finset.card_mul_cast_divConst, hasStrictFDerivAt_pi, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_sup_left, Polynomial.normalizedFactors_cyclotomic_card, ContinuousLinearMap.adjoint_innerSL_apply, NumberField.InfinitePlace.comap_embedding_of_isReal, ZLattice.coe_comap, LSeries.hasDerivAt_term, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, Valuation.Integers.bijective_algebraMap_of_subsingleton_units_mrange, Submodule.IsOrtho.comap, hasFDerivAt_iff_isLittleO_nhds_zero, Finset.expect_ite_eq', LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate, OrthogonalFamily.inner_right_fintype, Finset.dens_univ, geom_sum_Ico_le_of_lt_one, Finset.cast_addConst, Asymptotics.isLittleO_pow_pow_atTop_of_lt, Valuation.coeff_zero_minpoly, ContDiffMapSupportedIn.structureMapLM_apply, RatFunc.map_apply_div_ne_zero, Finset.mulConst_le_divConst_sq, RCLike.normSq_sub, trace_adjoinSimpleGen, IntermediateField.fixingSubgroup_sup, derivWithin_const_smul', ContinuousLinearMap.coprodEquivL_symm_apply, VectorPrebundle.contMDiffCoordChange_apply, isBoundedLinearMap_prod_multilinear, Module.length_eq_rank, AlgEquiv.eq_linearEquivConjAlgEquiv, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Orthonormal.inner_sum, differentiableWithinAt_fst, IntermediateField.normal_iff_normalClosure_eq, EuclideanGeometry.reflection_apply, continuousOn_coordChange, HasCompactSupport.convolution_integrand_bound_right_of_subset, LinearIsometryEquiv.comp_fderiv', IntermediateField.rank_adjoin_simple_eq_one_iff, Polynomial.coeff_preHilbertPoly_self, LinearPMap.adjoint_apply_of_dense, PadicInt.val_toZMod_eq_zmodRepr, HasStrictDerivAt_ofNat, Function.Periodic.const_inv_smul₀, Real.fourier_smul_convolution_eq, IsSepClosed.exists_eval₂_eq_zero, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, DoubleCentralizer.smul_snd, balancedCore_eq_iInter, RCLike.wInner_cWeight_eq_smul_wInner_one, inverse_mfderiv_add_left, postcomp_compactConvergenceCLM_apply, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, HasFiniteFPowerSeriesAt.comp, NumberField.ComplexEmbedding.orderOf_isConj_two_of_ne_one, ContinuousMap.idealOfSet_isMaximal_iff, IntermediateField.AdjoinPair.algebraMap_gen₂, ContinuousLinearMap.integral_id_map, HahnEmbedding.ArchimedeanStrata.iSupIndep_stratum, hasDerivWithinAt_iff_tendsto, NNRat.ofNat_lt_cast, PrimeSpectrum.nontrivial_iff_mem_rangeComap, MeasureTheory.condExpL2_const_inner, NumberField.house.basis_repr_norm_le_const_mul_house, balancedHull_convexHull_subseteq_absConvexHull, curveIntegrable_restrictScalars_iff, LinearMap.IsSymmetric.intCast, SpectrumRestricts.nnreal_iff_nnnorm, cyclotomicCharacter.continuous, IsCoercive.isClosed_range, Submodule.mem_traceDual_iff_isIntegral, LieAlgebra.IsKilling.rootSystem_root_apply, NumberField.IsCMField.Units.complexConj_eq_self_iff, ContinuousLinearMap.toWOT_apply, Polynomial.IsPrimitive.dvd_iff_fraction_map_dvd_fraction_map, IntermediateField.isIntegral_iff, Subfield.toIsStrictOrderedRing, LinearMap.finiteDimensional_range, mem_contMDiffFiberwiseLinear_iff, RatFunc.denom_zero, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, curveIntegralFun_def, ArchimedeanClass.FiniteResidueField.instIsOrderedRing, left_lt_add_div_two, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, ContinuousLinearMap.intervalIntegral_comp_comm, hasDerivAt_finCons, Asymptotics.IsThetaTVS.rfl, inner_eq_ofReal_norm_sq_right_iff, HasFDerivAt.smul, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, RatFunc.associated_denom_inv, ContinuousLinearMap.contMDiffAt, IsLocalRing.residue_surjective, isOpen_setOf_nat_le_rank, FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin, SchwartzMap.smulLeftCLM_smul, CurveIntegrable.neg, PadicInt.toZMod_spec, isClosed_setOf_isCompactOperator, DoubleCentralizer.coe_snd, ContinuousMultilinearMap.fin0_apply_norm, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, Algebra.botEquiv_symm_apply, WeierstrassCurve.Projective.isUnit_addZ_of_X_ne, tendsto_nhdsGT_zero_of_comp_inv_tendsto_atTop, MeasureTheory.integral_convolution, ValuationSubring.principalUnitGroup_injective, contractLeft_assoc_coevaluation', Int.clog_zero_right, ContinuousLinearMap.le_opNorm_enorm, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum, fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, DivisibleHull.nnqsmul_mk, separableClosure.normalClosure_eq_self, fderiv_sin, ArchimedeanClass.mk_inv, Affine.Simplex.centroid_vsub_point_eq_smul_vsub, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, hasStrictDerivAt_pow, Projectivization.Subspace.mem_submodule_iff, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, IsAlgClosed.dvd_iff_roots_le_roots, OrthonormalBasis.tensorProduct_repr_tmul_apply, Submodule.finiteDimensional_inf_left, Derivation.evalAt_apply, IntermediateField.coe_map, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, TrivSqZeroExt.snd_expSeries_of_smul_comm, ContinuousMultilinearMap.norm_curryMid, NNRat.instContinuousSMulRatReal, finrank_vectorSpan_insert_le_set, ConvexOn.univ_sSup_of_nat_affine_eq, AddChar.expect_eq_ite, NNRat.cast_mul_of_ne_zero, ContinuousLinearEquiv.comp_right_differentiable_iff, convexHull_range_eq_exists_affineCombination, LinearMap.trace_map, ContinuousAlternatingMap.ratio_le_opNorm, WeierstrassCurve.j_of_isCharThreeJNeZeroNF_of_char_three, IntermediateField.adjoin.powerBasis_dim, TensorProduct.assocIsometry_symm_apply, hasFDerivAt_exp_of_mem_ball, LaurentSeries.valuation_X_pow, InnerProductSpace.gramSchmidt_mem_span, SimpContFract.determinant_aux, ModelWithCorners.uniqueDiffOn, norm_iteratedFDeriv_fderiv, TrivSqZeroExt.inv_inr, NormedSpace.dual_def, finiteDimensional_finsupp, LinearMap.IsSymmetric.add, HasFDerivAtFilter.hasDerivAtFilter, NumberField.house_eq_sup', TensorProduct.inner_map_map, IsGalois.of_fixedField_normal_subgroup, RCLike.geometric_hahn_banach_open_open, IntermediateField.Lifts.nonempty_algHom_of_exist_lifts_finset, Polynomial.residueFieldMapCAlgEquiv_symm_C, const_smul_mfderiv, fderiv_norm_sq, Filter.EventuallyEq.hasDerivAtFilter_iff, instProperSpaceSubtypeMemSubmoduleOfCompleteSpaceOfLocallyCompactSpace, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, IntermediateField.essFiniteType_iff, Field.Emb.cardinal_separableClosure, HasMFDerivAt.const_smul, IntermediateField.AdjoinSimple.algebraMap_gen, Valuation.Integers.dvd_iff_le, Subspace.finrank_add_finrank_dualAnnihilator_eq, Lagrange.interpolate_singleton, Set.finrank_mono, IntermediateField.isPurelyInseparable_sup, Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosed, TensorProduct.toLinearMap_mapInclIsometry, NonUnitalCommCStarAlgebra.toIsScalarTower, mfderivWithin_snd, map_inv_intCast_smul, Function.HasTemperateGrowth.isBigO, Polynomial.eventually_no_roots, NumberField.FinitePlace.norm_def, FormalMultilinearSeries.hasFPowerSeriesOnBall, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, ContinuousLinearMap.coe_mulₗᵢ, deriv_fun_const_smul', OrthogonalFamily.inner_right_dfinsupp, ContinuousLinearMap.isUnit_iff_bijective, NumberField.mixedEmbedding.convexBodySum_mem, balancedCoreAux_empty, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', ClassGroup.equiv_mk, PowerSeries.X_eq_normalizeX, Real.smul_iInf_of_nonneg, UniqueDiffWithinAt.of_real, orthonormal_span, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, Asymptotics.IsBigO.smul_isLittleO, ContinuousLinearMap.innerSL_apply_comp, conformalAt_iff', TensorProduct.lidIsometry_symm_apply, ContinuousLinearMap.instStarOrderedRingRCLike, surjective_stereographic, Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModule, ContinuousLinearMap.mdifferentiableAt, Balanced.smul_mono, NonnegSpectrumClass.iff_spectrum_nonneg, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, Matrix.mulVec_injective_iff_isUnit, hasDerivAt_abs_pos, ContinuousAlternatingMap.instContinuousEvalConst, PiTensorProduct.injectiveSeminorm_def, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, Affine.Simplex.centroid_vsub_eq, hasStrictFDerivAt_id, HilbertBasis.hasSum_repr_symm, PosSMulStrictMono.toPosSMulReflectLT, ContinuousAlternatingMap.norm_image_sub_le, IsGalois.mem_bot_iff_fixed, hasStrictFDerivAt_sub_const, ContinuousLinearMap.coe_deriv₂, IsDedekindDomain.selmerGroup.valuation_ker_eq, IsMIntegralCurveAt.eventually_hasDerivAt, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, IsAlgClosed.exists_aeval_eq_zero, LinearMap.instIsSimpleModuleEndOfNontrivial, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, hasFDerivAt_stereoInvFunAux_comp_coe, LinearIsometryEquiv.comp_hasStrictFDerivAt_iff, LinearMap.adjoint_id, inner_smul_left, contDiff_succ_iff_hasFDerivAt, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, mfderiv_prod_eq_add_apply, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, FiniteField.finrank_extension, Matrix.linearIndependent_rows_iff_isUnit, ValuationSubring.principalUnitGroup_symm_apply, MeasureTheory.condExpL2_indicator_nonneg, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, PadicInt.coe_pow, DoubleCentralizer.add_toProd, PowerSeries.inv_mul_cancel, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, IntermediateField.algebra_adjoin_le_adjoin, HasFDerivWithinAt.sum, TemperedDistribution.smulLeftCLM_apply_apply, X_pow_sub_C_irreducible_iff_of_prime, IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, Subspace.dualPairing_eq, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, hasFDerivAt_pi, NumberField.InfinitePlace.IsUnramified.comap, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, mfderivWithin_comp, Polynomial.map_normalize, FiniteDimensional.span_singleton, fderiv_inner_apply, RatFunc.algebraMap_comp_C, differentiableOn_fst, AffineIsometryEquiv.pointReflection_midpoint_right, hasFDerivWithinAt_snd, finrank_vectorSpan_range_le, Icc_subset_segment, IsBoundedLinearMap.isLinearMap_and_continuous_iff_isBoundedLinearMap, ContMDiff.coordChangeL, RatFunc.ofFractionRing_algebraMap, RatFunc.eval_algebraMap, SeparationQuotient.outCLM_injective, Module.Basis.traceDual_injective, Submodule.map_smul, differentiableWithinAt_finCons, fderiv_const_apply, Real.hasStrictDerivAt_log_of_pos, FormalMultilinearSeries.ofScalars_norm, ContinuousMultilinearMap.norm_ofSubsingleton_id, IsPurelyInseparable.elemExponent_def, HasFDerivWithinAt.fun_mul, hasFTaylorSeriesUpToOn_pi, RCLike.normSq_conj, IsCyclotomicExtension.discr_prime_pow, NNRat.subsingleton_ringHom, HasStrictFDerivAt.smul, ContinuousLinearMap.orthogonal_ker, AnalyticAt.hasStrictDerivAt, LinearMap.ker_smul, Module.Dual.range_eq_top_of_ne_zero, Nonneg.segment_eq_Icc, iter_deriv_pow, Asymptotics.IsThetaTVS.refl, ContinuousLinearMap.continuousAt_uncurry_of_multilinear, inv_add_inv, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, HasStrictFDerivAt.finset_prod, ContMDiff.smul_section, contDiffWithinAt_succ_iff_hasFDerivWithinAt, Filter.EventuallyEq.hasDerivWithinAt_iff, Asymptotics.IsBigO.hasFDerivAt, WeierstrassCurve.Jacobian.isUnit_addU_of_Y_ne, hasFDerivWithinAt_apply, SeminormFamily.basisSets_smul_left, ArchimedeanClass.stdPart_eq_sSup, InnerProductSpace.norm_rankOne, Urysohns.CU.lim_eq_midpoint, LinearMap.instIsStablyFiniteRing, HasFDerivAt.fun_sub, Complex.hasDerivAt_Gamma_nat, Subspace.dualEquivDual_apply, Subfield.mem_comap, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two, ContMDiffMap.coeFnLinearMap_apply, Submodule.isHilbertSumOrthogonal, OnePoint.equivProjectivization_apply_infinity, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, RCLike.inv_re, DoubleCentralizer.neg_fst, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, LinearMap.BilinForm.apply_dualBasis_right, PiTensorProduct.mapLMultilinear_toFun_apply, FunctionField.ringOfIntegers.not_isField, IsAlgClosed.ringHom_bijective_of_isIntegral, HasFiniteFPowerSeriesOnBall.fderiv, ContinuousLinearEquiv.norm_pos, HasFDerivAt.comp, real_inner_I_smul_self, LinearIsometry.lTensor_def, Hyperreal.archimedeanClassMk_epsilon_pos, Finset.dens_pos, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, balancedCore_subset_balancedCoreAux, Orthonormal.inner_right_sum, circleEquivGen_apply, cfcUnits_zpow, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, add_div_eq_mul_add_div, ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff, IntermediateField.finite_of_fg_of_isAlgebraic, minpoly.isIntegrallyClosed_eq_field_fractions', add_div, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Finset.nonneg_subConst, fderiv_eq_smul_deriv, unitary.inner_map_map, NNRat.cast_lt_zero, LinearMap.IsPositive.conj_adjoint, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Polynomial.IsSplittingField.finiteDimensional, LinearMap.ker_toContinuousLinearMap, IntermediateField.isScalarTower_mid, IntermediateField.finSepDegree_bot, ZLattice.comap_refl, hasStrictFDerivAt_exp_smul_const_of_mem_ball, exists_pos_right_iff_sameRay_and_ne_zero, Hyperreal.tendsto_atTop_iff, RCLike.norm_nnqsmul, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, LinearMap.IsSymmetric.pow, hasFDerivAt_prodMk_right, DoubleCentralizer.toProdMulOppositeHom_apply, IsGalois.ofDual_intermediateFieldEquivSubgroup_apply, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', ContinuousLinearMap.coeFn_compLp', gal_X_isSolvable, LinearMap.withSeminorms_induced, RatFunc.num_denom_neg, IsCyclotomicExtension.discr_prime_pow_ne_two', ContinuousLinearEquiv.mfderivWithin_eq, Finpartition.IsEquipartition.card_interedges_sparsePairs_le', MDifferentiableWithinAt.smul_section, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, degree_radical_le, ContMDiffOn.smul_section, curveIntegralFun_zero, perfectClosure.isPurelyInseparable, AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn, iteratedFDeriv_add_apply', hasFDerivAtFilter_intCast, iteratedFDeriv_succ_apply_left, Polynomial.valuation_X_eq_neg_one, hahnEmbedding_isOrderedModule, IsSymmSndFDerivAt.eq, hasFDerivAtFilter_one, Submodule.orthogonalProjectionFn_mem, LinearMap.IsPositive.re_inner_nonneg_left, iteratedFDeriv_const_of_ne, IntermediateField.isSeparable_adjoin_iff_isSeparable, hasDerivWithinAt_sub_const_iff, AbsoluteValue.eq_trivial_of_isEquiv_trivial, Lagrange.eval_basis_not_at_node, ContinuousLinearMapWOT.zero_apply, add_self_div_two, LinearMap.range_lt_top_of_det_eq_zero, FDRep.finrank_hom_simple_simple, AffineSubspace.sOppSide_smul_vsub_vadd_right, HasFDerivWithinAt.list_prod', NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, prod_galRestrict_eq_norm, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', fderiv_inv', LinearMap.BilinForm.isCompl_span_singleton_orthogonal, IntermediateField.sepDegree_top, Module.Basis.traceDual_eq_iff, ContinuousLinearEquiv.contDiff, SeparationQuotient.outCLM_isUniformInducing, ContinuousLinearMapWOT.ext_inner_iff, ContinuousLinearMap.coeFn_ofIsClosedGraph, RatFunc.monic_denom, NormedSpace.exp_eq_expSeries_sum, ZMod.pow_div_two_eq_neg_one_or_one, Trivialization.localFrame_apply_of_mem_baseSet, Continuous.fderiv_one, GaloisField.splits_zmod_X_pow_sub_X, VectorField.mlieBracket_const_smul_right, norm_inner_div_norm_mul_norm_eq_one_iff, MeasureTheory.lpMeas.aestronglyMeasurable, IsLocalMinOn.fderivWithin_eq_zero, tendsto_zero_geometric_tsum_pnat, RCLike.geometric_hahn_banach_open_point, WeierstrassCurve.Affine.Point.map_id, FormalMultilinearSeries.comp_assoc, PiTensorProduct.tprodL_coe, ModelWithCorners.extChartAt_transContinuousLinearEquiv_target, egauge_smul_left, HasFPowerSeriesWithinAt.comp, NNRat.cast_listSum, Submodule.mem_iff_norm_starProjection, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, Real.hasDerivAt_negMulLog, Localization.subalgebra.instIsFractionRingSubtypeMemSubalgebra, LinearMap.BilinForm.span_singleton_sup_orthogonal_eq_top, continuousMultilinearCurryFin1_apply, IsCoercive.antilipschitz, PiLp.hasStrictFDerivAt_toLp, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, LineDifferentiableAt.smul, hasFDerivWithinAt_id, Orthonormal.comp_linearIsometry, hasStrictFDerivAt_euclidean, LinearMap.dualAnnihilator_ker_eq_range_flip, hasFDerivAt_finset_prod, Hyperreal.coeRingHom_toFun, unitary.linearIsometryEquiv_coe_apply, HilbertBasis.finite_spans_dense, nnnorm_cfcₙ_lt, Trivialization.coordChangeL_prod, mfderiv_id, IntermediateField.extendScalars_le_extendScalars_iff, Fintype.expect_eq_sum_div_card, IntermediateField.coe_one, Finset.centerMass_mem_convexHull_of_nonpos, mfderivWithin_comp_of_eq
zpow 📖	CompOp	3 math math: zpow_zero', zpow_neg', zpow_succ'

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
div_eq_mul_inv 📖	mathematical	—	toDiv NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring toSemiring toInv	—	—
inv_zero 📖	mathematical	—	toInv AddMonoid.toZero AddCommMonoid.toAddMonoid NonUnitalNonAssocSemiring.toAddCommMonoid NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring toSemiring	—	—
mul_inv_cancel 📖	mathematical	—	NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring toSemiring toInv Semiring.toOne	—	—
nnqsmul_def 📖	mathematical	—	nnqsmul NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring toSemiring NNRat.cast toNNRatCast	—	—
nnratCast_def 📖	mathematical	—	NNRat.cast toNNRatCast toDiv Semiring.toNatCast toSemiring NNRat.num NNRat.den	—	—
toNontrivial 📖	mathematical	—	Nontrivial	—	—
zpow_neg' 📖	mathematical	—	zpow toInv	—	—
zpow_succ' 📖	mathematical	—	zpow NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring toSemiring	—	—
zpow_zero' 📖	mathematical	—	zpow Semiring.toOne toSemiring	—	—

Field

Definitions

Name	Category	Theorems
nnqsmul 📖	CompOp	1 math math: nnqsmul_def
qsmul 📖	CompOp	1 math math: qsmul_def
toCommRing 📖	CompOp	1527 math math: one_le_div_iff, GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_one, RCLike.conj_re, fderiv_iteratedFDeriv, RCLike.sqrt_eq_ite, FormalMultilinearSeries.comp_rightInv_aux1, ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, FractionalIdeal.spanSingleton_inv_mul, FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_changeOrigin, AddCircle.coe_equivIco_mk_apply, ContinuousMultilinearMap.norm_mkPiRing, RCLike.im_le_neg_norm_iff_eq_neg_I_mul_norm, ContinuousLinearMap.derivWithin_of_bilinear, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, RCLike.one_re, AddCircle.exists_gcd_eq_one_of_isOfFinAddOrder, InnerProductSpace.isPositive_rankOne_self, FractionalIdeal.spanSingleton_mul_inv, ValuativeRel.zero_veq_iff, IntermediateField.exists_algHom_adjoin_of_splits, MvPowerSeries.zero_inv, ordinaryHypergeometric_sum_eq, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, RCLike.map_apply, MDifferentiableOn.clm_postcomp, ContinuousLinearMap.analyticWithinAt_bilinear, strictConvexOn_iff_slope_strict_mono_adjacent, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuous₂, RCLike.geometric_hahn_banach_point_open, FormalMultilinearSeries.comp_partialSum, selfAdjoint.val_div, Filter.Tendsto.div_atTop, AnalyticOn.exists_hasFTaylorSeriesUpToOn, tendsto_const_mul_pow_nhds_iff', Real.hasFDerivAt_fourierChar_neg_bilinear_left, RCLike.reCLM_apply, HahnSeries.mem_cardSuppLTSubfield, nnratCast_def, RCLike.div_re_ofReal, ValuationSubring.image_maximalIdeal, RCLike.separate_convex_open_set, Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col, InnerProductSpace.rankOne_one_left_eq_innerSL, ContDiff.fderiv_succ, Function.FactorizedRational.divisor, inv_atBot₀, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, ContinuousLinearMap.map_add_add, convex_iff_ordConnected, FormalMultilinearSeries.changeOriginSeries_sum_eq_partialSum_of_finite, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, IntermediateField.coe_algebraMap_over_bot, fderivWithin_fderivWithin_eq_of_mem_nhdsWithin, ContinuousLinearMap.toLinearMap₁₂_injective, Asymptotics.IsEquivalent.multisetProd, MDifferentiableAt.cle_arrowCongr, discrim_eq_zero_iff, ContinuousLinearMap.continuousSMul, RCLike.re_add_im, hasFTaylorSeriesUpToOn_top_iff_right, InnerProductSpace.Core.inner_mul_inner_self_le, concaveOn_iff_slope_anti_adjacent, arithGeom_eq', ContinuousMultilinearMap.analyticAt_uncurry_of_linear, ContDiff.iteratedFDeriv_right, InnerProductSpace.isIdempotentElem_rankOne_self, IntermediateField.isScalarTower_mid', FractionalIdeal.map_one_div, one_le_pow_mul_abs_eval_div, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Asymptotics.SuperpolynomialDecay.param_inv_mul, Submodule.re_inner_starProjection_eq_normSq, ValuationSubring.valuation_le_iff, ContinuousLinearMap.precompUniformConvergenceCLM_apply, quasispectrumRestricts_iff_spectrumRestricts_inr', IntermediateField.coe_prod, LinearMap.IsPositive.re_inner_nonneg_right, ContDiffAt.fderiv_right_succ, LinearMap.IsSymmetric.im_inner_self_apply, AnalyticOnNhd.iteratedFDeriv_of_isOpen, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, traceForm_nondegenerate_tfae, RCLike.sub_conj, iteratedFDerivWithin_succ_eq_comp_right, RCLike.re_sqrt_ofReal, Matrix.Pivot.listTransvecCol_mul_last_col, RCLike.pos_iff, Subfield.multiset_prod_mem, SeminormFamily.filter_eq_iInf, FractionalIdeal.instNontrivialNonZeroDivisors, HasFTaylorSeriesUpTo.hasFDerivAt, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, Unitization.splitMul_apply, geom₂_sum, ContMDiffOn.clm_postcomp, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Set.image_const_mul_uIcc, FormalMultilinearSeries.le_changeOriginSeries_radius, CauSeq.abv_pos_of_not_limZero, FormalMultilinearSeries.derivSeries_coeff_one, ContinuousLinearMap.opNorm_lsmul_apply_le, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Polynomial.SplittingFieldAux.succ, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, Filter.tendsto_const_mul_atBot_iff_neg, HahnSeries.single_zero_ofScientific, FractionalIdeal.isFractional_div_of_ne_zero, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, RCLike.ofReal_re, Height.logHeight₁_sum_le, AnalyticOn.iteratedFDerivWithin, ValuativeRel.inv_srel_one, Finpartition.IsEquipartition.card_biUnion_offDiag_le', Height.logHeight₁_add_le, RCLike.re_add_im_ax, ContinuousAlternatingMap.piLIE_apply_apply, IntermediateField.botEquiv_symm, RCLike.is_real_TFAE, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, tendsto_bdd_div_atTop_nhds_zero, FractionalIdeal.invertible_of_principal, ContinuousLinearMap.isometry_mul_flip, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, Subfield.relfinrank_eq_finrank_of_le, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, HasFDerivWithinAt.linear_multilinear_comp, Polynomial.SplittingFieldAux.algebraMap_succ, iteratedFDerivWithin_succ_eq_comp_left, ContFract.convs_eq_convs', RCLike.abs_im_div_norm_le_one, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, contDiffOn_iff_continuousOn_differentiableOn, norm_sub_mul_self, Height.fun_mulHeight_zero, ContinuousLinearMap.hasDerivWithinAt_of_bilinear, ValuationSubring.nonunits_subset, Bundle.ContinuousLinearMap.vectorBundle, starConvex_iff_ordConnected, Matrix.IsHermitian.eigenvalues_eq, exists_pos_right_iff_sameRay, AddCircle.homeomorphAddCircle_apply_mk, iter_deriv_zpow', im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, ConvexOn.univ_sSup_of_countable_affine_eq, IntermediateField.exists_algHom_of_adjoin_splits, InnerProductSpace.inner_left_rankOne_apply, ConditionallyCompleteLinearOrderedField.toZeroLEOneClass, ContinuousAlternatingMap.curryLeft_smul, RCLike.ofNat_re, FractionalIdeal.div_one, ContMDiffAt.clm_postcomp, ContMDiffWithinAt.clm_postcomp, Ring.choose_eq_smul, zpow_two_nonneg, FractionalIdeal.spanFinset_eq_zero, ContDiffAt.fderiv_succ, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, RCLike.nonpos_iff, RCLike.smul_re, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, HasFPowerSeriesAt.comp, InnerProductSpace.rankOne_apply, segment_eq_uIcc, IntermediateField.isScalarTower, HasFTaylorSeriesUpToOn.zero_eq', mul_inv_cancel, Nat.ceil_le_two_mul, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, WithSeminorms.withSeminorms_eq, ContinuousMultilinearMap.norm_smulRightL_le, AnalyticOnNhd.iteratedFDeriv, ContinuousLinearMap.precompL_apply, openSegment_eq_Ioo, RCLike.abs_re_le_norm, IntermediateField.adjoin_zero, RCLike.geometric_hahn_banach_closed_point, FractionalIdeal.le_div_iff_mul_le, exists_nonneg_left_iff_sameRay, AEMeasurable.im, FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal, MDifferentiable.clm_postcomp, iteratedDeriv_scomp_eq_sum_orderedFinpartition, NormedField.norm_mul, IntermediateField.lift_adjoin_simple, Algebra.isIntegral_trace, RCLike.norm_sq_eq_def_ax, ContinuousLinearMap.toSesqForm_apply_coe, HasFPowerSeriesWithinOnBall.fderivWithin, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, IntermediateField.coe_add, FractionalIdeal.coeIdeal_inj, SimpleGraph.farFromTriangleFree_iff, IntermediateField.prod_mem, FractionalIdeal.isNoetherian_coeIdeal, extDeriv_fun_smul, zpow_neg_two_nonneg, ContinuousAlternatingMap.toAlternatingMap_curryLeft, ContinuousLinearMap.toLinearMap₁₂_apply, VectorFourier.fourierPowSMulRight_eq_comp, RCLike.intCast_re, inv_lt_zero', ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, LinearOrderedField.inducedOrderRingIso_self, RCLike.im_eq_zero_iff_isSelfAdjoint, ContinuousLinearMap.opNorm_mul, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, inner_mul_inner_self_le, Algebra.IsAlgebraic.tower_top, MDifferentiable.cle_arrowCongr, PointwiseConvergenceCLM.postcomp_apply, Unitization.nnnorm_def, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, RCLike.mul_im_ax, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, InnerProductSpace.Core.norm_eq_sqrt_re_inner, FractionalIdeal.eq_zero_or_one_of_isField, ConditionallyCompleteLinearOrderedField.toPosMulStrictMono, Nat.ceil_le_mul, PiTensorProduct.mapL_smul, RCLike.abs_re_div_norm_le_one, norm_sub_sq, FormalMultilinearSeries.ofScalars_eq_zero, ContinuousAlternatingMap.instContinuousSMul, RCLike.I_re_ax, FractionalIdeal.inv_nonzero, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, SameRay.exists_eq_smul_add, IntermediateField.coe_inclusion, PiTensorProduct.projectiveSeminorm_apply, Nonneg.segment_eq_uIcc, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, RCLike.re_nonneg_of_nonneg, FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop, Finset.mem_convexHull', LinearMap.IsSymmetric.coe_re_inner_self_apply, FractionalIdeal.le_div_iff_of_ne_zero, Meromorphic.prod, div_neg_iff, OrderRingIso.eq_refl, div_le_one_iff, GenContFract.abs_sub_convergents_le', isBoundedBilinearMap_comp, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, Int.ceil_lt_two_mul, FractionalIdeal.le_div_iff_of_nonzero, GenContFract.compExactValue_correctness_of_stream_eq_some_aux_comp, Matrix.Pivot.mul_listTransvecRow_last_col, arithGeom_zero_eq_mul_div', MeromorphicOn.prod, FractionalIdeal.div_of_ne_zero, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, Odd.zpow_nonpos_iff, FractionalIdeal.inv_eq, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, EulerProduct.eulerProduct_completely_multiplicative, contDiff_succ_iff_fderiv, Nat.ceil_lt_two_mul, mul_sub_mul_div_mul_nonpos_iff, FractionalIdeal.mem_div_iff_of_nonzero, ContinuousLinearMap.mulLeftRight_apply, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField, SameRay.exists_eq_smul, ContinuousMultilinearMap.curryRight_norm, ContinuousLinearMap.analyticOn_bilinear, openSegment_eq_Ioo', MDifferentiableAt.clm_postcomp, RegularNormedAlgebra.isometry_mul', ContDiffWithinAt.hasFDerivWithinAt_nhds, inner_re_zero_right, QuasispectrumRestricts.map_zero, archimedean_iff_nat_le, OrderRingIso.subsingleton_right, hasFDerivAt_ringInverse, VectorFourier.fourierIntegral_iteratedFDeriv, isAlgebraic_rat, InnerProductSpace.nnnorm_rankOne, ContinuousLinearEquiv.arrowCongr_apply, RingPreordering.instIsPrimeSupport, ContinuousLinearMap.toUniformConvergenceCLM_apply, ContinuousAlternatingMap.curryLeft_apply_apply, ContinuousLinearMap.flip_smul, exists_basis_of_pairing_ne_zero, Unitization.quasispectrum_inr_eq, InnerProductSpace.isSymmetricProjection_rankOne_self, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, RCLike.re_monotone, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, FormalMultilinearSeries.ofScalars_add, Finset.centerMass_filter_ne_zero, RCLike.im_ofReal_pow, FloorSemiring.tendsto_pow_div_factorial_atTop, IntermediateField.equivOfEq_symm, ValuativeRel.div_vle_one_iff, selfAdjoint.val_zpow, Asymptotics.IsTheta.finsetProd, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, WeakDual.CharacterSpace.continuousMapEval_bijective, LowerSemicontinuousOn.isClosed_re_epigraph, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, HasFPowerSeriesOnBall.fderiv_eq, FractionalIdeal.one_div_spanSingleton, inner_self_im, ValuationSubring.nonunits_injective, IntermediateField.fieldRange_comp_val, PiTensorProduct.projectiveSeminorm_tprod_le, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, ValuativeRel.one_rel_inv, Module.Basis.traceDual_def, FractionalIdeal.fractional_div_of_nonzero, ContinuousLinearMap.fderiv_of_bilinear, Height.AdmissibleAbsValues.isNonarchimedean, IntermediateField.equivOfEq_rfl, iteratedFDerivWithin_succ_apply_right, ContinuousAlternatingMap.alternatizeUncurryFin_smul, contDiffAt_map_inverse, ValuativeRel.div_vle_iff, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, TrivSqZeroExt.eq_smul_exp_of_ne_zero, inner_re_zero_left, convexHull_basis_eq_stdSimplex, Module.Basis.trace_traceDual_mul, Filter.tendsto_const_mul_atBot_iff, AnalyticOn.fderivWithin, ContinuousLinearMap.opNorm_mul_apply, ContinuousLinearMap.norm_smulRightL, inner_self_ofReal_re, Set.preimage_mul_const_uIcc, Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec, ContDiffAt.fderiv_right, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousMultilinearMap.curryLeft_norm, InnerProductSpace.trace_rankOne, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, MDifferentiableWithinAt.cle_arrowCongr, RCLike.imLm_coe, Valuation.HasExtension.ofComapInteger, MDifferentiableWithinAt.clm_precomp, SimpleGraph.farFromTriangleFree.le_card_sub_card, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, ContDiffOn.fderiv_of_isOpen, Finset.centerMass_insert, isBoundedBilinearMap_compMultilinear, ConditionallyCompleteLinearOrderedField.toIsOrderedCancelAddMonoid, RCLike.div_im, SimpleGraph.isUniform_singleton, SimpContFract.determinant, Function.FactorizedRational.meromorphicOrderAt_eq, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, LinearOrderedField.cutMap_add, ContDiffAt.iteratedFDeriv_right, HasFPowerSeriesWithinAt.fderivWithin_eq, inCoordinates_apply_eq₂, RCLike.im_to_real, AnalyticOnNhd.fderiv_of_isOpen, FormalMultilinearSeries.id_comp', contDiffOn_infty_iff_fderivWithin, ContinuousLinearMap.flip_apply, CPolynomialOn.iteratedFDeriv, IntermediateField.adjoin_simple_adjoin_simple, Convex.mem_Ioo, RCLike.ext_iff, fderiv_inverse, FractionalIdeal.count_ne_zero, HasFPowerSeriesOnBall.fderiv, ContMDiffOn.clm_precomp, ContinuousMultilinearMap.restrictScalarsLinear_apply, contDiffOn_nat_iff_continuousOn_differentiableOn, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, IntermediateField.multiset_prod_mem, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, IntermediateField.range_val, InnerProductSpace.rankOne_eq_zero, Ideal.image_subset_nonunits_valuationSubring, Module.Basis.trace_mul_traceDual, Function.FactorizedRational.finprod_eq_fun, ContinuousAlternatingMap.norm_curryLeft, Asymptotics.IsEquivalent.finsetProd, Matrix.Pivot.listTransvecCol_getElem, RCLike.re_eq_norm_of_mul_conj, InnerProductSpace.inner_right_rankOne_apply, ContDiff.differentiable_iteratedFDeriv, ContinuousAlternatingMap.apply_apply, fderivWithin_inv', Polynomial.natDegree_removeFactor, HahnSeries.cardSuppLTSubfield_carrier, MvPowerSeries.coeff_inv, RCLike.conj_eq_iff_re, ContinuousLinearMap.fderivWithin_of_bilinear, IntermediateField.add_mem, PiTensorProduct.liftIsometry_tprodL, contDiffWithinAt_iff_of_ne_infty, UniformConvergenceCLM.continuousSMul, ValuativeRel.one_vle_div_iff, PiTensorProduct.injectiveSeminorm_le_projectiveSeminorm, ConvexOn.sSup_of_countable_affine_eq, AddCircle.addOrderOf_div_of_gcd_eq_one, Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero, InnerProductSpace.rankOne_eq_rankOne_iff_comm, RCLike.ofNat_mul_re, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, IntermediateField.lift_top, ContinuousLinearMap.precompR_apply, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, FormalMultilinearSeries.iteratedFDerivSeries_eq_zero, ordinaryHypergeometricSeries_apply_eq', InnerProductSpace.Core.inner_im_symm, ValuativeRel.rel_zero_iff, DirectLimit.exists_inv, iteratedFDerivWithin_eq_equiv_comp, dist_center_homothety, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, FormalMultilinearSeries.mkPiRing_coeff_eq, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, AlgebraicIndependent.lift_reprField, RCLike.conj_I_ax, GenContFract.zero_le_of_den, Polynomial.hilbertPoly_succ, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux, SameRay.exists_pos_right, RCLike.I_eq_zero_or_im_I_eq_one, gcd_zero_eq, Height.logHeight_zero, Height.mulHeight₁_add_le, ContinuousLinearMap.hasStrictDerivAt_of_bilinear, PointwiseConvergenceCLM.isInducing_inducingFn, ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier, zpow_two_pos_of_ne_zero, SimpleGraph.FarFromTriangleFree.nonpos, DirectLimit.nontrivial, ContinuousLinearEquiv.arrowCongr_symm, IntermediateField.coe_mul, ContinuousLinearMap.isBoundedBilinearMap, Filter.tendsto_mul_const_atTop_iff_neg, FractionalIdeal.div_nonzero, RCLike.le_iff_re_im, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, Affine.Simplex.mongePlane_def, ContinuousAlternatingMap.ofSubsingletonLIE_apply, Asymptotics.IsLittleO.multisetProd, FormalMultilinearSeries.compAlongComposition_bound, continuousMultilinearCurryRightEquiv_symm_apply, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, ContinuousLinearMap.bilinearComp_zero_right, zpow_zero', ContDiffWithinAt.fderivWithin'', AddCircle.equivAddCircle_apply_mk, ValuativeRel.one_rel_div_iff, Subfield.prod_mem, Height.fun_logHeight_zero, InnerProductSpace.rank_rankOne, ContMDiffOn.cle_arrowCongr, IsFractionRing.num_eq_zero, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, ContinuousLinearMap.adjointAux_apply, Int.fract_div_mul_self_add_zsmul_eq, RCLike.measurable_re, LocalSubring.instAtPrimeSubtypeMemSubringToSubringOfPrime, real_inner_eq_re_inner, RCLike.add_conj, RCLike.ofReal_re_ax, InnerProductSpace.Core.inner_self_eq_norm_mul_norm, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, RCLike.im_eq_conj_sub, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, segment_eq_Icc', InnerProductSpace.rankOne_def, arithGeom_same_eq_mul_div', EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers, RCLike.conj_im_ax, ContinuousLinearMap.coe_flipₗᵢ', div_eq_quo_add_sum_rem_div, PiTensorProduct.norm_eval_le_injectiveSeminorm, contDiffOn_succ_iff_fderiv_of_isOpen, fderivWithin_fderivWithin_eq_of_mem_nhds, contDiff_iff_continuous_differentiable, tendsto_pow_div_pow_atTop_zero, Finset.centerMass_smul_left, iter_deriv_zpow, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, tendsto_inv_atBot_nhdsLT_zero, SimpleGraph.IsUniform.pos, ContinuousMultilinearMap.prodL_apply, hasFTaylorSeriesUpToOn_succ_iff_right, ContinuousLinearMap.coe_flipMultilinearEquiv, NonUnitalAlgHom.coe_Lmul, ContinuousMultilinearMap.norm_map_init_le, Polynomial.SplittingFieldAux.scalar_tower', LinearOrderedField.inducedOrderRingHom_toFun, Set.image_mul_const_uIcc, RCLike.im_mul_ofReal, fderivWithin_fderivWithin_eq_of_eventuallyEq, EulerProduct.eulerProduct_completely_multiplicative_tprod, PiTensorProduct.liftEquiv_symm_apply, RCLike.geometric_hahn_banach_point_point, extDerivWithin_fun_smul, toIcoDiv_zero_one, LinearMap.span_singleton_sup_ker_eq_top, concaveOn_iff_div, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Int.ceil_lt_mul, eq_pos_convex_span_of_mem_convexHull, iteratedDerivWithin_scomp_eq_sum_orderedFinpartition, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, WithSeminorms.topology_eq_withSeminorms, segment_eq_Icc, OrderRingIso.subsingleton_left, FractionalIdeal.coe_ideal_span_singleton_div_self, HasFPowerSeriesWithinOnBall.hasSum_derivSeries_of_hasFDerivWithinAt, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, MonomialOrder.span_leadingTerm_eq_span_monomial', LinearMap.extendTo𝕜'_apply_re, iteratedDerivWithin_zpow, RCLike.re_to_real, FractionalIdeal.mul_generator_self_inv, ContinuousLinearMap.norm_precompR_le, DirectLimit.mul_inv_cancel, RCLike.neg_iff, IntermediateField.lift_inf, ContinuousLinearMap.isBoundedLinearMap_comp_right, RCLike.sqrt_eq_real_add_ite, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, RCLike.inv_im, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, PiTensorProduct.liftEquiv_apply, hasFTaylorSeriesUpTo_top_iff', fderivWithin_iteratedFDerivWithin, Height.mulHeight_zero, RCLike.ofReal_prod, ContinuousLinearMap.deriv_of_bilinear, sum_embeddings_eq_finrank_mul, henselian, IntermediateField.exists_algHom_of_splits, strictConvex_iff_convex, one_lt_div_iff, IsBoundedBilinearMap.isBoundedLinearMap_deriv, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, InnerProductSpaceable.inner_.norm_sq, ConvexOn.sSup_of_nat_affine_eq, ContinuousLinearMap.postcomp_apply, ContinuousLinearMap.prodMapL_apply, ContinuousLinearMap.uncurryLeft_apply, IntermediateField.restrictScalars_adjoin_eq_sup, RCLike.one_im, tendsto_inv_atBot_zero, RCLike.natCast_re, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, slope_pos_iff, contMDiffOn_continuousLinearMapCoordChange, Function.FactorizedRational.meromorphicNFOn_univ, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, InnerProductSpace.Core.inner_self_nonneg, RCLike.ofReal_finsuppProd, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, IntermediateField.Lifts.lt_iff, inner_re_symm, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, IntermediateField.extendScalars_le_iff, NormedField.dist_eq, IntermediateField.coe_sum, ContinuousMultilinearMap.apply_apply, ContDiff.smulRight, Rat.cast_finsuppProd, ContinuousMultilinearMap.flipLinear_apply_apply, RCLike.norm_le_re_iff_eq_norm, div_nonpos_iff, FormalMultilinearSeries.comp_id, FormalMultilinearSeries.cpolynomialAt_changeOrigin_of_finite, hasFTaylorSeriesUpTo_succ_nat_iff_right, FractionalIdeal.num_le_mul_inv, IntermediateField.coe_val, RCLike.ofReal_im, ContinuousLinearMap.uncurryBilinear_apply, iccHomeoI_apply_coe, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, RCLike.abs_im_le_norm, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, dist_homothety_self, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, iteratedFDeriv_eq_equiv_comp, tendsto_arithGeom_atTop_of_one_lt, sum_Ioo_inv_sq_le, ValuationSubring.nonunits_le_nonunits, Unitization.norm_eq_sup, RCLike.nonneg_iff, hasFTaylorSeriesUpToOn_succ_nat_iff_right, EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers, FloorRing.archimedean, FractionalIdeal.coe_inv_of_ne_zero, ordinaryHypergeometric_eq_tsum, RCLike.continuous_re, nndist_center_homothety, hasFDerivWithinAt_comp_smul_smul_iff, Rat.cast_multiset_prod, FractionalIdeal.isNoetherian_zero, Height.mulHeight₁_sum_le, IntermediateField.list_sum_mem, exists_nonneg_right_iff_sameRay, Bundle.ContinuousLinearMap.vectorPrebundle.isContMDiff, iteratedFDerivWithin_two_apply', FractionalIdeal.coeIdeal_injective, Polynomial.int_eval₂_eq, RCLike.zero_re, InnerProductSpace.Core.inner_re_symm, RCLike.smul_im, SimpleGraph.not_isUniform_iff, Rat.cast_det, dist_self_homothety, contDiffWithinAt_succ_iff_hasFDerivWithinAt', contDiffOn_succ_iff_hasFDerivWithinAt, GenContFract.convs_succ, ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', FormalMultilinearSeries.radius_unshift, HasFPowerSeriesAt.fderiv_eq, mul_sub_mul_div_mul_neg, arithGeom_eq, RCLike.re_eq_add_conj, continuousMultilinearCurryFin0_apply, PiTensorProduct.dualSeminorms_bounded, FractionalIdeal.map_eq_zero_iff, Function.FactorizedRational.analyticAt, extDeriv_smul, PointwiseConvergenceCLM.coeLMₛₗ_apply, ContinuousLinearMap.postcompCompactConvergenceCLM_apply, ContinuousMultilinearMap.curryMidEquiv_apply, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, HahnSeries.cardSupp_div_le, ContinuousLinearMap.reApplyInnerSelf_apply, DoubleCentralizer.algebraMap_snd, InfiniteGalois.restrict_fixedField, iteratedFDerivWithin_succ_apply_left, inner_self_eq_norm_mul_norm, IsStrictOrderedRing.topologicalRing, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvalues₀, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, round_eq, Polynomial.Chebyshev.iterate_derivative_U_eval_one_dvd, ConditionallyCompleteLinearOrderedField.to_archimedean, contDiffOn_infty_iff_fderiv_of_isOpen, EulerProduct.eulerProduct_completely_multiplicative_hasProd, Polynomial.Chebyshev.iterate_derivative_T_eval_one_dvd, ContinuousLinearMap.map_sub₂, ContinuousLinearMap.bilinearComp_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, Filter.tendsto_mul_const_atTop_iff, circleEquivGen_symm_apply, LinearMap.re_inner_adjoint_mul_self_nonneg, PointwiseConvergenceCLM.coeLM_apply, HasFTaylorSeriesUpToOn.fderivWithin, IntermediateField.restrictScalars_bot_eq_self, DoubleCentralizer.algebraMap_toProd, ValuationSubring.zero_mem, MeasureTheory.Integrable.re_im_iff, FormalMultilinearSeries.id_comp, Finset.mem_convexHull, ContinuousLinearMap.norm_map_tail_le, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, Finpartition.coe_energy, PiTensorProduct.injectiveSeminorm_apply, ValuativeRel.inv_rel_one, ContinuousLinearMap.isBoundedLinearMap_comp_left, LinearIsometryEquiv.toLinearEquiv_smul, FractionalIdeal.spanSingleton_div_spanSingleton, norm_fderiv_iteratedFDeriv, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, IntermediateField.mem_lift, Measurable.im, Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder, RCLike.norm_im_le_norm, ContMDiffAt.clm_precomp, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, iter_deriv_pow', ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, ConvexOn.convex_re_epigraph, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, ValuationSubring.valuation_eq_iff, ordinaryHypergeometricSeries_apply_eq, RCLike.sqrt_of_nonneg, HasFTaylorSeriesUpToOn.hasFDerivAt, IntermediateField.list_prod_mem, ContinuousLinearMap.flip_add, exists_pos_left_iff_sameRay, Polynomial.Chebyshev.derivative_U_eval_one_dvd, LinearMap.isPositive_iff_complex, inner_self_eq_norm_sq, RCLike.lipschitzWith_re, ContinuousMultilinearMap.uncurryRight_apply, Measurable.re, Asymptotics.IsTheta.multisetProd, ContinuousLinearMap.bilinearComp_zero, Convex.mem_toCone, inv_sub_inv, LinearOrderedField.inducedMap_add, IntermediateField.coe_zero, iteratedDeriv_eq_equiv_comp, Finset.convexHull_eq, norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, IntermediateField.instIsScalarTowerSubtypeMem_1, arithGeom_same_eq_mul_div, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, MeasureTheory.AEStronglyMeasurable.re, ValuationSubring.add_mem, RCLike.I_im, ArchimedeanClass.mk_ratCast, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, Asymptotics.superpolynomialDecay_mul_param_pow_iff, ContinuousLinearMap.le_opNorm₂, ContinuousLinearMap.norm_uncurryMid, FractionalIdeal.mul_one_div_le_one, InnerProductSpace.rankOne_def', ContinuousLinearMap.opNorm_mul_le, ContinuousLinearMap.uncurryLeft_norm, ContDiffWithinAt.fderivWithin', Int.ceil_le_two_mul, Pretrivialization.continuousLinearMap.isLinear, IsFractionRing.eq_zero_of_num_eq_zero, contDiffAt_succ_iff_hasFDerivAt, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, IntermediateField.lift_injective, FractionalIdeal.coeIdeal_eq_one, Asymptotics.IsBigO.multisetProd, RCLike.ofNat_mul_im, selfAdjoint.val_inv, FormalMultilinearSeries.compAlongComposition_norm, ContinuousLinearMap.isometry_mul, RCLike.isCauSeq_im, Matrix.Pivot.mul_listTransvecRow_last_row, InnerProductSpace.norm_sq_eq_re_inner, LocalSubring.le_ofPrime, archimedean_iff_nat_lt, ContinuousLinearMap.continuous_uncurry_of_multilinear, dist_homothety_center, ValuativeRel.vle_zero_iff, MDifferentiableOn.cle_arrowCongr, Filter.tendsto_const_mul_pow_atBot_iff, Ioo_subset_openSegment, Unitization.norm_def, Asymptotics.IsBigO.finsetProd, ValuativeRel.one_vlt_inv, tendsto_nhdsLT_zero_of_comp_inv_tendsto_atBot, RCLike.hasSum_re, ContinuousAlternatingMap.curryLeft_same, FractionalIdeal.isPrincipal_inv, ContinuousMultilinearMap.curryRight_apply, ValuationSubring.coe_mem_nonunits_iff, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, ValuationSubring.mem_nonunits_iff_exists_mem_maximalIdeal, FractionalIdeal.map_div, MDifferentiableAt.clm_precomp, DoubleCentralizer.coeHom_apply, ContinuousAlternatingMap.curryLeft_zero, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, ContinuousAlternatingMap.restrictScalarsLI_apply, Odd.zpow_nonneg_iff, FractionalIdeal.map_inv, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, iteratedFDeriv_succ_apply_right, FormalMultilinearSeries.leftInv_coeff_one, MeromorphicAt.prod, mdifferentiableOn_continuousLinearMapCoordChange, LinearOrderedField.inducedMap_zero, RCLike.mul_im_I_ax, PointwiseConvergenceCLM.precomp_apply, Polynomial.div_eq_quo_add_rem_div, Nat.one_sub_one_div_cast_nonneg, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, add_sub_div_two_lt, InnerProductSpace.isStarProjection_rankOne_self, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, Valuation.valuationSubring.integers, Set.preimage_const_mul_uIcc, HasFPowerSeriesAt.hasFDerivAt, AlgebraicIndependent.liftAlgHom_comp_reprField, Rat.cast_nonneg, Filter.tendsto_const_mul_atTop_iff_neg, PreInnerProductSpace.Core.re_inner_nonneg, IntermediateField.inclusion_self, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, IntermediateField.lift_bot, FractionalIdeal.exists_ne_zero_mem_isInteger, AbsoluteValue.hasBasis_uniformity, ArchimedeanClass.mk_le_mk_iff_ratCast, RCLike.re_mul_ofReal, IsFractionRing.restrictScalars_fieldEquivOfAlgEquiv, Matrix.Pivot.listTransvecCol_mul_last_row_drop, PiTensorProduct.mapLMultilinear_apply_apply, isBoundedBilinearMap_apply, ratCast_def, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational, inv_nhdsLT_zero, ContinuousLinearMap.IsInvertible.contDiffAt_map_inverse, hasStrictFDerivAt_ringInverse, ContinuousLinearMap.mul_apply', tendsto_const_mul_pow_nhds_iff, RCLike.im_tsum, GenContFract.le_of_succ_succ_get?_contsAux_b, InnerProductSpace.rankOne_comp_rankOne, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem, Module.Basis.traceDual_involutive, RCLike.norm_re_le_norm, ValuationSubring.mul_mem, re_inner_self_pos, Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row, IntermediateField.le_extendScalars_iff, InnerProductSpace.rankOne_comp, IsRealClosed.toIsSemireal, MeromorphicAt.fun_prod, FormalMultilinearSeries.apply_eq_prod_smul_coeff, InnerProductSpace.toMatrix_rankOne, Function.FactorizedRational.log_norm_meromorphicTrailingCoeffAt, PiTensorProduct.liftIsometry_comp_mapL, MvPowerSeries.inv_eq_zero, OrderRingIso.apply_eq_self, slope_pos_iff_gt, RCLike.geometric_hahn_banach_open, InnerProductSpace.isSymmetric_rankOne_self, Polynomial.natDegree_removeFactor', Positive.coe_inv, Rat.cast_nonpos, archimedean_iff_rat_le, continuousMultilinearCurryLeftEquiv_apply, selfAdjoint.val_qsmul, Algebra.trace_surjective, precomp_compactConvergenceCLM_apply, IntermediateField.inclusion_injective, ContinuousAlternatingMap.restrictScalarsCLM_apply, ValuativeRel.div_rel_one_iff, SimpleGraph.le_card_nonuniformWitness, AnalyticOnNhd.fderiv, PiTensorProduct.liftIsometry_symm_apply, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, InnerProductSpace.Core.inner_mul_symm_re_eq_norm, ContDiffWithinAt.differentiableWithinAt_iteratedFDerivWithin, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear, iteratedFDeriv_succ_eq_comp_right, ContinuousMultilinearMap.changeOriginSeries_support, ValuationSubring.inv_mem_nonunits_iff, AbsoluteValue.tendsto_div_one_add_pow_nhds_one, LinearOrderedField.inducedOrderRingIso_symm, FractionalIdeal.isNoetherian_iff, IsFractionRing.mk'_eq_zero_iff_eq_zero, DoubleCentralizer.algebraMap_fst, RCLike.re_le_re, RCLike.reLm_coe, fderiv_continuousLinearEquiv_comp, inv_zero, quasispectrumRestricts_iff_spectrumRestricts_inr, ContDiffOn.fderivWithin, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, RCLike.natCast_im, RingPreordering.instHasIdealSupport, MeasureTheory.MemLp.re, RCLike.ratCast_re, MeasureTheory.AEStronglyMeasurable.im, RCLike.ofReal_eq_re_of_isSelfAdjoint, Filter.tendsto_mul_const_atBot_iff_pos, Matrix.IsHermitian.coe_re_apply_self, MeasureTheory.Integrable.re, IsBoundedBilinearMap.toContinuousLinearMap_apply, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, mul_sub_mul_div_mul_nonpos, HasFPowerSeriesWithinOnBall.fderivWithin_eq, ContinuousMultilinearMap.piₗᵢ_symm_apply, integral_coe_re_add_coe_im, IntermediateField.LinearDisjoint.linearIndependent_right, RCLike.lt_iff_re_im, ContDiff.iteratedFDeriv_right', NumberField.linearDisjoint_of_isGalois_isCoprime_discr, ConvexOn.univ_sSup_affine_eq, SimpContFract.of_isContFract, tendsto_const_mul_zpow_atTop_zero, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, SameRay.exists_nonneg_left, Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow, FormalMultilinearSeries.radius_shift, norm_add_sq, RCLike.norm_sq_re_conj_add, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, AffineMap.homothety_isOpenMap, FractionalIdeal.mul_inv_cancel_iff, WeakDual.ker_isMaximal, FractionalIdeal.coe_ideal_span_singleton_inv_mul, ValuationSubring.mem_nonunits_iff_or, strictConvex_iff_ordConnected, contDiff_nat_iff_continuous_differentiable, norm_add_mul_self, IsFractionRing.num_zero, RCLike.conj_im, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, Subfield.relrank_eq_rank_of_le, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, ContinuousLinearMap.opNorm_lsmul_le, FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal, Matrix.Pivot.mul_listTransvecRow_last_col_take, Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero, InnerProductSpace.Core.inner_self_ofReal_re, FractionalIdeal.coe_inv_of_nonzero, ContinuousLinearMap.norm_compL_le, RCLike.hasSum_iff, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, RCLike.measurable_im, Odd.zpow_pos_iff, ValuativeRel.vle_div_iff, IntermediateField.topEquiv_symm_apply_coe, FractionalIdeal.spanFinset_coe, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, RCLike.re_eq_ofReal_of_isSelfAdjoint, ContinuousLinearMap.opNNNorm_mul_flip_apply, Finset.centerMass_ite_eq, IntermediateField.multiset_sum_mem, FractionalIdeal.div_spanSingleton, HasFPowerSeriesOnBall.hasFDerivAt, FirstOrder.Field.instModelField, ContinuousMultilinearMap.curryMid_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, Matrix.PosSemidef.re_dotProduct_nonneg, ContMDiff.clm_postcomp, IntermediateField.intermediateFieldMap_apply_coe, IntermediateField.topEquiv_apply, selfAdjoint.val_ratCast, iccHomeoI_symm_apply_coe, ContinuousLinearEquiv.arrowCongrSL_apply, crossProduct_ne_zero_iff_linearIndependent, MDifferentiableWithinAt.clm_postcomp, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, ValuativeRel.veq_zero_iff, iteratedDeriv_comp_eq_sum_orderedFinpartition, FormalMultilinearSeries.analyticAt_changeOrigin, mem_convexHull_iff_exists_fintype, ContinuousLinearMap.opNorm_mul_apply_le, RCLike.re_le_norm, Matrix.Pivot.listTransvecCol_mul_last_row, ContinuousLinearMap.isPositive_iff_complex, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply, ValuativeRel.valuation_surjective, round_le_add_half, HasFDerivAt.linear_multilinear_comp, Odd.zpow_neg_iff, OnePoint.exists_mem_SL2, NumberField.mixedEmbedding.logMap_apply, logDeriv_prod, meromorphicTrailingCoeffAt_prod, RCLike.ofNat_im, Rat.cast_lt_zero, convex_iff_div, HahnSeries.single_div_single, IntermediateField.mul_mem, SimpleGraph.right_nonuniformWitnesses_card, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, zpow_succ', tendsto_inv_nhdsLT_zero, ContinuousMultilinearMap.compContinuousLinearMapL_apply, MeromorphicOn.extract_zeros_poles, ContinuousLinearMap.norm_bilinearRestrictScalars, HasFPowerSeriesWithinOnBall.iteratedFDerivWithin, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, AlgebraicIndependent.aevalEquivField_apply_coe, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, HahnSeries.inv_def, Unitization.nnnorm_eq_sup, RCLike.norm_sq_eq_def, Matrix.IsHermitian.coe_re_diag, ContinuousLinearMap.bilinearComp_zero_left, div_pos_iff, FractionalIdeal.div_zero, ContinuousMultilinearMap.instContinuousSMul, Rat.cast_pos_of_pos, arithGeom_zero_eq_mul_div, FormalMultilinearSeries.ofScalars_smul, ContDiffAt.fderiv, Finsupp.logHeight_eq_log_mulHeight, RCLike.ratCast_im, FractionalIdeal.coeIdeal_eq_zero, MDifferentiableOn.clm_precomp, RCLike.I_mul_re, RCLike.conj_eq_iff_im, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, hasFTaylorSeriesUpToOn_succ_iff_left, ArchimedeanClass.mk_ratCast_nonneg, FractionalIdeal.bot_lt_mul_inv, MvPowerSeries.X_inv, Height.logHeight₁_zero, Even.zpow_pos_iff, LinearMap.span_singleton_inf_orthogonal_eq_bot, contDiffOn_succ_iff_fderivWithin, Finset.centerMass_pair, IsFractionRing.num_mul_den_eq_num_iff_eq, InnerProductSpace.toLinearMap_rankOne, div_eq_quo_add_rem_div_add_rem_div, Asymptotics.SuperpolynomialDecay.inv_param_mul, Convex.mem_Icc, ContDiffWithinAt.iteratedFDerivWithin_right, RCLike.conj_re_ax, IntermediateField.coe_smul, continuousMultilinearCurryRightEquiv_symm_apply', Filter.tendsto_div_const_atTop_iff_neg, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, ContDiffWithinAt.fderivWithin, FractionalIdeal.mul_inv_cancel_iff_isUnit, iteratedDerivWithin_eq_equiv_comp, ValuativeRel.one_vle_inv, AddCircle.addOrderOf_eq_pos_iff, iteratedFDerivWithin_two_apply, extDerivWithin_smul, Pretrivialization.continuousOn_continuousLinearMapCoordChange, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, inner_mul_symm_re_eq_norm, DoubleCentralizer.coe_fst, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, IntermediateField.coe_equivMap_apply, Submodule.re_inner_starProjection_nonneg, MeasureTheory.MemLp.im, ContinuousLinearMap.hasFDerivAt_of_bilinear, FormalMultilinearSeries.ofScalars_comp_neg_id, RCLike.realRingEquiv_apply, FirstOrder.Field.model_hasChar_of_charP, ContinuousAlternatingMap.curryLeft_add, ValuationSubring.nonunits_le, Unitization.quasispectrum_eq_spectrum_inr', RCLike.mul_im, FractionalIdeal.inv_zero', SimpleGraph.left_nonuniformWitnesses_card, ValuativeRel.div_rel_iff, ContinuousAlternatingMap.prodLIE_apply, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal, RCLike.im_sq_le_normSq, Asymptotics.SuperpolynomialDecay.param_zpow_mul, traceForm_nondegenerate, CPolynomialOn.fderiv, Function.FactorizedRational.extractFactor, LocalSubring.instIsScalarTowerSubtypeMemSubringToSubringOfPrime, toIcoMod_zero_one, ContinuousLinearMap.opNorm_flip, ContinuousLinearMap.precompCompactConvergenceCLM_apply, strictConcaveOn_iff_div, IsConformalMap.smul, archimedean_iff_int_lt, stdSimplex.barycenter_eq_centerMass, NNRat.Nonneg.coe_ofScientific, FormalMultilinearSeries.derivSeries_eq_zero, tendsto_const_mul_zpow_atTop_nhds_iff, ContDiffWithinAt.smulRight, FractionalIdeal.eq_zero_or_one, selfAdjoint.val_nnratCast, ContinuousMultilinearMap.curryLeft_apply, Asymptotics.superpolynomialDecay_mul_const_iff, LinearOrderedField.coe_inducedOrderRingIso, IsRealClosed.nonneg_iff_isSquare, AffineSubspace.direction_smul, algebraicIndependent_empty_type, Meromorphic.fun_prod, DirectLimit.inv_mul_cancel, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, Asymptotics.superpolynomialDecay_param_mul_iff, Asymptotics.SuperpolynomialDecay.mul_param_zpow, FractionalIdeal.exists_eq_spanSingleton_mul, RCLike.re_ofReal_pow, FormalMultilinearSeries.radius_le_radius_derivSeries, ContinuousAlternatingMap.curryLeftLI_apply, re_inner_self_nonpos, RCLike.norm_sq_re_add_conj, iteratedFDerivWithin_zero_eq_comp, LinearMap.IsSymmetric.im_inner_apply_self, ContinuousLinearMap.norm_compSL_le, AddCircle.nsmul_eq_zero_iff, archimedean_iff_rat_lt, RCLike.im_to_complex, AbsoluteValue.tendsto_div_one_add_pow_nhds_zero, trace_eq_sum_embeddings, InnerProductSpace.Core.cauchy_schwarz_aux', IntermediateField.botEquiv_def, ValuationSubring.mem_nonunits_iff, InnerProductSpace.isIdempotentElem_rankOne_self_iff, IsCauSeq.geo_series_const, fderivWithin_continuousLinearEquiv_comp, IntermediateField.adjoin_adjoin_comm, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn, IntermediateField.val_mk, RCLike.re_eq_complex_re, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Filter.Tendsto.const_div_atTop, FormalMultilinearSeries.ofScalars_series_eq_zero, Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, RCLike.norm_to_complex, ConvexCone.mem_hull_of_convex, Filter.tendsto_div_const_atBot_iff, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, RCLike.re_sq_le_normSq, LinearIsometryEquiv.symm_units_smul, algebraicIndependent_empty, SimpleGraph.not_isUniform_zero, IntermediateField.adjoin_simple_comm, OrthonormalBasis.sum_rankOne_eq_id, Asymptotics.IsLittleO.finsetProd, IntermediateField.inclusion_inclusion, div_nonneg_iff, sum_Ioc_inv_sq_le_sub, HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, RCLike.mul_re, IntermediateField.extendScalars_restrictScalars, ContinuousLinearMap.norm_smulRightL_le, LinearIsometryEquiv.symm_smul_apply, IntermediateField.zero_mem, IsRealClosed.isSquare_or_isSquare_neg, Rat.cast_pos, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, exists_add_lt_and_pos_of_lt, Even.zpow_nonneg, RCLike.re_le_neg_norm_iff_eq_neg_norm, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, Localization.subalgebra.ofField_eq, round_eq_iff, RCLike.to_complex_nonneg_iff, HasFiniteFPowerSeriesOnBall.fderiv', ValuativeRel.inv_vle_one, Filter.tendsto_div_const_atTop_iff, ContinuousMultilinearMap.currySum_apply, Module.Basis.traceDual_repr_apply, FormalMultilinearSeries.ofScalars_comp_neg, Unitization.norm_splitMul_snd_sq, Set.preimage_div_const_uIcc, FractionalIdeal.invertible_iff_generator_nonzero, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, FractionalIdeal.isNoetherian, ValuationRing.instValuationRingInteger, RCLike.im_ofReal_mul, inner_self_re_eq_norm, CompactConvergenceCLM.continuousSMul, convexHull_eq, inv_antitoneOn_Ioi, HasFiniteFPowerSeriesOnBall.hasFDerivAt, GenContFract.le_of_succ_get?_den, IntermediateField.lift_adjoin, ContinuousAlternatingMap.alternatizeUncurryFin_add, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, GenContFract.zero_le_of_contsAux_b, ContinuousLinearMap.flip_zero, RCLike.I_re, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, ConditionallyCompleteLinearOrderedField.toIsStrictOrderedRing, nndist_homothety_center, FormalMultilinearSeries.changeOriginSeries_finite_of_finite, div_sub', RCLike.im_eq_complex_im, Unitization.splitMul_injective, FractionalIdeal.spanSingleton_div_self, AddCircle.addOrderOf_div_of_gcd_eq_one', Nonneg.Icc_subset_segment, RCLike.ofReal_im_ax, iteratedDerivWithin_comp_eq_sum_orderedFinpartition, Asymptotics.superpolynomialDecay_const_mul_iff, ValuativeRel.inv_vlt_one, ContinuousLinearMap.toUniformConvergenceCLM_continuous, hasStrictFDerivAt_inv', IntermediateField.lift_sup, spectrum.nonzero_mul_comm, Set.Finite.convexHull_eq_image, Submodule.traceDual_span_of_basis, Polynomial.X_sub_C_mul_removeFactor, Affine.Triangle.prod_div_one_sub_eq_one_of_mem_line_point_lineMap, FractionalIdeal.isPrincipal, SameRay.exists_pos_left, deriv_descPochhammer_eval_eq_sum_prod_range_erase, InnerProductSpace.Core.inner_self_im, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, IntermediateField.adjoin_adjoin_left, qsmul_def, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, affineHomeomorph_apply, MDifferentiable.clm_precomp, convexHull_rangle_single_eq_stdSimplex, trace_eq_sum_automorphisms, AEMeasurable.re, continuousMultilinearCurryLeftEquiv_symm_apply, DoubleCentralizer.instStarModule, ContinuousMultilinearMap.smulRightL_apply, exists_pos_left_iff_sameRay_and_ne_zero, FractionalIdeal.coe_ideal_span_singleton_mul_inv, Filter.Tendsto.div_atBot, iteratedFDeriv_succ_eq_comp_left, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, IntermediateField.equivOfEq_apply, ContinuousLinearEquiv.arrowCongrSL_symm_apply, ContinuousLinearMap.opNorm_mulLeftRight_le, RCLike.re_ofReal_mul, norm_add_pow_two, PointwiseConvergenceCLM.evalCLM_apply, norm_eq_sqrt_re_inner, RCLike.iInter_halfSpaces_eq, inner_self_nonneg, ContinuousMultilinearMap.piₗᵢ_apply, Module.Basis.traceDual_powerBasis_eq, AddCircle.intCast_div_mul_eq_zsmul, ContMDiffWithinAt.clm_precomp, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, RCLike.continuous_im, norm_iteratedFDerivWithin_fderivWithin, IntermediateField.fieldRange_val, IntermediateField.liftAlgEquiv_apply, continuousMultilinearCurryFin1_symm_apply, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, RCLike.normSq_add, RCLike.div_re, ContinuousLinearMap.lsmul_flip_apply, ConvexCone.coe_hull_of_convex, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, Filter.Tendsto.const_div_atBot, setIntegral_re_add_im, RCLike.geometric_hahn_banach_compact_closed, ContDiffAt.differentiableAt_iteratedFDeriv, Height.mulHeight₁_zero, ContDiffOn.smulRight, Positive.coe_zpow, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, RCLike.geometric_hahn_banach_point_closed, ContinuousLinearMap.map_add₂, ContMDiff.clm_precomp, AddCircle.addOrderOf_coe_rat, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, FormalMultilinearSeries.derivSeries_apply_diag, SameRay.exists_nonneg_right, AnalyticAt.fderiv, fderiv_comp_smul, div_sub_div, ContinuousLinearMap.opNorm_lsmul, convexOn_iff_div, EuclideanGeometry.orthogonalProjection_mem_orthogonal, FormalMultilinearSeries.norm_changeOriginSeriesTerm, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, ValuativeRel.zero_srel_iff, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, GenContFract.sub_convs_eq, HasFTaylorSeriesUpTo.zero_eq', PointwiseConvergenceCLM.withSeminorms, norm_sub_pow_two, ContinuousLinearMap.map_zero₂, MeromorphicOn.fun_prod, ContDiff.fderiv_right, ContinuousMultilinearMap.curryFinFinset_symm_apply, homothety_inv_two, RCLike.conj_eq_re_sub_im, strictConvexOn_iff_div, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, HasFTaylorSeriesUpTo.fderiv, FractionalIdeal.coe_div, ValuativeRel.one_srel_inv, PiTensorProduct.injectiveSeminorm_tprod_le, ValuationRing.coe_equivInteger_apply, ContinuousLinearMap.precomp_apply, HahnSeries.inv_single, contDiff_infty_iff_fderiv, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, HasFPowerSeriesWithinOnBall.fderivWithin_of_mem_of_analyticOn, integral_re, ContinuousLinearMap.precomp_uniformConvergenceCLM_apply, IntermediateField.Lifts.eq_iff, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, geom_sum₂_Ico, Filter.tendsto_mul_const_atBot_iff_neg, mul_sub_mul_div_mul_neg_iff, ContinuousLinearMap.postcompUniformConvergenceCLM_apply, RCLike.normSq_apply, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, HasFiniteFPowerSeriesOnBall.fderiv_eq, ContinuousLinearMap.analyticAt_bilinear, ConvexOn.exists_affine_le_of_lt, HasFPowerSeriesAt.hasStrictFDerivAt, RingPreordering.supportAddSubgroup_eq_bot, ContinuousLinearMap.toPointwiseConvergenceCLM_apply, nnqsmul_def, div_lt_one_iff, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, FirstOrder.Field.model_fieldOfChar_of_charP, isBoundedLinearMap_continuousMultilinearMap_comp_linear, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, ContinuousLinearMap.toUniformConvergenceCLM_symm_apply, re_inner_le_norm, hasFDerivAt_inv', exists_continuousLinearEquiv_fderiv_symm_eq, FormalMultilinearSeries.rightInv_coeff, Convex.mem_toCone', IntermediateField.equivOfEq_trans, convexOn_zpow, RCLike.mul_re_ax, ContDiffOn.differentiableOn_iteratedFDerivWithin, LinearMap.im_inner_adjoint_mul_self_eq_zero, ContinuousLinearMap.map_neg₂, ConditionallyCompleteLinearOrderedField.toMulPosStrictMono, AddCircle.equivAddCircle_symm_apply_mk, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, integral_re_add_im, FormalMultilinearSeries.comp_rightInv_aux2, isConformalMap_const_smul, sub_div', IsFractionRing.num_mul_den_eq_num_iff_eq', IntermediateField.mem_restrict, div_eq_mul_inv, Int.ceil_le_mul, ContMDiffWithinAt.cle_arrowCongr, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, ValuationRing.of_field, continuousMultilinearCurryRightEquiv_apply, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, RCLike.norm_le_im_iff_eq_I_mul_norm, RCLike.re_to_complex, ContinuousAlternatingMap.prodLIE_symm_apply, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_apply, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, tendsto_pow_atTop_nhds_zero_iff, ContDiff.fderiv, gcd_eq, fderivWithin_comp_smul, RCLike.hasSum_im, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, ContinuousLinearMap.flipₗᵢ_symm, ContinuousLinearMap.postcomp_uniformConvergenceCLM_apply, exists_continuousLinearEquiv_fderivWithin_symm_eq, FormalMultilinearSeries.rightInv_coeff_one, RCLike.isCauSeq_re, Function.FactorizedRational.meromorphicTrailingCoeffAt_factorizedRational_off_support, RCLike.I_im', LinearMap.orthogonal_span_singleton_eq_to_lin_ker, archimedean_iff_int_le, FractionalIdeal.num_eq_zero_iff, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, IntermediateField.intermediateFieldMap_symm_apply_coe, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, inv_nonpos', VectorFourier.fourierIntegral_fderiv, ContinuousLinearMap.fpowerSeries_apply_one, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, Set.Finite.convexHull_eq, HahnSeries.cardSupp_inv_le, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, ValuativeRel.rel_div_iff, Complex.sum_div_factorial_le, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, FractionalIdeal.den_mem_inv, ContinuousLinearMap.opNNNorm_mul_apply, spectrum.zero_eq, ContinuousMultilinearMap.curryFinFinset_apply, ContDiffAt.smulRight, ConvexOn.sSup_affine_eq, nndist_self_homothety, FormalMultilinearSeries.changeOriginSeriesTerm_bound, RCLike.I_mul_I_ax, IntermediateField.coe_algebraMap_apply, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, LinearMap.IsSymmetric.coe_re_inner_apply_self, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, ContinuousLinearMap.norm_precompL_le, starConvex_iff_div, ContinuousLinearMap.apply_apply, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk, ContinuousLinearMap.norm_map_removeNth_le, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, IsSymmSndFDerivWithinAt.eq, ContinuousLinearMap.map_smulₛₗ₂, Asymptotics.superpolynomialDecay_param_pow_mul_iff, PiTensorProduct.mapLMultilinear_opNorm, Filter.tendsto_mul_const_atBot_iff, RCLike.geometric_hahn_banach_closed_compact, IntermediateField.restrictScalars_adjoin, RCLike.intCast_im, Filter.tendsto_div_const_atBot_iff_neg, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_symm_apply, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, inner_im_symm, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, isBoundedBilinearMap_smulRight, ContMDiffAt.cle_arrowCongr, IntermediateField.Lifts.le_iff, MeasureTheory.memLp_re_im_iff, ValuativeRel.ValueGroupWithZero.mk_eq_valuation, RCLike.normSq_sub, isBoundedLinearMap_prod_multilinear, nndist_homothety_self, IsFractionRing.isUnit_den_zero, RCLike.re_tsum, CauSeq.const_pos, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, RingPreordering.support_eq_bot, postcomp_compactConvergenceCLM_apply, HasFiniteFPowerSeriesAt.comp, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, FractionalIdeal.mem_div_iff_of_ne_zero, homothety_one_half, FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin, DoubleCentralizer.coe_snd, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, RCLike.imCLM_apply, ContinuousMultilinearMap.norm_curryMid, ConvexOn.univ_sSup_of_nat_affine_eq, Filter.tendsto_const_mul_atBot_iff_pos, convexHull_range_eq_exists_affineCombination, mod_eq, SimpContFract.determinant_aux, norm_iteratedFDeriv_fderiv, RCLike.geometric_hahn_banach_open_open, FractionalIdeal.coe_ideal_le_self_mul_inv, RCLike.lipschitzWith_im, inv_antitoneOn_Iio, Matrix.Pivot.listTransvecRow_getElem, ContinuousLinearMap.coe_mulₗᵢ, Nat.ceil_lt_mul, ContinuousLinearMap.toSesqForm_apply_norm_le, GenContFract.abs_sub_convs_le, PiTensorProduct.injectiveSeminorm_def, FirstOrder.Field.charP_iff_model_fieldOfChar, ContMDiff.cle_arrowCongr, ContinuousLinearMap.coe_deriv₂, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, contDiff_succ_iff_hasFDerivAt, ValuativeRel.zero_vlt_iff, integral_im, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, Convex.mem_Ioc, Filter.Tendsto.inv_tendsto_atBot, Valuation.HasExtension.algebraMap_injective, ValuationRing.instIsFractionRingInteger, selfAdjoint.val_nnqsmul, GenContFract.IntFractPair.nth_stream_fr_nonneg, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, RCLike.im_le_norm, FractionalIdeal.mem_inv_iff, Function.FactorizedRational.meromorphicNFOn, ContinuousLinearMap.hasDerivAt_of_bilinear, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, Icc_subset_segment, FractionalIdeal.spanSingleton_inv, FractionalIdeal.inv_of_ne_zero, Module.Basis.traceDual_injective, AddCircle.homeomorphAddCircle_symm_apply_mk, AddCircle.gcd_mul_addOrderOf_div_eq, Filter.tendsto_const_mul_atTop_iff, Affine.Simplex.altitude_def, IntermediateField.sum_mem, ContDiffWithinAt.fderivWithin_right, Rat.cast_prod, iter_deriv_pow, ContinuousLinearMap.continuousAt_uncurry_of_multilinear, contDiffWithinAt_succ_iff_hasFDerivWithinAt, FractionalIdeal.mul_div_self_cancel_iff, InnerProductSpace.norm_rankOne, arithGeom_strictMono, Convex.mem_Ico, RCLike.inv_re, PiTensorProduct.mapLMultilinear_toFun_apply, HasFiniteFPowerSeriesOnBall.fderiv, Matrix.PosDef.re_dotProduct_pos, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, circleEquivGen_apply, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, IntermediateField.isScalarTower_mid, exists_pos_right_iff_sameRay_and_ne_zero, Filter.tendsto_div_const_atBot_iff_pos, IntermediateField.LinearDisjoint.linearIndependent_left, MeasureTheory.Integrable.im, AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, LinearMap.IsPositive.re_inner_nonneg_left, ContinuousLinearMap.norm_iteratedFDerivWithin_le_of_bilinear_aux, AddCircle.natCast_div_mul_eq_nsmul, Asymptotics.superpolynomialDecay_mul_param_iff, RCLike.zero_im, fderiv_inv', Module.Basis.traceDual_eq_iff, RCLike.im_eq_zero, RCLike.geometric_hahn_banach_open_point, FormalMultilinearSeries.comp_assoc, HasFPowerSeriesWithinAt.comp, convexOn_iff_slope_mono_adjacent, continuousMultilinearCurryFin1_apply, Even.zpow_pos
toDiv 📖	CompOp	3 math math: nnratCast_def, ratCast_def, div_eq_mul_inv
toDivisionRing 📖	CompOp	2204 math math: IsPrimitiveRoot.subOneIntegralPowerBasis_gen_prime, Hyperreal.InfiniteNeg.neg, FiniteDimensional.of_exists_primitive_element, Polynomial.mul_div_eq_iff_isRoot, Padic.coe_neg, ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_one, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, FixedPoints.instFiniteDimensionalSubtypeMemSubfieldSubfield, one_le_div_iff, legendreSym.eq_neg_one_iff, NumberField.basisMatrix_eq_embeddingsMatrixReindex, WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', Lagrange.interpolate_one, Valued.continuous_extension, AddCircle.not_isOfFinAddOrder_iff_forall_rat_ne_div, Set.preimage_mul_const_Ioo_of_neg, exists_rat_pow_btwn, AddCircle.coe_equivIco_mk_apply, ValuationRing.mem_integer_iff, IntermediateField.isSeparable_of_mem_isSeparable, Algebra.charP_iff, LieAlgebra.IsKilling.iInf_ker_weight_eq_bot, Lagrange.eval_iterate_derivative_eq_sum, div_le_div_of_nonpos_of_le, Polynomial.eq_X_sub_C_of_separable_of_root_eq, Rat.intCast_lt_cast, mem_perfectClosure_iff_natSepDegree_eq_one, ordinaryHypergeometric_sum_eq, ArchimedeanClass.FiniteResidueField.mk_ratCast, discrim_le_zero_of_nonpos, IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', IntermediateField.aeval_gen_minpoly, IsUltrametricDist.isNonarchimedean_invariantExtension, strictConvexOn_iff_slope_strict_mono_adjacent, Algebra.instIsSeparableResidueFieldOfFormallyUnramified, Subfield.rank_comap, CauSeq.lt_irrefl, ValuationSubring.coe_mem_principalUnitGroup_iff, Hyperreal.infinite_neg, ValuationSubring.valuation_lt_one_iff, Convex.intrinsicClosure, IntermediateField.fieldRange_le, selfAdjoint.val_div, FixedPoints.finrank_eq_card, binomialSeries_eq_ordinaryHypergeometricSeries, zpow_eq_zpow_iff_of_ne_zero₀, Filter.Tendsto.div_atTop, IsUltrametricDist.algNormOfAlgEquiv_extends, IsPurelyInseparable.minpoly_natDegree_eq', ZMod.pow_card_sub_one, IntermediateField.sSup_toSubfield, Orientation.ne_iff_eq_neg, FixedPoints.minpoly.monic, HahnSeries.mem_cardSuppLTSubfield, SimpleGraph.lapMatrix_toLinearMap₂', ValuationSubring.image_maximalIdeal, NormedSpace.expSeries_eq_ofScalars, NumberField.InfinitePlace.sum_mult_eq, FixedPoints.minpoly.irreducible, Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col, RootPairing.coroot_eq_polarizationEquiv_apply_root, Ideal.exists_comap_galRestrict_eq, NumberField.canonicalEmbedding.mem_span_latticeBasis, NumberField.integralBasis_apply, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow, UniformSpace.Completion.mul_hatInv_cancel, ValuationSubring.integralClosure_algebraMap_injective, IsPurelyInseparable.minpoly_eq', FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, GenContFract.of_convergence, RootPairing.instIsRootSystemSubtypeMemSubmoduleSpanRangeCoeEmbeddingRootCorootRestrictScalars', X_pow_sub_C_splits_of_isPrimitiveRoot, NumberField.prod_nonarchAbsVal_eq, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, quadraticChar_card_card, FDRep.char_tensor, Lagrange.eval_interpolate_not_at_node', Valuation.mem_maximalIdeal_iff, NumberField.IsCMField.isConj_complexConj, Subfield.inf_relrank_left, Representation.IsIrreducible.instIsSimpleModuleMonoidAlgebraAsModule, ConvexOn.monotoneOn_slope_lt, abs_sub_round, round_neg_two_inv, NumberField.IsCMField.zpowers_complexConj_eq_top, IntermediateField.coe_algebraMap_over_bot, ValuationSubring.mem_toSubring, Subspace.instModuleDualFiniteDimensional, Algebra.normalizedTrace_eq_of_finiteDimensional, Subgroup.HasDetPlusMinusOne.isParabolic_iff_of_upperTriangular, CancelDenoms.cancel_factors_eq_div, NumberField.FinitePlace.mk_apply, discrim_eq_zero_iff, NumberField.instIsTotallyRealSubtypeMemSubfieldOfIsAlgebraic, CauSeq.sup_inf_distrib_right, NumberField.instFreeIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, concaveOn_iff_slope_anti_adjacent, WeierstrassCurve.Jacobian.add_of_Y_ne', arithGeom_eq', NumberField.canonicalEmbedding.latticeBasis_apply, NumberField.IsCMField.unitsComplexConj_torsion, Algebra.isInvariant_of_isGalois, Subfield.relfinrank_eq_one_iff, WeierstrassCurve.Affine.cyclic_sum_Y_mul_X_sub_X, IsPurelyInseparable.elemExponent_min', Padic.withValUniformEquiv_norm_le_one_iff, NumberField.norm_norm_le_norm_mul_house_pow, Valued.toNormedField.norm_le_one_iff, WeierstrassCurve.Jacobian.dblX_of_Z_ne_zero, NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd, Valued.extension_extends, one_le_pow_mul_abs_eval_div, Valued.valuedCompletion_surjective_iff, Polynomial.div_def, toIcoMod_eq_fract_mul, NumberField.RingOfIntegers.instIsIntegralClosureIntWithVal, NumberField.RingOfIntegers.instSMulDistribClass, ValuationSubring.valuation_le_iff, RootPairing.restrictScalars_coe_coroot, Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, FiniteField.isSquare_neg_one_iff, FixedPoints.isSeparable, Polynomial.exists_partition_polynomial, NumberField.IsCMField.equivInfinitePlace_symm_apply, Polynomial.fiberEquivQuotient_tmul, Int.fract_div_mul_self_mem_Ico, NumberField.IsCMField.units_rank_eq_units_rank, Subspace.dualLift_of_subtype, LieAlgebra.IsKilling.isCompl_ker_weight_span_coroot, WeierstrassCurve.Jacobian.Point.toAffine_of_Z_ne_zero, CancelDenoms.cancel_factors_le, LieAlgebra.finrank_engel, Subfield.relrank_comap_comap_eq_relrank_of_surjective, PadicComplex.coe_eq, Padic.coe_div, traceForm_nondegenerate_tfae, NumberField.mem_maximalRealSubfield_iff, Matrix.Pivot.listTransvecCol_mul_last_col, LaurentSeries.LaurentSeriesRingEquiv_def, FirstOrder.Field.realize_genericMonicPolyHasRoot, Subspace.dualRestrict_comp_dualLift, Lagrange.leadingCoeff_basis, LieModule.traceForm_eq_sum_finrank_nsmul', LinearMap.finiteDimensional_of_det_ne_one, Set.preimage_mul_const_Iio_of_neg, RatFunc.transcendental_X, FiniteField.isSquare_two_iff, IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, div_le_iff_of_neg, Valuation.HasExtension.instIsLocalHomSubtypeMemValuationSubringValuationSubringRingHomAlgebraMap, geom₂_sum, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, WeierstrassCurve.Projective.equiv_some_of_Z_ne_zero, Hyperreal.neg_lt_of_tendsto_zero_of_pos, Module.exists_dual_forall_apply_eq_one, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_apply, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Valuation.isEquiv_valuation_valuationSubring, ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_three, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, isSepClosure_iff, NumberField.mixedEmbedding.norm_eq_norm, IsRealClosed.exists_eq_zpow_of_isSquare, LieAlgebra.IsKilling.rootSystem_coroot_apply, round_two_inv, X_pow_sub_C_irreducible_iff_of_odd, StrictConcaveOn.slope_anti_adjacent, Subring.center.coe_div, Irreducible.natSepDegree_eq_one_iff_of_monic', NumberField.FinitePlace.norm_def', X_pow_sub_C_irreducible_of_odd, NumberField.mixedEmbedding.mem_idealLattice, IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers, sum_smul_minpolyDiv_eq_X_pow, FunctionField.inftyValuation.X_inv, Hyperreal.epsilon_mul_omega, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, NumberField.Units.regOfFamily_eq_det, IsPurelyInseparable.elemExponent_min, HahnSeries.single_zero_ofScientific, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible', FixedPoints.minpoly.eval₂', NumberField.FinitePlace.embedding_apply, IsAlgClosure.of_exists_root, WeierstrassCurve.Jacobian.negAddY_eq, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, Valuation.Integers.isPrincipal_iff_exists_isGreatest, IntermediateField.isAlgebraic_tower_bot, Rat.cast_fract, ZMod.exists_sq_eq_neg_one_iff, ValuativeRel.inv_srel_one, Normal.splits', IntermediateField.mem_adjoin_iff, instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Finpartition.IsEquipartition.card_biUnion_offDiag_le', isConjRoot_iff_exists_algEquiv, NumberField.FinitePlace.prod_eq_inv_abs_norm, IsPurelyInseparable.elemExponent_def', instIsAlgebraicResidueFieldOfIsIntegral, LaurentSeries.valuation_single_zpow, ZMod.wilsons_lemma, Cubic.disc_eq_prod_three_roots, FirstOrder.Field.charP_of_model_fieldOfChar, Set.preimage_const_mul_Ioc_of_neg, Normal.minpoly_eq_iff_mem_orbit, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', Padic.coe_sub, div_nonneg_of_nonpos, CauSeq.sup_idem, WeierstrassCurve.ofJ_1728_of_two_ne_zero, WeierstrassCurve.Projective.Y_eq_iff', Hyperreal.coe_ofNat, sbtw_midpoint_of_ne, ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl, GenContFract.exists_gcf_pair_rat_eq_nth_conts, tendsto_bdd_div_atTop_nhds_zero, WeierstrassCurve.Projective.nonsingular_of_Z_ne_zero, le_iff_forall_rat_lt_imp_le, FiniteDimensional.of_finite_intermediateField, Lagrange.eval_interpolate_not_at_node, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, Hyperreal.InfinitePos.neg, PadicComplex.norm_def, Orientation.eq_or_eq_neg, NumberField.RingOfIntegers.instIsFractionRing, Quaternion.coe_ratCast, ValuationSubring.valuation_unit, Hyperreal.infinitesimal_def, ContFract.convs_eq_convs', minpoly_algHom_toLinearMap, ArchimedeanClass.FiniteResidueField.mk_eq_zero, NumberField.abs_discr_ge', Matrix.mem_spectrum_iff_isRoot_charpoly, LieAlgebra.IsKilling.corootSpace_eq_bot_iff, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, Polynomial.abc, Subfield.relfinrank_top_left, AddCircle.homeomorphAddCircle_apply_mk, Polynomial.natSepDegree_X_sub_C_pow, NumberField.adjoin_eq_top_of_infinitePlace_lt, Polynomial.exists_partition_polynomial_aux, Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one, Quaternion.ratCast_re, quadraticChar_two, Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff, IsPrimitiveRoot.subOneIntegralPowerBasis_gen, Height.logHeight₁_sub_le, IsFractionRing.mk'_eq_one_iff_eq, sub_inv_antitoneOn_Ioi, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, IsAlgClosure.of_exist_roots, AffineMap.slope_comp, Subspace.dualAnnihilator_dualAnnihilator_eq, SimpleGraph.regularityReduced_adj, PowerSeries.derivative_inv', discrim_le_zero, Subfield.lift_relrank_comap_comap_eq_lift_relrank_of_surjective, WeierstrassCurve.Jacobian.negY_of_Z_ne_zero, IsDedekindDomain.HeightOneSpectrum.instIsNontrivialWithZeroMultiplicativeIntValuation, ConjRootClass.minpoly.map_eq_prod, Valuation.Integers.valuation_irreducible_lt_one, NumberField.Units.pos_at_place, IntermediateField.natCast_mem, WeierstrassCurve.Jacobian.addXYZ_of_X_eq, CancelDenoms.cancel_factors_lt, Height.logHeight₁_neg, Ring.choose_eq_smul, GenContFract.exists_rat_eq_nth_num, zpow_two_nonneg, div_two_sub_self, IsFractionRing.mk'_eq_div, IntermediateField.coe_neg, Subfield.splits_bot, ValuationSubring.mapOfLE_valuation_apply, WeierstrassCurve.Projective.add_of_Z_eq_zero, IntermediateField.isScalarTower, Padic.coe_zero, IntermediateField.LinearDisjoint.algebraMap_basisOfBasisRight_repr_apply, LinearOrderedField.lt_inducedMap_iff, WeierstrassCurve.Jacobian.negAddY_of_X_eq, Polynomial.roots_degree_eq_one, RatFunc.eval_one, NumberField.isTotallyReal_sup, IntermediateField.algebraAdjoinAdjoin.instIsAlgebraicSubtypeMemSubalgebraAdjoinAdjoin, IsAlgClosed.instIsAlgClosure, FixedPoints.rank_le_card, spectralAlgNorm_def, isPurelyInseparable_iff_fd_isPurelyInseparable, CauSeq.const_lt, spectrum_diagonal, LieAlgebra.IsKilling.le_chainBotCoeff_of_rootSpace_ne_top, IsUltrametricDist.invariantExtension_apply, PowerBasis.equivAdjoinSimple_symm_aeval, Orientation.map_eq_neg_iff_det_neg, IsCyclotomicExtension.Rat.nrComplexPlaces_eq_totient_div_two, NumberField.instFiniteDimensional, Height.logHeight₁_one, X_pow_sub_C_irreducible_iff_forall_prime_of_odd, Algebra.algebraMap_intNorm, SeparatingDual.exists_eq_one, finrank_algHom, exists_rat_gt, ValuationSubring.toSubring_top, FiniteField.orderOf_frobeniusAlgEquivOfAlgebraic, LieAlgebra.IsKilling.apply_coroot_eq_cast', NumberField.isTotallyReal_top_iff, SimpleGraph.farFromTriangleFree_iff, sbtw_iff_left_ne_and_right_mem_image_Ioi, FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation, NumberField.IsTotallyComplex.finrank, LinearMap.rank_diagonal, NumberField.RingOfIntegers.withValEquiv_symm_apply, zpow_neg_two_nonneg, LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, AffineBasis.convexHull_eq_nonneg_coord, Even.zpow_abs, ContinuousLinearMap.finiteDimensional, RootPairing.restrictScalars_pairing, CauSeq.inf_comm, Cubic.discr_eq_prod_three_roots, WeierstrassCurve.Projective.dblU_eq, FGModuleCat.instFiniteHomModuleCatObjIsFG, WeierstrassCurve.Projective.Point.toAffineLift_of_Z_ne_zero, LinearMap.span_singleton_sup_orthogonal_eq_top, NumberField.IsTotallyReal.finrank, le_one_div_of_neg, algebraicClosure.isAlgebraic, Height.mulHeight₁_zpow, NumberField.Units.coe_mul, AddCircle.isOfFinAddOrder_iff_exists_rat_eq_div, Projectivization.Subspace.span_sup, ValuationSubring.subtype_injective, Lagrange.coeff_eq_sum, RatFunc.coe_X, IsUltrametricDist.invariantExtension_extends, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow', Polynomial.Splits.eval_derivative_eq_eval_mul_sum, IntermediateField.finiteDimensional_right, ValuationRing.range_algebraMap_eq, IntermediateField.isAlgebraic_iff, AffineSubspace.wOppSide_iff_exists_wbtw, IntermediateField.charZero, NumberField.instIsTotallyRealSubtypeMemIntermediateFieldRatOfIsAlgebraic, Algebra.FormallyUnramified.iff_map_maximalIdeal_eq, IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower', NumberField.house_intCast, FiniteField.cast_card_eq_zero, padicNormE.eq_padic_norm', SimpleGraph.posSemidef_lapMatrix, WeierstrassCurve.Jacobian.add_of_Y_eq, zpow_eq_neg_zpow_iff₀, SameRay.exists_eq_smul_add, affineHomeomorph_symm_apply, Valued.exists_coe_eq_v, FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop, Matrix.minpoly_dvd_charpoly, Finset.mem_convexHull', Subfield.lift_relrank_map_map, Subfield.relrank_top_left, Hyperreal.infinite_abs_iff, List.SortedLE.wbtw, LinearMap.BilinForm.apply_dualBasis_left, div_neg_iff, Basis.linearEquiv_dual_iff_finiteDimensional, NumberField.FinitePlace.norm_embedding_eq, div_le_one_iff, IsNormalClosure.adjoin_rootSet, NumberField.RingOfIntegers.instIsDedekindDomainWithVal, Derivation.leibniz_div, IntermediateField.LinearDisjoint.trace_algebraMap, Polynomial.separable_X_pow_sub_C, NormedSpace.exp_eq_tsum, NumberField.IsCMField.isQuadraticExtension, Polynomial.valuation_of_mk, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, Rat.intCast_le_cast, Subspace.finrank_dualCoannihilator_eq, GenContFract.compExactValue_correctness_of_stream_eq_some_aux_comp, Polynomial.Gal.restrictDvd_def, Matrix.Pivot.mul_listTransvecRow_last_col, IntermediateField.div_mem, Polynomial.X_pow_sub_one_splits, arithGeom_zero_eq_mul_div', Odd.zpow_nonpos_iff, OrderIso.smulRightDual_apply, IsCyclotomicExtension.Rat.discr_prime_pow', WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, Quaternion.inv_def, Subspace.finiteDimensional_quot_dualCoannihilator_iff, CauSeq.not_limZero_of_pos, mul_sub_mul_div_mul_nonpos_iff, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, discrim_eq_zero_of_existsUnique, IntermediateField.minpoly_gen, sub_half_lt_round, ValuationSubring.eq_top_iff, LaurentSeries.inducing_coe, isSplittingField_X_pow_sub_C_of_root_adjoin_eq_top, Polynomial.exists_finset_of_splits, Rat.isNat_intCeil_ofIsNNRat, WeierstrassCurve.Projective.addY_of_Z_ne_zero, LaurentSeries.continuous_coe, SameRay.exists_eq_smul, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, ZMod.exists_sq_eq_two_iff, WeierstrassCurve.Projective.negAddY_of_X_eq, NumberField.IsCMField.orderOf_complexConj, IsCyclotomicExtension.Rat.absdiscr_prime_pow, gal_X_pow_sub_C_isSolvable, Lagrange.interpolate_eq_sum, IsIdempotentElem.spectrum_subset, normalClosure_eq_iSup_adjoin', ConcaveOn.antitoneOn_slope_gt, IsPrimitiveRoot.adjoinEquivRingOfIntegers_symm_apply, AffineSubspace.wOppSide_self_iff, IntermediateField.iInf_toSubfield, RootPairing.Base.exists_mem_span_pairingIn_ne_zero_and_pairwise_ne, CauSeq.coe_sup, Hyperreal.archimdeanClassMk_coe, FiniteField.roots_X_pow_card_sub_X, Int.floor_div_natCast, Algebra.discr_powerBasis_eq_norm, ConvexOn.secant_mono_aux3, Normal.splits, Subfield.mem_bot_iff_pow_eq_self, archimedean_iff_nat_le, IsPrimitiveRoot.norm_eq_neg_one_pow, Subfield.isTotallyReal_bot, abs_inv, Valued.integer.exists_norm_lt_one, ValuationSubring.valuation_lt_one_or_eq_one, WeierstrassCurve.Projective.addXYZ_of_X_eq, PowerSeries.intValuation_eq_of_coe, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, FiniteField.instIsSplittingFieldExtensionHSubPolynomialHPowNatXCard, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, Hyperreal.infinitePos_neg, Quaternion.coe_zpow, FormalMultilinearSeries.ofScalars_series_of_subsingleton, CauSeq.mul_pos, solvableByRad.isSolvable, WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero, WeierstrassCurve.Jacobian.equiv_zero_of_Z_eq_zero, FirstOrder.Field.instModelACFOfCharPOfIsAlgClosed, Quaternion.imJ_nnratCast, divRadical_dvd_derivative, Polynomial.leadingCoeff_mul_prod_normalizedFactors, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, Polynomial.squarefree_cyclotomic, FDRep.instFiniteDimensionalHom, NormedSpace.expSeries_sum_eq, Hyperreal.isSt_iff_abs_sub_lt_delta, FiniteField.instIsScalarTowerZModExtension, NumberField.RingOfIntegers.instIsTorsionFree_2, Subfield.mem_closure_iff, GenContFract.succ_nth_conv_eq_squashGCF_nth_conv, FloorSemiring.tendsto_pow_div_factorial_atTop, IntermediateField.coe_type_toSubfield, ValuationSubring.isLocalRing, ValuativeRel.div_vle_one_iff, OnePoint.smul_some_eq_ite, selfAdjoint.val_zpow, Polynomial.X_pow_sub_C_separable_iff, IntermediateField.restrictRestrictAlgEquivMapHom_apply, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen_prime, Valued.extension_eq_zero_iff, Algebra.norm_eq_prod_embeddings, isAlgebraic_of_finite_intermediateField, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_def, IsPurelyInseparable.minpoly_eq, NumberField.canonicalEmbedding.integralBasis_repr_apply, IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer, WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, Set.preimage_const_mul_Ico_of_neg, IsDiscreteValuationRing.isRankOneDiscrete, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, minpoly.degree_le, Filter.Tendsto.atTop_div_const_of_neg, WeierstrassCurve.Affine.slope_of_Y_ne, ValuativeRel.one_rel_inv, Algebra.FormallyUnramified.iff_isSeparable, Module.Basis.traceDual_def, iInf_valuationSubring_superset, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integers, NumberField.Units.regulator_eq_det, Rat.preimage_cast_Ioi, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, Height.logHeight₁_div_eq_logHeight, SimpleGraph.isUniform_one, FixedPoints.normal, FGModuleCat.FGModuleCatEvaluation_apply, ValuativeRel.div_vle_iff, IsPurelyInseparable.natSepDegree_eq_one, TrivSqZeroExt.eq_smul_exp_of_ne_zero, Derivation.leibniz_inv, div_le_div_right_of_neg, mem_perfectClosure_iff_pow_mem, CauSeq.add_pos, NumberField.AdeleRing.algebraMap_snd_apply, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, convexHull_basis_eq_stdSimplex, Module.Basis.trace_traceDual_mul, coevaluation_apply_one, Filter.Eventually.ratCast_atBot, ValuationSubring.idealOfLE_le_of_le, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, Projectivization.card'', Subfield.finrank_comap, div_le_one_of_ge, WithAbs.tendsto_one_div_one_add_pow_nhds_one, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, Set.preimage_mul_const_uIcc, StrictConvexOn.secant_strict_mono_aux3, Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec, IsLocalRing.map_tensorProduct_mk_eq_top, FunctionField.valuedFqtInfty.def, Rat.preimage_cast_Icc, IntermediateField.isTotallyReal_bot, AdjoinRoot.mul_div_root_cancel, NumberField.Units.coe_coe, Valued.isClopen_valuationSubring, SimpleGraph.farFromTriangleFree.le_card_sub_card, Algebra.map_intNormAux, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', Finset.centerMass_insert, Matrix.finite_spectrum, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime, IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem, abs_one_div, Algebra.coe_norm_int, IsNormalClosure.splits, LinearOrderedField.cutMap_add, Valuation.exists_isUniformizer_of_isCyclic_of_nontrivial, DualNumber.maximalIdeal_eq_span_singleton_eps, Projectivization.Subspace.span_empty, NumberField.Units.finrank_mul_regOfFamily_eq_det, FormalMultilinearSeries.ofScalars_sub, Valuation.mem_unitGroup_iff, abs_div, midpoint_le_right, Set.image_div_const_uIcc, abs_sub_round_div_natCast_eq, NumberField.instIsTotallyRealSubtypeMemSubfieldTop, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, instIsSeparableResidueFieldOfQuotientIdeal, normalClosure.restrictScalars_eq, Valued.isClosed_valuationSubring, IsDedekindDomain.HeightOneSpectrum.valuation_def, Convex.mem_Ioo, Hyperreal.coe_eq_one, Rat.cast_min, Int.floor_div_cast_of_nonneg, IsPrimitiveRoot.adjoinEquivRingOfIntegers_apply, NumberField.det_basisOfFractionalIdeal_eq_absNorm, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, Valuation.Integers.isIntegrallyClosed_integers, Rat.round_cast, ValuationSubring.valuation_le_one, FGModuleCat.instIsMonoidalClosedModuleCatIsFG, FixedPoints.finrank_le_card, padicNormE.defn, ArchimedeanClass.FiniteElement.mk_intCast, ConvexOn.secant_mono_aux2, Ideal.image_subset_nonunits_valuationSubring, Projectivization.cross_mk_of_cross_ne_zero, finrank_quotient_span_eq_natDegree, Module.Basis.trace_mul_traceDual, Rep.instProjective, Matrix.Pivot.listTransvecCol_getElem, StrictConcaveOn.secant_strict_mono, gal_X_pow_sub_one_isSolvable, bddAbove_slope_gt_of_mem_interior, Finpartition.IsEquipartition.sum_nonUniforms_lt', NumberField.RingOfIntegers.coe_eq_zero_iff, spectralAlgNorm_mul, spectralNorm_eq_invariantExtension, HahnSeries.cardSuppLTSubfield_carrier, IntermediateField.LinearDisjoint.basisOfBasisLeft_apply, MvPowerSeries.coeff_inv, algebraicClosure.isIntegralClosure, sub_inv_antitoneOn_Icc_left, Subfield.relfinrank_comap_comap_eq_relfinrank_inf, Polynomial.natSepDegree_C_mul_X_sub_C_pow, Algebra.normalizedTrace_intermediateField, LinearMap.finrank_genEigenspace_le, Matrix.projVandermonde_apply_of_ne_zero, div_lt_one_of_neg, Algebra.FormallyEtale.iff_isSeparable, sub_smul_slope_vadd, AlgebraicClosure.instCharP, ValuativeRel.one_vle_div_iff, NumberField.InfinitePlace.map_ratCast, NumberField.Units.norm, LinearOrderedField.cutMap_coe, AddCircle.addOrderOf_div_of_gcd_eq_one, FDRep.instFiniteDimensionalCarrierVFGModuleCat, FGModuleCat.instFiniteHom, Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero, WeierstrassCurve.Projective.negY_of_Z_ne_zero, NumberField.IsCMField.complexConj_apply_apply, NNRat.intCeil_cast, WeierstrassCurve.Affine.addPolynomial_slope, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, ConvexOn.slope_mono_adjacent, AffineSubspace.wSameSide_and_wOppSide_iff, LocalSubring.eq_iInf_of_isIntegrallyClosedIn, List.exists_map_eq_of_sorted_nonempty_iff_sbtw, Set.preimage_mul_const_Iic_of_neg, Derivation.leibniz_zpow, ordinaryHypergeometricSeries_apply_eq', IsStrictOrderedRing.toIsTopologicalDivisionRing, Projectivization.Subspace.span_coe, spectrum.one_eq, Subfield.relrank_comap, NumberField.RingOfIntegers.instIsLocalizationAlgebraMapSubmonoidIntNonZeroDivisors, Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, spectralMulAlgNorm_def, NumberField.of_subfield, Rat.floor_cast, NumberField.mixedEmbedding.span_idealLatticeBasis, ConcaveOn.slope_anti, Valuation.HasExtension.maximalIdeal_comap_algebraMap_eq_maximalIdeal, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, Matrix.instFiniteSpectrum, mul_gaussSum_inv_eq_gaussSum, IntermediateField.LinearDisjoint.basisOfBasisRight_apply, Odd.zpow_nonpos, Quaternion.imI_nnratCast, AlgebraicIndependent.lift_reprField, GenContFract.zero_le_of_den, X_pow_sub_C_irreducible_iff_of_prime_pow, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, WeierstrassCurve.Jacobian.dblXYZ_of_Z_ne_zero, Set.preimage_const_mul_Ioi_of_neg, Finpartition.isUniform_one, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux, IsCyclotomicExtension.splits_cyclotomic, Quaternion.imK_nnratCast, FDRep.average_char_eq_finrank_invariants, Polynomial.IsRoot.mul_div_eq, Height.logHeight_one, NumberField.IsCMField.coe_ringOfIntegersComplexConj, PowerSeries.normalized_count_X_eq_of_coe, WeierstrassCurve.Jacobian.addX_of_Z_ne_zero, ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier, zpow_two_pos_of_ne_zero, WeierstrassCurve.Jacobian.negMap_of_Z_eq_zero, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, WeierstrassCurve.Affine.addX_eq_addX_negY_sub, ConjRootClass.minpoly_mk, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, IsTranscendenceBasis.isAlgebraic_field, Ring.instIsFractionRingNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, isPurelyInseparable_iff_pow_mem, quadraticCharFun_one, FiniteField.norm_surjective, div_lt_div_right_of_neg, IsFractionRing.charP_of_isFractionRing, IntermediateField.toSubfield_map, WeierstrassCurve.Affine.slope_of_X_ne, PowerBasis.equivAdjoinSimple_aeval, Rat.cast_lt_natCast, FiniteDimensional.of_subalgebra_toSubmodule, IntermediateField.isPurelyInseparable_tower_bot, IntermediateField.neg_mem, le_separableClosure_iff, IntermediateField.charP', Polynomial.preHilbertPoly_eq_choose_sub_add, tendsto_nat_floor_mul_div_atTop, Polynomial.roots_C_mul_X_add_C, Subfield.relrank_comap_comap_eq_relrank_inf, IsSepClosure.isSeparable, affineHomeomorph_image_I, ConcaveOn.comp_affineMap, AddCircle.equivAddCircle_apply_mk, ValuativeRel.one_rel_div_iff, NumberField.FinitePlace.norm_lt_one_iff_mem, uniform_continuous_npow_on_bounded, isStronglyTranscendental_iff_of_field, Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing, Rat.preimage_cast_Ico, IntermediateField.botContinuousSMul, NumberField.IsCMField.equivInfinitePlace_apply, Rat.valuation_le_one_iff_den, eq_separableClosure_iff, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, WeierstrassCurve.Affine.C_addPolynomial_slope, Int.fract_div_mul_self_add_zsmul_eq, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, LocalSubring.instAtPrimeSubtypeMemSubringToSubringOfPrime, Valuation.mem_valuationSubring_iff, Rat.cast_max, ValuationSubring.coe_unitGroupMulEquiv_apply, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, div_le_one_of_neg, Submodule.mk_mem_projectivization_iff, LinearMap.minpoly_dvd_charpoly, PowerBasis.trace_gen_eq_nextCoeff_minpoly, IntermediateField.mem_toSubfield, mem_algebraicClosure_iff, arithGeom_same_eq_mul_div', NumberField.IsCMField.is_quadratic, div_eq_quo_add_sum_rem_div, IsFractionRing.mk'_num_den', sbtw_iff_right_ne_and_left_mem_image_Ioi, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, Char.card_pow_card, Valuation.pow_Uniformizer_is_pow_generator, AddCircle.coe_fract, instLawfulOfScientificOfCharZero, tendsto_pow_div_pow_atTop_zero, IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered, WeierstrassCurve.isGoodReduction_iff, FGModuleCat.FGModuleCatDual_obj, Finset.centerMass_smul_left, NumberField.IsCMField.complexConj_apply_eq_self, Rat.cast_lt_intCast, toIcoMod_eq_add_fract_mul, Valuation.Integers.le_iff_dvd, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, toIocMod_eq_sub_fract_mul, IsCyclotomicExtension.isSplittingField_X_pow_sub_one, IsPurelyInseparable.hasExponent_of_finiteDimensional, IsFractionRing.div_surjective, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, IsCyclotomicExtension.Rat.discr, Algebra.norm_inv, LaurentSeries.exists_Polynomial_intValuation_lt, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, Valued.continuous_extensionValuation, IntermediateField.instSubfieldClass, Padic.coe_mul, FiniteField.algebraMap_norm_eq_pow, trace_eq_finrank_mul_minpoly_nextCoeff, ValuationSubring.valuation_le_one_iff, Valued.coe_valuation_eq_rankOne_hom_comp_valuation, ValuationSubring.mem_unitGroup_iff, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_sup, GenContFract.exists_gcf_pair_rat_eq_of_nth_contsAux, Rat.natCast_le_cast, Odd.zpow_neg, IntermediateField.isAlgebraic_tower_top, Polynomial.separable_X_pow_sub_C', ConcaveOn.antitoneOn_slope_lt, Subfield.algebraMap_ofSubfield, GenContFract.of_convergence_epsilon, IsCyclotomicExtension.splits_X_pow_sub_one, IntermediateField.adjoin_one, transcendental_aeval_iff, Valuation.ideal_isPrincipal, toIcoDiv_zero_one, concaveOn_iff_div, Algebra.normalizedTrace_eq_of_fininteDimensional, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, one_div_le_one_div_of_neg, ValuationSubring.pointwise_smul_toSubring, eq_pos_convex_span_of_mem_convexHull, FiniteField.isSquare_neg_two_iff, NumberField.mixedEmbedding.covolume_idealLattice, Representation.isSemisimpleRepresentation_iff_isSemisimpleModule_asModule, Differential.logDeriv_div, Rat.cast_lt, Filter.tendsto_div_const_atTop_of_neg, Hyperreal.archimedeanClassMk_pos_of_tendsto, ArchimedeanClass.FiniteElement.val_sub, FGModuleCat.FGModuleCatCoevaluation_apply_one, ValuationSubring.mem_carrier, SimpleGraph.nonuniformWitnesses_spec, one_lt_div_of_neg, Subspace.dualRestrict_leftInverse, FiniteField.algebraMap_norm_eq_prod_pow, WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_ne_zero, Rat.preimage_cast_uIcc, CancelDenoms.cancel_factors_ne, Subfield.bot_eq_of_zMod_algebra, Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_det, trace_eq_trace_adjoin, IntermediateField.coe_isIntegral_iff, Set.preimage_const_mul_Iio_of_neg, instIsAlgebraicQuotientIdealResidueField, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, WeierstrassCurve.Jacobian.addY_of_Z_ne_zero, IsLocalRing.instFiniteDimensionalResidueFieldCotangentSpaceOfIsNoetherianRing, MonomialOrder.span_leadingTerm_eq_span_monomial', List.exists_map_eq_of_sorted_nonempty_iff_wbtw, Polynomial.SplittingField.instExpChar, Submodule.traceDual_le_span_map_traceDual, IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, NumberField.Embeddings.card, StrictConvexOn.secant_strict_mono_aux1, Valuation.instNonemptyUniformizer, LieAlgebra.IsKilling.coroot_mem_corootSpace, WeierstrassCurve.Jacobian.dblY_of_Z_ne_zero, ArchimedeanClass.stdPart_one, one_div_lt_of_neg, LinearOrderedField.cutMap_nonempty, NormedSpace.expSeries_apply_eq, AddCircle.card_addOrderOf_eq_totient, LocalSubring.map_maximalIdeal_eq_top_of_isMax, NumberField.IsCMField.complexEmbedding_complexConj, sum_embeddings_eq_finrank_mul, mem_perfectClosure_iff, tendsto_nat_floor_div_atTop, IsFractionRing.closure_range_algebraMap, ZMod.pow_card_sub_one_eq_one, WeierstrassCurve.Affine.derivative_addPolynomial_slope, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, one_lt_div_iff, PowerBasis.equivAdjoinSimple_gen, WeierstrassCurve.Jacobian.X_eq_iff, le_div_iff_of_neg', NumberField.CMExtension.equivMaximalRealSubfield_apply, div_le_iff_of_neg', Ideal.ResidueField.exists_smul_eq_tmul_one, Rat.comap_cast_atBot, GenContFract.terminates_iff_rat, NumberField.Units.mem_torsion, LinearMap.finiteDimensional', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, separableClosure.eq_top_iff, Valued.integer.norm_le_one, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, LieAlgebra.IsKilling.apply_coroot_eq_cast, slope_pos_iff, IntermediateField.mem_adjoin_iff_div, NumberField.to_finiteDimensional, Hyperreal.infinitesimal_sub_st, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, NumberField.isTotallyReal_iff_le_maximalRealSubfield, IsCyclotomicExtension.Rat.discr_prime_pow_ne_two', AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, Subfield.roots_X_pow_char_sub_X_bot, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', Representation.isSimpleModule_iff_irreducible_ofModule, Polynomial.natSepDegree_X_pow_char_pow_sub_C, Subfield.inf_relfinrank_left, Rat.cast_finsuppProd, GenContFract.convs_eq_convs', div_nonpos_iff, WeierstrassCurve.Jacobian.addMap_of_Z_ne_zero, Subfield.relfinrank_top_right, Lagrange.leadingCoeff_eq_sum, Hyperreal.infinitePos_abs_iff_infinite_abs, PowerBasis.equivAdjoinSimple_symm_gen, FiniteField.isSplittingField_of_nat_card_eq, legendreSym.eq_one_iff, Algebra.isUnramifiedAt_iff_map_eq, ArchimedeanClass.FiniteElement.mk_ratCast, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, IsCyclotomicExtension.Rat.absdiscr_prime_pow_succ, ArchimedeanClass.stdPart_intCast, NumberField.maximalRealSubfield_eq_top_iff_isTotallyReal, AlgHom.fieldRange_toSubfield, NumberField.IsCMField.card_infinitePlace_eq_card_infinitePlace, groupCohomology.norm_ofAlgebraAutOnUnits_eq, iccHomeoI_apply_coe, Valued.isOpen_valuationSubring, div_lt_iff_of_neg, ModP.preVal_mk, midpoint_le_left, RatFunc.valuation_eq_LaurentSeries_valuation, ModP.v_p_lt_preVal, sum_Ioo_inv_sq_le, NumberField.Units.coe_neg_one, Valuation.IsRankOneDiscrete.generator_zpowers_eq_range, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, WeierstrassCurve.Projective.addZ_eq, isPurelyInseparable_iff_natSepDegree_eq_one, RatFunc.liftRingHom_apply, Subfield.relfinrank_inf_mul_relfinrank, Irreducible.natSepDegree_eq_one_iff_of_monic, instSubsingletonSubfieldZMod, FiniteField.two_pow_card, PadicInt.coe_adicCompletionIntegersEquiv_apply, ordinaryHypergeometric_eq_tsum, quadraticChar_neg_two, LinearOrderedField.exists_mem_cutMap_mul_self_of_lt_inducedMap_mul_self, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, NumberField.mixedEmbedding.logMap_eq_logEmbedding, Rat.cast_multiset_prod, ValuationSubring.neg_mem, IsRealClosed.exists_eq_zpow_of_odd, Subfield.extendScalars_top, NumberField.isFinitePlace_iff, IntermediateField.coe_toSubfield, AbsoluteValue.exists_one_lt_lt_one_pi_of_not_isEquiv, FGModuleCat.ihom_obj, StrictConvexOn.slope_strict_mono_adjacent, LinearOrderedField.coe_mem_cutMap_iff, NumberField.is_primitive_element_of_infinitePlace_lt, SimpleGraph.not_isUniform_iff, Rat.cast_det, RatFunc.liftRingHom_apply_div', IsCyclotomicExtension.Rat.discr_prime_pow_succ, exists_rat_btwn, GenContFract.convs_succ, Padic.coe_inj, Polynomial.sub_mod, List.exists_map_eq_of_sorted_iff_sbtw, Ring.instIsSeparableFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Valued.toNormedField.norm_le_iff, FDRep.char_linHom, Sbtw.of_lt_of_lt, IsGaloisGroup.finiteDimensional, Submodule.restrictScalars_traceDual, LinearMap.BilinForm.dualBasis_eq_iff, NumberField.RingOfIntegers.rank, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, Height.mulHeight₁_sub_le, NumberField.IsTotallyReal.maximalRealSubfield_eq_top, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_essFiniteType, Differential.logDeriv_one, arithGeom_eq, NumberField.integralBasis_repr_apply, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, Polynomial.separable_prod_X_sub_C_iff', WithAbs.instFiniteDimensional, ValuationSubring.instIsDomainSubtypeMem, ConjRootClass.mk_neg, FiniteField.splits_X_pow_nat_card_sub_X, Padic.coe_one, LaurentSeries.coe_X_compare, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, AffineMap.image_uIcc, Matrix.val_planeConformalMatrix, Quaternion.coe_div, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, IsPrimitiveRoot.exists_pow_or_neg_mul_pow_of_isOfFinOrder, Valuation.Integers.dvdNotUnit_iff_lt, FractionalIdeal.mem_dual, Polynomial.rootOfSplits'_eq_rootOfSplits, Height.fun_logHeight_one, Valuation.Integers.valuation_unit, Polynomial.natDegree_hilbertPoly_of_ne_zero, round_eq, Polynomial.Chebyshev.iterate_derivative_U_eval_one_dvd, Configuration.ofField.instNondegenerateProjectivizationForallFinOfNatNat, Algebra.normalizedTrace_self, Polynomial.Chebyshev.iterate_derivative_T_eval_one_dvd, jacobiSum_eq_gaussSum_mul_gaussSum_div_gaussSum, RootPairing.GeckConstruction.instIsIrreducible, IntermediateField.algebraMap_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, tendsto_ratCast_atBot_iff, NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, PowerSeries.invOfUnit_eq', Algebra.norm_eq_norm_adjoin, NumberField.FinitePlace.coe_apply, Subspace.quotAnnihilatorEquiv_apply, circleEquivGen_symm_apply, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, PadicAlgCl.isAlgebraic, Rat.preimage_cast_Iic, Projectivization.mk_eq_mk_iff_crossProduct_eq_zero, IntermediateField.LinearDisjoint.norm_algebraMap, Valued.closure_coe_completion_v_lt, functionField_iff, ValuationSubring.instIsFractionRingSubtypeMem, WeierstrassCurve.Projective.negDblY_of_Z_ne_zero, Valued.valuation_isClosedMap, Lagrange.iterate_derivative_interpolate, Finset.mem_convexHull, PowerBasis.toMatrix_isIntegral, Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, Finpartition.coe_energy, ValuativeRel.inv_rel_one, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, Valued.closure_coe_completion_v_mul_v_lt, Valuation.HasExtension.instIsScalarTower_valuationSubring', FractionalIdeal.spanSingleton_div_spanSingleton, NumberField.RingOfIntegers.mk_zero, Finset.centroid_eq_centerMass, ConvexOn.secant_mono, Valued.valuedCompletion_apply, RatFunc.liftRingHom_apply_div, ValuationSubring.algebraMap_apply, le_div_iff_of_neg, Normal.isIntegral, Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder, LinearMap.hasEigenvalue_zero_tfae, NumberField.mixedEmbedding.norm_smul, sbtw_pointReflection_of_ne, LinearOrderedField.inducedMap_one, Wbtw.of_le_of_le, ValuationSubring.valuation_eq_iff, ordinaryHypergeometricSeries_apply_eq, ConvexOn.secant_mono_aux1, WeierstrassCurve.Affine.addY_sub_negY_addY, IntermediateField.list_prod_mem, WeierstrassCurve.Projective.negMap_of_Z_ne_zero, Polynomial.Chebyshev.derivative_U_eval_one_dvd, LinearMap.finiteDimensional, isAlgebraic_of_adjoin_eq_adjoin, ConvexOn.slope_mono, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, Valued.norm_def, CancelDenoms.cancel_factors_eq, SimpleGraph.unreduced_edges_subset, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, NumberField.FinitePlace.norm_def_int, Projectivization.Subspace.subset_span, spectralNorm_one, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Polynomial.Monic.natSepDegree_eq_one_iff, Valuation.valuationSubring_isPrincipalIdealRing, vectorSpan_segment, inv_sub_inv, IntermediateField.coe_zero, X_pow_sub_C_irreducible_of_prime, CauSeq.le_sup_left, Finset.convexHull_eq, WeierstrassCurve.Projective.neg_of_Z_ne_zero, IsLocalRing.exists_factor_valuationRing, arithGeom_same_eq_mul_div, slope_def_field, Subfield.relrank_map_map, ArchimedeanClass.stdPart_neg, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, Polynomial.separable_prod_X_sub_C_iff, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, LinearMap.charpoly_constantCoeff_eq_zero_iff, ArchimedeanClass.mk_ratCast, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, Subfield.bot_eq_of_charZero, NumberField.RingOfIntegers.withValEquiv_apply, Hyperreal.IsSt.sub, ZMod.gauss_lemma, NumberField.isTotallyReal_maximalRealSubfield, ValuationSubring.isIntegral_of_mem_ringOfIntegers', WeierstrassCurve.Projective.negDblY_eq, Rat.preimage_cast_Ici, left_le_lineMap_iff_le, Algebra.norm_eq_prod_automorphisms, Subfield.relrank_inf_mul_relrank, slope_fun_def, Set.preimage_const_mul_Ici_of_neg, Matrix.sub_scalar_sq_eq_disc, Polynomial.exists_approx_polynomial, Set.preimage_mul_const_Ici_of_neg, Set.preimage_mul_const_Ioc_of_neg, Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField, natDegree_radical_le, IsCyclotomicExtension.finiteDimensional, IsUltrametricDist.algNormOfAlgEquiv_apply, GenContFract.of_den_mono, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, StrictConvexOn.secant_strict_mono_aux2, selfAdjoint.val_inv, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, LieAlgebra.IsKilling.biSup_corootSpace_eq_top, IsPRadical.isPurelyInseparable, Algebra.IsUnramifiedAt.not_minpoly_sq_dvd, Subspace.finrank_add_finrank_dualCoannihilator_eq, Algebra.instIsSeparableResidueFieldOfIsUnramifiedAt, Rat.castOrderEmbedding_apply, IsFractionRing.mk'_mk_eq_div, Polynomial.X_pow_sub_one_separable_iff, NumberField.RingOfIntegers.coe_injective, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, LieAlgebra.IsKilling.disjoint_ker_weight_corootSpace, List.Sorted.sbtw, Matrix.Pivot.mul_listTransvecRow_last_row, LocalSubring.le_ofPrime, lt_div_iff_of_neg, wbtw_iff_right_eq_or_left_mem_image_Ici, CauSeq.const_le, IsPrimitiveRoot.exists_neg_pow_of_isOfFinOrder, one_mem_inv_coe_ideal, archimedean_iff_nat_lt, Valued.integer.coe_span_singleton_eq_closedBall, IntermediateField.mem_adjoin_range_iff, RatFunc.liftAlgHom_apply_div, FDRep.instHasKernels, WeierstrassCurve.Projective.addX_eq, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, wbtw_iff_left_eq_or_right_mem_image_Ici, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, IsSeparable.tower_bot, WittVector.RecursionBase.solution_spec, ValuativeRel.one_vlt_inv, WeierstrassCurve.Projective.addMap_of_Y_eq, SimpleGraph.FarFromTriangleFree.lt_half, round_eq_zero_iff, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, ArchimedeanClass.stdPart_natCast, ValuationSubring.coe_mem_nonunits_iff, NormedSpace.expSeries_apply_eq', gal_X_sub_C_isSolvable, Polynomial.hilbertPoly_mul_one_sub_succ, toIocDiv_eq_neg_floor, exists_primitive_element_iff_finite_intermediateField, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Valued.toNormedField.one_lt_norm_iff, IsCyclotomicExtension.Rat.natAbs_discr, UniformSpace.Completion.instIsTopologicalDivisionRing, FiniteField.isSplittingField_of_card_eq, LieModule.traceForm_eq_sum_finrank_nsmul, Rat.cast_mono, WeierstrassCurve.Projective.Y_eq_iff, NumberField.RingOfIntegers.isIntegral_coe, Polynomial.dickson_one_one_zmod_p, ValuationSubring.mem_nonunits_iff_exists_mem_maximalIdeal, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, Filter.Tendsto.atBot_div_const, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, IsDedekindDomain.HeightOneSpectrum.coe_mem_adicCompletionIntegers, NumberField.Units.complexEmbedding_apply, IsStronglyTranscendental.iff_of_isFractionRing, Subfield.inf_relfinrank_right, OnePoint.smul_infty_eq_ite, IntermediateField.AdjoinPair.algebraMap_gen₁, Odd.zpow_nonneg_iff, NumberField.fractionalIdeal_rank, ValuationSubring.top_coe_div, PowerSeries.invOfUnit_eq, Polynomial.IsSplittingField.IsScalarTower.isAlgebraic, doublyStochastic_eq_convexHull_permMatrix, LaurentSeries.valuation_LaurentSeries_equal_extension, IntermediateField.sub_mem, IsPrimitiveRoot.norm_eq_one_of_linearly_ordered, CauSeq.sup_comm, NumberField.finite_of_discr_bdd, FixedPoints.toAlgAut_surjective, Padic.exi_rat_seq_conv, IsPurelyInseparable.minpoly_natDegree_eq, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_apply, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, RatFunc.v_def, RingOfIntegers.coe_norm, minpoly.add_algebraMap, RatFunc.instCharZero, divRadical_dvd_wronskian_right, ArchimedeanClass.FiniteResidueField.mk_ne_zero, Polynomial.div_eq_quo_add_rem_div, LieAlgebra.IsKilling.chainTopCoeff_add_chainBotCoeff, Nat.one_sub_one_div_cast_nonneg, add_sub_div_two_lt, NumberField.Units.coe_pow, Set.preimage_const_mul_uIcc, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, LaurentSeries.LaurentSeries_coe, Finset.centroid_mem_convexHull, root_X_pow_sub_C_pow, AlgebraicIndependent.liftAlgHom_comp_reprField, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, Subalgebra.finiteDimensional_toSubmodule, legendreSym.eq_zero_iff, NumberField.RingOfIntegers.mk_one, FixedPoints.isIntegral, bddBelow_slope_lt_of_mem_interior, Rat.preimage_cast_Iio, Rat.cast_nonneg, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_adjoin_eq_top, NumberField.IsCMField.unitsMulComplexConjInv_apply, LaurentSeries.powerSeries_ext_subring, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, Set.unit_valuation_eq_one, Submodule.mem_projectivization_iff_submodule_le, Lagrange.eval_basisDivisor_left_of_ne, PowerSeries.instIsDiscreteValuationRing, Projectivization.card_of_finrank, NumberField.Units.abs_det_eq_abs_det, FDRep.instInjectiveOfNeZeroCastCard, RatFunc.liftAlgHom_apply_ofFractionRing_mk, stdSimplex.barycenter_apply, Valuation.isNontrivial_valuation_valuationSubring_iff, Hyperreal.lt_neg_of_pos_of_infinitesimal, Quaternion.imK_ratCast, IsCyclotomicExtension.Rat.absdiscr_prime, Algebra.FormallyUnramified.isSeparable, Rat.preimage_cast_uIoc, ArchimedeanClass.mk_le_mk_iff_ratCast, Algebra.discr_powerBasis_eq_prod, FDRep.char_one, Subfield.lift_relrank_comap, IntermediateField.charP, Algebra.IsAlgebraic.isNormalClosure_iff, Matrix.Pivot.listTransvecCol_mul_last_row_drop, IntermediateField.intCast_mem, jacobiSum_nontrivial_inv, InfiniteGalois.isOpen_iff_finite, RootPairing.restrictScalars_coe_root, IsPurelyInseparable.trans, IsFractionRing.ringHom_fieldRange_eq_of_comp_eq, Subspace.dualAnnihilator_iInf_eq, Polynomial.leadingCoeff_preHilbertPoly, ValuationSubring.isIntegral_of_mem_ringOfIntegers, spectralAlgNorm_one, LinearMap.finrank_maxGenEigenspace, Projectivization.Subspace.sup_span, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, Valued.integer.isDiscreteValuationRing_of_compactSpace, div_lt_div_of_neg_of_lt, NumberField.inverse_basisMatrix_mulVec_eq_repr, Projectivization.Subspace.monotone_span, NumberField.RingOfIntegers.instIsIntegralClosureInt, FixedPoints.smul_polynomial, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, Rat.cast_abs, lt_div_iff_of_neg', NumberField.IsCMField.ringOfIntegersComplexConj_eq_self_iff, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, Height.logHeight₁_zpow, CauSeq.inf_le_right, NumberField.Units.coe_injective, ValuationSubring.mem_or_inv_mem', FunctionField.inftyValuation.X_zpow, RatFunc.rank_ratFunc_ratFunc, Height.mulHeight₁_eq_mulHeight, div_lt_iff_of_neg', Polynomial.cyclotomic_eq_minpoly_rat, NumberField.Units.coe_one, spectralAlgNorm_extends, Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row, Valued.integer.norm_unit, LaurentSeries.powerSeriesRingEquiv_coe_apply, Valuation.leIdeal_zero, IsRealClosed.toIsSemireal, Polynomial.C_div, ValuationSubring.prime_idealOfLE, Filter.tendsto_div_const_atBot_of_neg, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, minpoly.ofSubring, NumberField.IsCMField.mem_realUnits_iff, exists_isTranscendenceBasis_and_isSeparable_of_perfectField, normal_iff, Int.sub_floor_div_mul_nonneg, AlgHom.card, Hyperreal.not_infinite_neg, IntermediateField.adjoin_intCast, slope_pos_iff_gt, Quaternion.im_nnratCast, FiniteDimensional.finiteDimensional_subalgebra, Rat.cast_nonpos, IntermediateField.iSup_toSubfield, archimedean_iff_rat_le, instIsDiscreteValuationRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, IsCyclotomicExtension.Rat.discr_prime_pow, Subfield.relfinrank_comap, selfAdjoint.val_qsmul, LaurentSeries.powerSeriesEquivSubring_apply, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff, NumberField.mixedEmbedding.unitSMul_smul, ArchimedeanClass.FiniteElement.val_one, Finpartition.IsEquipartition.sum_nonUniforms_lt, WeierstrassCurve.Jacobian.add_of_X_ne, LinearMap.det_eq_one_of_finrank_eq_zero, FDRep.simple_iff_end_is_rank_one, ValuativeRel.div_rel_one_iff, SimpleGraph.le_card_nonuniformWitness, FunctionField.inftyValuation.X, primitive_element_iff_minpoly_degree_eq, WeierstrassCurve.Jacobian.Y_eq_iff', IsPurelyInseparable.tower_bot, CauSeq.exists_lt, Projectivization.orthogonal_mk, Projectivization.cross_mk, WeierstrassCurve.Projective.Point.toAffine_of_Z_ne_zero, LieAlgebra.IsKilling.root_apply_coroot, ValuationSubring.ofPrime_scalar_tower, Quaternion.imJ_ratCast, separableClosure.isAlgebraic, IsAlgClosure.ofAlgebraic, tendsto_nat_ceil_div_atTop, Subfield.extendScalars.orderIso_apply, FiniteField.X_pow_card_sub_X_natDegree_eq, IntermediateField.expChar, Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull, FiniteField.pow_dichotomy, isGalois_iff, gaussSum_mul_gaussSum_pow_orderOf_sub_one, isPurelyInseparable_iff_perfectClosure_eq_top, Int.map_round, lineMap_le_lineMap_iff_of_lt, AlgHom.card_le, FiniteField.splits_X_pow_card_sub_X, Algebra.isSeparable_tower_bot_of_isSeparable, IsGaloisGroup.intermediateField, List.exists_map_eq_of_sorted_iff_wbtw, ValuationSubring.principalUnitGroupEquiv_apply, Module.End.eigenspace_div, abs_neg_one_zpow, WeierstrassCurve.Projective.X_eq_iff, Polynomial.SplittingField.instCharZero, Hyperreal.coe_one, Projectivization.Subspace.span_le_subspace_iff, FunctionField.inftyValuedFqt.def, NumberField.Embeddings.coeff_bdd_of_norm_le, Polynomial.divByMonic_eq_div, Subfield.relrank_top_right, LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul, ValuationSubring.instSubringClass, Ring.instFiniteDimensionalFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin, spectralNorm.eq_of_normalClosure', SimpContFract.of_isContFract, ZMod.Ico_map_valMinAbs_natAbs_eq_Ico_map_id, tendsto_const_mul_zpow_atTop_zero, NumberField.exists_ideal_in_class_of_norm_le, algebraicClosure.eq_top_iff, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow, ValuationSubring.one_mem, spectralNorm.spectralNorm_eq_norm_coeff_zero_rpow, Quaternion.ratCast_im, Valued.integer.exists_nnnorm_lt_one, WeierstrassCurve.Projective.dblY_of_Z_ne_zero, Rat.isNat_intFloor_ofIsNNRat, Algebra.normalizedTrace_minpoly, Set.preimage_mul_const_Ico_of_neg, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, separatingDual_iff_injective, minpoly.eq_X_sub_C', Valued.integer.properSpace_iff_compactSpace_integer, isVisible_iff_lineMap, Differential.logDeriv_pow, primitive_element_iff_minpoly_natDegree_eq, RatFunc.liftRingHom_apply_ofFractionRing_mk, Submodule.traceDual_eq_span_map_traceDual_of_linearDisjoint, extremePoints_doublyStochastic, Valuation.Integers.valuation_pos_iff_ne_zero, Subspace.dualEquivDual_def, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', legendreSym.eq_one_iff', List.Sorted.wbtw, FixedBy.intermediateField_mem_iff, IsAlgClosure.isAlgebraic, RootPairing.polarizationEquiv_symm_apply_coroot, IntermediateField.isScalarTower_over_bot, IntermediateField.isSeparable_tower_bot, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, FiniteField.isSquare_iff, IntermediateField.minpoly_eq, RatFunc.instExpChar, Nat.one_sub_one_div_cast_le_one, LinearMap.BilinForm.IsSymm.polarization, max_div_div_right_of_nonpos, Quaternion.ratCast_imI, Matrix.Pivot.mul_listTransvecRow_last_col_take, Int.fract_div_natCast_eq_div_natCast_mod, Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero, IsAlgClosure.separable, legendreSym.eq_pow, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_surjective, PowerSeries.coeff_inv, exists_integral_multiples, IntermediateField.bot_toSubfield, Odd.zpow_pos_iff, WeierstrassCurve.Affine.slope_of_Y_ne_eq_evalEval, ValuativeRel.vle_div_iff, NumberField.RingOfIntegers.coe_eq_algebraMap, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, Subspace.dualLift_rightInverse, IsPurelyInseparable.pow_mem, Valuation.valuationSubring_not_isField, isPurelyInseparable_iff_finSepDegree_eq_one, LieAlgebra.rank_le_finrank_engel, CauSeq.le_total, ValuationSubring.mem_principalUnitGroup_iff, NumberField.mem_span_integralBasis, quadraticCharFun_eq_pow_of_char_ne_two, WeierstrassCurve.Projective.add_of_Y_eq, Ideal.coe_smul_primesOver_eq_map_galRestrict, IntermediateField.adjoin_eq_range_algebraMap_adjoin, Quaternion.normSq_zpow, Polynomial.resultant_eq_prod_roots_sub, Quaternion.coe_nnratCast, Finset.centerMass_ite_eq, ValuationSubring.toSubring_injective, NumberField.IsCMField.exists_isConj, spectralAlgNorm_of_finiteDimensional_normal_def, isPurelyInseparable_of_finSepDegree_eq_one, WeierstrassCurve.Projective.negAddY_eq, FirstOrder.Field.instModelField, OnePoint.smul_infty_def, Height.fun_mulHeight_one, MonoidAlgebra.Submodule.instIsSemisimpleRingAddMonoidAlgebra, Hyperreal.infinite_iff_abs_lt_abs, Module.instFiniteDimensionalOfIsReflexive, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, WeierstrassCurve.Jacobian.addX_eq, WeierstrassCurve.Projective.add_of_X_ne, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, selfAdjoint.val_ratCast, iccHomeoI_symm_apply_coe, FixedPoints.toAlgHom_bijective, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, FiniteField.isSquare_odd_prime_iff, Algebra.normalizedTrace_def, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, Subfield.isClosed_topologicalClosure, IntermediateField.adjoin_natCast, NumberField.Units.coe_zpow, NumberField.mem_span_basisOfFractionalIdeal, Polynomial.IsSplittingField.instFiniteDimensionalSplittingField, FiniteField.minpoly_frobeniusAlgHom, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, mem_convexHull_iff_exists_fintype, IntermediateField.coe_inv, IntermediateField.AdjoinSimple.isIntegral_gen, RatFunc.instCharP, IsGaloisGroup.fixedPoints, Matrix.Pivot.listTransvecCol_mul_last_row, perfectField_iff_isSeparable_algebraicClosure, LieAlgebra.IsKilling.rootSystem_pairing_apply, LieAlgebra.IsKilling.chainTopCoeff_zero_right, quadraticChar_odd_prime, le_iff_forall_lt_rat_imp_le, Valued.extensionValuation_apply_coe, round_le_add_half, Odd.zpow_neg_iff, IsDedekindDomain.HeightOneSpectrum.valuation_surjective, NumberField.mixedEmbedding.logMap_apply, Quaternion.ratCast_imK, Algebra.FormallyEtale.iff_exists_algEquiv_prod, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, Rat.cast_lt_zero, Rat.cast_strictMono, convex_iff_div, HahnSeries.single_div_single, IntermediateField.isPurelyInseparable_bot, NumberField.mixedEmbedding.latticeBasis_apply, mem_algebraicClosure_iff', Polynomial.mem_normalizedFactors_iff, SimpleGraph.right_nonuniformWitnesses_card, FiniteField.sum_pow_units, pow_div_pow_eventuallyEq_atTop, List.SortedLT.sbtw, LaurentSeries.valuation_coe_ratFunc, Quaternion.ratCast_imJ, Hyperreal.archimedeanClassMk_omega_neg, ValuationSubring.coe_unitGroupMulEquiv_symm_apply, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, WeierstrassCurve.Projective.add_of_Y_ne', IntermediateField.top_toSubfield, WeierstrassCurve.Jacobian.negAddY_of_Z_ne_zero, Hyperreal.archimedeanClassMk_coe_nonneg, Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable, Normal.toIsAlgebraic, AlgebraicIndependent.aevalEquivField_apply_coe, LieAlgebra.IsKilling.orthogonal_span_coroot_eq_ker, ZMod.instSubsingletonSubfield, Height.logHeight₁_eq_logHeight, HahnSeries.inv_def, Valuation.Integer.not_isUnit_iff_valuation_lt_one, CauSeq.le_sup_right, IsCyclotomicExtension.Rat.nrRealPlaces_eq_zero, Ideal.factors_span_eq, minpoly_algEquiv_toLinearMap, exists_rat_mem_uIoo, div_pos_iff, minpoly.natSepDegree_eq_one_iff_pow_mem, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, Rat.cast_pos_of_pos, arithGeom_zero_eq_mul_div, FormalMultilinearSeries.ofScalars_smul, Polynomial.mod_X_sub_C_eq_C_eval, NumberField.FinitePlace.norm_eq_one_iff_notMem, Valuation.exists_pow_Uniformizer, Submodule.mem_traceDual, Projectivization.Subspace.mem_span, IntermediateField.finiteDimensional_left, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, legendreSym.card_sqrts, minpoly.one, ZMod.gauss_lemma_aux, Matrix.finiteDimensional, LaurentSeries.valuation_compare, ArchimedeanClass.mk_ratCast_nonneg, isConjRoot_iff_orbitRel, AlgebraicClosure.instIsScalarTower, Hyperreal.tendsto_atBot_iff, le_perfectClosure_iff, perfectClosure.isAlgebraic, IsPreconnected.eq_or_eq_neg_of_sq_eq, Polynomial.SplittingField.instCharP, NumberField.IsCMField.complexConj_eq_self_iff, Even.zpow_pos_iff, PadicInt.zmod_congr_of_sub_mem_max_ideal, SimpleGraph.nonuniformWitness_spec, IntermediateField.isSeparable_sup, lineMap_le_left_iff_le, Finset.centerMass_pair, one_div_lt_one_div_of_neg_of_lt, FiniteGaloisIntermediateField.finiteDimensional, minpoly.neg, div_eq_quo_add_rem_div_add_rem_div, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, Polynomial.natSepDegree_X_sub_C, Convex.mem_Icc, Rat.denseRange_cast, IsSepClosure.isAlgClosure_of_perfectField_top, Filter.tendsto_div_const_atTop_iff_neg, ZMod.nonsquare_iff_jacobiSym_eq_neg_one, lt_one_div_of_neg, Rat.cast_le_intCast, RatFunc.liftAlgHom_apply, Polynomial.roots_C_mul_X_sub_C, ValuativeRel.one_vle_inv, AddCircle.addOrderOf_eq_pos_iff, slope_sub_smul, LaurentSeries.tendsto_valuation, IsGaloisGroup.subgroup, normalClosure_eq_iSup_adjoin, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, left_le_midpoint, isSepClosed_iff_isPurelyInseparable_algebraicClosure, NumberField.abs_discr_ge_of_isTotallyComplex, Module.End.genEigenspace_div, WeierstrassCurve.Projective.negMap_of_Z_eq_zero, AlgebraicClosure.isAlgebraic, NumberField.mixedEmbedding.latticeBasis_repr_apply, RatFunc.transcendental, IsGalois.finiteDimensional_of_finite, IntermediateField.mem_adjoin_simple_iff, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField, Set.preimage_const_mul_Ioo_of_neg, krullTopology_mem_nhds_one_iff, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, FormalMultilinearSeries.ofScalars_comp_neg_id, FiniteField.unitsMap_norm_surjective, gaussSum_pow_eq_prod_jacobiSum, IntermediateField.one_mem, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, MonoidAlgebra.Submodule.instIsSemisimpleModule, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, Rat.ceil_cast, Matrix.posDef_inv_iff, Valued.integer.mem_iff, pow_div_pow_eventuallyEq_atBot, FirstOrder.Field.model_hasChar_of_charP, WeierstrassCurve.Projective.addMap_of_Z_ne_zero, X_pow_sub_C_irreducible_of_prime_pow, WeierstrassCurve.Projective.equiv_zero_of_Z_eq_zero, WeierstrassCurve.Affine.Point.map_some, ValuationSubring.nonunits_le, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', RatFunc.finrank_ratFunc_ratFunc, SimpleGraph.FarFromTriangleFree.lt_one, WeierstrassCurve.Jacobian.nonsingular_of_Z_ne_zero, SimpleGraph.left_nonuniformWitnesses_card, ValuativeRel.div_rel_iff, Padic.rat_dense', PowerSeries.intValuation_X, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, AlgebraicGeometry.Proj.valuativeCriterion_existence_aux, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal, Asymptotics.SuperpolynomialDecay.param_zpow_mul, Finpartition.mk_mem_sparsePairs, one_div_le_of_neg, sub_smul_slope, Valued.completable, IsCyclotomicExtension.Rat.finrank, LocalSubring.instIsScalarTowerSubtypeMemSubringToSubringOfPrime, toIcoMod_zero_one, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', Polynomial.Monic.eq_X_pow_char_pow_sub_C_of_natSepDegree_eq_one_of_irreducible, Subspace.dualLift_injective, strictConcaveOn_iff_div, Hyperreal.coe_div, krullTopology_mem_nhds_one_iff_of_normal, IsRealClosed.exists_eq_zpow_of_nonneg, IsGalois.integral, IntermediateField.sInf_toSubfield, Rat.cast_le_natCast, archimedean_iff_int_lt, IsPurelyInseparable.elemExponent_le_exponent, stdSimplex.barycenter_eq_centerMass, NNRat.Nonneg.coe_ofScientific, tendsto_const_mul_zpow_atTop_nhds_iff, Subfield.relfinrank_map_map, Set.preimage_mul_const_Icc_of_neg, NumberField.mixedEmbedding.finrank, ConjRootClass.mk_def, selfAdjoint.val_nnratCast, NumberField.to_charZero, NumberField.IsTotallyReal.le_maximalRealSubfield, AffineSubspace.direction_smul, Valuation.leAddSubgroup_zero, NumberField.isUnit_iff_norm, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, toIcoDiv_eq_floor, FGModuleCat.FGModuleCatDual_coe, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Subfield.lift_rank_comap, Projectivization.cross_mk_of_ne, Asymptotics.SuperpolynomialDecay.mul_param_zpow, Algebra.isSeparable_self, tendsto_nat_ceil_mul_div_atTop, NumberField.house_nat_mul, StrictConvexOn.secant_strict_mono, separableClosure.isSeparable, minpoly.natDegree_le, LieAlgebra.IsKilling.chainBotCoeff_le_chainLength, AddCircle.nsmul_eq_zero_iff, wbtw_or_wbtw_smul_vadd_of_nonneg, IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen, archimedean_iff_rat_lt, IsCyclotomicExtension.splitting_field_cyclotomic, Valued.integer.isUnit_iff_norm_eq_one, trace_eq_sum_embeddings, ValuationSubring.mem_nonunits_iff, ArchimedeanClass.FiniteElement.mk_one, le_algebraicClosure_iff, Valued.toNormedField.norm_lt_iff, Valued.integer.isPrincipalIdealRing_of_compactSpace, FDRep.char_orthonormal, NumberField.RingOfIntegers.instIsScalarTower, Projectivization.Subspace.span_union, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Hyperreal.infiniteNeg_neg, Filter.Tendsto.const_div_atTop, CSA.fin_dim, Hyperreal.coe_abs, WittVector.RecursionBase.solution_pow, Subfield.relrank_eq_one_iff, FormalMultilinearSeries.ofScalars_series_eq_zero, Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec, finSepDegree_eq_finrank_iff, IsFractionRing.isAlgebraic_iff', Filter.tendsto_div_const_atBot_iff, Valuation.Integers.valuation_irreducible_pos, RootPairing.restrictScalars_toLinearMap_apply_apply, LinearMap.finrank_maxGenEigenspace_zero_eq, NumberField.RingOfIntegers.instIsScalarTower_1, LaurentSeries.comparePkg_eq_extension, NumberField.toNNReal_valued_eq_adicAbv, FiniteDimensional.exists_is_basis_integral, IntermediateField.coe_pow, exists_pos_rat_lt, Rat.preimage_cast_Ioo, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, Normal.out, Representation.irreducible_iff_isSimpleModule_asModule, LinearOrderedField.coe_lt_inducedMap_iff, WeierstrassCurve.Jacobian.Point.toAffine_zero, FixedPoints.minpoly_eq_minpoly, algebraicClosure.isAlgClosure, IsAlgebraic.inv_iff, IsPurelyInseparable.of_injective_comp_algebraMap, Quaternion.im_ratCast, Set.preimage_mul_const_Ioi_of_neg, legendreSym.eq_neg_one_iff', ModP.v_p_lt_val, jacobiSum_mul_jacobiSum_inv, RatFunc.single_zpow, IntermediateField.pow_mem, div_nonneg_iff, LaurentSeries.valuation_def, Subspace.dualAnnihilator_le_dualAnnihilator_iff, FiniteField.X_pow_card_pow_sub_X_natDegree_eq, RatFunc.liftAlgHom_apply_div', FiniteField.bijective_frobeniusAlgEquivOfAlgebraic_pow, ConvexOn.comp_affineMap, sum_Ioc_inv_sq_le_sub, WeierstrassCurve.Jacobian.negDblY_of_Z_ne_zero, AddCircle.addOrderOf_period_div, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, ConvexOn.monotoneOn_slope_gt, NumberField.isAlgebraic, Algebra.discr_powerBasis_eq_prod'', IsRealClosed.isSquare_or_isSquare_neg, MvPowerSeries.invOfUnit_eq', Rat.cast_pos, IsPrimitiveRoot.coe_toInteger, sub_inv_antitoneOn_Icc_right, FunctionField.inftyValuation.C, Valued.instFaithfulSMulCompletionOfUniformContinuousConstSMul, one_div_lt_one_div_of_neg, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, Even.zpow_nonneg, Polynomial.coeff_eq_esymm_roots_of_splits, NumberField.Embeddings.finite_of_norm_le, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one, NumberField.mixedEmbedding.norm_real, Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, Valuation.Integers.isUnit_iff_valuation_eq_one, ZMod.isSquare_of_jacobiSym_eq_one, round_eq_iff, isAlgClosure_iff, LieAlgebra.IsKilling.traceForm_coroot, ValuativeRel.inv_vle_one, Ideal.Factors.finiteDimensional_quotient_pow, Filter.tendsto_div_const_atTop_iff, Cubic.eq_sum_three_roots, IntermediateField.expChar', FDRep.char_dual, FormalMultilinearSeries.ofScalars_comp_neg, Complex.rank_rat_complex, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow, FiniteField.card', FGModuleCat.FGModuleCatEvaluation_apply', LieModule.traceForm_eq_sum_finrank_nsmul_mul, discrim_lt_zero, convexHull_eq_union, Set.preimage_div_const_uIcc, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, Height.mulHeight₁_div_eq_mulHeight, ValuationRing.instValuationRingInteger, quadraticChar_eq_pow_of_char_ne_two, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, convexHull_eq, IntermediateField.inf_toSubfield, NumberField.basisOfFractionalIdeal_apply, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, GenContFract.zero_le_of_contsAux_b, LieAlgebra.IsKilling.chainBotCoeff_zero_right, Polynomial.leadingCoeff_div, tendsto_pow_div_pow_atTop_atTop, slope_fun_def_field, mem_separableClosure_iff, NumberField.InfinitePlace.card_add_two_mul_card_eq_rank, div_sub', discrim_lt_zero_of_neg, AddCircle.addOrderOf_div_of_gcd_eq_one', quadraticChar_eq_pow_of_char_ne_two', RingOfIntegers.algebraMap_norm_algebraMap, WeierstrassCurve.Jacobian.Y_eq_iff, bijective_rangeRestrict_comp_of_valuationRing, Padic.coe_add, isSeparable_iff_finInsepDegree_eq_one, Set.integer_valuation_le_one, Polynomial.separable_cyclotomic, OrderIso.smulRightDual_symm_apply, one_le_div_of_neg, CyclotomicField.instCharZero, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, ValuativeRel.inv_vlt_one, PowerSeries.inv_eq_inv_aux, Algebra.discr_powerBasis_eq_prod', Polynomial.X_sub_C_mul_removeFactor, wbtw_total_of_sameRay_vsub_left, LieAlgebra.IsKilling.chainBotCoeff_add_chainTopCoeff, NumberField.FinitePlace.isFinitePlace, LinearMap.BilinForm.toLin_restrict_ker_eq_inf_orthogonal, wbtw_or_wbtw_smul_vadd_of_nonpos, LinearMap.isCompl_span_singleton_orthogonal, FixedPoints.toAlgAut_bijective, Cubic.eq_prod_three_roots, right_le_midpoint, FiniteField.isSplittingField_sub, NumberField.InfinitePlace.map_intCast, MvPowerSeries.invOfUnit_eq, Complex.isIntegral_rat_I, CauSeq.lt_total, IsUltrametricDist.isNonarchimedean_algNormOfAlgEquiv, Hyperreal.abs_omega, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, FDRep.instHasFiniteLimits, Valued.integer.totallyBounded_iff_finite_residueField, divRadical_dvd_wronskian_left, instIsPrincipalIdealRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, LieAlgebra.IsKilling.rootSpace_two_smul, LieAlgebra.isRegular_iff_finrank_engel_eq_rank, NumberField.instFiniteIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, Set.preimage_const_mul_Icc_of_neg, NumberField.mixedEmbedding.euclidean.finrank, convexHull_rangle_single_eq_stdSimplex, AffineSubspace.SOppSide.exists_sbtw, IsUltrametricDist.isPowMul_algNormOfAlgEquiv, LaurentSeries.ratfuncAdicComplRingEquiv_apply, FixedPoints.smul, IsIdempotentElem.quasispectrum_subset, separableClosure_le_iff, solvableByRad.isIntegral, IntermediateField.LinearDisjoint.basisOfBasisLeft_repr_apply, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, Projectivization.Subspace.span_univ, Valuation.Uniformizer.is_generator, Filter.Tendsto.div_atBot, Rat.cast_le, WeierstrassCurve.Projective.Point.toAffine_zero, WeierstrassCurve.Jacobian.neg_of_Z_ne_zero, Representation.is_simple_module_iff_irreducible_ofModule, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, quadraticChar_neg_one, gauge_smul_left, Hyperreal.infinitesimal_neg, LinearOrderedField.cutMap_self, Module.End.mem_spectrum_iff_isRoot_charpoly, ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdeal, NumberField.IsCMField.infinitePlace_complexConj, Hyperreal.coe_neg, IntermediateField.isAlgebraic_adjoin_iff_bot, Module.Basis.traceDual_powerBasis_eq, ConcaveOn.slope_anti_adjacent, Derivation.leibniz_div_const, AddCircle.intCast_div_mul_eq_zsmul, LinearOrderedField.cutMap_bddAbove, ValuationSubring.subtype_apply, isAlgebraic_of_mem_rootSet, Rat.isNNRat_intFract_of_isNNRat, Module.End.genEigenspace_restrict_eq_top, FixedPoints.smulCommClass', Subring.eq_iInf_of_isIntegrallyClosedIn, IsFractionRing.lift_fieldRange, div_neg_of_neg_of_pos, Quaternion.re_ratCast, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, IsGalois.of_fixed_field, FixedPoints.coe_algebraMap, ValuationSubring.valuation_eq_one_iff, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, Filter.Tendsto.const_div_atBot, Subfield.card_bot, WeierstrassCurve.Projective.dblX_eq, CauSeq.exists_gt, FiniteDimensional.subalgebra_toSubmodule, Cubic.d_eq_three_roots, Set.integer_eq, WeierstrassCurve.Projective.addX_of_Z_ne_zero, Positive.coe_zpow, zpow_eq_one_iff_cases₀, Valuation.valuationSubring_eq_top_iff, Hyperreal.abs_lt_real_iff_infinitesimal, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, Projectivization.cross_mk_of_cross_eq_zero, Subfield.extendScalars.orderIso_symm_apply_coe, Finset.centerMass_neg_left, LieAlgebra.IsKilling.chainTopCoeff_le_chainLength, LinearMap.not_hasEigenvalue_zero_tfae, AddCircle.addOrderOf_coe_rat, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly, Projectivization.card_of_finrank_two, IntermediateField.sup_toSubfield, IsCyclotomicExtension.Rat.discr_odd_prime', ValuationSubring.ofPrime_localization, ArchimedeanClass.mk_div, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, GenContFract.of_convs_eq_convs', div_sub_div, convexOn_iff_div, zpow_eq_zpow_iff_cases₀, Valuation.HasExtension.instIsScalarTower_valuationSubring, FDRep.instProjectiveOfNeZeroCastCard, MvPolynomial.comp_C_integral_of_surjective_of_isJacobsonRing, Filter.tendsto_div_const_atBot_of_pos, Subfield.relfinrank_comap_comap_eq_relfinrank_of_surjective, NumberField.coe_discr, ZMod.prod_Ico_one_prime, LinearMap.finrank_maxGenEigenspace_eq, IntermediateField.adjoin_toSubfield, spectralAlgNorm_isPowMul, Polynomial.hilbertPoly_mul_one_sub_pow_add, homothety_inv_two, IntermediateField.finiteDimensional_map, strictConvexOn_iff_div, CauSeq.trichotomy, NumberField.Units.finrank_mul_regulator_eq_det, Configuration.ofField.mem_iff, ValuativeRel.one_srel_inv, NumberField.InfinitePlace.prod_eq_abs_norm, IsSepClosure.isAlgClosure_of_perfectField, LieAlgebra.IsKilling.span_weight_eq_top, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, ValuationRing.coe_equivInteger_apply, Algebra.IsSeparable.of_algHom, IsAdjoinRoot.primitive_element_root, IsCyclotomicExtension.Rat.discr_prime, wbtw_pointReflection, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype, Algebra.isSeparable_residueField_iff, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, NumberField.FinitePlace.norm_le_one, geom_sum₂_Ico, mul_sub_mul_div_mul_neg_iff, NumberField.InfinitePlace.map_natCast, NumberField.Units.sum_mult_mul_log, WeierstrassCurve.Projective.add_of_Y_ne, LinearMap.BilinForm.finrank_add_finrank_orthogonal, Valuation.leSubmodule_zero, Subfield.extendScalars_self, Algebra.coe_trace_int, NumberField.Embeddings.range_eval_eq_rootSet_minpoly, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton, Valued.integer.norm_coe_unit, WeierstrassCurve.j_of_isShortNF, WithAbs.instIsSeparable, Lagrange.eval_basis_self, IntermediateField.forall_mem_adjoin_smul_eq_self_iff, GenContFract.exists_rat_eq_nth_conv, LaurentSeries.mem_integers_of_powerSeries, div_lt_one_iff, one_div_le_one_div_of_neg_of_le, FirstOrder.Field.model_fieldOfChar_of_charP, WeierstrassCurve.IsGoodReduction.goodReduction, RingOfIntegers.coe_algebraMap_norm, min_div_div_right_of_nonpos, IsPrimitiveRoot.minpoly_dvd_cyclotomic, Algebra.IsAlgebraic.tower_bot, Projectivization.Subspace.span_eq_span_iff, NumberField.mixedEmbedding.convexBodySum_volume, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, LieModule.Weight.toLinear_neg, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, WeierstrassCurve.Projective.negAddY_of_Z_ne_zero, WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero, IntermediateField.isPurelyInseparable_tower_top, Algebra.Etale.iff_exists_algEquiv_prod, NumberField.RingOfIntegers.minpoly_coe, ZMod.fieldRange_castHom_eq_bot, Rat.preimage_cast_Ioc, Subspace.map_dualCoannihilator, lineMap_slope_lineMap_slope_lineMap, FDRep.scalar_product_char_eq_finrank_equivariant, Subfield.lift_relrank_comap_comap_eq_lift_relrank_inf, convexOn_zpow, IntermediateField.toSubfield_injective, WeierstrassCurve.Jacobian.dblXYZ_of_Y_eq, WeierstrassCurve.Jacobian.equation_of_Z_ne_zero, WeierstrassCurve.Projective.dblX_of_Z_ne_zero, Projectivization.Subspace.mem_carrier_iff, Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, ValuationSubring.algebraMap_injective, NNRat.intFloor_cast, autAdjoinRootXPowSubC_root, Hyperreal.infinitePos_abs_iff_infinite, AddCircle.equivAddCircle_symm_apply_mk, Polynomial.cyclotomic_eq_minpoly, IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers, ZMod.euler_criterion, NumberField.hermiteTheorem.rank_le_rankOfDiscrBdd, ValuationSubring.valuation_surjective, Cubic.b_eq_three_roots, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, Valued.norm_pos_iff_valuation_pos, wbtw_midpoint, Subfield.completableTopField, sub_div', sub_self_div_two, Hyperreal.IsSt.neg, Valuation.HasExtension.instLiesOverSubtypeMemValuationSubringValuationSubringMaximalIdeal, Rat.natCast_lt_cast, perfectClosure.perfectRing, MvPolynomial.isAlgebraic_of_mem_vars_of_forall_totalDegree_le, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, algebraMap.coe_ratCast, NumberField.Units.dirichletUnitTheorem.exists_unit, ZMod.exists_sq_eq_neg_two_iff, FixedPoints.mem_intermediateField_iff, LieAlgebra.IsKilling.exists_isSl2Triple_of_weight_isNonZero, CauSeq.sup_inf_distrib_left, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible, abs_zpow, ArchimedeanClass.FiniteElement.mk_natCast, lineMap_slope_slope_sub_div_sub, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, tendsto_pow_atTop_nhds_zero_iff, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int, Valued.toNormedField.norm_lt_one_iff, CauSeq.inf_idem, two_mul_le_add_mul_sq, WeierstrassCurve.Jacobian.add_of_Z_eq_zero, gaussSum_mul_gaussSum_eq_card, IsGalois.splits, Quaternion.normSq_div, Projectivization.Subspace.span_eq_sInf, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Subfield.inf_relrank_right, NumberField.RingOfIntegers.instIsIntegralClosure, Polynomial.mod_def, GenContFract.of_isSimpContFract, Polynomial.pairwise_coprime_X_sub_C, Matrix.sub_scalar_sq_eq_discr, archimedean_iff_int_le, RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_u, IsUltrametricDist.isPowMul_invariantExtension, ZMod.eisenstein_lemma_aux, IsNonarchimedeanLocalField.instIsTopologicalDivisionRing, NumberField.mixedEmbedding.norm_unit, Algebra.prod_embeddings_eq_finrank_pow, IsSepClosure.separable, Set.Finite.convexHull_eq, FiniteField.card_algHom_of_finrank_dvd, wbtw_iff_of_le, minpoly.eq_X_sub_C, ValuativeRel.rel_div_iff, WeierstrassCurve.j_of_isCharTwoJNeZeroNF_of_char_two, AlgebraicClosure.instCharZero, Complex.sum_div_factorial_le, Lagrange.nodal_erase_eq_nodal_div, exists_rat_lt, div_pos_of_neg_of_neg, Subspace.dualAnnihilator_inf_eq, FunctionField.inftyValuation_apply, IsGalois.separable, FiniteField.algebraMap_norm_eq_pow_sum, WeierstrassCurve.Jacobian.addMap_of_Y_eq, NumberField.instIsAlgebraicSubtypeMemSubfield, Hyperreal.st_neg, ValuationSubring.integer_valuation, ValuationSubring.primeSpectrumEquiv_apply, Height.mulHeight₁_neg, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, zpow_eq_one_iff_of_ne_zero₀, NumberField.IsCMField.complexConj_torsion, ValuationSubring.mapOfLE_comp_valuation, starConvex_iff_div, LieModule.range_traceForm_le_span_weight, sub_inv_antitoneOn_Iio, ArchimedeanClass.stdPart_ratCast, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, IsGalois.to_isSeparable, Quaternion.normSq_ratCast, FDRep.dualTensorIsoLinHom_hom_hom, instIsIntegrallyClosedSubtypeMemSubring, LieAlgebra.IsKilling.corootSpace_zero_eq_bot, LaurentSeries.exists_ratFunc_eq_v, MvPolynomial.instFiniteDimensionalROfFinite, FixedPoints.minpoly.eval₂, IntermediateField.zsmul_mem, Valued.toNormedField.one_le_norm_iff, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, WeierstrassCurve.Projective.dblXYZ_of_Y_eq, gaussSum_sq, LinearOrderedField.inducedMap_rat, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, IntermediateField.isSeparable_tower_top, slope_def_module, Filter.tendsto_div_const_atBot_iff_neg, LinearMap.finrank_eigenspace_le, Module.End.eigenspace_aeval_polynomial_degree_1, inv_eq_of_aeval_divX_ne_zero, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, exists_eq_sum_perm_of_mem_doublyStochastic, ValuationSubring.coe_subtype, Rat.comap_cast_atTop, Ideal.Fiber.exists_smul_eq_one_tmul, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, normalClosure.is_finiteDimensional, Algebra.IsSeparable.trans, IntermediateField.finiteDimensional_sup, Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin, separableClosure.eq_bot_iff, Algebra.normalizedTrace_self_apply, ConjRootClass.mk_eq_mk, Polynomial.normalizedFactors_cyclotomic_card, ValuativeRel.ValueGroupWithZero.mk_eq_valuation, LinearOrderedField.mem_cutMap_iff, Subfield.le_topologicalClosure, Valuation.coeff_zero_minpoly, Polynomial.coeff_preHilbertPoly_self, Projectivization.Subspace.span_iUnion, exists_rat_near, CauSeq.const_pos, IntermediateField.AdjoinPair.algebraMap_gen₂, Valuation.IsRankOneDiscrete.generator_mem_range, Height.mulHeight₁_one, irreducible_X_pow_sub_C_of_root_adjoin_eq_top, NumberField.house.basis_repr_norm_le_const_mul_house, Valued.integer.exists_norm_coe_lt_one, Submodule.mem_traceDual_iff_isIntegral, LieAlgebra.IsKilling.rootSystem_root_apply, Hyperreal.coe_sub, NumberField.IsCMField.Units.complexConj_eq_self_iff, IntermediateField.isIntegral_iff, Subfield.toIsStrictOrderedRing, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, homothety_one_half, Set.preimage_const_mul_Iic_of_neg, WeierstrassCurve.Jacobian.neg_of_Z_eq_zero, Algebra.IsAlgebraic.isSeparable_of_perfectField, ArchimedeanClass.mk_inv, Projectivization.Subspace.mem_submodule_iff, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, IsFractionRing.lift_mk', PadicComplexInt.integers, Subfield.extendScalars_injective, convexHull_range_eq_exists_affineCombination, WeierstrassCurve.j_of_isCharThreeJNeZeroNF_of_char_three, wbtw_iff_sameRay_vsub, mod_eq, IsRealClosed.isSquare_neg_of_not_isSquare, Int.sub_floor_div_mul_lt, IsCyclotomicExtension.isSeparable, Complex.nonempty_linearEquiv_real, IntermediateField.AdjoinSimple.algebraMap_gen, Valuation.Integers.dvd_iff_le, Subspace.finrank_add_finrank_dualAnnihilator_eq, LieModule.Weight.coe_neg, IntermediateField.isPurelyInseparable_sup, Matrix.Pivot.listTransvecRow_getElem, NumberField.FinitePlace.norm_def, CauSeq.coe_inf, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, Rat.ringOfIntegersWithValEquiv_apply, Filter.Eventually.ratCast_atTop, Int.fract_div_intCast_eq_div_intCast_mod, Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModule, div_neg_of_pos_of_neg, NumberField.IsCMField.regOfFamily_realFunSystem, Valuation.isNontrivial_iff_not_a_field, FirstOrder.Field.charP_iff_model_fieldOfChar, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, ValuationSubring.principalUnitGroup_symm_apply, Convex.mem_Ioc, Quaternion.re_nnratCast, FDRep.simple_iff_char_is_norm_one, Valuation.HasExtension.algebraMap_injective, ValuationRing.instIsFractionRingInteger, X_pow_sub_C_irreducible_iff_of_prime, selfAdjoint.val_nnqsmul, CauSeq.inf_le_left, Subspace.dualPairing_eq, inv_eq_of_root_of_coeff_zero_ne_zero, zpow_eq_neg_one_iff₀, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, Height.mulHeight_one, IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow', AddCircle.homeomorphAddCircle_symm_apply_mk, AddCircle.gcd_mul_addOrderOf_div_eq, IsPurelyInseparable.elemExponent_def, WeierstrassCurve.Jacobian.add_of_Y_ne, separableClosure.isPurelyInseparable, Rat.cast_prod, WeierstrassCurve.Projective.negDblY_of_Y_eq, tendsto_ratCast_atTop_iff, IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers, Subspace.dualEquivDual_apply, Convex.mem_Ico, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, LinearMap.BilinForm.apply_dualBasis_right, FixedBy.subfield_mem_iff, Hyperreal.archimedeanClassMk_epsilon_pos, circleEquivGen_apply, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, isCyclic_tfae, Polynomial.IsSplittingField.finiteDimensional, Hyperreal.IsSt.infinitesimal_sub, Hyperreal.tendsto_atTop_iff, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, Filter.tendsto_div_const_atBot_iff_pos, LinearOrderedField.toPosSMulStrictMono_rat, Valuation.HasExtension.algebraMap_mem_maximalIdeal_iff, RatFunc.num_denom_neg, IsIntegral.tower_bot_of_field, Finpartition.IsEquipartition.card_interedges_sparsePairs_le', IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, degree_radical_le, perfectClosure.isPurelyInseparable, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Polynomial.valuation_X_eq_neg_one, IntermediateField.isSeparable_adjoin_iff_isSeparable, AddCircle.natCast_div_mul_eq_nsmul, Lagrange.eval_basis_not_at_node, Hyperreal.Infinitesimal.neg, FDRep.finrank_hom_simple_simple, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, prod_galRestrict_eq_norm, Module.Basis.traceDual_eq_iff, IsGaloisGroup.fixedPoints_eq_bot, GenContFract.exists_rat_eq_nth_den, ZMod.pow_div_two_eq_neg_one_or_one, Quaternion.imI_ratCast, GaloisField.splits_zmod_X_pow_sub_X, Polynomial.comp_C_integral_of_surjective_of_isJacobsonRing, WeierstrassCurve.Projective.equation_of_Z_ne_zero, Valuation.isEquiv_iff_valuationSubring, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, Polynomial.Monic.eq_X_sub_C_pow_of_natSepDegree_eq_one_of_splits, IntermediateField.adjoin_contains_field_as_subfield, Rep.instInjective, Even.zpow_pos, NormedSpace.exp_eq_ofScalarsSum, IntermediateField.coe_one, Polynomial.modByMonic_eq_mod, instIsInvariantSubringOfIsInvariantSubfield, IsFractionRing.charZero_of_isFractionRing, IsPurelyInseparable.tower_top
toInv 📖	CompOp	4 math math: mul_inv_cancel, zpow_neg', inv_zero, div_eq_mul_inv
toNNRatCast 📖	CompOp	2 math math: nnratCast_def, nnqsmul_def
toRatCast 📖	CompOp	2 math math: ratCast_def, qsmul_def
toSemifield 📖	CompOp	7922 math math: ArithmeticFunction.vonMangoldt.residueClass_eq, withSeminorms_iff_mem_nhds_isVonNBounded, FiniteDimensional.of_exists_primitive_element, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, IsLocalMaxOn.fderivWithin_nonpos, Polynomial.mul_div_eq_iff_isRoot, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, FiniteField.Extension.frob_apply, LinearMap.det_toContinuousLinearMap, RatFunc.instFaithfulSMulPolynomialLaurentSeries, mfderiv_sumSwap, TangentBundle.continuousLinearMapAt_model_space, hasFDerivAt_iff_hasDerivAt, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, ContinuousLinearEquiv.antilipschitz, VectorBundleCore.toFiberBundleCore_coordChange, ContMDiffAt.coordChangeL, iteratedDeriv_scomp_two, TensorProduct.mapInclIsometry_apply, MvPolynomial.vanishingIdeal_anti_mono, ContinuousLinearMap.rayleigh_smul, Polynomial.Gal.galActionHom_restrict, AffineSubspace.sOppSide_iff_exists_right, mfderiv_prod_eq_add, Real.hasDerivAt_arccos, Real.hasDerivAt_fourier, InnerProductSpace.Core.inner_smul_right, AffineSpace.asymptoticNhds_smul, RCLike.conj_re, NumberField.basisMatrix_eq_embeddingsMatrixReindex, LinearIsometryEquiv.strictConvex_preimage, WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero, Polynomial.degree_normalize, TemperedDistribution.lineDerivOpCLM_eq, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', PiTensorProduct.mapL_id, Algebra.IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, ContinuousLinearMap.instT2Space, Submodule.starProjection_apply_eq_isComplProjection, Lagrange.interpolate_one, DiffContOnCl.smul, nhds_hasBasis_absConvex_open, fderiv_iteratedFDeriv, Polynomial.differentiableWithinAt, MeasureTheory.convolution_flip, Trivialization.pullback_linear, Algebra.normalizedTrace_map, FormalMultilinearSeries.comp_rightInv_aux1, ContinuousLinearMap.hasFPowerSeriesOnBall, MDifferentiable.coordChangeL, AlgEquiv.restrictNormal_trans, RatFunc.laurent_injective, IsAlgClosed.roots_eq_zero_iff_degree_nonpos, IntermediateField.extendScalars_toSubfield, exists_rat_pow_btwn, ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, AddCircle.coe_equivIco_mk_apply, hasStrictFDerivAt_apply, differentiableWithinAt_finCons', NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, Orthonormal.linearIndependent, fderiv_snd, LinearIsometryEquiv.hasStrictFDerivAt, Bundle.Trivial.continuousLinearEquivAt_trivialization, ContinuousLinearMap.derivWithin_of_bilinear, HasStrictFDerivAt.isLittleOTVS, ValuationRing.mem_integer_iff, SchwartzMap.lineDerivOpCLM_eq, NumberField.InfinitePlace.isNontrivial, MeasureTheory.lpNorm_conj, Algebra.normalizedTrace_algebraMap_eq_id, AddChar.card_addChar_le, NumberField.InfinitePlace.eq_iff_isEquiv, TensorProduct.enorm_lid, IntermediateField.finInsepDegree_top, LieAlgebra.IsKilling.iInf_ker_weight_eq_bot, InfiniteGalois.normal_iff_isGalois, LinearMap.BilinForm.dualSubmoduleParing_spec, Height.logHeight₁_pow, ProbabilityTheory.cdf_measure_stieltjesFunction, LinearMap.IsSymmetric.conj_eigenvalue_eq_self, SpectrumRestricts.nnreal_of_nonneg, hasDerivWithinAt_Iio_iff_Iic, RatFunc.ofFractionRing_mk', HasStrictFDerivAt.fun_mul', unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, TensorProduct.inner_tmul, fderivWithin_ofNat, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, HasMFDerivAt.mul, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, Submodule.coe_continuous_linearProjOfClosedCompl', InnerProductSpace.isPositive_rankOne_self, LinearIsometryEquiv.comp_fderiv, Polynomial.natSepDegree_le_natDegree, MeasureTheory.condExpL1_smul, Seminorm.absorbent_closedBall_zero, ContinuousLinearMap.isBigO_comp, Lagrange.interpolate_eq_of_values_eq_on, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, ContinuousAlternatingMap.opNorm_prod, LinearMap.ortho_smul_right, Orthonormal.inner_left_finsupp, ordinaryHypergeometric_sum_eq, LeftInvariantDerivation.lift_zero, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ArchimedeanClass.FiniteResidueField.mk_ratCast, Polynomial.coe_normUnit_of_ne_zero, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, norm_cfcₙHom, IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', IntermediateField.aeval_gen_minpoly, OrthonormalBasis.orthogonalProjection_eq_sum, IntermediateField.adjoin_eq_top_iff_of_isAlgebraic, hasDerivWithinAt_ofNat, ContinuousLinearMap.analyticWithinAt_bilinear, ValuationSubring.mem_comap, IsIntegralClosure.rank, MvPolynomial.radical_le_vanishingIdeal_zeroLocus, strictConvexOn_iff_slope_strict_mono_adjacent, HasCompactSupport.convolution_integrand_bound_left, Subfield.rank_comap, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuous₂, LinearMap.IsSymmetric.inner_map_polarization, RCLike.geometric_hahn_banach_point_open, Polynomial.IsSplittingField.mul, ValuationSubring.coe_mem_principalUnitGroup_iff, fderivWithin_comp_derivWithin_of_eq, ContinuousLinearEquiv.differentiable, ContinuousLinearMap.opNorm_prod, hasDerivWithinAt_add_const_iff, ValuationSubring.valuation_lt_one_iff, IsLocalRing.ResidueField.algebraMap_residue, LinearMap.coe_toSeminorm, ContinuousLinearMap.integral_compLp, FormalMultilinearSeries.comp_partialSum, Real.sSup_smul_of_nonpos, IntermediateField.fieldRange_le, tendsto_birkhoffAverage_apply_sub_birkhoffAverage', LinearMap.adjoint_adjoint, DoubleCentralizer.star_snd, ContinuousLinearMap.norm_inr_le_one, quadraticChar_card_sqrts, IntermediateField.LinearDisjoint.iff_inf_eq_bot, IntermediateField.normal_inf, TensorProduct.ext_iff_inner_left, FixedPoints.finrank_eq_card, Valuation.FiniteField.algebraMap_le_one, binomialSeries_eq_ordinaryHypergeometricSeries, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, Matrix.IsHermitian.isClosedEmbedding_cfcAux, InnerProductSpace.toLinearIsometry_toDual, IsUltrametricDist.algNormOfAlgEquiv_extends, Valuation.FiniteField.algebraMap_eq_one, RCLike.normSq_to_real, ZMod.pow_card_sub_one, Polynomial.cardPowDegree_zero, Seminorm.continuous_of_continuous_comp, HasMFDerivAt.add, AlgEquiv.coe_adjoinSingletonEquivAdjoinRootMinpoly_symm, galRestrict_symm_algebraMap_apply, NumberField.InfinitePlace.norm_embedding_of_isReal, Subspace.dualAnnihilator_dualAnnihilator_eq_map, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, Filter.IsBoundedUnder.smul_tendsto_zero, tendsto_const_mul_pow_nhds_iff', PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, RatFunc.num_div, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal, IsSelfAdjoint.commute_cfcHom, Real.hasFDerivAt_fourierChar_neg_bilinear_left, InnerProductSpace.span_gramSchmidtNormed, LinearIsometryEquiv.analyticOnNhd, QuadraticMap.lineDeriv, hasStrictDerivAt_intCast, ContinuousAlternatingMap.uniformContinuous_eval_const, cfcₙ_norm_nonneg, IsGalois.tower_top_intermediateField, LeftInvariantDerivation.leibniz, MeasureTheory.convolution_eq_right', Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, hasStrictFDerivAt_exp_of_mem_ball, quasispectrum.algebraMap_mem, hasFDerivAt_iff_hasGradientAt, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, FixedPoints.minpoly.monic, cfcₙHom_apply_mem_elemental, ContinuousMultilinearMap.cpolynomialOn, LinearIsometry.norm_compContinuousAlternatingMap, IsHilbertSum.surjective_isometry, SimpleGraph.lapMatrix_toLinearMap₂', curveIntegral_smul, FormalMultilinearSeries.ofScalars_apply_eq', ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, ValuationSubring.image_maximalIdeal, Submodule.reflection_trans_reflection, AddDissociated.randomisation, NormedSpace.expSeries_eq_ofScalars, CFC.abs_eq_cfc_norm, NumberField.InfinitePlace.sum_mult_eq, FixedPoints.minpoly.irreducible, extDeriv_constOfIsEmpty, RCLike.separate_convex_open_set, RootPairing.coroot_eq_polarizationEquiv_apply_root, Bundle.Trivial.symmL_trivialization, Ideal.exists_comap_galRestrict_eq, NumberField.canonicalEmbedding.mem_span_latticeBasis, Real.fderiv_fourierIntegral, Submodule.orthogonalDecomposition_symm_apply, hasStrictFDerivAt_list_prod_finRange', RatFunc.coe_mapAlgHom_eq_coe_map, OrthogonalFamily.linearIsometry_apply_single, NumberField.integralBasis_apply, AbsoluteValue.isEquiv_trivial_iff_eq_trivial, CFC.sqrt_eq_one_iff', ContinuousLinearMapWOT.neg_apply, LinearIsometry.nnnorm_toContinuousLinearMap, ContinuousLinearMap.isStarProjection_iff_isSymmetricProjection, CFC.posPart_one, InnerProductSpace.rankOne_one_left_eq_innerSL, ContDiff.fderiv_succ, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow, Submodule.IsOrtho.starProjection_comp_starProjection, FormalMultilinearSeries.ofScalars_eq_zero_of_scalar_zero, convexHull_insert, fderiv_intCast, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, IntermediateField.adjoin.finrank, Subalgebra.spectrum_sUnion_connectedComponentIn, ValuationSubring.integralClosure_algebraMap_injective, ContMDiffMap.coeFnAlgHom_apply, IsPurelyInseparable.minpoly_eq', IntermediateField.algebraMap_mem, NonUnitalCStarAlgebra.toStarModule, NormedSpace.expSeries_summable_of_mem_ball, hasDerivAt_sqrt_mul_log, Filter.EventuallyEq.fderivWithin, IsLocalRing.finrank_CotangentSpace_eq_one_iff, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, LinearMap.IsSymmetric.restrictScalars, bddBelow_smul_iff_of_neg, Matrix.GeneralLinearGroup.val_mkOfDetNeZero, PrimeSpectrum.residueField_specComap, fderivWithin_one, ContinuousLinearMap.continuous_det, HasFiniteFPowerSeriesAt.neg, inv_atBot₀, Polynomial.isEquivalent_atBot_div, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, NumberField.mixedEmbedding.convexBodyLT'_mem, NumberField.InfinitePlace.comap_mk, PiTensorProduct.mapLMonoidHom_apply, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv, ClosedSubmodule.toSubmodule_orthogonal_eq, RootPairing.instIsRootSystemSubtypeMemSubmoduleSpanRangeCoeEmbeddingRootCorootRestrictScalars', ContinuousLinearMap.map_add_add, NumberField.prod_nonarchAbsVal_eq, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, ContinuousAlternatingMap.isEmbedding_restrictScalars, ContinuousAlternatingMap.norm_constOfIsEmpty, HasFDerivWithinAt.pow, ContinuousLinearMap.sSup_unit_ball_eq_norm, Lagrange.eval_interpolate_not_at_node', Valuation.mem_maximalIdeal_iff, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, convex_iff_ordConnected, WeakDual.isCompact_polar, hasFDerivWithinAt_const, MeromorphicOn.divisor_fun_smul, ContinuousAlternatingMap.isClosedEmbedding_toContinuousMultilinearMap, nnnorm_cfc_lt, hasFDerivAt_one, Representation.IsIrreducible.instIsSimpleModuleMonoidAlgebraAsModule, Real.hasDerivAt_sigmoid, taylorWithinEval_hasDerivAt_Ioo, Lagrange.nodalWeight_eq_eval_nodal_erase_inv, Manifold.IsImmersionAtOfComplement.target_subset_preimage_target, convexHull_multiset_sum, Polynomial.Gal.smul_def, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center, WeierstrassCurve.Jacobian.baseChange_add, IsGalois.card_aut_eq_finrank, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, NormedSpace.Dual.isClosed_image_polar_of_mem_nhds, ContinuousLinearMap.analyticWithinAt, AdjoinRoot.minpoly_root, round_neg_two_inv, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, HasFDerivWithinAt.add, IntermediateField.extendScalars_sup, NumberField.IsCMField.zpowers_complexConj_eq_top, IntermediateField.coe_algebraMap_over_bot, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, Matrix.IsHermitian.det_abs, MDifferentiableAt.mfderiv_prod, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, Algebra.normalizedTrace_surjective, LinearMap.IsPositive.ne_zero_iff, Submodule.iUnion_ssubset_of_forall_ne_top_of_card_lt, hasFDerivAtFilter_pi, ModularForm.mul_slash, ContinuousLinearMap.toLinearMap₁₂_injective, Height.mulHeight₁_eq, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, Subspace.instModuleDualFiniteDimensional, curveIntegrable_segment, Algebra.normalizedTrace_eq_of_finiteDimensional, hasFDerivAt_multiset_prod, IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot, NumberField.FinitePlace.mk_apply, LinearMap.isPositive_adjoint_comp_self, Matrix.GeneralLinearGroup.IsParabolic.parabolicFixedPoint_pow, Manifold.IsImmersionAt.map_target_subset_target, BoundedContinuousFunction.algebraMap_apply, Submodule.toLinearEquiv_orthogonalDecomposition_symm, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, spectrum.subset_closedBall_norm_mul, OrthonormalBasis.repr_injective, spectrum.instCompactSpace, NumberField.instFreeIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', ContinuousLinearMap.continuousSMul, CFC.posPart_natCast, hasFTaylorSeriesUpToOn_top_iff_right, DirichletCharacter.LSeries_eulerProduct_tprod, ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, concaveOn_iff_slope_anti_adjacent, arithGeom_eq', SeparableClosure.isSepClosed, MeasureTheory.convolution_mul, IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable', expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, RootPairing.GeckConstruction.instHasTrivialRadical, HasFPowerSeriesWithinOnBall.hasSum_sub, AffineSubspace.setOf_sSameSide_eq_image2, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots, intervalIntegral.integral_hasDerivWithinAt_right, Matrix.spectrum_toEuclideanLin, ContDiff.iteratedFDeriv_right, Bornology.isVonNBounded_add_of_nonempty, NumberField.canonicalEmbedding.latticeBasis_apply, IsLocalRing.ker_residue, NumberField.IsCMField.unitsComplexConj_torsion, FormalMultilinearSeries.radius_pi_eq_iInf, ContinuousLinearMap.norm_inl_le_one, MeasureTheory.norm_condExpL2_le, RatFunc.num_div_dvd, ContinuousLinearEquiv.contDiff_comp_iff, Ideal.exists_mem_span_singleton_map_residueField_eq, mem_subalgebraEquivIntermediateField, SchwartzMap.pairing_apply_apply, Submodule.instStrictConvexSpace, InnerProductSpace.isIdempotentElem_rankOne_self, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, minpoly.algEquiv_apply, Algebra.isInvariant_of_isGalois, ContinuousMultilinearMap.norm_map_snoc_le, MonoidAlgebra.Submodule.exists_isCompl, NumberField.InfinitePlace.le_iff_le, LineDifferentiableWithinAt.smul, MeasureTheory.Measure.MapLinearEquiv.isAddHaarMeasure, IsPurelyInseparable.elemExponent_min', Meromorphic.fun_inv, ImplicitFunctionData.isInvertible_fderiv_prodFun, Trivialization.continuousLinearMapAt_apply, iteratedFDerivWithin_eventually_congr_set, ApproximatesLinearOn.lipschitz, NumberField.norm_norm_le_norm_mul_house_pow, IntermediateField.isScalarTower_mid', Real.hasStrictDerivAt_rpow_const_of_ne, FractionalIdeal.map_one_div, ConjRootClass.aeval_minpoly_iff, Polynomial.Gal.restrict_smul, ContinuousAlternatingMap.isUniformEmbedding_toContinuousMultilinearMap, StrongDual.polarSubmodule_eq_setOf, ContinuousLinearMap.continuous_integral_comp_L1, ContinuousLinearMap.isBigOWith_sub, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd, one_le_pow_mul_abs_eval_div, ContinuousLinearMap.isUniformEmbedding_restrictScalars, CFC.sq_sqrt, hasDerivWithinAt_taylorWithinEval, RCLike.star_def, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, Polynomial.div_def, HasFTaylorSeriesUpTo.cont, ImplicitFunctionData.isCompl_ker, CategoryTheory.finrank_hom_simple_simple_le_one, ContinuousLinearMap.hasDerivAtFilter, finrank_quotient_span_eq_natDegree_norm, fderivWithin_csinh, DoubleCentralizer.intCast_snd, FractionRing.instIsScalarTower, toIcoMod_eq_fract_mul, AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpen, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, DoubleCentralizer.range_toProdMulOpposite, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, ContinuousLinearMapWOT.withSeminorms, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, NumberField.InfinitePlace.nat_card_stabilizer_eq_one_or_two, Submodule.re_inner_starProjection_eq_normSq, HasFPowerSeriesOnBall.add, differentiableWithinAt_pi'', Ideal.ker_algebraMap_residueField, RatFunc.laurent_X, Lagrange.degree_basisDivisor_self, VectorField.fderiv_apply_lieBracket, NumberField.RingOfIntegers.instSMulDistribClass, MeasureTheory.inner_condExpL2_left_eq_right, ValuationSubring.mem_or_inv_mem, Polynomial.idealX_span, QuadraticForm.posDef_toMatrix', RootPairing.restrictScalars_coe_coroot, Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, NumberField.isInfinitePlace_iff, AnalyticOnNhd.compContinuousLinearMap, AffineIsometryEquiv.linear_eq_linear_isometry, ClassGroup.Quot_mk_eq_mk, IsGaloisGroup.iff_isFractionRing, NumberField.InfinitePlace.isUnramified_iff_card_stabilizer_eq_one, Bornology.isVonNBounded_add_self, WeakDual.isClosed_image_polar_of_mem_nhds, Polynomial.exists_partition_polynomial, fderiv_id, ZLattice.covolume_eq_det_inv, one_add_cpow_hasFPowerSeriesAt_zero, RCLike.algebraMap_eq_ofReal, NumberField.IsCMField.equivInfinitePlace_symm_apply, Module.Basis.constrL_basis, IsPrimitiveRoot.minpoly_dvd_pow_mod, IsIntegralClosure.isFractionRing_of_finite_extension, Submodule.reflection_orthogonal_apply, NumberField.InfinitePlace.IsUnramified.comap_algHom, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, RCLike.inner_apply', Polynomial.Gal.galActionHom_injective, convex_iff_sum_mem, Polynomial.fiberEquivQuotient_tmul, ContinuousLinearMap.comp_memLp, ZMod.units_pow_card_sub_one_eq_one, OrderRingHom.eq_id, MeasureTheory.integral_fintype_prod_volume_eq_pow, Real.fderiv_fourierChar_neg_bilinear_right_apply, NumberField.InfinitePlace.isometry_embedding, quasispectrumRestricts_iff_spectrumRestricts_inr', LinearMap.IsSymmetric.diagonalization_apply_self_apply, Matrix.isParabolic_iff_exists, Module.rankAtStalk_eq, IntermediateField.coe_bot, Subspace.dualLift_of_subtype, LinearMap.IsPositive.re_inner_nonneg_right, ContinuousAlternatingMap.instIsUniformAddGroup, WeierstrassCurve.Projective.comp_equiv_comp, Real.fourier_continuousLinearMap_apply, Ideal.ramificationIdx_le_finrank, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, LieAlgebra.IsKilling.isCompl_ker_weight_span_coroot, norm_iteratedFDeriv_mul_le, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, Padic.complete', intervalIntegral.fderiv_integral_of_tendsto_ae, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplex, ContDiffAt.fderiv_right_succ, flip_innerSL_real, WeierstrassCurve.Jacobian.Point.toAffine_of_Z_ne_zero, Submodule.starProjection_orthogonal', RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, NormedSpace.isBounded_iff_subset_smul_ball, AffineIsometryEquiv.ofTop_apply, LieAlgebra.finrank_engel, DoubleCentralizer.natCast_fst, hasFPowerSeriesOnBall_pi_iff, LinearMap.IsSymmetric.im_inner_self_apply, RatFunc.num_one, DifferentiableAt.prodMap, ContinuousLinearMap.IsPositive.toLinearMap, AnalyticOnNhd.iteratedFDeriv_of_isOpen, Polynomial.natSepDegree_pow, ZMod.charpoly_pow_card, ContinuousLinearMap.norm_compLp_le, Submodule.toLinearEquiv_orthogonalDecomposition, Continuous.convolution_integrand_fst, PadicComplex.coe_eq, MDifferentiableOn.smul_const_section, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, ContinuousLinearEquiv.symm_toDiffeomorph, ContDiffMapSupportedIn.structureMapCLM_apply, RCLike.sub_conj, OrthonormalBasis.toBasis_tensorProduct, TensorProduct.congrIsometry_refl_refl, eventually_enorm_mfderivWithin_symm_extChartAt_lt, ContinuousAlternatingMap.opNNNorm_pi, NumberField.mem_maximalRealSubfield_iff, HasFPowerSeriesWithinAt.const_smul, norm_smul_inv_norm', MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, tangentMap_snd, LaurentSeries.LaurentSeriesRingEquiv_def, Emb.Cardinal.directed_filtration, SchwartzMap.lineDerivOp_fourier_eq, FirstOrder.Field.realize_genericMonicPolyHasRoot, Subspace.dualRestrict_comp_dualLift, isClosedEmbedding_cfcₙAux, Lagrange.leadingCoeff_basis, AddChar.wInner_cWeight_self, LieModule.traceForm_eq_sum_finrank_nsmul', IntermediateField.lift_insepDegree_bot', Ring.ordFrac_eq_div, LeftInvariantDerivation.coe_derivation, Int.ceil_div_ceil_inv_sub_one, TensorProduct.enorm_comm, innerSL_apply_apply, ContinuousLinearMapWOT.instIsUniformAddGroup, DirichletCharacter.LSeries_modOne_eq, Submodule.isOrtho_sup_right, RCLike.norm_expect_le, Quaternion.coe_inv, fderiv_multiset_prod, Polynomial.eventually_atBot_not_isRoot, HasFPowerSeriesWithinOnBall.restrictScalars, NormedSpace.isVonNBounded_iff, CFC.abs_eq_cfcₙ_coe_norm, ContinuousLinearEquiv.subsingleton_or_norm_symm_pos, AlgebraicGeometry.ValuativeCommSq.isFractionRing, aemeasurable_smul_const, LinearIsometry.rTensor_def, IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, LinearMap.adjoint_innerₛₗ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, VectorField.fderiv_apply_lieBracket_of_isSymmSndFDerivAt, EuclideanSpace.inner_single_left, HasFTaylorSeriesUpTo.hasFDerivAt, HasFDerivAtFilter.fun_sum, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, LinearMap.continuousLinearMapClassOfFiniteDimensional, hasDerivAt_neg', ContMDiffWithinAt.mfderivWithin_const, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, Valuation.HasExtension.instIsLocalHomSubtypeMemValuationSubringValuationSubringRingHomAlgebraMap, HasFDerivAtFilter.sub, Unitization.splitMul_apply, geom₂_sum, inner_eq_norm_mul_iff, ContinuousLinearMap.toBilinForm_apply, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, DoubleCentralizer.nnnorm_def', ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, LinearMap.adjoint_eq_toCLM_adjoint, HasFDerivAt.fun_mul, Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, ClosedSubmodule.orthogonal_gc, LinearMap.isPositive_id, IsCyclotomicExtension.discr_odd_prime, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Seminorm.bddAbove_range_iff, fderivWithin_zero_of_not_accPt, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, NormedSpace.image_isVonNBounded_iff, VectorField.mpullbackWithin_smul, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_apply, eqOn_dslope_sub_smul, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Submodule.orthogonalProjection_mem_subspace_eq_self, IsPurelyInseparable.insepDegree_eq, ContinuousLinearMap.nnnorm_def, ContinuousLinearMap.IsPositive.inner_nonneg_right, MvPolynomial.le_vanishingIdeal_zeroLocus, gauge_smul_of_nonneg, DoubleCentralizer.zero_snd, LeftInvariantDerivation.left_invariant', insepDegree_le_rank, selfAdjoint.expUnitaryPathToOne_apply, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, hasDerivAt_bernoulliFun, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, FormalMultilinearSeries.le_changeOriginSeries_radius, algebraMap.coe_logDeriv, ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff, derivWithin_fderivWithin, HasFDerivWithinAt.prodMap, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Emb.Cardinal.filtration_succ, RatFunc.denom_one, Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField, Set.unit_eq, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, NumberField.mixedEmbedding.norm_eq_norm, IntermediateField.relfinrank_mul_finrank_top, Polynomial.map_div, LieAlgebra.IsKilling.rootSystem_coroot_apply, instLiesOverFiberOfIsPrime, PowerSeries.eq_divided_by_X_pow_order_Iff_Unit, mfderiv_comp, round_two_inv, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, X_pow_sub_C_irreducible_iff_of_odd, IsLocalRing.finrank_cotangentSpace_eq_zero, WittVector.RecursionMain.succNthVal_spec', InnerProductSpace.span_gramSchmidtNormed_range, HasFDerivWithinAt.hasLineDerivWithinAt, DirichletCharacter.LSeriesSummable_of_one_lt_re, ContinuousLinearMap.opNorm_comp_linearIsometryEquiv, Submodule.orthogonal_disjoint, algebraicClosure.algebraicClosure_eq_bot, ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverse, ContDiffPointwiseHolderAt.isBigO, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, NumberField.FinitePlace.norm_def', SchwartzMap.decay', Module.Basis.ofZLatticeBasis_apply, Seminorm.smul_inf, ContinuousAlternatingMap.map_insertNth, PowerSeries.Inv_divided_by_X_pow_order_leftInv, FormalMultilinearSeries.derivSeries_coeff_one, instIsTorsionFreeCyclotomicFieldOfIsDomainOfIsFractionRing, Polynomial.isCoveringMapOn_eval, Submodule.starProjection_add_starProjection_orthogonal, Matrix.spectrum_toLpLin, HasDerivAt.comp_ofReal, OrderedFinpartition.norm_compAlongOrderedFinpartition_le, tangentConeAt_nonempty_of_properSpace, instIsZLatticeComap, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_right, mdifferentiableOn_symm_coordChangeL, X_pow_sub_C_irreducible_of_odd, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, Continuous.integral_hasStrictDerivAt, Polynomial.mod_eq_self_iff, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Submodule.mem_orthogonal_singleton_iff_inner_right, NumberField.mixedEmbedding.mem_idealLattice, Polynomial.one_le_prod_max_one_norm_roots, RatFunc.denom_mul_dvd, IsFractionRing.fieldEquivOfAlgEquivHom_apply, Complex.re_balance, mdifferentiableWithinAt_smul_const_section, InnerProductSpace.Core.inner_smul_left, SchwartzMap.bilinLeftCLM_apply, ContinuousMap.setOfIdeal_ofSet_eq_interior, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, FunctionField.inftyValuation.X_inv, IsConformalMap.is_complex_or_conj_linear, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, NumberField.Units.regOfFamily_eq_det, Submodule.IsLattice.rank', FiniteField.frobeniusAlgEquivOfAlgebraic_apply, ContinuousLinearMap.nhds_zero_eq_of_basis, HasGradientAt.hasDerivAt', IsHilbertSum.linearIsometryEquiv_symm_apply, SmoothBumpCovering.exists_immersion_euclidean, PowerSeries.Unit_of_divided_by_X_pow_order_zero, OrderedFinpartition.norm_applyOrderedFinpartition_le, iteratedDeriv_pow, ContinuousLinearMap.cpolynomialAt, HasMFDerivWithinAt.prodMk, differentiableOn_pi, InfiniteGalois.normalAutEquivQuotient_apply, IsPurelyInseparable.elemExponent_min, AffineMap.hasDerivWithinAt, Submodule.starProjection_singleton, RCLike.conj_nat_cast, IsGaloisGroup.fixingSubgroup_top, HasFPowerSeriesAt.eventually_hasSum, instIsFractionRing, LeftInvariantDerivation.left_invariant, mfderiv_comp_apply_of_eq, PowerSeries.degree_weierstrassMod_lt, PowerSeries.maximalIdeal_eq_span_X, FractionalIdeal.isFractional_div_of_ne_zero, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, hasStrictFDerivAt_snd, WeierstrassCurve.Projective.dblU_smul, NumberField.FinitePlace.embedding_apply, NormedSpace.toIsBoundedSMul, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, WeierstrassCurve.Jacobian.negAddY_eq, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, ContinuousAlternatingMap.isClosed_range_toContinuousMultilinearMap, CategoryTheory.finrank_hom_simple_simple_eq_one_iff, Valuation.Integers.isPrincipal_iff_exists_isGreatest, curveIntegralFun_smul, addInvariantVectorField_smul, IntermediateField.isAlgebraic_tower_bot, Module.Basis.exists_opNorm_le, ClosedSubmodule.mem_orthogonal', CFC.sqrt_rpow, ConjRootClass.separable_minpoly, egauge_ball_le_of_one_lt_norm, Subspace.dualCoannihilator_dualAnnihilator_eq, MeasureTheory.charFun_toDual_symm_eq_charFunDual, IsGaloisGroup.fixedPoints_top, hasDerivWithinAt_iff_isLittleO, hasStrictFDerivAt_iff_isLittleOTVS, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, ValuativeRel.inv_srel_one, Normal.splits', IntermediateField.mem_adjoin_iff, IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply, RatFunc.laurent_algebraMap, instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, isConjRoot_iff_exists_algEquiv, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, OrthogonalFamily.orthonormal_sigma_orthonormal, Set.unitEquivUnitsInteger_symm_apply_coe, IsPurelyInseparable.finInsepDegree_eq, isDomain, ContinuousAlternatingMap.piLIE_apply_apply, PreInnerProductSpace.Core.smul_left, Matrix.PosSemidef.sqrt_eq_zero_iff, IntermediateField.mem_carrier, IsPurelyInseparable.elemExponent_def', Differentiable.fderiv_norm_rpow, UniqueMDiffOn.uniqueDiffOn, FDerivMeasurableAux.le_of_mem_A, lintegral_fderiv_lineMap_eq_edist, NumberField.InfiniteAdeleRing.algebraMap_apply, RCLike.normSq_neg, ContinuousLinearMap.isBigOWith_id, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, curveIntegrable_fun_neg_iff, hasDerivWithinAt_zero, IntermediateField.botEquiv_symm, ContDiffAt.hasStrictDerivAt, ContinuousLinearEquiv.coe_toDiffeomorph_symm, Submodule.reflection_symm, Normal.minpoly_eq_iff_mem_orbit, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', TensorProduct.ext_iff_inner_right_threefold', Subfield.relfinrank_mul_finrank_top, padicNormE.nonarchimedean', CurveIntegrable.zero, fderiv_comp_deriv, ContinuousMultilinearMap.contDiffAt, finSepDegree_eq_of_isAlgClosed, hasDerivAtFilter_ofNat, iteratedDeriv_comp_const_mul, RCLike.is_real_TFAE, sbtw_midpoint_of_ne, ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, curveIntegrable_smul_iff, TensorProduct.toLinearEquiv_lidIsometry, NormedSpace.exp_series_hasSum_exp', HasFPowerSeriesOnBall.restrictScalars, contractLeft_assoc_coevaluation, FiniteDimensional.of_finite_intermediateField, Complex.im_expect, Lagrange.eval_interpolate_not_at_node, FiniteField.frobeniusAlgHom_apply, ContinuousLinearMap.opNNNorm_le_iff, ContinuousLinearMap.isometry_mul_flip, OrthonormalBasis.toBasis_singleton, ZSpan.smul, AnalyticOnNhd.eval_linearMap', IsIntegralClosure.isLocalization, HasStrictFDerivAt.mul', NumberField.RingOfIntegers.instIsFractionRing, isPowMul_spectralNorm_of_finiteDimensional_normal, fderiv_fun_pow, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, Module.Basis.ofZLatticeComap_apply, ValuationSubring.valuation_unit, IntermediateField.relrank_mul_rank_top, IsGalois.card_fixingSubgroup_eq_finrank, Subfield.relfinrank_eq_finrank_of_le, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, InnerProductSpace.smul_left, ClosedSubmodule.inf_orthogonal, HasFDerivAtFilter.const_sub, LinearMap.coe_toContinuousLinearMap', balanced_ball_zero, HasFDerivWithinAt.linear_multilinear_comp, Polynomial.SplittingFieldAux.algebraMap_succ, iteratedFDerivWithin_succ_eq_comp_left, ContinuousLinearMap.isPositive_natCast, tendsto_birkhoffAverage_apply_sub_birkhoffAverage, isGalois_iff_isGalois_top, DiffContOnCl.inv, ContinuousMultilinearMap.opNorm_zero_iff, ModularForm.prod_slash, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, Polynomial.hilbertPoly_smul, hasStrictFDerivAt_exp_smul_const_of_mem_ball', ArchimedeanClass.FiniteResidueField.mk_eq_zero, NumberField.abs_discr_ge', hasFDerivWithinAt_comp_smul_iff_smul, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Matrix.mem_spectrum_iff_isRoot_charpoly, convexJoin_segments, Submodule.starProjection_comp_starProjection_eq_zero_iff, FDerivMeasurableAux.differentiable_set_subset_D, Submodule.one_le_traceDual_one, Ideal.algebraMap_quotient_residueField_mk, SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, MeromorphicOn.fun_smul, monomial_has_deriv_aux, finSepDegree_mul_finInsepDegree, continuous_equivFun_basis, DirichletCharacter.LSeries_twist_vonMangoldt_eq, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, LinearEquiv.toLinearEquiv_toContinuousLinearEquiv_symm, LinearIsometryEquiv.conjStarAlgEquiv_apply, MeasureTheory.smul_convolution, IsLocalRing.ResidueField.map_comp, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, IsPurelyInseparable.finrank_eq_pow, VectorField.mlieBracketWithin_const_smul_right, starConvex_iff_ordConnected, FractionalIdeal.coe_extendedHomₐ_eq_span, HasFDerivAt.le_of_lipschitzOn, Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, mem_principal_ideals_iff, LinearMap.toMatrixOrthonormal_reindex, contDiff_one_iff_fderiv, AlgebraicGeometry.functionField_isFractionRing_of_affine, MeasureTheory.ConvolutionExistsAt.integrable, HasStrictFDerivAt.pow, InfiniteGalois.mem_bot_iff_fixed, Real.hasDerivAt_mul_log, ConjRootClass.rootSet_minpoly_eq_carrier, exists_pos_right_iff_sameRay, AddCircle.homeomorphAddCircle_apply_mk, Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, Polynomial.natSepDegree_X_sub_C_pow, Asymptotics.isLittleOTVS_prodMk_left, inner_smul_left_eq_star_smul, fderivWithin_sinh, RCLike.mul_conj, RCLike.norm_conj, ValueDistribution.logCounting_pow_top, OnePoint.smul_infty_eq_self_iff, WithSeminorms.continuousSMul, CyclotomicRing.instIsFractionRingCyclotomicFieldOfIsDomainOfNeZeroCast, LinearMap.ortho_smul_left, hasLineDerivAt_iff_isLittleO_nhds_zero, deriv.scomp_of_eq, HasFDerivWithinAt.comp_of_tendsto, smul_unitClosedBall, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, Real.hasStrictDerivAt_sinh, TestFunction.continuous_iff_continuous_comp, Polynomial.exists_partition_polynomial_aux, HasFiniteFPowerSeriesOnBall.sum, HasStrictFDerivAt.const_mul, isSeparable_algebraMap, Subring.center.coe_inv, Algebra.normalizedTrace_comp_algHom, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, LinearMap.IsSymmetricProjection.ext_iff, ConvexOn.univ_sSup_of_countable_affine_eq, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, ContinuousLinearMap.ebound, RatFunc.laurent_div, Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff, CFC.negPart_algebraMap, InnerProductSpace.inner_left_rankOne_apply, Polynomial.IsSplittingField.splits_iff, cfcₙHom_nnreal_eq_restrict, AlgebraicClosure.maxIdeal.isMaximal, IsFractionRing.mk'_eq_one_iff_eq, sub_inv_antitoneOn_Ioi, TestFunction.toBoundedContinuousFunctionCLM_apply, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, RCLike.continuous_normSq, IsLocalFrameOn.coeff_apply_of_mem, ClosedSubmodule.orthogonal_injective, ContinuousAlternatingMap.norm_def, HasFDerivAt.finset_prod, ENNReal.orderIsoRpow_symm_apply, DirichletCharacter.LFunction_eq_LSeries, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, IntermediateField.normal_iff_forall_map_eq, Subspace.dualAnnihilator_dualAnnihilator_eq, ContinuousLinearMap.smul_compLp, PowerSeries.derivative_inv', hasDerivWithinAt_abs_pos, Submodule.norm_starProjection_apply_le, instIsLocalRingTensorProductResidueFieldOfIsLocalHomRingHomAlgebraMap, ContinuousLinearMap.norm_extendTo𝕜, IsLocalMax.fderiv_eq_zero, ContinuousLinearMap.contMDiff, ContinuousLinearMap.mdifferentiable, NumberField.InfinitePlace.IsUnramified.stabilizer_eq_bot, HasStrictFDerivAt.fun_sum, LieModule.exists_nontrivial_weightSpace_of_lieIdeal, HasSum.hasSum_at_zero, WeierstrassCurve.Affine.Point.toClass_zero, Pretrivialization.continuousLinearMap_symm_apply', HasFPowerSeriesAt.add, WeierstrassCurve.Jacobian.negY_of_Z_ne_zero, HasFDerivAt.norm_sq, VectorBundleCore.coordChange_self, lineDifferentiableAt_smul_iff, differentiable_fst, ContinuousAlternatingMap.curryLeft_smul, derivWithin.scomp_of_eq, fderiv_const_smul_field, IntermediateField.extendScalars_injective, HasFTaylorSeriesUpToOn.comp_continuousAffineMap, LinearIsometry.map_starProjection', ContinuousLinearMap.hasBasis_nhds_zero, polynomialFunctions.starClosure_topologicalClosure, HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, DifferentiableAt.fderiv_prodMk, ConjRootClass.minpoly.map_eq_prod, NumberField.mixedEmbedding.commMap_apply_of_isComplex, Valuation.Integers.valuation_irreducible_lt_one, innerₛₗ_apply_apply, hasFDerivWithinAt_inv, eventually_nhds_norm_smul_sub_lt, LinearIsometryEquiv.coe_toAffineIsometryEquiv, NumberField.Units.pos_at_place, DoubleCentralizer.pow_snd, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, finite_of_finite_type_of_isJacobsonRing, OrthonormalBasis.repr_self, NumberField.InfinitePlace.Completion.norm_coe, RCLike.ofReal_balance, Submodule.symmetric_isOrtho, SpectrumRestricts.nnreal_iff, iteratedDeriv_scomp_three, padicNormE.image', ContDiffAt.continuousAt_fderiv, fderiv_fun_pow', Polynomial.hilbertPoly_eq_zero_of_le_rootMultiplicity_one, hasDerivWithinAt_pi, IsometryEquiv.midpoint_fixed, minpoly.aux_inj_roots_of_min_poly, Real.integrable_prod_sub, NormedSpace.isVonNBounded_ball, OrthogonalFamily.norm_sq_diff_sum, MDifferentiable.smul, IsAlgClosed.card_roots_eq_natDegree, DirichletCharacter.norm_LSeries_product_ge_one, Ring.choose_eq_smul, norm_smul_inv_norm, ContinuousLinearEquiv.comp_hasFDerivAt_iff, ContinuousLinearMap.eq_adjoint_iff, hasMFDerivAt_sumSwap, ContinuousLinearMap.hasFDerivAt, fderivWithin_intCast, IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable, NumberField.InfinitePlace.comap_apply, ContDiffAt.fderiv_succ, ContMDiffVectorBundle.pullback, toMatrix_rotation, ContinuousLinearMap.topologicalAddGroup, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, RCLike.smul_re, IsFractionRing.mk'_eq_div, SchwartzMap.toLpCLM_apply, Polynomial.div_tendsto_zero_iff_degree_lt, LinearMap.IsSymmetric.directSum_decompose_apply, Real.volume_val, derivWithin.scomp, IntermediateField.LinearDisjoint.map', ZMod.trace_pow_card, gal_X_pow_isSolvable, Subfield.splits_bot, spectrum.nonempty_of_isAlgClosed_of_finiteDimensional, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, HasFPowerSeriesAt.comp, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, ContinuousLinearMap.IsPositive.smul_of_nonneg, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, Algebra.instFiniteResidueFieldOfQuasiFiniteAt, Unitary.coe_linearIsometryEquiv_apply, segment_eq_uIcc, MeromorphicOn.divisor_pow, ModularForm.prod_slash_sum_weights, WeierstrassCurve.Projective.add_of_Z_eq_zero, MeasureTheory.convolution_tendsto_right, NumberField.InfinitePlace.card_stabilizer, ContinuousLinearMap.coe_toContinuousLinearEquivOfDetNeZero, gelfandStarTransform_apply_apply, IntermediateField.restrictScalars_normal, Submodule.reflection_singleton_apply, RCLike.nonUnitalContinuousFunctionalCalculus, IntermediateField.isScalarTower, HasFDerivAt.of_notMem_tsupport, HasFTaylorSeriesUpToOn.zero_eq', Polynomial.Gal.mapRoots_bijective, IsFractionRing.fieldEquivOfAlgEquiv_trans, fderiv_sum, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, AffineIsometryEquiv.pointReflection_midpoint_left, HarmonicAt.analyticAt_complex_partial, FormalMultilinearSeries.ofScalars_apply_eq, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, Polynomial.splits_map_iff, Ring.ordFrac_eq_ord, IsNonarchimedeanLocalField.instIsDiscreteValuationRingSubtypeMemSubringIntegerValueGroupWithZeroValuation, NormedSpace.Dual.toWeakDual_continuous, PowerSeries.inv_eq_iff_mul_eq_one, HasFiniteFPowerSeriesAt.finite, HasFDerivWithinAt.const_mul, isClosed_setOf_tendsto_birkhoffAverage, IsGalois.mem_range_algebraMap_iff_fixed, deriv_fun_inv'', fderiv_ofNat, Algebra.FormallySmooth.adjoin_of_algebraicIndependent, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ValuationSubring.mem_inv_pointwise_smul_iff, FormalMultilinearSeries.id_apply_one', ContinuousMultilinearMap.norm_smulRightL_le, tensorIteratedFDerivTwo_eq_iteratedFDeriv, AnalyticOnNhd.iteratedFDeriv, ContinuousLinearEquiv.contDiffAt_comp_iff, IntermediateField.algebraAdjoinAdjoin.instIsAlgebraicSubtypeMemSubalgebraAdjoinAdjoin, IsAlgClosed.instIsAlgClosure, Asymptotics.isTheta_inv, FixedPoints.rank_le_card, ContinuousLinearMap.precompL_apply, DoubleCentralizer.nnnorm_snd, Algebra.normalizedTrace_algebraMap, Set.inv_Iio₀, ContinuousLinearEquiv.isBigO_comp, isPurelyInseparable_iff_fd_isPurelyInseparable, Set.inv_Ioo_0_right, Algebra.WeaklyQuasiFiniteAt.finite_residueField, HasStrictFDerivAt.star, inv_le_inv_of_neg, OrderRingHom.apply_eq_self, OrthonormalBasis.measurePreserving_repr, Submodule.reflection_apply, openSegment_eq_Ioo, RCLike.ofReal_comp_balance, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, curveIntegralFun_segment, ContinuousMultilinearMap.norm_mkPiAlgebra_le, DifferentiableAt.hasDerivAt, Finpartition.IsEquipartition.card_biUnion_offDiag_le, fderivWithin_zero, AlgEquiv.restrictNormalHom_surjective, spectrum_diagonal, finInsepDegree_self, LieAlgebra.IsKilling.le_chainBotCoeff_of_rootSpace_ne_top, RCLike.geometric_hahn_banach_closed_point, differentiable_finCons', Submodule.orthogonal_eq_bot_iff, TensorProduct.adjoint_map, IsUltrametricDist.invariantExtension_apply, Real.hasDerivAt_arcosh, curveIntegral_neg, exists_nonneg_left_iff_sameRay, ConjRootClass.minpoly_injective, Polynomial.add_mod, Matrix.linearIndependent_rows_of_invertible, HasFDerivAt.sub, VectorBundleCore.contMDiffOn_coordChange, FormalMultilinearSeries.radius_le_smul, LinearIsometryEquiv.lTensor_apply, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, mfderiv_comp_of_eq, PowerBasis.equivAdjoinSimple_symm_aeval, FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal, InnerProductSpace.gramSchmidt_def, HasFDerivAt.star, NumberField.instFiniteDimensional, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, iteratedFDerivWithin_succ_const, enorm_fderiv_norm_rpow_le, ContinuousLinearMap.isPositive_self_comp_adjoint, Lagrange.basis_singleton, iteratedDeriv_scomp_eq_sum_orderedFinpartition, trivialization_linear, formalMultilinearSeries_geometric_apply_norm_le, ContinuousLinearMap.hasFPowerSeriesAt, Bundle.Trivial.continuousLinearMapAt_trivialization, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, LinearMap.adjoint_toContinuousLinearMap, WeierstrassCurve.integralModel_Δ_eq, FunctionField.ringOfIntegers.instIsIntegralClosureSubtypeMemSubalgebraPolynomial, X_pow_sub_C_irreducible_iff_forall_prime_of_odd, hasDerivAt_iff_isLittleO, IntermediateField.lift_adjoin_simple, spectrum.isOpen_resolventSet, DirichletCharacter.LFunction_changeLevel, NumberField.InfinitePlace.smul_apply, HasDerivWithinAt.hasFDerivWithinAt, Algebra.algebraMap_intNorm, Unitary.linearIsometryEquiv_coe_apply, algebraicClosure.normalClosure_eq_self, NormedSpace.isBounded_iff_subset_smul_closedBall, LDL.lowerInv_eq_gramSchmidtBasis, SeparatingDual.exists_eq_one, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, hasFPowerSeriesAt_const, hasStrictFDerivAt_pi', IntermediateField.AdjoinDouble.normal_algebraicClosure, Polynomial.natSepDegree_eq_zero_iff, HasFDerivAtFilter.neg, fderiv_eq_deriv_mul, algebraicClosure.map_eq_of_algebraicClosure_eq_bot, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, IsPurelyInseparable.exists_pow_mem_range_tensorProduct, finrank_algHom, FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius, ContinuousMultilinearMap.curry0_apply, HasFDerivWithinAt.fun_const_smul, norm_iteratedFDerivWithin_zero, iteratedFDerivWithin_of_isOpen, HasStrictFDerivAt.const_smul, hasStrictFDerivAt_natCast, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, inTangentCoordinates_eq_mfderiv_comp, FormalMultilinearSeries.radius_compNeg, hasFDerivAtFilter_ofNat, FiniteField.orderOf_frobeniusAlgEquivOfAlgebraic, LieAlgebra.IsKilling.apply_coroot_eq_cast', hasFDerivAtFilter_zero, HasFDerivAt.multilinear_comp, Polynomial.differentiableOn_aeval, NormedSpace.expSeries_apply_eq_div', IsLocalRing.residue_eq_zero_iff, Polynomial.mem_iff_eq_smul_annIdealGenerator, Real.fourierIntegral_continuousMultilinearMap_apply, EuclideanGeometry.oangle_midpoint_right, FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation, NumberField.IsTotallyComplex.finrank, LinearMap.rank_diagonal, NumberField.RingOfIntegers.withValEquiv_symm_apply, LinearIsometryEquiv.adjoint_eq_symm, Polynomial.natDegree_hilbertPoly_of_ne_zero_of_rootMultiplicity_lt, extDeriv_fun_smul, RatFunc.liftMonoidWithZeroHom_apply_div', fderivWithin_ccosh, TensorProduct.mapIsometry_id_id, galRestrict'_id, ContinuousAlternatingMap.toAlternatingMap_curryLeft, MeromorphicAt.inv_iff, Matrix.toEuclideanLin_apply, inner_self_eq_norm_sq_to_K, InfiniteGalois.krullTopology_mem_nhds_one_iff_of_isGalois, IsContDiffImplicitAt.hasFDerivAt, LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, AffineBasis.convexHull_eq_nonneg_coord, Complex.im_nnqsmul, iteratedDerivWithin_eq_iteratedFDerivWithin, ContinuousLinearMap.toLinearMap₁₂_apply, FiniteField.coe_frobeniusAlgEquivOfAlgebraic, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, HasFDerivWithinAt.mul, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, LinearMap.IsPositive.isPositive_smul_iff, ContinuousLinearMap.sSup_sphere_eq_nnnorm, analyticOrderAt_smul_eq_top_of_left, Polynomial.IsSplittingField.adjoin_rootSet, VectorFourier.fourierPowSMulRight_eq_comp, ContinuousLinearMap.finiteDimensional, inv_lt_zero', ContinuousAlternatingMap.le_opNNNorm, LinearIsometryEquiv.trans_smul, IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable, Polynomial.isUnit_map, AffineSubspace.sSameSide_iff_exists_left, HasFPowerSeriesOnBall.tendsto_partialSum_prod, RootPairing.restrictScalars_pairing, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, hasFDerivWithinAt_pi', HasFDerivWithinAt.multiset_prod, IsHilbertSum.hasSum_linearIsometryEquiv_symm, Algebra.instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced, IntermediateField.isAlgebraic_adjoin_iff_top, WeierstrassCurve.Projective.dblU_eq, ContinuousLinearMap.opNorm_mul, Algebra.isGeometricallyReduced_iff, Submodule.IsOrtho.map_iff, MeasureTheory.integral_fintype_prod_eq_pow, DoubleCentralizer.smul_toProd, mfderivWithin_projIcc_one, sepDegree_self, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, FiniteField.card_algEquiv_extension, FGModuleCat.instFiniteHomModuleCatObjIsFG, NumberField.mixedEmbedding.convexBodyLT_mem, NumberField.InfinitePlace.coe_apply, Real.sInf_smul_of_nonneg, Algebra.IsAlgebraic.algHom_bijective, InnerProductSpace.Core.inner_smul_ofReal_right, NumberField.IsTotallyReal.finrank, IntermediateField.inf_toSubalgebra, algebraicClosure.isAlgebraic, HasFDerivAt.arctan, NumberField.ComplexEmbedding.IsConj.coe_stabilizer_mk, PiTensorProduct.mapL_one, NumberField.Units.coe_mul, IsFractionRing.exists_reduced_fraction, Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg, Real.hasStrictDerivAt_arccos, DoubleCentralizer.toProdMulOpposite_injective, RCLike.conjCLE_apply, ContinuousLinearMap.norm_fst_le, PowerSeries.eq_mul_inv_iff_mul_eq, PointwiseConvergenceCLM.postcomp_apply, ContMDiffAt.mfderiv_apply, hasFDerivAt_snd, PowerSeries.isUnit_divided_by_X_pow_order, IsGalois.normalClosure, ValuationSubring.subtype_injective, DoubleCentralizer.norm_fst_eq_snd, AlgEquiv.adjoinSingletonEquivAdjoinRootMinpoly_symm_toAlgHom, Unitization.nnnorm_def, RatFunc.coe_X, NumberField.InfinitePlace.comp_of_comap_eq, UpperHalfPlane.coe_pos_real_smul, MvPowerSeries.eq_inv_iff_mul_eq_one, IsUnit.cfcSqrt, IsPurelyInseparable.iterateFrobenius_algebraMap, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, ContinuousLinearMap.le_opNorm, IsUltrametricDist.invariantExtension_extends, convexHull_toCone_eq_sInf, ImplicitFunctionData.range_leftDeriv, HasFDerivAt.fun_smul, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, Orthonormal.inner_left_fintype, Height.mulHeight₁_pow, IntermediateField.finiteDimensional_right, HasLineDerivAt.tendsto_slope_zero_right, RatFunc.isCoprime_num_denom, ZLattice.comap_toAddSubgroup, ValuationRing.range_algebraMap_eq, FunctionField.inftyValuation.polynomial, Complex.hasDerivAt_GammaIntegral, NormedSpace.expSeries_eq_expSeries, NormedSpace.expSeries_summable, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, compactOperator_topologicalClosure, RCLike.wInner_cWeight_eq_expect, IsFractionRing.algHom_commutes, Submodule.coe_orthogonalDecomposition_symm, IntermediateField.isAlgebraic_iff, Complex.starConvex_ofReal_slitPlane, NumberField.ComplexEmbedding.conjugate_comp, PiTensorProduct.mapL_smul, Subfield.relrank_mul_rank_top, BoundedContinuousFunction.coe_toContinuousMapStarₐ, MeasureTheory.aestronglyMeasurable_condExpL2, Lagrange.basisDivisor_self, Submodule.orthogonalProjection_bot, Real.fderiv_fourier, DoubleCentralizer.norm_def', ContinuousLinearMap.adjointAux_norm, RCLike.toIsStrictOrderedModule, IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower', differentiable_apply, Submodule.range_starProjection, ContinuousLinearMap.fderiv, fderiv_neg, RCLike.toIsStrictOrderedRing, LinearIsometryEquiv.inner_map_eq_flip, MeasureTheory.convolution_smul, LeftInvariantDerivation.lift_add, hasDerivAtFilter_natCast, Matrix.PosSemidef.sq_eq_sq_iff, padicNormE.eq_padic_norm', FormalMultilinearSeries.ofScalarsSum_op, Polynomial.isEquivalent_atTop_lead, LinearMap.flip_injective_iff₁, FormalMultilinearSeries.ofScalars_eq_zero, EuclideanGeometry.orthogonalProjection_apply_mem, meromorphicOrderAt_ne_top_iff, ContDiffAt.inv, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, Hyperreal.infinitesimal_inv_of_infinite, FormalMultilinearSeries.ofScalars_apply_zero, ContinuousAlternatingMap.instContinuousSMul, LinearMap.toMatrixOrthonormal_apply_apply, FractionalIdeal.inv_nonzero, HasFDerivAt.restrictScalars, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, ContinuousLinearMap.fpowerSeries_apply_zero, IntermediateField.instSMulMemClass, VectorPrebundle.mk_contMDiffCoordChange, IntermediateField.coe_inclusion, Submodule.exists_add_mem_mem_orthogonal, PiTensorProduct.projectiveSeminorm_apply, PadicInt.algebraMap_apply, Nonneg.segment_eq_uIcc, VectorFourier.fourierIntegral_continuousLinearMap_apply, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, AffineSubspace.coe_subtypeₐᵢ, FractionRing.algebraMap_liftAlgebra, FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop, closedConvexHull_eq_closure_convexHull, le_inv_of_neg, Finset.mem_convexHull', LinearMap.IsSymmetric.coe_re_inner_self_apply, Lagrange.eq_interpolate_iff, RatFunc.coe_coe, finSepDegree_self, ContinuousLinearMap.comp_memLp', HasStrictFDerivAt.list_prod', PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, FiniteField.sum_pow_lt_card_sub_one, SchwartzMap.fourier_lineDerivOp_eq, Manifold.IsImmersionAtOfComplement.map_target_subset_target, Complex.starConvex_one_slitPlane, Real.sSup_smul_of_nonneg, AddChar.wInner_cWeight_eq_zero_iff_ne, ContinuousLinearMapWOT.inducingFn_apply, TemperedDistribution.instLineDerivLeftSMulReal, AffineSubspace.sOppSide_iff_exists_left, DirichletCharacter.norm_le_one, Basis.linearEquiv_dual_iff_finiteDimensional, ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, NumberField.FinitePlace.norm_embedding_eq, hasStrictDerivAt_exp_smul_const, IsNormalClosure.adjoin_rootSet, Derivation.leibniz_div, ContinuousMap.setOfIdeal_ofSet_of_isOpen, Polynomial.separable_X_pow_sub_C, isBoundedBilinearMap_comp, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, Polynomial.span_singleton_annIdealGenerator, fderivWithin_sin, NormedSpace.exp_eq_tsum, set_smul_sphere_zero, NumberField.IsCMField.isQuadraticExtension, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, DirichletCharacter.mul_delta, Polynomial.valuation_of_mk, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, Module.Basis.mulOpposite_is_orthonormal_iff, Subspace.finrank_dualCoannihilator_eq, ContMDiff.smul, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, FormalMultilinearSeries.nnnorm_changeOrigin_le, hasStrictDerivAt_add_const_iff, Trivialization.continuousLinearEquivAt_apply, hasLineDerivWithinAt_smul_iff, Emb.Cardinal.two_le_deg, NumberField.ComplexEmbedding.Extension.not_isReal_of_not_isReal, Asymptotics.IsTheta.smul, MDifferentiable.const_smul, hasMFDerivAt_fst, MeasureTheory.condExpL2_indicator_ae_eq_smul, AbsoluteValue.isEquiv_iff_lt_one_iff, fderiv_fun_sub, mfderivWithin_comp_projIcc_one, NumberField.InfinitePlace.comap_comp, RootPairing.finrank_corootSpanIn_int, LeftInvariantDerivation.lift_smul, IsMIntegralCurveOn.hasDerivWithinAt, FormalMultilinearSeries.rightInv_removeZero, Polynomial.X_pow_sub_one_splits, arithGeom_zero_eq_mul_div', Rat.IsIntegralClosure.intEquiv_apply_eq_ringOfIntegersEquiv, IsPrimitiveRoot.powerBasis_gen_mem_adjoin_zeta_sub_one, isCompactOperator_iff_isCompact_closure_image_ball, FractionalIdeal.div_of_ne_zero, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, DoubleCentralizer.norm_def, ClosedSubmodule.orthogonal_closure'', hasStrictDerivAt_exp_smul_const', InfiniteGalois.fixingSubgroup_fixedField, HasCompactSupport.fderiv, OrderIso.smulRightDual_apply, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlane, LinearIsometry.toAffineIsometry_toAffineMap, MeromorphicAt.fun_smul, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, IsCyclotomicExtension.Rat.discr_prime_pow', SchwartzMap.smulLeftCLM_real_smul, InnerProductSpace.toDualMap_apply_apply, WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, Submodule.le_orthogonal_orthogonal, hasFDerivWithinAt_intCast, IntermediateField.finInsepDegree_le_of_left_le, LinearMap.eq_adjoint_iff_basis_left, contDiff_succ_iff_fderiv, ContinuousLinearMap.opNNNorm_prod, ContinuousLinearEquiv.comp_differentiableOn_iff, Lagrange.basisDivisor_add_symm, MDifferentiableOn.smul, Quaternion.inv_def, Matrix.ker_mulVecLin_conjTranspose_mul_self, ZLattice.rank, hasDerivAtFilter_zero, Subspace.finiteDimensional_quot_dualCoannihilator_iff, HasMFDerivAt.neg, smul_closedBall', spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, ZSpan.quotientEquiv_apply_mk, Polynomial.map_mod, LinearMap.IsSymmetricProjection.isIdempotentElem, HasFDerivAt.fun_const_smul, Polynomial.cardPowDegree_isEuclidean, IntermediateField.isAlgebraic_adjoin_iff, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, IntermediateField.minpoly_gen, Emb.Cardinal.isLeast_leastExt, Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem, Matrix.PosSemidef.posDef_iff_isUnit, Algebra.IsQuadraticExtension.isMulCommutative_galoisGroup, LaurentSeries.inducing_coe, SeparatingDual.exists_continuousLinearEquiv_apply_eq, NonUnitalSubalgebra.unitization_injective, Manifold.pathELength_def, PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision, WeakDual.toStrongDual_inj, TrivSqZeroExt.fst_expSeries, EuclideanSpace.volume_closedBall_fin_three, NumberField.exists_conjugate_one_le_norm, NumberField.InfinitePlace.conjugate_embedding_injective, ContinuousLinearMap.uniformContinuous_restrictScalars, Cubic.splits_iff_card_roots, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, NumberField.InfinitePlace.norm_embedding_eq, isModuleTopologyOfFiniteDimensional, isSeparable_algebraMap, LinearMap.extendTo𝕜'_apply, IntermediateField.aeval_coe, LinearIsometryEquiv.fderiv, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, PrimeSpectrum.coe_preimageOrderIsoFiber_symm_apply_coe_asIdeal, IsGalois.self, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, ContinuousLinearMap.holderₗ_apply_apply, Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, dslope_sub_smul, hasDerivAt_id', rescale_to_shell_semi_normed_zpow, ContinuousMultilinearMap.unit_le_opNorm, LaurentSeries.continuous_coe, IsLocalRing.instIsLocalHomResidueFieldRingHomResidue, convexJoin_segment_singleton, ContinuousMultilinearMap.curryRight_norm, hasDerivWithinAt_Iic_of_tendsto_deriv, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, Submodule.instHasOrthogonalProjectionOfCompleteSpace, fderiv.log, openSegment_eq_Ioo', FDerivMeasurableAux.norm_sub_le_of_mem_A, HasFDerivAt.add, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, MeasureTheory.convolution_lsmul, NumberField.IsCMField.orderOf_complexConj, ContinuousAlternatingMap.instContinuousConstSMul, Normal.algHomEquivAut_symm_apply, curveIntegral_fun_zero, gal_X_pow_sub_C_isSolvable, meromorphicNFOn_smul_iff_right_of_analyticOnNhd, ModelWithCorners.uniqueDiffOn_preimage, LinearMap.nonneg_iff_isPositive, Lagrange.interpolate_eq_sum, IsIdempotentElem.spectrum_subset, Bornology.isVonNBounded_covers, hasDerivAt_abs_neg, coe_innerSL_apply, normalClosure_eq_iSup_adjoin', MvPolynomial.rank_R, HasFDerivWithinAt.const_sub, IsAlgClosed.splits_codomain, LinearMap.IsSymmetric.inner_map_self_eq_zero, ContinuousLinearMap.isCompact_image_coe_closedBall, IntermediateField.map_map, Real.deriv_sqrt_aux, OrthonormalBasis.prod_apply, iteratedFDeriv_add_apply, deriv_fderiv, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, PowerSeries.normUnit_X, RegularNormedAlgebra.isometry_mul', convexJoin_singleton_segment, ContDiffWithinAt.hasFDerivWithinAt_nhds, IsPrimitiveRoot.adjoinEquivRingOfIntegers_symm_apply, FiniteDimensional.nonempty_continuousLinearEquiv_iff_finrank_eq, IntermediateField.fixingSubgroup_top, HasFDerivAt.sum, HasStrictDerivAt.real_of_complex, ContinuousLinearMap.isClosed_image_coe_closedBall, IntermediateField.coe_toSubalgebra, DoubleCentralizer.central, instIsAbelianGalois, RootPairing.Base.exists_mem_span_pairingIn_ne_zero_and_pairwise_ne, ModelWithCorners.hasMFDerivAt, WeierstrassCurve.Projective.isUnit_dblU_of_Y_eq, Matrix.PosSemidef.det_sqrt, Hyperreal.archimdeanClassMk_coe, MeasureTheory.integral_condExpL2_eq, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, FiniteField.roots_X_pow_card_sub_X, HasFPowerSeriesOnBall.coeff_zero, IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_one, integral_smul_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, quadraticCharFun_eq_zero_iff, hasFDerivAtFilter_const, VectorBundleCore.localTriv_symm_fst, range_cfcₙHom, Emb.Cardinal.succEquiv_coherence, IntermediateField.bot_toSubalgebra, HasMFDerivWithinAt.prodMap, IntermediateField.isScalarTower_bot, Algebra.discr_powerBasis_eq_norm, hasDerivWithinAt_abs, hasFPowerSeriesOnBall_const, hasFDerivAtFilter_iff_isLittleO, IsAlgebraic.inv, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, TensorProduct.lidIsometry_apply, IsSepClosed.lift_def, ContDiffMapSupportedIn.seminorm_le_iff, eventually_norm_mfderivWithin_symm_extChartAt_lt, NumberField.InfinitePlace.mkReal_coe, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, Hyperreal.inv_omega, Normal.splits, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, NumberField.InfinitePlace.smul_eq_comap, Hyperreal.infinite_iff_infinitesimal_inv, Submodule.exists_forall_notMem_of_forall_ne_top, Trivialization.comp_continuousLinearEquivAt_eq_coord_change, Subfield.mem_bot_iff_pow_eq_self, UniqueMDiffOn.uniqueDiffOn_target_inter, IsPrimitiveRoot.norm_eq_neg_one_pow, convex_halfSpace_re_le, VectorFourier.hasFDerivAt_fourierIntegral, Polynomial.factor_dvd_of_natDegree_ne_zero, abs_inv, Finset.centerMass_id_mem_convexHull, LinearMap.flip_surjective_iff₁, Seminorm.ball_norm_mul_subset, DirichletCharacter.unit_norm_eq_one, coeSubmodule_differentIdeal, coe_galRestrict_apply, WeierstrassCurve.Projective.Point.toAffineLift_zero, minpoly.sub_algebraMap, IntermediateField.sup_toSubalgebra_of_isAlgebraic_left, iteratedFDeriv_sum, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, hasFDerivAt_ringInverse, LinearMap.IsPositive.inner_nonneg_left, IntermediateField.relfinrank_top_right, norm_cfcₙ_lt, ContinuousMultilinearMap.opNorm_smul_le, contDiffAt_one_iff, Function.HasTemperateGrowth.fun_smul, Filter.HasBasis.isLittleOTVS_iff, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, NumberField.InfinitePlace.smul_mk, HasFDerivWithinAt.of_notMem_tsupport, ContinuousLinearMap.instCStarRingId, WeierstrassCurve.Projective.addXYZ_of_X_eq, WeakDual.coe_toStrongDual, fermatLastTheoremWith'_polynomial, NormedSpace.eq_zero_iff_forall_dual_eq_zero, hasFDerivAt_finCons, PowerSeries.intValuation_eq_of_coe, Matrix.linfty_opNNNorm_eq_opNNNorm, HasMFDerivWithinAt.neg, Algebra.FormallySmooth.iff_injective_lTensor_residueField, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, AffineIsometryEquiv.map_vsub, Finset.centerMass_id_mem_convexHull_of_nonpos, hasFDerivWithinAt_finCons, coeSubmodule_differentIdeal_fractionRing, Ideal.Fiber.lift_residueField_surjective, InformationTheory.hasDerivAt_klFun, isConjRoot_iff_aeval_eq_zero, MeasureTheory.setIntegral_condExpL2_indicator, InnerProductSpace.nnnorm_rankOne, RatFunc.mk_eq_mk', rank_mul_sepDegree_of_isSeparable, ContinuousMultilinearMap.norm_restr, WeierstrassCurve.Jacobian.comp_equiv_comp, ContinuousMultilinearMap.norm_image_sub_le, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, PreInnerProductSpace.Core.conj_inner_symm, convexHull_add, ProbabilityTheory.isPosSemidef_covarianceBilin, fderiv_smul, stereographic_apply_neg, LinearIsometry.norm_toContinuousLinearMap, OrthonormalBasis.orthogonalProjection_apply_eq_sum, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, FiniteField.instIsSplittingFieldExtensionHSubPolynomialHPowNatXCard, hasMFDerivAt_inr, ValuationRing.iff_isInteger_or_isInteger, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, ContinuousLinearEquiv.arrowCongr_apply, differentiable_snd, FiniteField.algebraMap_trace_eq_sum_pow, IsLocalRing.maximalIdeal_eq_bot, HasFDerivWithinAt.star, ArithmeticFunction.vonMangoldt.residueClass_apply, hasDerivAt_of_tendstoLocallyUniformlyOn, hasDerivAtFilter_iff_tendsto_slope, ContinuousLinearMap.norm_toSpanSingleton, NumberField.ComplexEmbedding.involutive_conjugate, fderivWithin_eventually_congr_set', intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left, ContinuousLinearMap.setIntegral_compLp, LinearMap.trace_eq_sum_inner, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, ContinuousLinearMap.toUniformConvergenceCLM_apply, FormalMultilinearSeries.ofScalars_series_of_subsingleton, ContinuousAlternatingMap.curryLeft_apply_apply, NormedSpace.isVonNBounded_closedBall, ContinuousLinearMap.flip_smul, logDeriv_fun_pow, Representation.IsIrreducible.finrank_eq_one_of_isMulCommutative, solvableByRad.isSolvable, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, mfderivWithin_sumInr, exists_basis_of_pairing_ne_zero, MeromorphicOn.divisor_inv, Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos, WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero, ContinuousMap.spectrum_eq_preimage_range, ContinuousLinearEquiv.isBigO_sub, HasFDerivAt.isBigOTVS_sub, Unitization.quasispectrum_inr_eq, IntermediateField.linearDisjoint_comm, ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem, HasCompactSupport.hasDerivAt_convolution_right, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, InnerProductSpace.isSymmetricProjection_rankOne_self, hasDerivWithinAt_neg, Subspace.dualPairing_nondegenerate, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, divRadical_dvd_derivative, Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRing, Polynomial.leadingCoeff_mul_prod_normalizedFactors, Module.Basis.constrL_apply, MeromorphicOn.divisor_fun_pow, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, Bundle.ContinuousRiemannianMetric.continuous, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, hasMFDerivAt_neg, HasFDerivWithinAt.const_smul, Matrix.IsHermitian.charpoly_cfc_eq, NormedSpace.norm_expSeries_summable, ContinuousLinearEquiv.hasMFDerivAt, MeasureTheory.ConvolutionExistsAt.integrable_swap, isPowMul_spectralNorm, NormedSpace.expSeries_sum_eq, Polynomial.deriv_aeval, VectorBundleCore.trivializationAt_coordChange_eq, hasGradientWithinAt_iff_hasFDerivWithinAt, DoubleCentralizer.nnnorm_def, norm_inner_eq_norm_iff, Real.volume_eq_stieltjes_id, spectrum.isCompact, HasFiniteFPowerSeriesOnBall.eq_partialSum, FiniteField.instIsScalarTowerZModExtension, Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, NumberField.RingOfIntegers.instIsTorsionFree_2, ContinuousLinearMap.measurable_apply₂, IsLocalFrameOn.coeff_congr, FormalMultilinearSeries.ofScalars_add, DifferentiableAt.fderiv_norm_self, continuousOn_tangentCoordChange, ContinuousAlternatingMap.isEmbedding_toContinuousMultilinearMap, RootPairing.finrank_rootSpanIn_int, Polynomial.monic_mapAlg_iff, RCLike.im_ofReal_pow, FloorSemiring.tendsto_pow_div_factorial_atTop, IntermediateField.equivOfEq_symm, LinearIsometryEquiv.smul_apply, LaurentSeries.val_le_one_iff_eq_coe, ValuationSubring.isLocalRing, Matrix.card_GL_field, CFC.sqrt_eq_rpow, inner_eq_norm_mul_iff_div, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, LinearIsometryEquiv.contDiff, OnePoint.smul_some_eq_ite, HasFDerivAt.comp_hasFDerivWithinAt, ContDiff.continuous_fderiv_apply, FiniteDimensional.RCLike.properSpace_submodule, AffineMap.hasDerivAt_lineMap, Polynomial.dvd_C_mul, Function.hasTemperateGrowth_iff_isBigO, range_stereographic_symm, Seminorm.convexOn, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, Polynomial.X_pow_sub_C_separable_iff, Submodule.traceDual_top', HasGradientAtFilter.hasDerivAtFilter', IntermediateField.restrictRestrictAlgEquivMapHom_apply, Algebra.norm_eq_prod_embeddings, DifferentiableWithinAt.prodMk, PiLp.volume_preserving_toLp, MonomialOrder.isUnit_leadingCoeff, IsPurelyInseparable.minpoly_eq, SeparatingDual.dualMap_surjective_iff, NumberField.canonicalEmbedding.integralBasis_repr_apply, ValuationSubring.smul_mem_pointwise_smul_iff, IsLocalExtr.fderiv_eq_zero, EuclideanGeometry.orthogonalProjection_apply', Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed, WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, IsGalois.intermediateFieldEquivSubgroup_apply, ContMDiffAt.smul, isOpenEmbedding_stereographic_symm, Polynomial.natSepDegree_zero, intervalIntegral.integral_hasDerivWithinAt_left, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, Polynomial.ofReal_eval, HasFPowerSeriesOnBall.fderiv_eq, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, strictConvex_closedBall, NormedSpace.toNormSMulClass, FractionalIdeal.one_div_spanSingleton, Ideal.algebraMap_residueField_surjective, mfderivWithin_comp_of_preimage_mem_nhdsWithin_of_eq, AlgHom.fieldRange_toSubalgebra, ContinuousMultilinearMap.nnnorm_constOfIsEmpty, ContinuousLinearMapWOT.instLocallyConvexSpace, ContinuousLinearMap.instLocallyConvexSpace, Ideal.sum_ramification_inertia, PadicAlgCl.norm_extends, FunctionField.classNumber_eq_one_iff, Asymptotics.IsLittleOTVS.zero, ContinuousLinearMap.flip_mul, minpoly.degree_le, DirichletCharacter.LSeriesSummable_mul, IsAlgClosed.card_roots_map_eq_natDegree_of_isUnit_leadingCoeff, NormedSpace.inclusionInDoubleDual_norm_eq, IsFractionRing.integerNormalization_eq_zero_iff, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, WeierstrassCurve.Projective.isUnit_Y_of_Z_eq_zero, IntermediateField.fieldRange_comp_val, VectorBundle.trivialization_linear', SchwartzMap.smulLeftCLM_sum, PiTensorProduct.projectiveSeminorm_tprod_le, IsRealClosed.exists_eq_pow_of_nonneg, IntermediateField.linearDisjoint_iff, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff', FractionRing.instIsScalarTower_1, AffineMap.hasDerivWithinAt_lineMap, IntermediateField.adjoin.powerBasis_gen, WeierstrassCurve.Affine.slope_of_Y_ne, ValuativeRel.one_rel_inv, NumberField.ComplexEmbedding.IsConj.eq, mfderiv_prod_eq_add_comp, FractionalIdeal.fractional_div_of_nonzero, ContinuousLinearMap.fderiv_of_bilinear, IsDedekindDomain.integer_empty, Ideal.card_primesOverFinset_le_finrank, NumberField.Units.regulator_eq_det, logDeriv_eqOn_iff, Matrix.PosSemidef.posSemidef_sqrt, hasFDerivAt_of_subsingleton, Real.hasDerivWithinAt_arccos_Ici, unitary.linearIsometryEquiv_coe_symm_apply, PiTensorProduct.tprodL_toFun, IntermediateField.toSubalgebra_map, ContinuousLinearMap.isPositive_def, IntermediateField.equivOfEq_rfl, Seminorm.gaugeSeminorm_ball, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, ContinuousLinearMap.nnnorm_toSpanSingleton, continuousOn_cfc_setProd, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, EuclideanGeometry.oangle_midpoint_rev_left, IntermediateField.map_fixingSubgroup, Polynomial.abs_tendsto_atTop_iff, IsLocalRing.finrank_CotangentSpace_eq_one, ContinuousLinearEquiv.hasMFDerivWithinAt, ContinuousAlternatingMap.alternatizeUncurryFin_smul, contDiffAt_map_inverse, fderiv_mul_const', LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, FGModuleCat.FGModuleCatEvaluation_apply, Complex.hasDerivAt_Gammaℝ_one, SchwartzMap.toBoundedContinuousFunctionCLM_apply, RCLike.conj_ofReal, curveIntegral_segment, Asymptotics.isLittleOTVS_fun_neg_left, TestFunction.postcompCLM_apply, Module.End.map_genEigenrange_le, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, IntermediateField.normal_iff_normalClosure_le, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, IsLocalRing.finrank_cotangentSpace_eq_zero_iff, TrivSqZeroExt.eq_smul_exp_of_ne_zero, Asymptotics.isBigOTVS_iff_smallSets, Derivation.leibniz_inv, ContinuousAlternatingMap.norm_restrictScalars, Real.fourierIntegral_continuousLinearMap_apply, OrthonormalBasis.coe_ofRepr, Submodule.starProjection_top', ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, MvPowerSeries.inv_eq_iff_mul_eq_one, mem_perfectClosure_iff_pow_mem, OrthonormalBasis.toBasis_mulOpposite, Submodule.adjoint_subtypeL, MeasureTheory.convolutionExistsAt_flip, ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, hasStrictFDerivAt_exp, NumberField.AdeleRing.algebraMap_snd_apply, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, convexHull_basis_eq_stdSimplex, Module.Basis.trace_traceDual_mul, IntermediateField.relrank_top_right, IsCoercive.range_eq_top, RingPreordering.inv_mem, coevaluation_apply_one, Emb.Cardinal.noMaxOrder_rank_toType, MvPolynomial.vanishingIdeal_pointToPoint, LinearMap.isSymmetric_adjoint_mul_self, InnerProductSpace.Core.cauchy_schwarz_aux, ValuationSubring.idealOfLE_le_of_le, ContinuousLinearMap.opNorm_mul_apply, gelfandStarTransform_symm_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, ContinuousLinearMap.norm_smulRightL, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, NumberField.InfinitePlace.card_filter_mk_eq, RatFunc.num_denom_add, Convex.radon_partition, Submodule.le_traceDual_traceDual, Subfield.finrank_comap, mfderiv_comp_mfderivWithin, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1, Algebra.instFiniteResidueFieldOfFormallyUnramified, IsPurelyInseparable.bijective_comp_algebraMap, RCLike.conjLIE_apply, Submodule.reflection_orthogonalComplement_singleton_eq_neg, deriv_fun_div, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, ContinuousLinearEquiv.comp_fderiv, IsLocalRing.map_tensorProduct_mk_eq_top, HasFDerivWithinAt.fun_smul, Complex.orthonormalBasisOneI_repr_apply, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, ContinuousLinearMap.isBigO_id, GaloisField.finrank, IsLocalRing.residue_def, RCLike.conj_mul, ContDiffAt.fderiv_right, AnalyticOn.compContinuousLinearMap, hasStrictFDerivAt_iff_isLittleO, MeasureTheory.convolution_def, WeierstrassCurve.Affine.slope_of_Y_ne', Affine.Triangle.dist_circumcenter_reflection_orthocenter, HasStrictFDerivAt.prodMk, MeasureTheory.norm_condExpL2_coe_le, FunctionField.valuedFqtInfty.def, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousMultilinearMap.curryLeft_norm, HasStrictFDerivAt.of_notMem_tsupport, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, RatFunc.instIsFractionRingPolynomial, HasDerivAt.hasFDerivAt, NormedAlgebra.exists_isMinOn_norm_sub_smul, MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable, InnerProductSpace.trace_rankOne, coe_toPrincipalIdeal, RatFunc.eval_X, AdjoinRoot.mul_div_root_cancel, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, IntermediateField.continuousSMul, NumberField.Units.coe_coe, minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_pow, ContinuousMultilinearMap.uncurry0_norm, hasMFDerivWithinAt_inr, FunctionField.algebraMap_injective, HasFPowerSeriesWithinOnBall.prod, MvPolynomial.instIsPrimeVanishingIdealSingletonForallSet, NormedSpace.eq_iff_forall_dual_eq, Set.coe_unit, ContinuousLinearEquiv.integral_comp_comm, Algebra.IsCentral.baseField_essentially_unique, Algebra.map_intNormAux, PrimeSpectrum.isOpenMap_comap_algebraMap_tensorProduct_of_field, ContinuousMultilinearMap.le_opNorm, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, ContDiffOn.fderiv_of_isOpen, Bundle.Trivial.linearMapAt_trivialization, Matrix.PosDef.isUnit, continuousOn_cfcₙ, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', ContinuousLinearMap.continuous_restrictScalars, HasFDerivWithinAt.neg, hasStrictDerivAt_const_add_iff, iteratedFDeriv_const_smul_apply, Finset.centerMass_insert, isBoundedBilinearMap_compMultilinear, DirichletCharacter.LSeries_changeLevel, ContinuousLinearEquiv.comp_right_fderiv, hasLineDerivAt_smul_iff, RatFunc.intDegree_inv, Submodule.isIdempotentElem_starProjection, differentiableOn_finCons', VectorField.lieBracket_const_smul_left, RCLike.div_im, Real.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, SimpContFract.determinant, hasFDerivAt_norm_rpow, Matrix.finite_spectrum, Complex.re_comp_balance, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers, dist_birkhoffAverage_apply_birkhoffAverage, IsGaloisGroup.mulEquivCongr_apply_smul, Algebra.ringChar_eq, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, ZSpan.repr_ceil_apply, Asymptotics.isEquivalent_nat_ceil, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime, IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem, Ideal.ResidueField.ringHom_ext_iff, HasFPowerSeriesOnBall.uniform_geometric_approx, LinearIsometry.inner_map_map, DoubleCentralizer.neg_snd, IsNormalClosure.splits, FiniteField.forall_pow_eq_one_iff, top_fixedByFinite, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ZLattice.comap_equiv_apply, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, ContinuousAlternatingMap.instIsTopologicalAddGroup, ContinuousLinearMap.analyticAt, iteratedFDeriv_succ_const, absoluteGaloisGroup.commutator_closure_isNormal, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, LaurentSeries.algebraMap_apply, DualNumber.maximalIdeal_eq_span_singleton_eps, IntermediateField.relfinrank_dvd_finrank_bot, Asymptotics.isBigOTVS_fun_neg_left, UniqueFactorizationMonoid.integer_of_integral, WeierstrassCurve.Projective.isUnit_addU_of_Y_ne, IsGalois.sup_right, ContDiffAt.iteratedFDeriv_right, NumberField.Units.finrank_mul_regOfFamily_eq_det, ContDiffBump.convolution_tendsto_right, isCoveringMap_zpow, Matrix.linfty_opNNNorm_toMatrix, HasFTaylorSeriesUpToOn.cont, RatFunc.laurent_at_zero, Asymptotics.isBigOTVS_fun_neg_right, Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm, IsLocalRing.ResidueField.map_comp_residue, RCLike.instContinuousMapUniqueHom, AnalyticOnNhd.fderiv_of_isOpen, Module.Basis.coe_constrL, ContinuousAlternatingMap.le_opNorm, WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_neg_mul, MvPowerSeries.constantCoeff_inv, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, Seminorm.rescale_to_shell_zpow, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, IsDedekindDomain.selmerGroup.monotone, FormalMultilinearSeries.ofScalars_sub, Valuation.mem_unitGroup_iff, Asymptotics.IsEquivalent.smul, differentiableAt_apply, ConjRootClass.monic_minpoly, NormedSpace.expSeries_hasSum_exp, isConjRoot_iff_eq_algebraMap, midpoint_le_right, ContinuousMultilinearMap.range_toUniformOnFun, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, derivWithin_fun_div, tangentMapWithin_snd, algebraMap_galRestrict_apply, Matrix.toEuclideanCLM_toLp, Seminorm.smul_closedBall_zero, WeakDual.CharacterSpace.homeoEval_naturality, minpoly.map_eq_of_isSeparable_of_isPurelyInseparable, DifferentiableWithinAt.hasDerivWithinAt, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, CPolynomialOn.iteratedFDeriv, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, ContinuousLinearMap.isPositive_id, IntermediateField.adjoin_simple_adjoin_simple, FormalMultilinearSeries.coeff_eq_zero, analyticOrderAt_centeredMonomial, CFC.posPart_algebraMap_nnreal, IntermediateField.adjoin_simple_toSubalgebra_of_integral, normalClosure.restrictScalars_eq, differentiableAt_pi'', RCLike.conjCLE_coe, Height.mulHeight_pow, HasFPowerSeriesOnBall.sum, Module.End.hasUnifEigenvalue_iff_mem_spectrum, NumberField.InfinitePlace.isUnramified_self, contDiffOn_stereoToFun, Real.hasFDerivAt_fourier, ContinuousLinearMap.isUniformAddGroup, LeftInvariantDerivation.evalAt_coe, Unitary.coe_symm_linearIsometryEquiv_apply, mfderivWithin_sumInl, fderiv_inverse, smul_sphere', hasStrictFDerivAt_exp_smul_const', SchwartzMap.smulLeftCLM_fun_neg, FractionalIdeal.count_ne_zero, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_right, IsRealClosed.exists_eq_pow_of_odd, IsPrimitiveRoot.adjoinEquivRingOfIntegers_apply, HasFPowerSeriesOnBall.fderiv, range_cfcₙ, LinearMap.adjoint_rTensor, NumberField.det_basisOfFractionalIdeal_eq_absNorm, convex_halfSpace_im_gt, dist_midpoint_midpoint_le, RCLike.normSq_inv, Matrix.PosSemidef.sqrt_eq_one_iff, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, LinearMap.IsPositive.add, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, NumberField.InfinitePlace.isUnramified_smul_iff, ImplicitFunctionData.leftDeriv_fderiv_implicitFunction, Emb.cardinal_eq_of_isSeparable, IntermediateField.AdjoinSimple.norm_gen_eq_one, FixedPoints.finrank_le_card, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, NumberField.InfinitePlace.orbitRelEquiv_apply_mk'', LinearMap.adjoint_inner_right, padicNormE.defn, MeasureTheory.mem_lpMeas_indicatorConstLp, iteratedFDeriv_const_smul_apply', IsAbelianGalois.toIsMulCommutative, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, PiLp.hasFDerivAt_toLp, stereoInvFun_apply, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, IntermediateField.range_val, PiTensorProduct.mapL_coe, IntermediateField.instFiniteSubtypeMemBot, ArchimedeanClass.FiniteElement.mk_intCast, NumberField.InfinitePlace.Completion.locallyCompactSpace, IntermediateField.isCyclotomicExtension_lcm_sup, Filter.EventuallyEq.hasDerivAt_iff, Manifold.IsImmersionAt.writtenInCharts, fderiv_pow, InnerProductSpace.rankOne_eq_zero, ContinuousLinearMap.lipschitz, Polynomial.differentiable_aeval, Ideal.image_subset_nonunits_valuationSubring, DoubleCentralizer.range_toProd, map_mem_perfectClosure_iff, fderiv_one, AlgEquiv.card_le, Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, finrank_quotient_span_eq_natDegree, RCLike.mul_wInner_left, padicNormE.add_eq_max_of_ne', TensorProduct.ext_iff_inner_left_threefold', Convex.toWeakSpace_closure, Module.Basis.trace_mul_traceDual, Submodule.isOrtho_sSup_right, LinearIsometry.lTensor_apply, AddChar.expect_apply_eq_zero_iff_ne_zero, ClosedSubmodule.bot_orthogonal_eq_top, LinearIsometry.norm_compContinuousMultilinearMap, ContinuousAlternatingMap.norm_curryLeft, minpoly.frobenius_of_isSeparable, hasDerivAtFilter_neg, RatFunc.numDenom_div, Complex.ofReal_balance, tsum_pow_div_one_sub_eq_tsum_sigma, IntermediateField.linearDisjoint_iff', Real.hasDerivAt_binEntropy, Submodule.norm_sq_eq_add_norm_sq_starProjection, hasDerivAt_gronwallBound_shift, AffineIsometry.linear_eq_linearIsometry, RCLike.re_eq_norm_of_mul_conj, Algebra.IsGeometricallyReduced.isReduced_algebraicClosure_tensorProduct, UniqueDiffOn.of_real, ContMDiffOn.coordChangeL, IsGaloisGroup.fixedPoints_fixingSubgroup, gal_X_pow_sub_one_isSolvable, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, integralClosure.isFractionRing_of_finite_extension, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, IsLiouville.rfl, SchwartzMap.pairing_apply, HasFDerivAt.pow, Polynomial.int_cyclotomic_rw, IsSimpleModule.algebraMap_end_bijective_of_isAlgClosed, ContinuousLinearMapWOT.smul_apply, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, spectrum.eventually_isUnit_resolvent, Asymptotics.isBigOTVS_iff_isBigO, ContinuousMultilinearMap.isLeast_opNorm, Polynomial.existsUnique_hilbertPoly, fderivWithin_comp_derivWithin, ContDiff.continuous_fderiv, ContinuousAlternatingMap.apply_apply, Finpartition.IsEquipartition.sum_nonUniforms_lt', hasFDerivAt_id, Bornology.isVonNBounded_sub_of_nonempty, Real.hasDerivAt_qaryEntropy, NumberField.RingOfIntegers.coe_eq_zero_iff, innerSL_inj, AffineIsometryEquiv.coe_ofEq_apply, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, MeasureTheory.condExpIndSMul_smul, hasDerivAt_add_const_iff, IntermediateField.extendScalars.orderIso_apply, hasDerivWithinAt_pow, Submodule.closed_of_finiteDimensional, hasDerivWithinAt_iff_hasFDerivWithinAt, Polynomial.natDegree_removeFactor, RatFunc.instIsScalarTowerOfPolynomial_1, Padic.norm_p_pow, MeasureTheory.ae_ae_add_linearMap_mem_iff, AffineSubspace.wOppSide_iff_exists_left, NumberField.InfinitePlace.IsRamified.comap_embedding_conjugate, TensorProduct.ext_iff_inner_left_threefold, MeasureTheory.lintegral_nnnorm_condExpL2_le, MvPowerSeries.coeff_inv, RCLike.conj_eq_iff_re, Monotone.ae_hasDerivAt, IsPurelyInseparable.injective_comp_algebraMap, StrongDual.toLp_of_not_memLp, AffineSubspace.isometryEquivMap.toAffineMap_eq, algebraicClosure.isIntegralClosure, Ideal.surjectiveOnStalks_residueField, DoubleCentralizer.add_fst, Quaternion.expSeries_odd_of_imaginary, deriv_pi, LinearMap.IsSymmetric.coe_toSelfAdjoint, sub_inv_antitoneOn_Icc_left, Polynomial.natSepDegree_C_mul_X_sub_C_pow, Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_map, AlgebraicClosure.instIsAlgClosureOfIsAlgebraic, quasispectrum.isCompact, HasFPowerSeriesWithinAt.coeff_zero, Algebra.normalizedTrace_intermediateField, TensorProduct.inner_lid_lid, NumberField.InfinitePlace.even_card_aut_of_not_isUnramified, EuclideanSpace.volume_closedBall_fin_two, OrthonormalBasis.toBasis_map, ContDiffMapSupportedIn.uniformSpace_eq_iInf, NormedSpace.norm_expSeries_summable_of_mem_ball', hasFDerivAt_apply, RatFunc.num_C, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, Matrix.piLp_ofLp_toEuclideanLin, LinearMap.finrank_genEigenspace_le, cfcₙAux_id, LinearMap.IsSymmetric.diagonalization_symm_apply, minpoly.dvd_iff, PiTensorProduct.liftIsometry_tprodL, HasStrictFDerivAt.cexp, WeierstrassCurve.Jacobian.map_add, maximal_orthonormal_iff_basis_of_finiteDimensional, Matrix.projVandermonde_apply_of_ne_zero, VectorField.mpullback_smul_apply, OnePoint.map_smul, TensorProduct.norm_comm, contDiffWithinAt_iff_of_ne_infty, NormedSpace.inclusionInDoubleDual_norm_le, mfderiv_sumInl, ValuationSubring.principalUnitGroup_le_principalUnitGroup, RatFunc.smul_eq_C_mul, SeparatingDual.instNontrivialContinuousLinearMapIdOfContinuousSMul, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, AnalyticOnNhd.eval_linearMap, LinearEquiv.coe_toContinuousLinearEquiv_symm, hasFTaylorSeriesUpToOn_pi', curveIntegral_segment_const, IsFractionRing.fieldEquivOfAlgEquiv_refl, hasDerivWithinAt_one, mfderiv_sub, sub_smul_slope_vadd, galLift_algebraMap_apply, VectorBundleCore.localTriv_symm_apply, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, WeakDual.isCompact_closedBall, ArchimedeanClass.stdPart_eq_sInf, AffineSubspace.setOf_wOppSide_eq_image2, ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv, NumberField.Units.norm, ContinuousLinearMap.isPositive_toLinearMap_iff, instPolynormableSpaceProd, TangentBundle.trivializationAt_apply, PiTensorProduct.injectiveSeminorm_le_projectiveSeminorm, ConvexOn.sSup_of_countable_affine_eq, isNormalClosure_normalClosure, VectorFourier.iteratedFDeriv_fourierIntegral, TestFunction.coe_ofSupportedInCLM, Real.differentiableAt_rpow_of_ne, PointedContMDiffMap.smul_def, CFC.sqrt_eq_one_iff, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, Hyperreal.stdPart_coe, Polynomial.natSepDegree_X, FGModuleCat.instFiniteHom, ContDiffBump.normed_convolution_eq_right, Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero, IsScalarTower.AlgEquiv.restrictNormalHom_comp, PiTensorProduct.bddBelow_projectiveSemiNormAux, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, ContinuousLinearMap.uniformContinuousConstSMul, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContDiffMapSupportedIn.continuous_iff_comp_withOrder, HasLineDerivAt.tendsto_slope_zero, IntermediateField.mem_fixedField_iff, NumberField.IsCMField.complexConj_apply_apply, ContinuousAlternatingMap.instUniformContinuousConstSMul, IntermediateField.finrank_eq_one_iff, ContinuousLinearMap.holder_smul_left, RatFunc.laurent_laurent, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, IntermediateField.lift_top, ContinuousLinearMap.precompR_apply, HarmonicAt.differentiableAt_complex_partial, LaurentSeries.exists_ratFunc_val_lt, Algebra.IsCentral.right_of_tensor_of_field, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, WeierstrassCurve.Affine.addPolynomial_slope, IsGaloisGroup.fixingSubgroup_le_of_le, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, instIsLocalRing, isSymmSndFDerivAt_iff_iteratedFDeriv, RatFunc.num_algebraMap, IntermediateField.sInf_toSubalgebra, HasFDerivWithinAt.mul_const, absorbent_nhds_zero, ContMDiffAt.const_smul_section, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, Polynomial.natSepDegree_map, Matrix.GeneralLinearGroup.IsParabolic.pow, Derivation.leibniz_zpow, ordinaryHypergeometricSeries_apply_eq', MeasureTheory.hasFDerivAt_convolution_right_with_param, ContinuousLinearEquiv.differentiableAt, fderiv_pow', spectrum.one_eq, ContMDiffAt.mfderiv_const, AnalyticOn.domDomCongr_iteratedFDeriv, NumberField.RingOfIntegers.instIsLocalizationAlgebraMapSubmonoidIntNonZeroDivisors, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, ContMDiffSection.coe_smul, fderiv_mul, FormalMultilinearSeries.coeff_ofScalars, IntermediateField.adjoin_map, Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, StieltjesFunction.measurable_measure, Asymptotics.IsLittleO.isLittleOTVS, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, hasDerivAt_ofNat, LinearIsometry.isConformalMap, LinearIsometryEquiv.reflections_generate, ContinuousLinearMap.ratio_le_opNorm, IntermediateField.finrank_lt_of_gt, Submodule.map_orthogonal_equiv, mfderiv_prodMap, iteratedFDerivWithin_eq_equiv_comp, Algebra.WeaklyQuasiFiniteAt.finite_locoalization, DifferentiableAt.isBigOTVS_sub, Matrix.l2_opNNNorm_mulVec, NumberField.mixedEmbedding.span_idealLatticeBasis, Valuation.HasExtension.maximalIdeal_comap_algebraMap_eq_maximalIdeal, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, hasFDerivAt_prodMk_left, Matrix.instFiniteSpectrum, Lagrange.degree_interpolate_erase_lt, NumberField.ComplexEmbedding.IsConj.symm, Orthonormal.inner_left_right_finset, map_mem_separableClosure_iff, HasStrictFDerivAt.isLittleO, IntermediateField.insepDegree_bot', HasCompactSupport.hasFDerivAt_convolution_right, Set.coe_integer, IntermediateField.fixedField_antitone, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, ClosedSubmodule.top_orthogonal_eq_bot, PrimeSpectrum.mem_image_comap_basicOpen, ZMod.card_units, ArchimedeanClass.FiniteResidueField.ofArchimedean_inj, differentialIdeal_le_iff, differentiableAt_inv_iff, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, SchwartzMap.norm_iteratedFDeriv_le_seminorm, Submodule.norm_orthogonalProjection_apply_le, Filter.tendsto_neg_const_mul_pow_atTop, instPolynormableSpaceSubtypeMemSubmodule, LinearMap.deriv, VectorPrebundle.linear_trivializationOfMemPretrivializationAtlas, AlgebraicIndependent.lift_reprField, RCLike.conj_I_ax, uniqueDiffWithinAt_convex_of_isRCLikeNormedField, Continuous.fderiv, Polynomial.hilbertPoly_succ, X_pow_sub_C_irreducible_iff_of_prime_pow, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, TensorProduct.norm_assoc, TensorProduct.nnnorm_tmul, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, IntermediateField.isAlgebraic_adjoin, galLift_comp, DoubleCentralizer.smul_fst, norm_fderiv_le_of_lipschitz, IsCyclotomicExtension.splits_cyclotomic, IsLocalRing.ResidueField.instIsScalarTower_1, mem_subalgebraEquivIntermediateField_symm, InnerProductSpace.toDualMap_apply, FDRep.average_char_eq_finrank_invariants, TotallyBounded.isVonNBounded, instIsLiouvilleSubtypeMemIntermediateField, Polynomial.factor_dvd_of_degree_ne_zero, Algebra.adjoin.powerBasis_dim, RCLike.normSq_nonneg, CategoryTheory.finrank_endomorphism_eq_one, NumberField.mixedEmbedding.convexBodySumFun_smul, hasFDerivWithinAt_finCons', IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two, NumberField.InfinitePlace.instMonoidWithZeroHomClassReal, NumberField.IsCMField.coe_ringOfIntegersComplexConj, Subalgebra.LinearDisjoint.exists_field_of_isDomain_of_injective, DifferentiableAt.conj_conj, AffineIsometryEquiv.ofTop_symm_apply_coe, InfiniteGalois.mulEquivToLimit_symm_continuous, TangentBundle.coordChange_model_space, ZMod.pow_card, NumberField.mixedEmbedding.logMap_real_smul, ContinuousLinearMap.adjoint_inner_left, PowerSeries.normalized_count_X_eq_of_coe, fderivWithin_cos, WeierstrassCurve.Jacobian.addX_of_Z_ne_zero, PointwiseConvergenceCLM.isInducing_inducingFn, ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, TensorProduct.inner_mapIncl_mapIncl, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, WeierstrassCurve.Affine.addX_eq_addX_negY_sub, DirectLimit.nontrivial, ContinuousLinearEquiv.arrowCongr_symm, ContinuousLinearMap.isBoundedBilinearMap, Valuation.FiniteField.instIsTrivialOn, FractionalIdeal.div_nonzero, nnnorm_algebraMap, ArchimedeanClass.stdPart_map_real, fdifferential_apply, ContinuousMultilinearMap.opNorm_nonneg, ContinuousMultilinearMap.hasBasis_nhds_zero, ContinuousMultilinearMap.instIsUniformAddGroup, ball_normSeminorm, HasFPowerSeriesWithinOnBall.sum, instTotallySeparatedSpaceAlgEquivOfIsIntegral, InnerProductSpace.AlgebraOfCoalgebra.mul_def, SeparableClosure.hasEnoughRootsOfUnity_pow, Real.hasStrictDerivAt_arcosh, toIsField, LinearMap.extendTo𝕜_apply, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq, Hyperreal.infinitePos_iff_infinitesimal_inv_pos, Filter.EventuallyEq.iteratedFDerivWithin, RatFunc.liftMonoidWithZeroHom_apply_div, MeromorphicAt.fun_pow, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, HasLineDerivWithinAt.smul, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, IsTranscendenceBasis.isAlgebraic_field, LinearMap.range_dualMap_eq_dualAnnihilator_ker, mdifferentiable_smul_const_section, FormalMultilinearSeries.apply_eq_pow_smul_coeff, RatFunc.num_dvd, hasDerivAtFilter_id, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Ideal.ResidueField.liftₐ_comp_toAlgHom, Filter.Tendsto.atTop_smul_nhds_tendsto_asymptoticNhds, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, minpoly.isIntegrallyClosed_eq_field_fractions, ContinuousLinearEquiv.integrable_comp_iff, Asymptotics.isBigOTVS_congr, ContinuousLinearMap.instContinuousEvalConst, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, fderivWithin_ccos, Ring.instIsFractionRingNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, FiniteField.frobeniusAlgEquiv_symm_apply, isPurelyInseparable_iff_pow_mem, Asymptotics.isBigOTVS_neg_right, MDifferentiableOn.coordChangeL, hasDerivAt_update, quadraticCharFun_one, VectorField.mlieBracketWithin_const_smul_left, Lagrange.degree_interpolate_lt, ContinuousLinearMap.IsPositive.isSymmetric, ContinuousAlternatingMap.ofSubsingletonLIE_apply, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, fderiv_fun_add, MeromorphicOn.fun_pow, Real.one_div_sub_hasFPowerSeriesOnBall_zero, FormalMultilinearSeries.compAlongComposition_bound, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_fst, RCLike.uniqueNonUnitalContinuousFunctionalCalculus, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, IntermediateField.toSubfield_map, ContinuousLinearMap.lipschitz_apply, PowerBasis.equivAdjoinSimple_aeval, Trivialization.prod.isLinear, inner_eq_sum_norm_sq_div_four, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, IntermediateField.extendScalars_adjoin, NumberField.InfinitePlace.isInfinitePlace, IsAlgClosed.exists_pow_nat_eq, fderiv_pow_ring, constFormalMultilinearSeries_apply_zero, FiniteDimensional.of_subalgebra_toSubmodule, IntermediateField.isPurelyInseparable_tower_bot, le_separableClosure_iff, DifferentiableAt.fderiv_restrictScalars, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, Normal.algHomEquivAut_apply, inTangentCoordinates_eq, LinearIsometryEquiv.conjStarAlgEquiv_trans, IsCyclotomicExtension.finrank, FormalMultilinearSeries.radius_smul_eq, Polynomial.preHilbertPoly_eq_choose_sub_add, DifferentiableAt.comp_ringHom, selfAdjoint.unitarySelfAddISMul_coe, AffineIsometryEquiv.ofEq_symm, RatFunc.laurentAux_div, HasDerivWithinAt.complexToReal_fderiv, Polynomial.abs_tendsto_atBot_iff, ContinuousLinearMap.bilinearComp_zero_right, FractionalIdeal.coe_dual_one, RootPairing.finrank_corootSpanIn, tendsto_nat_floor_mul_div_atTop, Polynomial.roots_C_mul_X_add_C, ZMod.instIsDomain, LinearMap.IsSymmetric.continuous, IsContMDiffRiemannianBundle.exists_contMDiff, Module.End.IsSemisimple.pow, AddCircle.equivAddCircle_apply_mk, ContinuousMap.ideal_isMaximal_iff, PrimeSpectrum.iInf_localization_eq_bot, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, Valuation.Integers.isFractionRing, DirichletCharacter.LSeries.mul_mu_eq_one, BaireSpace.instBarrelledSpace, integral_conj, hasDerivAtFilter_add_const_iff, LinearIsometry.extend_apply, NumberField.FinitePlace.norm_lt_one_iff_mem, IntermediateField.extendScalars_inf, Polynomial.Gal.instIsScalarTowerSplittingField, hasDerivAt_jacobiTheta₂_fst, AdjoinRoot.span_maximal_of_irreducible, IsGaloisGroup.of_isGalois, uniform_continuous_npow_on_bounded, InnerProductSpace.rank_rankOne, LinearMap.isSymmetric_sum, FiniteField.pow_finrank_eq_natCard, MDifferentiableAt.const_smul, LinearMap.toSeminorm_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, Submodule.isOrtho_top_left, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_inner, IntermediateField.botContinuousSMul, NumberField.IsCMField.equivInfinitePlace_apply, IsometricContinuousFunctionalCalculus.toNonUnital, RatFunc.mk_eq_div, contMDiffAt_coordChangeL, meromorphicNFAt_inv, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isReal, HasFDerivWithinAt.fun_sub, LinearMap.flip_bijective_iff₁, InnerProductSpace.toDual_apply_apply, LinearMap.flip_bijective_iff₂, WittVector.frobeniusPoly_zmod, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, ContinuousLinearMap.nonneg_iff_isPositive, Real.hasDerivAt_arcsin, RCLike.real_smul_eq_coe_smul, eq_separableClosure_iff, WeierstrassCurve.Affine.C_addPolynomial_slope, LinearMap.BilinForm.mem_dualSubmodule, coe_lpBCFₗᵢ, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, Submodule.linearEquiv_det_reflection, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, LinearMap.isSymmetric_linearIsometryEquiv_conj_iff, MvPolynomial.map_restrict_dom_evalₗ, LocalSubring.instAtPrimeSubtypeMemSubringToSubringOfPrime, Trivialization.symmL_continuousLinearMapAt, ValuationSubring.coe_unitGroupMulEquiv_apply, ProperCone.innerDual_singleton, quadraticCharFun_mul, algebraMap_isometry, RCLike.add_conj, Submodule.IsOrtho.map, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, Polynomial.isPrimitive_iff_ne_zero, LinearIsometryEquiv.comp_differentiableOn_iff, RingOfIntegers.norm_algebraMap, LinearIsometryEquiv.comp_differentiableAt_iff, differentiable_inner, HasFPowerSeriesWithinOnBall.sub, CFC.exp_eq_normedSpace_exp, CFC.abs_natCast, HasLineDerivAt.tendsto_slope_zero_left, Submodule.mk_mem_projectivization_iff, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, ContDiffWithinAt.continuousLinearMap_comp, NumberField.InfinitePlace.smul_coe_apply, LinearMap.minpoly_dvd_charpoly, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, RCLike.im_eq_conj_sub, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, spectrum.pow_image_subset, ValuationRing.isFractionRing_iff, HasFDerivWithinAt.prodMk, ContinuousAlternatingMap.norm_ofSubsingleton, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_list_prod', segment_eq_Icc', Submodule.toLinearMap_starProjection_eq_isComplProjection, Matrix.cRank_diagonal, FunctionField.ringOfIntegers.instIsDomainSubtypeMemSubalgebraPolynomial, hasStrictFDerivAt_finCons, InnerProductSpace.rankOne_def, MDifferentiableWithinAt.coordChangeL, Diffeomorph.mfderivToContinuousLinearEquiv_coe, TensorProduct.nnnorm_map, Module.Basis.ofZLatticeBasis_span, arithGeom_same_eq_mul_div', MvPowerSeries.inv_mul_cancel, RCLike.conj_im_ax, ContinuousLinearMap.coe_flipₗᵢ', HasMFDerivAt.prodMap, ValuationSubring.unitGroup_injective, NumberField.IsCMField.is_quadratic, div_eq_quo_add_sum_rem_div, PiTensorProduct.norm_eval_le_injectiveSeminorm, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, IsFractionRing.mk'_num_den', deriv_inv, IntermediateField.normal_iff_forall_fieldRange_le, Submodule.sub_starProjection_mem_orthogonal, ContinuousLinearMap.fpowerSeriesBilinear_apply_add_three, contDiffOn_succ_iff_fderiv_of_isOpen, PointwiseConvergenceCLM.equivWeakDual_apply, Polynomial.fderiv_aeval, fderivWithin_fderivWithin_eq_of_mem_nhds, inner_self_conj, Char.card_pow_card, ContinuousLinearMap.norm_smulRight_apply, Valuation.pow_Uniformizer_is_pow_generator, Real.hasStrictDerivAt_cosh, Module.End.maxUnifEigenspaceIndex_le_finrank, contDiff_iff_continuous_differentiable, tendsto_pow_div_pow_atTop_zero, dist_birkhoffAverage_birkhoffAverage, IsPrimitiveRoot.discr_zeta_eq_discr_zeta_sub_one, hasDerivAt_const, dslope_sub_smul_of_ne, Polynomial.prod_max_one_norm_roots_le_mahlerMeasure_of_one_le_leadingCoeff, Algebra.bijective_algebraMap_iff, FiniteField.finrank_zmod_extension, FGModuleCat.FGModuleCatDual_obj, Finset.centerMass_smul_left, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Module.Basis.equivFunL_symm_apply_repr, ArchimedeanClass.FiniteResidueField.ofArchimedean_injective, PrincipalIdeals.normal, IsometryEquiv.map_midpoint, fderiv_mul', LinearIsometryEquiv.conjStarAlgEquiv_ext_iff, OrthonormalBasis.repr_apply_apply, IsGalois.normalAutEquivQuotient_apply, IsGalois.normalBasis_apply, UniformSpace.Completion.norm_toComplL, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, NumberField.IsCMField.complexConj_apply_eq_self, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, instSMulDistribClassAlgEquiv, Complex.hasDerivAt_Gammaℂ_one, VectorField.lieBracket_fmul_left, HasFDerivAtFilter.sum, RatFunc.num_zero, toIcoMod_eq_add_fract_mul, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right, tendsto_inv_atBot_nhdsLT_zero, ContinuousMultilinearMap.analyticAt, hasMFDerivAt_id, ClosedSubmodule.orthogonal_eq_inter, Valuation.Integers.le_iff_dvd, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, IntermediateField.adjoin_simple_eq_top_iff_of_isAlgebraic, ContinuousMultilinearMap.prodL_apply, toIocMod_eq_sub_fract_mul, FormalMultilinearSeries.radius_inv_eq_limsup, Real.hasStrictDerivAt_log, Polynomial.hilbertPoly_zero_left, HasFDerivWithinAt.cexp, IsCyclotomicExtension.isSplittingField_X_pow_sub_one, hasFDerivWithinAt_iff_hasDerivWithinAt, IsAlgClosed.card_roots_map_eq_natDegree_from_simpleRing, IsFractionRing.div_surjective, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet, hasFTaylorSeriesUpToOn_succ_iff_right, ContinuousLinearMap.coe_flipMultilinearEquiv, PowerSeries.instUniqueFactorizationMonoid, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, Seminorm.bddAbove_iff, Algebra.norm_inv, LaurentSeries.exists_Polynomial_intValuation_lt, NonUnitalAlgHom.coe_Lmul, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, QuadraticForm.equivalent_weightedSumSquares, ContinuousMultilinearMap.norm_map_init_le, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, hasMFDerivWithinAt_id, LeftInvariantDerivation.left_invariant'', ordinaryHypergeometricSeries_apply_zero, Lagrange.basis_empty, SchwartzMap.compCLMOfAntilipschitz_apply, Polynomial.SplittingFieldAux.scalar_tower', ContinuousAlternatingMap.hasStrictFDerivAt, FiniteField.algebraMap_norm_eq_pow, SchwartzMap.fourierInv_apply_eq, trace_eq_finrank_mul_minpoly_nextCoeff, SchwartzMap.smulRightCLM_apply_apply, NormedSpace.expSeries_summable', LinearOrderedField.inducedOrderRingHom_toFun, NormedSpace.norm_expSeries_summable_of_mem_ball, gal_prod_isSolvable, LinearIsometryEquiv.conjStarAlgEquiv_refl, CurveIntegrable.fun_zero, Emb.Cardinal.strictMono_leastExt, IntermediateField.rank_adjoin_eq_one_iff, InnerProductSpace.laplacian_smul, hasStrictFDerivAt_iff_hasStrictDerivAt, ValuationSubring.mem_unitGroup_iff, mem_segment_iff_sameRay, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, binomialSeries_apply, eventually_singleton_add_smul_subset, VectorField.mpullback_apply, LinearMap.IsSymmetric.toSelfAdjoint_apply, RatFunc.liftOn_div, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure_1, RCLike.conj_div, Submodule.coe_continuous_linearProjOfClosedCompl, ContinuousLinearMapWOT.instIsTopologicalAddGroup, fderiv_mem_iff, galLiftEquiv_apply, iteratedFDeriv_neg_apply, Submodule.coe_orthogonalDecomposition, VectorField.lieBracket_eq, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, hasMFDerivWithinAt_fst, ContinuousLinearMap.coe_restrict_scalarsL', HasDerivAt.complexToReal_fderiv, differentiableAt_fst, ContinuousLinearMapWOT.isInducing_inducingFn, fderivWithin_fderivWithin_eq_of_eventuallyEq, NumberField.InfinitePlace.LiesOver.comap_eq, DoubleCentralizer.star_fst, differentiableOn_pi'', InnerProductSpace.laplacianWithin_smul, IntermediateField.isAlgebraic_tower_top, StrongDual.polarSubmodule_eq_polar, Polynomial.separable_X_pow_sub_C', StrictConvex.affinity, NumberField.InfinitePlace.even_finrank_of_not_isUnramifiedIn, Submodule.finrank_orthogonal_span_singleton, summable_prod_mul_pow, IsAlgClosed.factors, instIsScalarTowerAtPrimeFractionRing, PiTensorProduct.liftEquiv_symm_apply, IsLocalRing.ResidueField.lift_comp_residue, Subfield.algebraMap_ofSubfield, RCLike.summable_conj, Polynomial.fact_irreducible_factor, RCLike.geometric_hahn_banach_point_point, IsCyclotomicExtension.splits_X_pow_sub_one, Quaternion.normSq_inv, Algebra.TensorProduct.isField_of_isAlgebraic, ContinuousLinearMap.fpowerSeries_apply_add_two, TestFunction.coe_ofSupportedInLM, IntermediateField.rank_top, mfderivWithin_eventually_congr_set', meromorphicOrderAt_inv, transcendental_aeval_iff, Valuation.ideal_isPrincipal, toIcoDiv_zero_one, LinearMap.span_singleton_sup_ker_eq_top, LinearMap.dualMap_injective_iff, concaveOn_iff_div, LinearMap.isPositive_natCast, inner_smul_real_right, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Algebra.normalizedTrace_eq_of_fininteDimensional, TensorProduct.toLinearEquiv_congrIsometry, Asymptotics.isLittleOTVS_fun_neg_right, ContinuousMultilinearMap.opNorm_zero, hasFDerivAt_exp_smul_const', ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, PowerSeries.IsWeierstrassFactorization.natDegree_eq_toNat_order_map, Complex.one_add_cpow_hasFPowerSeriesAt_zero, FormalMultilinearSeries.ofScalars_norm_le, Submodule.isOrtho_iSup_left, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall, IsCoercive.bounded_below, IsLocalFrameOn.toBasisAt_coe, NumberField.mixedEmbedding.covolume_idealLattice, Representation.isSemisimpleRepresentation_iff_isSemisimpleModule_asModule, IntermediateField.finrank_eq_fixingSubgroup_index, Commute.cfcₙHom, LinearMap.dualPairing_nondegenerate, Hyperreal.archimedeanClassMk_pos_of_tendsto, NumberField.place_apply, Submodule.norm_subtypeL, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, RatFunc.num_inv_dvd, ContinuousLinearMapWOT.hasBasis_seminorms, Submodule.mem_orthogonal', ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, FGModuleCat.FGModuleCatCoevaluation_apply_one, MvPolynomial.finrank_R, hasFDerivAt_finCons', LinearMap.toMatrixOrthonormal_symm_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, contDiffPointwiseHolderAt_iff, ContinuousLinearMap.IsStarNormal.orthogonal_range, segment_eq_Icc, ContinuousLinearMap.aestronglyMeasurable_comp₂, Subspace.dualRestrict_leftInverse, FiniteField.algebraMap_norm_eq_prod_pow, Matrix.posDef_gram_iff_linearIndependent, instPolynormableSpaceForall, WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_ne_zero, SchwartzMap.smulLeftCLM_const, hasStrictFDerivAt_piLp, NumberField.house_pow_le, MDifferentiableAt.smul_section, Subfield.bot_eq_of_zMod_algebra, Lagrange.eval_basisDivisor_right, trace_eq_trace_adjoin, IntermediateField.coe_isIntegral_iff, LinearMap.toMatrix_innerₛₗ_apply, strictConvexSpace_iff, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, Valuation.associated_of_isUniformizer, HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub, PointwiseConvergenceCLM.equivWeakDual_symm_apply, PadicAlgCl.instUniformContinuousConstSMulPadic, hasDerivAt_of_tendstoUniformlyOn, TensorProduct.toLinearEquiv_commIsometry, PadicInt.Coe.ringHom_apply, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, WeierstrassCurve.Jacobian.addY_of_Z_ne_zero, EuclideanGeometry.oangle_midpoint_left, PowerSeries.X_inv, fderiv_fun_sum, AffineMap.hasDerivAt, hasDerivWithinAt_congr_set, MonomialOrder.span_leadingTerm_eq_span_monomial', Submodule.norm_sq_eq_add_norm_sq_projection, smul_sphere, LinearMap.extendTo𝕜'_apply_re, IntermediateField.adjoin_root_eq_top, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, tangentCoordChange_comp, Matrix.ker_mulVecLin_transpose_mul_self, HasFDerivWithinAt.fun_neg, LinearIsometry.norm_iteratedFDeriv_comp_left, LinearMap.range_toContinuousLinearMap, IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, Submodule.orthogonal_gc, NumberField.Embeddings.card, fderiv_const_smul_of_invertible, ContinuousLinearEquiv.dimH_image, meromorphicOrderAt_eq_int_iff, FractionalIdeal.mul_generator_self_inv, ContinuousLinearMap.norm_precompR_le, hasFDerivWithinAt_pow', ContDiffMapSupportedIn.structureMapLM_apply_withOrder, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_right, IsGaloisGroup.fixingSubgroup_fixedPoints, HasFTaylorSeriesUpToOn.continuousLinearMap_comp, IsGaloisGroup.mulEquivAlgEquiv_apply_apply, IsFractionRing.stabilizerHom_surjective, hasStrictDerivAt_finCons', InfiniteGalois.proj_adjoin_singleton_val, normalClosure_def, Polynomial.Splits.def, hasDerivWithinAt_taylorWithinEval_at_Icc, dist_iteratedFDerivWithin_zero, curveIntegral_restrictScalars, ContinuousLinearMap.hasFDerivAtFilter, IntermediateField.lift_inf, HasFPowerSeriesOnBall.hasSum, ContinuousLinearMap.isBoundedLinearMap_comp_right, Algebra.QuasiFinite.finite_fiber, quadraticChar_exists_neg_one', Matrix.PosSemidef.toLinearMap₂'_zero_iff, Submodule.starProjection_isSymmetric, convex_halfSpace_im_lt, HasFDerivAt.iterate, Polynomial.rootSet_C_mul_X_pow, Submodule.starProjection_apply, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, Algebra.QuasiFinite.instFiniteResidueField, NumberField.Embeddings.instNonemptyRingHomOfIsAlgebraicRatOfIsAlgClosed, HasFPowerSeriesWithinAt.pi, Matrix.eRank_diagonal, NormedSpace.isVonNBounded_iff', Polynomial.rootSet_derivative_subset_convexHull_rootSet, IsLocalRing.ResidueField.mapEquiv_apply, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv', RCLike.inv_im, WeakDual.isSeqCompact_closedBall, hasStrictDerivAt_finCons, IsFractional.div_of_nonzero, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, PiTensorProduct.liftEquiv_apply, HasFDerivAt.cexp, DoubleCentralizer.add_snd, Lagrange.degree_basisDivisor_of_ne, has_antideriv_at_fourier_neg, NumberField.InfinitePlace.isRamified_iff, hasFTaylorSeriesUpTo_top_iff', NumberField.InfinitePlace.card_isUnramified, hasStrictDerivAt_zpow, NormedSpace.expSeries_apply_eq, rank_mul_insepDegree_of_isPurelyInseparable, MvPowerSeries.C_inv, fderivWithin_iteratedFDerivWithin, IntermediateField.linearDisjoint_comm', LocalSubring.map_maximalIdeal_eq_top_of_isMax, rescale_to_shell, Matrix.det_eq_prod_roots_charpoly_of_splits, ContinuousLinearMap.rayleighQuotient_add, ContinuousMultilinearMap.contDiff, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, LinearIsometry.toSpanSingleton_apply, hasFDerivAt_iff_tendsto, IsFractionRing.fieldEquivOfAlgEquiv_algebraMap, WeakDual.exists_countable_separating, PolynormableSpace.induced, Polynomial.natSepDegree_eq_natDegree_iff, LinearMap.isSelfAdjoint_iff', Subspace.dual_finrank_eq, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, NumberField.IsCMField.complexEmbedding_complexConj, ContinuousLinearMap.deriv_of_bilinear, ContDiffWithinAt.inv, sum_embeddings_eq_finrank_mul, Orientation.areaForm'_apply, Padic.padicNormE.is_norm, mem_perfectClosure_iff, VectorBundleCore.coe_coordChange, IntermediateField.smul_mem, Subalgebra.algebraicClosure_eq_integralClosure, tendsto_nat_floor_div_atTop, hasFDerivAtFilter_iff_hasDerivAtFilter, NumberField.InfinitePlace.isComplex_smul_iff, AlgHom.map_fieldRange, innerSLFlip_apply_apply, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable, ContinuousLinearEquiv.mdifferentiableOn, ContinuousLinearMap.nnnorm_holder_apply_apply_le, IsFractionRing.closure_range_algebraMap, Polynomial.annIdealGenerator_mem, PadicAlgCl.spectralNorm_eq, Affine.Triangle.dist_orthocenter_reflection_circumcenter, OrthogonalFamily.hasSum_linearIsometry, Polynomial.hasFDerivAt, ZMod.pow_card_sub_one_eq_one, Asymptotics.isTheta_const_smul_left, FiniteField.instFiniteExtension_1, strictConvex_iff_convex, IntermediateField.extendScalars_self, Polynomial.splits_iff, upperBounds_smul_of_neg, Distribution.mapCLM_apply, WeierstrassCurve.Affine.derivative_addPolynomial_slope, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, Subalgebra.isField_of_algebraic, finrank_euclideanSpace, Polynomial.IsSplittingField.splits, FormalMultilinearSeries.norm_compContinuousLinearMap_le, PowerBasis.equivAdjoinSimple_gen, RatFunc.ofFractionRing_comp_algebraMap, LieModule.exists_nontrivial_weightSpace_of_isNilpotent, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, WeierstrassCurve.Jacobian.X_eq_iff, Ideal.ResidueField.map_algebraMap, algebraMap_mk, LinearMap.IsPositive.isSelfAdjoint, Emb.Cardinal.equivSucc_coherence, ContinuousLinearMap.bilinear_hasTemperateGrowth, FiniteField.frobeniusAlgEquivOfAlgebraic_symm_apply, Polynomial.IsSplittingField.splits', IntermediateField.finrank_top, LinearMap.mem_span_iff_continuous_of_finite, IsContinuousRiemannianBundle.exists_continuous, Bornology.isVonNBounded_iff_smul_tendsto_zero, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, RatFunc.algebraMap_X, Module.AEval.isTorsion_of_finiteDimensional, NumberField.InfinitePlace.IsRamified.isReal, DoubleCentralizer.norm_snd, NumberField.CMExtension.equivMaximalRealSubfield_apply, Submodule.top_orthogonal_eq_bot, Lagrange.basisDivisor_eq_zero_iff, ConvexOn.sSup_of_nat_affine_eq, ContinuousLinearMap.postcomp_apply, FunctionField.ringOfIntegers.instIsIntegrallyClosedSubtypeMemSubalgebraPolynomial, convexJoin_assoc, Ideal.ResidueField.exists_smul_eq_tmul_one, Submodule.fst_orthogonalDecomposition_apply, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, minpoly.ker_aeval_eq_span_minpoly, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, LinearEquiv.coe_toContinuousLinearEquiv', hasFDerivWithinAt_one, Matrix.rank_eq_finrank_span_row, IsDedekindDomain.FiniteAdeleRing.instIsScalarTower, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, map_equiv_traceDual, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, IntermediateField.restrictScalars_adjoin_eq_sup, Submodule.orthogonal_orthogonal_eq_closure, RatFunc.intDegree_C, SpectrumRestricts.mul_comm_iff, ContinuousLinearEquiv.nhds, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, Submodule.smul_starProjection_singleton, NumberField.Units.mem_torsion, FiniteGaloisIntermediateField.isGalois, ContinuousLinearMap.opNorm_comp_le, contMDiff_smul, MeasureTheory.dist_convolution_le, DoubleCentralizer.nnnorm_fst, LinearMap.finiteDimensional', ContinuousLinearMap.isUnit_iff_isUnit_toLinearMap, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, tendsto_inv_atBot_zero, with_gaugeSeminormFamily, TensorProduct.ext_iff_inner_right, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, NonUnitalStarSubalgebra.unitization_injective, PowerSeries.constantCoeff_inv, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, LieAlgebra.IsKilling.apply_coroot_eq_cast, slope_pos_iff, IntermediateField.mem_adjoin_iff_div, IsGalois.is_separable_splitting_field, contMDiffOn_continuousLinearMapCoordChange, LinearEquiv.isPositive_symm_iff, NumberField.to_finiteDimensional, ContinuousLinearMap.instCompleteSpace, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, Module.Basis.exists_opNNNorm_le, aestronglyMeasurable_smul_const_iff, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, absConvexHull_add_subset, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, PiTensorProduct.mapL_mul, cfcHom_real_eq_restrict, Finset.centerMass_mem_convexHull, hasDerivWithinAt_taylor_coeff_within, IntermediateField.Lifts.lt_iff, ContinuousLinearMap.toLinearMap_innerSL_apply, Polynomial.Gal.restrictComp_surjective, IsCyclotomicExtension.Rat.discr_prime_pow_ne_two', NumberField.ComplexEmbedding.IsConj.isReal_comp, HasFPowerSeriesAt.hasStrictDerivAt, Submodule.orthogonalFamily_self, AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, IsAlgClosure.equivOfEquiv_comp_algebraMap, IntermediateField.top_toSubalgebra, hasFDerivAt_ofNat, Subfield.roots_X_pow_char_sub_X_bot, IntermediateField.extendScalars_le_iff, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Module.Basis.equivFunL_apply, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', Representation.isSimpleModule_iff_irreducible_ofModule, Polynomial.natSepDegree_X_pow_char_pow_sub_C, hasFDerivAt_list_prod_finRange', NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, LinearMap.IsSymmetric.adjoint_eq, Trivialization.continuousLinearEquivAt_apply', LinearMap.isPositive_sum, ContinuousMultilinearMap.flipLinear_apply_apply, Submodule.starProjection_norm_le, HasStrictFDerivAt.neg, mfderiv_add, ContinuousAlternatingMap.norm_toContinuousMultilinearMap, HasGradientAt.hasFDerivAt, Lagrange.natDegree_basisDivisor_self, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, PowerSeries.mul_inv_cancel, LinearMap.hasDerivWithinAt, PiLp.volume_preserving_ofLp, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, MeromorphicOn.inv_iff, rescale_to_shell_semi_normed, Localization.subalgebra.isLocalization_ofField, FormalMultilinearSeries.comp_id, ContinuousMultilinearMap.hasStrictFDerivAt, Submodule.inner_orthogonalProjection_eq_of_mem_right, Subfield.relfinrank_top_right, Submodule.reflection_reflection, fderivWithin_comp_smul_eq_fderivWithin_smul, ContinuousLinearMap.isLeast_opNNNorm, RatFunc.num_denom_mul, Hyperreal.inv_epsilon, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_one, Matrix.trace_eq_sum_roots_charpoly, ContinuousMap.adjoin_id_eq_span_one_union, IsSelfAdjoint.spectrumRestricts, IsGaloisGroup.fixedPoints_bot, Submodule.isOrtho_iff_le, MeasureTheory.condExp_smul, Polynomial.hilbertPoly_add_left, Polynomial.logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots, hasFTaylorSeriesUpTo_succ_nat_iff_right, PowerBasis.equivAdjoinSimple_symm_gen, FiniteField.isSplittingField_of_nat_card_eq, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, iteratedFDeriv_add, SeparableClosure.hasEnoughRootsOfUnity, hasFDerivWithinAt_zero, ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun, HasFDerivWithinAt.norm_sq, minpoly.prime, CFC.abs_algebraMap, hasFDerivWithinAt_piLp, IntermediateField.coe_val, Complex.restrictScalars_one_smulRight, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, ContinuousLinearMapWOT.isEmbedding_inducingFn, inv_lt_inv_of_neg, IsPrimitiveRoot.minpoly_dvd_mod_p, differentiableOn_piLp, Polynomial.SplittingField.splits, ClosedSubmodule.iInf_orthogonal, WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne, Asymptotics.isLittleOTVS_iff_smallSets, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, hasDerivAt_fourier_neg, nhds_hasBasis_absConvex, Module.End.IsSemisimple.aeval, EuclideanGeometry.reflection_apply_of_mem, norm_fderiv_norm_rpow_le, AlgHom.fieldRange_toSubfield, HasFPowerSeriesOnBall.neg, VectorFourier.fderiv_fourierIntegral, Polynomial.splits_id_iff_splits, ContinuousLinearMap.uncurryBilinear_apply, LinearMap.IsSymmetric.isSymmetric_smul_iff, Matrix.isStrictlyPositive_iff_posDef, groupCohomology.norm_ofAlgebraAutOnUnits_eq, VectorBundle.continuousOn_coordChange', CategoryTheory.finrank_hom_simple_simple_eq_zero_iff, LinearMap.isPositive_linearIsometryEquiv_conj_iff, ZSpan.coe_floor_self, HasFDerivWithinAt.smul_const, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, IntermediateField.fixingSubgroup_le, ContinuousLinearMap.mfderiv_eq, Seminorm.sSup_empty, ModP.preVal_mk, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, hasFDerivWithinAt_singleton, LinearEquiv.coe_toContinuousLinearEquiv_symm', OrthonormalBasis.equiv_self_rfl, Matrix.IsHermitian.roots_charpoly_eq_eigenvalues, ContinuousAlternatingMap.isLeast_opNorm, midpoint_le_left, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, RatFunc.valuation_eq_LaurentSeries_valuation, InnerProductSpace.coe_gramSchmidtBasis, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, NormedSpace.isVonNBounded_of_isBounded, HasStrictFDerivAt.add, IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero, iteratedFDeriv_eq_equiv_comp, Submodule.reflection_inv, sum_Ioo_inv_sq_le, NumberField.Units.coe_neg_one, Real.smul_iInf_of_nonpos, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, meromorphicTrailingCoeffAt_inv, Unitization.norm_eq_sup, WeierstrassCurve.Projective.addZ_eq, Real.hasDerivAt_cos, mfderivWithin_comp_of_preimage_mem_nhdsWithin, Matrix.ofLp_toEuclideanCLM, Quaternion.expSeries_even_of_imaginary, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Nat.cast_le_pow_sub_div_sub, summable_pow_div_add, hasDerivAtFilter_iff_isLittleO, Polynomial.IsSplittingField.instIsTorsionFreeSplittingField, AlgebraicClosure.instIsAlgClosure, IsStrictlyPositive.nnrpow, PrimeSpectrum.residueField_comap, HasStrictFDerivAt.restrictScalars, NumberField.InfinitePlace.card_isUnramified_compl, FiniteField.two_pow_card, AffineIsometry.map_vsub, RatFunc.map_apply_div, PiTensorProduct.mapL_comp, PadicInt.coe_adicCompletionIntegersEquiv_apply, IntermediateField.finrank_eq_finrank_subalgebra, Submodule.norm_starProjection, isCompactOperator_iff_image_closedBall_subset_compact, IntermediateField.finrank_eq_one_iff_eq_top, fderiv_cos, FractionalIdeal.coe_inv_of_ne_zero, CancelDenoms.inv_subst, Algebra.Transcendental.rank_eq_cardinalMk, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, ordinaryHypergeometric_eq_tsum, FormalMultilinearSeries.isLittleO_one_of_lt_radius, Algebra.instFiniteResidueFieldOfIsUnramifiedAt, hasDerivAt_exp_smul_const, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', WeierstrassCurve.Affine.map_slope, NormedSpace.algebraMap_exp_comm, Meromorphic.fun_smul, Unitary.linearIsometryEquiv_coe_symm_apply, Asymptotics.isBigOTVS_neg_left, NormedSpace.expSeries_apply_eq_div, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, Polynomial.isRoot_gcd_iff_isRoot_left_right, ContDiff.comp_continuousLinearMap, ZMod.sq_add_sq, exists_dual_vector, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, NumberField.mixedEmbedding.logMap_eq_logEmbedding, hasFDerivWithinAt_comp_smul_smul_iff, IntermediateField.restrictRestrictAlgEquivMapHom_injective, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_apply, ContinuousLinearMap.rayleighQuotient_le_norm, Mathlib.Meta.NormNum.IsRat.natFloor, IsLocalRing.ResidueField.map_map, IsSepClosed.exists_pow_nat_eq, ZMod.euler_criterion_units, ProbabilityTheory.hasDerivAt_complexMGF, gauge_smul_left_of_nonneg, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff, AffineIsometryEquiv.symm_constVSub, DifferentiableWithinAt.isBigOTVS_sub, ContMDiffWithinAt.smul, LinearMap.isPositive_toContinuousLinearMap_iff, ContinuousLinearMap.norm_def, OrthogonalFamily.summable_of_lp, meromorphicNFOn_inv, IsLocalRing.exists_surjective_of_not_isLocalRing, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, LinearIsometryEquiv.analyticWithinAt, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', HasFPowerSeriesAt.apply_eq_zero, Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', fderivWithin_zero_of_notMem_closure, AddChar.wInner_cWeight_eq_one_iff_eq, ContinuousLinearMap.le_opNorm_of_le, iteratedDeriv_comp_const_smul, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDual, iteratedDerivWithin_one_div, norm_inner_eq_norm_tfae, Cubic.splits_iff_roots_eq_three, ContinuousMultilinearMap.opNorm_pi, curveIntegral_fun_add, ContinuousLinearEquiv.lipschitz, iteratedDeriv_vcomp_three, Algebra.IsCentral.left_of_tensor_of_field, Submodule.isCompl_orthogonal_of_hasOrthogonalProjection, Algebra.adjoin_eq_top_of_primitive_element, exists_nonneg_right_iff_sameRay, IsCyclotomicExtension.discr_prime_pow_ne_two, Submodule.reflection_mul_reflection, Height.mulHeight_smul_eq_mulHeight, Polynomial.isEquivalent_atTop_div, Real.hasDerivWithinAt_arcsin_Ici, OpenPartialHomeomorph.MDifferentiable.comp_symm_deriv, UniqueDiffWithinAt.smul_iff, HasStrictFDerivAt.arctan, curveIntegral_fun_neg, hasMFDerivAt_inl, HasStrictDerivAt.hasStrictFDerivAt, PowerSeries.mul_inv_rev, FiniteField.coe_frobeniusAlgEquivOfAlgebraic_iterate, NumberField.isFinitePlace_iff, Transcendental.algebraicClosure, RCLike.inner_tmul_eq, gal_C_isSolvable, deriv.scomp, AnalyticAt.analyticOrderAt_eq_natCast, HasFDerivAtFilter.const_smul, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, differentiableAt_finCons, InnerProductSpace.gramSchmidt_triangular, Algebra.normalizedTrace_algebraMap_apply_eq_self, ContinuousMultilinearMap.instContinuousConstSMul, NormedSpace.equicontinuous_TFAE, ContinuousLinearMap.differentiable, hasDerivAt_taylorWithinEval_succ, Submodule.starProjection_map_apply, RCLike.smul_im, Bornology.IsBounded.smul₀, LinearMap.dualMap_bijective_iff, NumberField.InfinitePlace.IsUnramified.eq, HasFDerivAt.multiset_prod, LinearMap.star_eq_adjoint, SpectrumRestricts.real_iff, LinearEquiv.toLinearEquiv_toContinuousLinearEquiv, contDiffWithinAt_succ_iff_hasFDerivWithinAt', IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two, IsLocalFrameOn.eventually_eq_sum_coeff_smul, MvPolynomial.pointToPoint_zeroLocus_le, Filter.EventuallyEq.iteratedFDerivWithin', contDiffOn_succ_iff_hasFDerivWithinAt, HasFDerivAt.mul_const, GenContFract.convs_succ, Set.val_unitEquivUnitsInteger_apply_coe, Polynomial.sub_mod, Nat.div_two_lt_floor, differentiableWithinAt_euclidean, ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', unitary.spectrum_subset_circle, IntermediateField.finrank_adjoin_eq_one_iff, ContinuousLinearMap.opNorm_add_le, IsLocalRing.ResidueField.map_residue, Ring.instIsSeparableFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, WittVector.isDiscreteValuationRing, exists_integral_inj_algHom_of_quotient, ContinuousLinearMap.sSup_sphere_eq_norm, FDRep.char_linHom, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, DoubleCentralizer.neg_toProd, FormalMultilinearSeries.radius_unshift, IsGaloisGroup.finiteDimensional, HasFPowerSeriesAt.fderiv_eq, CategoryTheory.endomorphism_simple_eq_smul_id, LinearPMap.adjointDomainMkCLM_apply, IntermediateField.normal_iff_forall_map_le', Submodule.restrictScalars_traceDual, NumberField.RingOfIntegers.rank, hasStrictFDerivAt_zero, Matrix.isPositive_toEuclideanLin_iff, ContinuousLinearMap.coe_restrictScalarsIsometry, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, TensorProduct.enorm_tmul, ContinuousLinearMap.memLp_of_bilin, PadicInt.isFractionRing, HasFPowerSeriesOnBall.tendstoUniformlyOn, IntermediateField.normal_iff_forall_fieldRange_eq, Polynomial.aeval_conj, ProbabilityTheory.hasFPowerSeriesAt_mgf, ContinuousLinearMap.norm_inr, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, IsPrimitiveRoot.separable_minpoly_mod, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, Submodule.starProjection_bot, arithGeom_eq, RootPairing.polarizationEquiv_apply, RCLike.re_eq_add_conj, instIsAbelianGaloisSubtypeMemIntermediateField_1, NumberField.integralBasis_repr_apply, ContinuousLinearMap.differentiableWithinAt, continuousMultilinearCurryFin0_apply, exists_finite_inj_algHom_of_fg, IsLocalRing.PrimeSpectrum.comap_residue, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, IsNonarchimedeanLocalField.instFiniteResidueFieldSubtypeMemSubringIntegerValueGroupWithZeroValuation, Polynomial.separable_prod_X_sub_C_iff', EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HasFDerivWithinAt.mapsTo_tangent_cone, finSepDegree_le_finrank, WithAbs.instFiniteDimensional, PiTensorProduct.dualSeminorms_bounded, ValuationSubring.instIsDomainSubtypeMem, LinearMap.hasBasis_weakBilin, RootPairing.linearIndepOn_root_baseOf, CommCStarAlgebra.toStarModule, FormalMultilinearSeries.radius_neg, VectorPrebundle.pretrivialization_linear', nonempty_algHom_of_range_minpoly_subset, FiniteField.splits_X_pow_nat_card_sub_X, HasFDerivWithinAt.mul_const', extDeriv_smul, PointwiseConvergenceCLM.coeLMₛₗ_apply, ContinuousLinearMap.postcompCompactConvergenceCLM_apply, spectrum.isClosed, HasStrictFDerivAt.iterate, LaurentSeries.coe_X_compare, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, WeakBilin.locallyConvexSpace, Submodule.orthogonal_closure, MvPolynomial.zeroLocus_bot, LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, TensorProduct.inner_assoc_assoc, ContinuousMultilinearMap.curryMidEquiv_apply, StrictConvexSpace.strictConvex_closedBall, fderiv_const_mul, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq, ApproximatesLinearOn.lipschitz_sub, Matrix.val_planeConformalMatrix, ContinuousMultilinearMap.iteratedFDeriv_eq, FormalMultilinearSeries.le_mul_pow_of_radius_pos, ZSpan.norm_fract_le, differentialIdeal_le_fractionalIdeal_iff, HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal, IntermediateField.finrank_bot, IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zero, ConjRootClass.splits_minpoly, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, isSeparable_inv, ContinuousLinearMap.reApplyInnerSelf_apply, ZSpan.fundamentalDomain_reindex, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, fderiv_exp, Affine.Simplex.direction_mongePlane, DoubleCentralizer.algebraMap_snd, NormedSpace.expSeries_apply_zero, WeakDual.polar_def, ConvexCone.smul_mem_iff, IntermediateField.fixingSubgroup_antitone, ContinuousLinearMap.differentiableAt, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, RCLike.wInner_const_left, Valuation.Integers.dvdNotUnit_iff_lt, AnalyticAt.analyticOrderNatAt_eq_iff, fderiv_arctan, fderivWithin_const, RatFunc.laurentAux_algebraMap, RCLike.wInner_cWeight_const_left, MeasureTheory.integrable_smul_const, hasFiniteFPowerSeriesOnBall_const, InfiniteGalois.restrict_fixedField, LinearMap.le_def, FormalMultilinearSeries.ofScalarsSum_zero, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, contDiffAt_inv, iteratedFDerivWithin_succ_apply_left, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, HasFDerivAtFilter.fun_const_smul, hasStrictFDerivAt_norm_sq, FractionalIdeal.mem_dual, Matrix.linearIndependent_cols_iff_isUnit, Submodule.starProjection_unit_singleton, SchwartzMap.fourier_evalCLM_eq, RatFunc.algebraMap_eq_C, LinearIsometryEquiv.comp_differentiableWithinAt_iff, tfae_of_isNoetherianRing_of_isLocalRing_of_isDomain, LinearMap.adjoint_toSpanSingleton, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvalues₀, DoubleCentralizer.one_snd, Valuation.Integers.valuation_unit, OrthonormalBasis.coe_toBasis, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, Polynomial.natDegree_hilbertPoly_of_ne_zero, Polynomial.div_eq_zero_iff, Polynomial.IsSplittingField.adjoin_rootSet', AlgebraicGeometry.instIsFractionRingCarrierStalkCommRingCatPresheafFunctionField, IsLocalRing.ResidueField.map_id, IntermediateField.sepDegree_bot, convexJoin_convexJoin_convexJoin_comm, ContinuousMultilinearMap.norm_mkPiAlgebra, ValuationSubring.unitGroup_strictMono, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, contDiffOn_infty_iff_fderiv_of_isOpen, hasDerivWithinAt_natCast, Asymptotics.superpolynomialDecay_iff_isLittleO, Algebra.normalizedTrace_self, NumberField.canonicalEmbedding.nnnorm_eq, RatFunc.algebraMap_apply_div, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, algebraMap_memℓp_infty, galLiftEquiv_symm_apply, jacobiSum_eq_gaussSum_mul_gaussSum_div_gaussSum, convexHull_sum, Hyperreal.IsSt.inv, ContinuousLinearEquiv.analyticOn, RatFunc.div_smul, DirichletCharacter.LSeriesSummable_twist_vonMangoldt, ContinuousMultilinearMap.opNorm_add_le, fderiv_pow_ring', ContinuousLinearMap.map_sub₂, ContinuousLinearMap.bilinearComp_apply, RootPairing.GeckConstruction.instIsIrreducible, IntermediateField.algebraMap_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, ContinuousMultilinearMap.instContinuousEval, differentiableAt_piLp, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Submodule.reflection_sub, InfiniteGalois.instCompactSpaceAlgEquivOfIsGalois, IsAlgClosure.equivOfEquiv_symm_algebraMap, TemperedDistribution.instLineDerivSMulReal, iteratedDeriv_comp_neg, fderiv_natCast, IsConjRoot.exists_algEquiv, IntermediateField.finInsepDegree_bot', NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_le, RCLike.inner_apply, SchwartzMap.evalCLM_apply_apply, Algebra.norm_eq_norm_adjoin, Algebra.IsAlgebraic.algHom_bijective₂, LinearMap.IsSymmetric.natCast, HasFDerivAtFilter.fun_sub, upperHemicontinuous_quasispectrum, spectrum.isBounded, OpenPartialHomeomorph.MDifferentiable.mfderiv_bijective, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, ClosedSubmodule.mem_orthogonal, IsSelfAdjoint.sq_spectrumRestricts, Height.mulHeight_eq, fderiv_const, DiffContOnCl.smul_const, NumberField.FinitePlace.coe_apply, Matrix.posDef_iff_eq_conjTranspose_mul_self, MeasureTheory.condExpIndL1_smul', Polynomial.differentiableAt_aeval, Subspace.quotAnnihilatorEquiv_apply, circleEquivGen_symm_apply, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, ContinuousLinearMap.toContinuousLinearEquivOfDetNeZero_apply, WeakDual.CharacterSpace.compContinuousMap_apply, Subalgebra.frontier_subset_frontier, LinearMap.re_inner_adjoint_mul_self_nonneg, PointwiseConvergenceCLM.coeLM_apply, hasDerivAt_id, differentiable_pi, HasFTaylorSeriesUpToOn.fderivWithin, Real.hasDerivAt_rpow_const, IntermediateField.restrictScalars_bot_eq_self, DirichletCharacter.convolution_twist_vonMangoldt, ContinuousLinearEquiv.hasFDerivWithinAt, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, ContinuousMultilinearMap.isLeast_opNNNorm, Complex.ofReal_comp_balance, functionField_iff, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff, ValuationSubring.instIsFractionRingSubtypeMem, RCLike.normSq_mul, LinearMap.isPositive_self_comp_adjoint, PadicInt.toZMod_eq_residueField_comp_residue, RatFunc.eval_C, Polynomial.hilbertPoly_X_pow_succ, RCLike.hasSum_conj, Polynomial.isEquivalent_atBot_lead, Lagrange.iterate_derivative_interpolate, FormalMultilinearSeries.id_comp, Finset.mem_convexHull, fderivWithin.log, circleIntegral.integral_smul, ContinuousLinearMap.norm_map_tail_le, deriv_update, finSepDegree_eq_finrank_of_isSeparable, HasFPowerSeriesAt.restrictScalars, AlgebraicClosure.Monics.splits_finsetProd, contMDiffOn_symm_coordChangeL, hasDerivAt_integral_of_dominated_loc_of_deriv_le, tangentBundleCore_coordChange_model_space, MvPolynomial.le_zeroLocus_iff_le_vanishingIdeal, ContinuousLinearMap.instStarModuleId, NumberField.mixedEmbedding.mixedEmbedding_apply_isReal, Polynomial.hasFDerivAt_aeval, IntermediateField.adjoin.range_algebraMap_subset, Seminorm.convex_ball, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, Height.mulHeight₁_inv, LinearIsometryEquiv.toLinearEquiv_lTensor, DoubleCentralizer.instIsCentralScalar, Hyperreal.coe_inv, spectrum.isUnit_one_sub_smul_of_lt_inv_radius, NormedField.continuousAt_inv, Matrix.linearIndependent_of_posDef_gram, ContDiffAt.restrictScalars_iteratedFDeriv, IsUnit.cfcNNRpow, exists_dual_vector'', ContinuousLinearMapWOT.instContinuousSMul, Finpartition.coe_energy, PiTensorProduct.injectiveSeminorm_apply, ValuativeRel.inv_rel_one, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, ContinuousLinearMap.isBoundedLinearMap_comp_left, LinearIsometryEquiv.toLinearEquiv_smul, MeasureTheory.MemLp.continuousLinearMap_comp, Valuation.HasExtension.instIsScalarTower_valuationSubring', RingHom.SurjectiveOnStalks.residueFieldMap_bijective, Algebra.adjoin.powerBasis_gen, Matrix.trace_eq_sum_roots_charpoly_of_splits, NumberField.RingOfIntegers.mk_zero, norm_fderiv_iteratedFDeriv, curveIntegralFun_neg, meromorphicOrderAt_smul, Asymptotics.isLittleOTVS_map, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, conformalFactorAt_inner_eq_mul_inner', InfiniteGalois.limitToAlgEquiv_apply, hasFDerivAtFilter_snd, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, IsFractionRing.mk'_num_den, LinearIsometryEquiv.analyticOn, Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv, ValuationSubring.algebraMap_apply, LinearIsometryEquiv.analyticAt, IsLocalRing.ResidueField.map_id_apply, Matrix.l2_opNNNorm_def, hasMFDerivAt_const, NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConj, ContinuousLinearEquiv.strictConvex_image, ContinuousMultilinearMap.instIsBoundedSMul, IntermediateField.mem_lift, IntermediateField.isAlgebraic_adjoin_pair, MeromorphicOn.inv, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, PowerSeries.inv_eq_zero, hasDerivAtFilter_sub_const_iff, CyclotomicRing.instIsScalarTowerCyclotomicField, RatFunc.faithfulSMul, IsRealClosed.exists_eq_pow_of_isSquare, ContinuousLinearMap.integrable_comp, ContinuousLinearMap.adjointAux_adjointAux, HasStrictFDerivAt.const_sub, RatFunc.num_X, Submodule.coe_inner, Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, fderiv_sub, LinearMap.det_map, NumberField.Embeddings.instNonemptyRingHom, hasDerivAt_exp, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, ZSpan.span_top, LinearMap.hasEigenvalue_zero_tfae, AffineSubspace.wSameSide_iff_exists_left, hasFDerivAt_single, Ideal.finrank_quotient_map, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_orthonormalBasis, MeasureTheory.condExpL2_indicator_of_measurable, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, Complex.hasDerivAt_logTaylor, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, iteratedDeriv_vcomp_eq_sum_orderedFinpartition, LinearMap.eq_adjoint_iff, ContinuousLinearMapWOT.instContinuousAdd, WittVector.exists_frobenius_solution_fractionRing, NumberField.mixedEmbedding.norm_smul, Real.hasStrictDerivAt_arsinh, VectorField.mpullbackWithin_smul_apply, Algebra.discr_mul_isIntegral_mem_adjoin, NNReal.coe_nnqsmul, iter_deriv_pow', HasFDerivWithinAt.iterate, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, hasDerivAt_iff_tendsto_slope_zero, HasMFDerivWithinAt.sum, IntermediateField.finrank_sup_le, Orthonormal.inner_right_finsupp, ConvexOn.convex_re_epigraph, Differential.instDifferentialAlgebraSubtypeMemIntermediateField_1, ValuationSubring.valuation_eq_iff, NumberField.InfinitePlace.IsRamified.comap_embedding, ordinaryHypergeometricSeries_apply_eq, LinearMap.norm_extendTo𝕜'_apply_sq, Asymptotics.isLittleOTVS_iff_isLittleO, OrthonormalBasis.tensorProduct_apply', WithSeminorms.equicontinuous_TFAE, EuclideanSpace.basisFun_repr, ImplicitFunctionData.hasStrictFDerivAt, ContinuousLinearMap.integral_comp_id_comm', Height.AdmissibleAbsValues.mulSupport_finite, UniqueMDiffWithinAt.uniqueDiffWithinAt, NumberField.InfinitePlace.LiesOver.embedding_comp_eq_or_conjugate_embedding_comp_eq, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, ContinuousLinearMap.coprodEquivL_apply_apply, HasFTaylorSeriesUpToOn.hasFDerivAt, Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zero, mfderiv_prod_right, LinearIsometry.norm_toContinuousLinearMap_comp, galRestrictHom_symm_algebraMap_apply, hasStrictFDerivAt_inv, RatFunc.algebraMap_C, ContinuousLinearMap.isBigOWith_comp, ContinuousLinearMap.flip_add, exists_pos_left_iff_sameRay, IntermediateField.adjoinRootEquivAdjoin_apply_root, LinearMap.finiteDimensional, hasFiniteFPowerSeriesAt_const, continuous_clm_apply, IntermediateField.normalClosureOperator_apply, IntermediateField.fixingSubgroup_isClosed, AffineSubspace.isometryEquivMap.coe_apply, ContinuousAlternatingMap.hasBasis_nhds_zero, IsFractionRing.associated_num_den_inv, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, LinearIsometry.coe_toSpanSingleton, Bornology.isBounded_iff_isVonNBounded, Polynomial.cardPowDegree_apply, ContinuousLinearEquiv.isBigO_sub_rev, ContinuousLinearMap.isSelfAdjoint_iff', Submodule.sndL_comp_coe_orthogonalDecomposition, HasFDerivWithinAt.restrictScalars, DoubleCentralizer.pow_toProd, OrthonormalBasis.equiv_apply_euclideanSpace, measurable_fderiv_apply_const, Submodule.le_traceDual, stereographic_neg_apply, IsConjRoot.add_algebraMap, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, IsLocalFrameOn.coeff_apply_of_notMem, isSelfAdjoint_starProjection, krullTopology_isTotallySeparated, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, InnerProductSpace.gramSchmidt_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, VectorBundleCore.localTriv_coordChange_eq, ContinuousMultilinearMap.uncurryRight_apply, IntermediateField.rank_bot, eventually_norm_symmL_trivializationAt_self_comp_lt, RCLike.ofReal_pow, ContinuousLinearMap.isVonNBounded_iff, NumberField.FinitePlace.norm_def_int, InnerProductSpace.Core.inner_smul_ofReal_left, mfderivWithin_zero_of_not_mdifferentiableWithinAt, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, fderiv_inv, FiniteField.unit_isSquare_iff, Differentiable.prodMk, Complex.orthonormalBasisOneI_repr_symm_apply, ModelWithCorners.hasMFDerivWithinAt, derivWithin_comp_mul_left, Manifold.riemannianEDist_def, HasFDerivAtFilter.prodMk, hasDerivAt_circleMap, HasFDerivAtFilter.isLittleO, convexHullAddMonoidHom_apply, curveIntegralFun_fun_zero, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, Valuation.valuationSubring_isPrincipalIdealRing, vectorSpan_segment, RCLike.ofReal_alg, ContinuousLinearMap.bilinearComp_zero, HasFDerivAt.fun_pow', IsAlgClosed.card_aroots_eq_natDegree, inv_sub_inv, le_restrictScalars_separableClosure, ZSpan.map, IsSimpleModule.finrank_eq_one_of_isMulCommutative, IntermediateField.coe_zero, NumberField.InfinitePlace.isRamified_iff_card_stabilizer_eq_two, X_pow_sub_C_irreducible_of_prime, Submodule.IsLattice.finrank_of_pi, DifferentiableAt.prodMk, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, Finset.convexHull_eq, HasMFDerivWithinAt.mul', ContinuousLinearEquiv.norm_symm_pos, Submodule.sInf_orthogonal, ContinuousAlternatingMap.uniformContinuous_coe_fun, WeierstrassCurve.Projective.neg_of_Z_ne_zero, ContinuousMultilinearMap.cpolynomialAt, ContinuousLinearMap.NonlinearRightInverse.right_inv, norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, curveIntegralFun_def', PointedContMDiffMap.instIsScalarTowerSomeENatTop, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace, NumberField.RingOfIntegers.instIsTorsionFree, FormalMultilinearSeries.ofScalarsSum_eq_tsum, NumberField.discr_eq_basisMatrix_det_sq, IntermediateField.adjoin.algebraMap_mem, Submodule.isOrtho_span, IsStrictlyPositive.sqrt, contDiffOn_fderiv_coord_change, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, IsLocalRing.exists_factor_valuationRing, IntermediateField.instIsScalarTowerSubtypeMem_1, RatFunc.num_eq_zero_iff, ZSpan.exist_unique_vadd_mem_fundamentalDomain, ContinuousMultilinearMap.ratio_le_opNorm, arithGeom_same_eq_mul_div, HasFDerivAtFilter.fun_add, ContinuousLinearEquiv.subsingleton_or_nnnorm_symm_pos, ContinuousLinearMap.norm_extendTo𝕜'_bound, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff, MvPolynomial.mem_zeroLocus_iff, slope_def_field, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, HasFDerivWithinAt.hasDerivWithinAt, Matrix.PosSemidef.isUnit_sqrt_iff, spectralNorm_smul, hasDerivAt_iff_hasFDerivAt, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, Complex.im_balance, Polynomial.eventually_atTop_not_isRoot, HasFiniteFPowerSeriesOnBall.neg, RCLike.conj_tsum, Complex.ofReal_expect, Padic.complete'', Algebra.IsCentral.instContinuousLinearMap, IsSemisimpleRing.exists_algEquiv_pi_matrix_of_isAlgClosed, HasFDerivAtFilter.comp, Polynomial.separable_prod_X_sub_C_iff, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, LinearMap.charpoly_constantCoeff_eq_zero_iff, LinearMap.weakBilin_withSeminorms, norm_derivWithin_eq_norm_fderivWithin, Asymptotics.IsEquivalent.pow, lineDifferentiableWithinAt_smul_iff, NumberField.ComplexEmbedding.isConj_apply_apply, ArchimedeanClass.mk_ratCast, iteratedFDeriv_zero_apply, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, ContinuousLinearMap.le_def, isSolvable_of_isScalarTower, WeakDual.isClosed_closedBall, contDiff_succ_iff_fderiv_apply, WeierstrassCurve.Projective.map_dblU, hasDerivAt_fourier, AlgebraicGeometry.ValuativeCommSq.commSq, coe_lpPiLpₗᵢ, Submodule.complete_of_finiteDimensional, Subfield.bot_eq_of_charZero, ProbabilityTheory.instIsProbabilityMeasureCondCDF, MvPolynomial.eval_indicator_apply_eq_zero, VectorBundleCore.localTriv_apply, NumberField.RingOfIntegers.withValEquiv_apply, LinearIsometry.inr_apply, fderiv_ccos, LinearMap.isPositive_zero, DoubleCentralizer.zero_fst, IntermediateField.finrank_bot_mul_relfinrank, fderiv_update, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, FiniteField.Matrix.charpoly_pow_card, Asymptotics.superpolynomialDecay_mul_param_pow_iff, ContinuousLinearMap.hasFDerivWithinAt, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, fdifferential_comp, minpoly.dvd_map_of_isScalarTower, LinearIsometry.orthonormal_comp_iff, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv, WeierstrassCurve.Projective.negDblY_eq, Diffeomorph.uniqueDiffOn_image, ContinuousLinearMap.le_opNorm₂, Algebra.norm_eq_prod_automorphisms, ContinuousLinearMap.lpPairing_eq_integral, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, slope_fun_def, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, Seminorm.continuous_iff, HasFDerivAt.smul_const, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, ContinuousLinearMap.norm_uncurryMid, IsLocalFrameOn.linearIndependent, RCLike.wInner_const_right, lift_rank_mul_lift_insepDegree_of_isPurelyInseparable, Matrix.sub_scalar_sq_eq_disc, InnerProductSpace.rankOne_def', ContDiff.fderiv_apply, EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, ContinuousLinearMap.opNorm_mul_le, ContinuousLinearMap.uncurryLeft_norm, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_right, hasFDerivAtFilter_fst, Polynomial.exists_approx_polynomial, Submodule.isClosed_orthogonal, Submodule.IsLattice.rank_of_pi, ContinuousLinearMap.opNorm_subsingleton, hasStrictDerivAt_abs_neg, ContinuousLinearMap.holder_smul_right, Filter.EventuallyEq.fderiv, Height.logHeight₁_inv, HasFDerivWithinAt.multilinear_comp, HasFPowerSeriesOnBall.tendstoUniformlyOn', Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField, HasFPowerSeriesWithinOnBall.const_smul, natDegree_radical_le, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, FiniteField.trace_pow_card, fderiv_apply_one_eq_deriv, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, IsCyclotomicExtension.finiteDimensional, HasFTaylorSeriesUpToOn.compContinuousLinearMap, hasFDerivAt_zero_of_eventually_const, OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_top, IsUltrametricDist.algNormOfAlgEquiv_apply, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, IntermediateField.bot_eq_top_iff_finrank_eq_one, ContinuousAlternatingMap.continuous_restrictScalars, HasFPowerSeriesOnBall.sub, IntermediateField.finiteDimensional_adjoin, contDiffAt_succ_iff_hasFDerivAt, ContinuousLinearMap.IsPositive.inner_nonneg_left, IntermediateField.isTranscendenceBasis_adjoin_iff, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, hasFDerivAt_const, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_left, HasFDerivAt.inner, LinearMap.adjoint_lTensor, DirichletCharacter.LSeriesSummable_iff, EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, LinearEquiv.smulOfNeZero_apply, LinearMap.slope_comp, IntermediateField.lift_injective, PadicComplex.instIsScalarTowerPadicPadicAlgCl, RCLike.conj_eq_iff_real, MeasureTheory.Integrable.convolution_integrand, HasFDerivAtFilter.star, RatFunc.intDegree_add, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, OrthonormalBasis.map_apply, LinearMap.toMatrixOrthonormal_apply, MeasureTheory.condExpL1CLM_lpMeas, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, fderivWithin_exp, FiniteGaloisIntermediateField.adjoin_map, NumberField.InfinitePlace.embedding_of_isReal_apply, Submodule.isSymmetricProjection_starProjection, CFC.sqrt_sq, deriv_inv'', ContinuousLinearMap.mdifferentiableWithinAt, SeparatingDual.completeSpace_continuousLinearMap_iff, selfAdjoint.val_inv, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, convex_halfSpace_re_ge, OrthogonalFamily.inner_sum, LinearMap.IsPositive.smul_of_nonneg, NormedSpace.vonNBornology_eq, HasStrictFDerivAt.fun_sub, ClosedSubmodule.mem_orthogonal_toSubmodule_iff, HasFDerivAt.lim, hasDerivWithinAt_const, FormalMultilinearSeries.compAlongComposition_norm, Polynomial.tendsto_nhds_iff, ContinuousLinearMap.isometry_mul, Subspace.finrank_add_finrank_dualCoannihilator_eq, Matrix.IsHermitian.spectrum_eq_image_range, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', ContinuousLinearMap.isOpen_injective, isCoveringMapOn_npow, NonUnitalCommCStarAlgebra.toStarModule, Submodule.le_traceDual_comm, ContDiff.continuous_iteratedFDeriv', IsFractionRing.mk'_mk_eq_div, IntermediateField.coe_extendScalars, NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding, Polynomial.X_pow_sub_one_separable_iff, NumberField.RingOfIntegers.coe_injective, OrthonormalBasis.sum_repr_symm, HasFDerivAt.const_mul, Meromorphic.pow, CFC.rpow_sqrt_nnreal, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, LieAlgebra.IsKilling.disjoint_ker_weight_corootSpace, MvPolynomial.frobenius_zmod, StrongDual.toLpₗ_apply, IntermediateField.AdjoinSimple.trace_gen_eq_zero, integralClosure.isFractionRing_of_algebraic, Orthonormal.inner_left_sum, DoubleCentralizer.sub_toProd, formalMultilinearSeries_geometric_apply_norm, IntermediateField.lift_sepDegree_bot', ContinuousLinearMap.continuous_uncurry_of_multilinear, Valued.integer.coe_span_singleton_eq_closedBall, IntermediateField.mem_adjoin_range_iff, Polynomial.differentiableOn, Pi.orthonormalBasis.toBasis, LinearIsometry.map_starProjection, IsLocalFrameOn.coeff_apply_zero_at, CyclotomicRing.adjoin_algebra_injective, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, egauge_ball_one_le_of_one_lt_norm, HasFTaylorSeriesUpToOn.add, NormedSpace.norm_expSeries_summable', MeasureTheory.dist_convolution_le', instLiesOverResidueFieldBotIdeal, instIsTopologicalGroupAlgEquiv, isQuotientCoveringMap_zpow, Polynomial.natSepDegree_C_mul, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, HasFDerivAt.mul, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, IsLocalRing.split_injective_iff_lTensor_residueField_injective, VectorField.lieBracket_const_smul_right, WeierstrassCurve.Projective.addX_eq, Asymptotics.IsBigO.hasFDerivWithinAt, LinearMap.continuous_of_nonzero_on_open, Submodule.inf_orthogonal, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, RatFunc.denom_X, InnerProductSpace.innerSL_norm, hasFDerivAt_exp_zero, LinearIsometryEquiv.strictConvex_image, Filter.tendsto_const_mul_pow_atBot_iff, fderiv_add, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, SchwartzMap.le_seminorm, Ioo_subset_openSegment, IsLocalDiffeomorph.mfderivToContinuousLinearEquiv_coe, DoubleCentralizer.nnnorm_fst_eq_snd, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, toWeakSpace_closedConvexHull_eq, Unitization.norm_def, IntermediateField.relrank_dvd_rank_top_of_le, convexHull_pi, Submodule.IsOrtho.le, Submodule.reflection_map, ContinuousAlternatingMap.instT3Space, LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpace, WittVector.RecursionBase.solution_spec, xInTermsOfW_vars_subset, AlgebraicClosure.le_maxIdeal, ValuativeRel.one_vlt_inv, Polynomial.gcd_map, InnerProductSpace.span_gramSchmidt_Iic, MDifferentiableAt.smul, SimpleGraph.FarFromTriangleFree.lt_half, Submodule.det_reflection, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, ContinuousLinearMap.measurable_apply, selfAdjoint.star_coe_unitarySelfAddISMul, IsSepClosed.algebraMap_surjective, hasFDerivAtFilter_iff_isLittleOTVS, IntermediateField.finSepDegree_adjoin_simple_le_finrank, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, IsAlgClosed.card_aroots_eq_natDegree_of_leadingCoeff_ne_zero, ContinuousAlternatingMap.curryLeft_same, ContinuousMultilinearMap.curryRight_apply, TensorProduct.inner_comm_comm, ValuationSubring.coe_mem_nonunits_iff, NormedSpace.expSeries_apply_eq', ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Submodule.inner_orthogonalProjection_eq_of_mem_left, ContMDiffWithinAt.mfderivWithin, gal_X_sub_C_isSolvable, Polynomial.IsSplittingField.splittingField, convex_halfSpace_im_ge, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, Polynomial.hilbertPoly_mul_one_sub_succ, differentiableWithinAt_pi, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, toIocDiv_eq_neg_floor, contDiffOn_inv, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Hyperreal.instIsStrictOrderedRing, ContinuousLinearMap.extendTo𝕜_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, eventually_norm_symmL_trivializationAt_comp_self_lt, ContinuousLinearMap.IsPositive.add, EuclideanSpace.volume_ball_fin_three, Subspace.dualAnnihilator_inj, Emb.Cardinal.filtration_apply, FiniteField.isSplittingField_of_card_eq, Polynomial.natSepDegree_mul_eq_iff, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff', InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis, CurveIntegrable.fun_neg, MeromorphicAt.pow, AffineSubspace.subtypeₐᵢ_linear, AlgebraicClosure.toSplittingField_coeff, LieModule.traceForm_eq_sum_finrank_nsmul, NumberField.RingOfIntegers.isIntegral_coe, mfderivWithin_const, IntermediateField.relrank_dvd_rank_bot, hasStrictFDerivAt_pow', Polynomial.hasStrictDerivAt_aeval, AnalyticOn.iteratedFDeriv_comp_perm, ContinuousLinearMap.norm_single, LinearMap.flip_injective_iff₂, VectorPrebundle.exists_coordChange, Asymptotics.superpolynomialDecay_iff_isBigO, ValuationSubring.mem_nonunits_iff_exists_mem_maximalIdeal, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, DoubleCentralizer.one_fst, ContinuousLinearMap.norm_extendTo𝕜', ValuationSubring.unitGroup_le_unitGroup, Lagrange.degree_basis, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, IsDedekindDomain.HeightOneSpectrum.coe_mem_adicCompletionIntegers, StrongDual.polar_univ, IsLocalRing.ResidueField.algebraMap_eq, AlgHom.liftNormal_commutes, NormedAlgebra.instRegularNormedAlgebra, fderivWithin_eventually_congr_set, Lagrange.eval_basis_of_ne, NumberField.Units.complexEmbedding_apply, IsStronglyTranscendental.iff_of_isFractionRing, convex_halfSpace_re_lt, LinearIsometry.coe_toAffineIsometry, NumberField.count_multisetInfinitePlace_eq_mult, FractionalIdeal.map_div, Polynomial.isUnit_or_eq_zero_of_isUnit_integerNormalization_primPart, linearIndependent_of_ne_zero_of_inner_eq_zero, WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne', ContDiffMapSupportedIn.postcompCLM_apply, ValuationSubring.principal_units_le_units, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ContinuousAlternatingMap.curryLeft_zero, IsContDiffImplicitAt.bijective, DirichletCharacter.absicssaOfAbsConv_eq_one, Polynomial.natSepDegree_smul_nonzero, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, OnePoint.smul_infty_eq_ite, ContinuousAlternatingMap.restrictScalarsLI_apply, fderivWithin_fun_const, Complex.restrictScalars_toSpanSingleton, ProbabilityTheory.measure_cdf, PerfectField.splits_of_natSepDegree_eq_one, ContinuousMultilinearMap.opNNNorm_prod, IntermediateField.AdjoinPair.algebraMap_gen₁, ContinuousLinearEquiv.comp_right_differentiableOn_iff, Padic.isAbsoluteValue, OpenPartialHomeomorph.MDifferentiable.mfderiv_surjective, NumberField.fractionalIdeal_rank, ContinuousLinearMap.opENorm_comp_le, hasGradientAt_iff_hasFDerivAt, Asymptotics.IsTheta.isThetaTVS, Asymptotics.isEquivalent_nat_floor, RatFunc.denom_div, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, IsLocalRing.finrank_cotangentSpace_le_one_iff, curveIntegrable_neg_iff, PowerSeries.invOfUnit_eq, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, HasFPowerSeriesOnBall.tendsto_partialSum, maximal_orthonormal_iff_orthogonalComplement_eq_bot, ValuationRing.of_integers, hasMFDerivWithinAt_const, FractionalIdeal.map_inv, iteratedFDeriv_one_apply, ContinuousLinearEquiv.iteratedFDeriv_comp_left, Filter.Tendsto.zero_smul_isBoundedUnder_le, NumberField.InfinitePlace.not_isUnramified_iff, Submodule.reflection_orthogonal, quasispectrum.algebraMap_mem_iff, hasFDerivAt_exp_smul_const_of_mem_ball, fderiv_fun_mul', NumberField.InfinitePlace.isUnramified_iff, IsDiscreteValuationRing.exists_lift_of_le_one, Finset.centerMass_segment', ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, HasFPowerSeriesOnBall.factorial_smul, HasFDerivAt.const_smul, HasFDerivAt.hasLineDerivAt, WeierstrassCurve.Affine.Point.map_map, doublyStochastic_eq_convexHull_permMatrix, derivWithin_pi, ContinuousAlternatingMap.norm_image_sub_le', NormedSpace.expSeries_sum_eq_rat, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, HasFPowerSeriesWithinAt.prod, Valuation.HasExtension.algebraMap_mem_valuationSubring, Module.End.finite_spectrum, LaurentSeries.valuation_LaurentSeries_equal_extension, IsGalois.intermediateFieldEquivSubgroup_symm_apply, ContMDiffMap.coe_smul, Polynomial.natSepDegree_expand, iteratedFDeriv_succ_apply_right, NumberField.InfinitePlace.denseRange_algebraMap_pi, Submodule.isOrtho_top_right, FormalMultilinearSeries.leftInv_coeff_one, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, ContinuousLinearMap.hasMFDerivAt, IsAlgClosed.exists_eval₂_eq_zero, TensorProduct.assocIsometry_apply, NumberField.finite_of_discr_bdd, Matrix.toLin_conjTranspose, RCLike.instStarModuleReal, mdifferentiableOn_continuousLinearMapCoordChange, hasDerivAtFilter_intCast, FixedPoints.toAlgAut_surjective, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, Orthonormal.inner_finsupp_eq_sum_left, cfcHom_nnreal_eq_restrict, fderiv_deriv, Padic.exi_rat_seq_conv, Matrix.IsHermitian.spectral_theorem, WithLp.unitizationAlgEquiv_symm_apply_ofLp, PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable, IsPurelyInseparable.minpoly_natDegree_eq, hasFPowerSeriesAt_pi_iff, Module.Basis.continuous_toMatrix, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_apply, NumberField.RingOfIntegers.mapRingHom_apply, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, IntermediateField.LinearDisjoint.of_inf_eq_bot, RatFunc.intDegree_polynomial, norm_cfcₙ_le, toPrincipalIdeal_eq_iff, NumberField.InfinitePlace.isReal_smul_iff, AlgHom.coe_fieldRange, hasDerivWithinAt_univ, Asymptotics.isLittleOTVS_neg_right, MulChar.star_apply', LinearIsometryEquiv.hasFDerivAt, IntermediateField.adjoin_simple_toSubalgebra_of_isAlgebraic, ContinuousAlternatingMap.uniformContinuous_toContinuousMultilinearMap, Seminorm.ball_zero_absorbs_ball_zero, RCLike.continuous_conj, RatFunc.v_def, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm, minpoly.add_algebraMap, RatFunc.instCharZero, Subfield.relrank_dvd_rank_top_of_le, HasFDerivAtFilter.add, Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap, ContinuousLinearEquiv.contDiffWithinAt_comp_iff, PointwiseConvergenceCLM.precomp_apply, divRadical_dvd_wronskian_right, NormedSpace.exp_def, Matrix.PosSemidef.sq_sqrt, uniqueMDiffWithinAt_iff, ArchimedeanClass.FiniteResidueField.mk_ne_zero, ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff, LinearIsometryEquiv.rTensor_apply, Polynomial.div_eq_quo_add_rem_div, LinearIsometryEquiv.inner_map_map, norm_algebraMap, LieAlgebra.IsKilling.chainTopCoeff_add_chainBotCoeff, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, NumberField.Units.coe_pow, CategoryTheory.finrank_hom_simple_simple, IsPurelyInseparable.algebraMap_elemReduct_eq', Subspace.dualLift_of_mem, InnerProductSpace.isStarProjection_rankOne_self, coord_norm', StrictConvex.smul, Trivialization.apply_eq_prod_continuousLinearEquivAt, HasFDerivWithinAt.comp, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, ContinuousLinearMapWOT.ext_dual_iff, LinearIsometry.integral_comp_comm, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, LaurentSeries.LaurentSeries_coe, contDiff_clm_apply_iff, HasFPowerSeriesAt.hasFDerivAt, OrthonormalBasis.measurePreserving_repr_symm, Polynomial.SplittingFieldAux.instIsSplittingFieldNatDegree, Finset.centroid_mem_convexHull, WeakDual.isClosed_polar, hasStrictFDerivAt_finCons', WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal', spec_cfcₙAux, norm_fderiv_norm, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, root_X_pow_sub_C_pow, ClosedSubmodule.orthogonal_eq_top_iff, fderiv_comp, eventually_enorm_mfderiv_extChartAt_lt, AlgebraicIndependent.liftAlgHom_comp_reprField, QuadraticMap.lineDifferentiableAt, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, Subalgebra.finiteDimensional_toSubmodule, EuclideanSpace.piLpCongrLeft_single, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, NumberField.RingOfIntegers.mk_one, hasFDerivAt_exp_smul_const, LinearIsometryEquiv.norm_iteratedFDeriv_comp_right, HasFPowerSeriesOnBall.eventually_hasSum, Algebra.IsSeparable.finSepDegree_eq, ContinuousLinearMap.hasStrictFDerivAt, IntermediateField.finrank_top', inv_antitoneOn_Icc_right, NumberField.conj_basisMatrix, WeierstrassCurve.Projective.baseChange_add, NumberField.IsCMField.unitsMulComplexConjInv_apply, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, oneTangentSpaceIcc_def, smul_unitBall, LaurentSeries.powerSeries_ext_subring, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, Set.unit_valuation_eq_one, Submodule.mem_projectivization_iff_submodule_le, Lagrange.eval_basisDivisor_left_of_ne, PowerSeries.instIsDiscreteValuationRing, PowerSeries.isNoetherianRing, IsSymmSndFDerivAt.iteratedFDeriv_cons, IntermediateField.inclusion_self, NumberField.Units.abs_det_eq_abs_det, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, Complex.im_comp_balance, IntermediateField.lift_bot, IsPurelyInseparable.algebraMap_iterateFrobenius, Lagrange.natDegree_basisDivisor_of_ne, RCLike.normSq_eq_def', Polynomial.C_mul_dvd, ContinuousLinearMap.comp_analyticOn, Polynomial.isBoundedUnder_abs_atBot_iff, analyticOrderAt_pow, hasStrictDerivAt_const, PerfectField.toPerfectRing, ContinuousLinearMap.continuousConstSMul, RootPairing.ker_rootForm_eq_dualAnnihilator, fderiv_finset_prod, ModelWithCorners.hasMFDerivWithinAt_symm, IsGalois.fixedField_top, Bundle.Trivial.trivialization.isLinear, ContinuousLinearMap.coeFn_compLpL, hasStrictFDerivAt_list_prod_attach', stdSimplex.barycenter_apply, IsPrimitiveRoot.norm_pow_sub_one_two, deriv_single, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, IntermediateField.normalClosure_of_normal, StrongDual.norm_toLpₗ_le, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, hasFDerivWithinAt_euclidean, FractionalIdeal.exists_ne_zero_mem_isInteger, ClosedSubmodule.mem_orthogonal_iff, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, HasFPowerSeriesWithinAt.restrictScalars, DoubleCentralizer.sub_fst, tangentConeAt_real_subset_isRCLikeNormedField, range_deriv_subset_closure_span_image, AbsoluteValue.hasBasis_uniformity, Matrix.PosDef.isStrictlyPositive, Module.Basis.parallelepiped_eq_map, ArchimedeanClass.mk_le_mk_iff_ratCast, Algebra.discr_powerBasis_eq_prod, ContDiffMapSupportedIn.norm_apply_le_seminorm, Polynomial.mem_iff_annIdealGenerator_dvd, contDiffOn_clm_apply, ContinuousLinearMap.le_opNNNorm, spectrum.subset_polynomial_aeval, FDRep.char_one, nnnorm_cfc_le, ContinuousLinearEquiv.det_coe_symm, NumberField.InfinitePlace.isometry_embedding_of_isReal, IsFractionRing.restrictScalars_fieldEquivOfAlgEquiv, LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range, FormalMultilinearSeries.id_apply_zero, SchwartzMap.hasDerivAt, stabilizer_isOpen_of_isIntegral, FunctionField.ringOfIntegers.instIsDedekindDomainSubtypeMemSubalgebraPolynomialOfIsSeparableRatFunc, Algebra.IsAlgebraic.isNormalClosure_iff, Submodule.starProjection_orthogonal, Seminorm.inf_apply, ClassGroup.mk_eq_mk, PiTensorProduct.mapLMultilinear_apply_apply, ContinuousLinearMap.instNonnegSpectrumClassRealId, iteratedDeriv_comp_two, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, ContinuousLinearMap.uncurryMid_apply, ContinuousMap.setOfIdeal_eq_compl_singleton, hasFDerivAt_update, Polynomial.div_C, IntermediateField.sup_toSubalgebra_of_left, spectralNorm_extends, isBoundedBilinearMap_apply, HasFPowerSeriesWithinOnBall.coeff_zero, InfiniteGalois.isOpen_iff_finite, RootPairing.restrictScalars_coe_root, FormalMultilinearSeries.analyticOnNhd, galLift_id, InfiniteGalois.mem_range_algebraMap_iff_fixed, hasDerivAtFilter_iff_tendsto, MeromorphicOn.divisor_fun_inv, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, inv_nhdsLT_zero, Matrix.IsHermitian.eigenvectorUnitary_coe, Polynomial.natSepDegree_pow_of_ne_zero, Polynomial.natSepDegree_one, hasStrictFDerivAt_ringInverse, Subspace.dualAnnihilator_iInf_eq, NumberField.InfinitePlace.even_finrank_of_not_isUnramified, ContDiffOn.continuousOn_fderiv_of_isOpen, Polynomial.leadingCoeff_preHilbertPoly, ContinuousLinearMap.mul_apply', AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, Hyperreal.infinitesimal_iff_infinite_inv, LinearMap.finrank_maxGenEigenspace, Emb.Cardinal.deg_lt_aleph0, WeierstrassCurve.Δ_integral_of_isIntegral, ContDiffOn.continuousLinearMap_comp, HasFDerivAt.fun_sum, stereographic_target, fderiv_zero_of_not_differentiableAt, Unitary.norm_map, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, Valued.integer.isDiscreteValuationRing_of_compactSpace, tendsto_const_mul_pow_nhds_iff, LinearMap.instStarModuleId, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, Submodule.starProjection_apply_mem, NumberField.inverse_basisMatrix_mulVec_eq_repr, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, RatFunc.denom_div_dvd, InnerProductSpace.rankOne_comp_rankOne, ContinuousLinearMap.opNorm_zero, MeasureTheory.convolution_lsmul_swap, IntermediateField.relfinrank_bot_left, NumberField.RingOfIntegers.instIsIntegralClosureInt, NNReal.coe_expect, Real.hasStrictDerivAt_arctan, HasFTaylorSeriesUpToOn.prodMk, FixedPoints.smul_polynomial, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, ContinuousMultilinearMap.norm_iteratedFDeriv_le, ContDiffAt.domDomCongr_iteratedFDeriv, Module.Basis.traceDual_involutive, CFC.abs_ofNat, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, RatFunc.laurent_C, AnalyticAt.hasFPowerSeriesAt, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, LinearMap.BilinForm.orthogonal_span_singleton_eq_toLin_ker, ZLattice.volume_image_eq_volume_div_covolume, hasDerivAtFilter_finCons', NumberField.InfinitePlace.card_real_embeddings, mfderivWithin_prodMap, Polynomial.Gal.splits_in_splittingField_of_comp, LinearIsometry.toLinearMap_rTensor, PiLp.hasStrictFDerivAt_apply, hasStrictFDerivAt_fst, DifferentiableAt.comp_semilinear₁, CFC.negPart_one, Matrix.toEuclideanLin_eq_toLin, IsAlgClosed.exists_root, NumberField.Units.coe_injective, ValuationSubring.mem_or_inv_mem', UniqueMDiffOn.uniqueDiffOn_inter_preimage, CFC.log_smul', DoubleCentralizer.pow_fst, FunctionField.inftyValuation.X_zpow, RatFunc.rank_ratFunc_ratFunc, IntermediateField.toSubalgebra_injective, StrongDual.toLpₗ_of_not_memLp, isConformalMap_complex_linear_conj, MeromorphicAt.meromorphicTrailingCoeffAt_smul, fderiv_smul_const, PiTensorProduct.mapL_apply, hasDerivWithinAt_finCons', Matrix.isHermitian_iff_isSymmetric, Subspace.dualRestrict_surjective, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, mfderiv_sumInr, ContinuousMultilinearMap.norm_iteratedFDeriv_le', support_iteratedFDeriv_subset, hasStrictFDerivAt_finset_prod, convex_RCLike_iff_convex_real, NumberField.Units.coe_one, instContMDiffInv₀ModelWithCornersSelf, spectralAlgNorm_extends, Submodule.le_orthogonal_iff_le_orthogonal, fderiv_fun_neg, Valued.integer.norm_unit, Lagrange.degree_interpolate_le, curveIntegral_zero, IntermediateField.le_extendScalars_iff, Complex.isOpenQuotientMap_zpow_compl_zero, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, DirichletCharacter.norm_LFunction_product_ge_one, Submodule.IsOrtho.comap_iff, InnerProductSpace.rankOne_comp, LaurentSeries.powerSeriesRingEquiv_coe_apply, spectrum.map_inv, Polynomial.C_div, Submodule.mem_orthogonal, ValuationSubring.prime_idealOfLE, StrongDual.mem_polarSubmodule, exists_dual_vector', derivWithin_inv', Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Asymptotics.IsTheta.const_smul_left, Asymptotics.isLittleOTVS_comm, RatFunc.instIsScalarTowerOfPolynomial, ContinuousLinearMap.hasBasis_nhds_zero_of_basis, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable', minpoly.ofSubring, hasFPowerSeriesWithinAt_pi_iff, isCompactOperator_iff_isCompact_closure_image_closedBall, NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, gal_one_isSolvable, IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace, LinearMap.continuous_of_finiteDimensional, hasDerivAt_iff_isLittleO_nhds_zero, HasFDerivAt.le_of_lip', inner_smul_right, Filter.Tendsto.atTop_smul_const_tendsto_asymptoticNhds, Polynomial.normalize_eq_self_iff_monic, SchwartzMap.tsupport_smulLeftCLM_subset, HasMFDerivAt.sub, IntermediateField.extendScalars.orderIso_symm_apply_coe, exists_isTranscendenceBasis_and_isSeparable_of_perfectField, InnerProductSpace.toMatrix_rankOne, PowerSeries.Unit_of_divided_by_X_pow_order_nonzero, IsFractionRing.injective_comp_algebraMap, eventually_norm_symmL_trivializationAt_lt, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, cfcₙHom_real_eq_restrict, normal_iff, CFC.abs_algebraMap_nnreal, LinearMap.polar_AbsConvex, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, differentiableAt_euclidean, ConjRootClass.nodup_aroots_minpoly, AlgHom.card, FormalMultilinearSeries.changeOriginSeries_summable_aux₁, hasFDerivAtFilter_finCons, PiTensorProduct.liftIsometry_comp_mapL, MvPowerSeries.inv_eq_zero, iteratedFDeriv_smul_const_apply, IsAlgClosure.equivOfEquiv_symm_comp_algebraMap, Seminorm.continuous_from_bounded, OrthonormalBasis.reindex_toBasis, ContinuousLinearMap.opNorm_le_iff, slope_pos_iff_gt, RCLike.geometric_hahn_banach_open, RCLike.conj_wInner_symm, InnerProductSpace.isSymmetric_rankOne_self, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, FiniteDimensional.finiteDimensional_subalgebra, Positive.coe_inv, FractionalIdeal.smul_mem_dual_one, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, Commute.cfcHom, Padic.valuation_pow, Real.hasDerivAt_cosh, fderiv_const_sub, continuousMultilinearCurryLeftEquiv_apply, tsupport_fderiv_subset, HasFPowerSeriesAt.deriv, NumberField.InfinitePlace.isReal_comap_iff, IsPurelyInseparable.bijective_restrictDomain, fderiv_id', ArchimedeanClass.FiniteResidueField.mk_le_mk, LinearIsometryEquiv.symm_rTensor, LinearMap.isSymmetricProjection_iff, uniqueMDiffWithinAt_iff_inter_range, mfderiv_snd, HasMFDerivWithinAt.add, LaurentSeries.powerSeriesEquivSubring_apply, IntermediateField.sepDegree_bot', Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, RootPairing.polarizationEquiv_toLinearMap, cfc_apply_mem_elemental, HasCompactSupport.iteratedFDeriv, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, TensorProduct.commIsometry_symm, isStarProjection_starProjection, precomp_compactConvergenceCLM_apply, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff, unitary.norm_map, Asymptotics.IsBigOTVS.rfl, Set.EqOn.iteratedFDerivWithin, NumberField.mixedEmbedding.unitSMul_smul, ContinuousLinearEquiv.fderiv, IntermediateField.inclusion_injective, Differential.instDifferentialAlgebraSubtypeMemIntermediateField, Seminorm.bddBelow_range_add, ContinuousAlternatingMap.restrictScalarsCLM_apply, ContMDiffWithinAt.mfderivWithin_apply, Asymptotics.IsLittleOTVS.bot, SchwartzMap.tsupport_fderivCLM_subset, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_left, ContinuousLinearMap.isBigOTVS_comp, Finpartition.IsEquipartition.sum_nonUniforms_lt, WeierstrassCurve.Jacobian.add_of_X_ne, ContinuousLinearEquiv.mdifferentiableWithinAt, FDRep.simple_iff_end_is_rank_one, hfdifferential_apply, Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sq, IntermediateField.LinearDisjoint.bot_right, ContinuousLinearMap.NonlinearRightInverse.right_inv', ContinuousLinearEquiv.mdifferentiable, MvPolynomial.quotient_mk_comp_C_injective, AffineSubspace.midpoint_mem_perpBisector, AnalyticAt.exists_eq_sum_add_pow_mul, Ideal.ResidueField.algHom_ext_iff, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, ContinuousLinearMap.integral_comp_L1_comm, Polynomial.sum_derivRootWeight_pos, curveIntegralFun_add, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, ContinuousLinearMap.opNorm_zero_iff, IsPrimitiveRoot.squarefree_minpoly_mod, LinearEquiv.isSymmetric_symm_iff, Polynomial.isSplittingField_C, FunctionField.inftyValuation.X, InnerProductSpace.gramSchmidt_def'', Real.hasDerivAt_fourierChar, OrthonormalBasis.equiv_symm, AnalyticOnNhd.fderiv, AlgebraicClosure.Monics.map_eq_prod, primitive_element_iff_minpoly_degree_eq, WeierstrassCurve.Jacobian.Y_eq_iff', hasDerivAt_intCast, nndist_midpoint_midpoint_le, HasFDerivWithinAt.sub, Seminorm.absorbent_ball_zero, LindemannWeierstrass.integral_exp_mul_eval, minpoly.dvd_map_of_isScalarTower', HasFDerivAtFilter.fun_neg, LinearEquiv.coe_toContinuousLinearEquiv, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcₙHom, SchwartzMap.smulLeftCLM_neg, IntermediateField.map_fixingSubgroup_index, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, AlgHom.fieldRange_eq_top, ContinuousLinearEquiv.comp_differentiableAt_iff, IntermediateField.normal_iff_forall_map_le, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, mfderiv_zero_of_not_mdifferentiableAt, DirichletCharacter.LSeries_eulerProduct_hasProd, NumberField.AdeleRing.algebraMap_injective, Algebra.IsAlgebraic.bijective_of_isScalarTower', Asymptotics.IsTheta.pow, spectrum.differentiableOn_inverse_one_sub_smul, ValuationSubring.ofPrime_scalar_tower, Trivialization.continuousLinearEquivAt_prod, IsAlgClosed.algebraMap_bijective_of_isIntegral, HasFPowerSeriesAt.const_smul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, iteratedFDeriv_succ_eq_comp_right, SchwartzMap.iteratedPDeriv_eq_iteratedFDeriv, RCLike.inv_pos_of_pos, ContinuousMultilinearMap.changeOriginSeries_support, ContinuousLinearEquiv.comp_hasFDerivAt_iff', separableClosure.isAlgebraic, IntermediateField.adjoin_toSubalgebra, IsAlgClosure.ofAlgebraic, ValuationSubring.inv_mem_nonunits_iff, tendsto_nat_ceil_div_atTop, curveIntegralFun_sub, Asymptotics.isBigOTVS_fun_comm, FunctionField.ringOfIntegers.algebraMap_injective, ContDiffMapSupportedIn.seminorm_apply, sepDegree_mul_insepDegree, FormalMultilinearSeries.isLittleO_of_lt_radius, tsupport_iteratedFDeriv_subset, OrthogonalFamily.eq_ite, AffineSubspace.sSameSide_smul_vsub_vadd_right, FiniteField.X_pow_card_sub_X_natDegree_eq, IsFractionRing.mk'_eq_zero_iff_eq_zero, logDeriv_inv, Complex.card_primitiveRoots, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, ContinuousMultilinearMap.hasFDerivAt, ODE.hasDerivWithinAt_picard_Icc, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, MeasureTheory.lpNorm_const_smul, VectorField.lieBracket_smul_left, Real.iteratedFDeriv_fourier, RatFunc.denom_inv_dvd, Seminorm.smul_closedBall_subset, LieModule.exists_nontrivial_weightSpace_of_isSolvable, instIsScalarTowerCyclotomicField, DoubleCentralizer.algebraMap_fst, NumberField.ComplexEmbedding.isConj_symm, differentiableOn_euclidean, hasDerivWithinAt_diff_singleton, ValuationSubring.surjective_unitGroupToResidueFieldUnits, fderiv_continuousLinearEquiv_comp, FiniteField.pow_dichotomy, nnnorm_fderiv_norm_rpow_le, hasFDerivWithinAt_natCast, Real.hasFPowerSeriesOnBall_linear_zero, NumberField.mixedEmbedding.indexEquiv_apply_isReal, NumberField.ComplexEmbedding.Extension.comp_eq, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, hasStrictFDerivAt_exp_zero_of_radius_pos, ContinuousLinearMap.toBilinForm_injective, quasispectrumRestricts_iff_spectrumRestricts_inr, Ideal.ramificationIdx_mul_inertiaDeg_of_isLocalRing, rootOfSplitsXPowSubC_pow, AlgHom.card_le, InnerProductSpace.mem_span_gramSchmidt, ContinuousLinearMap.mfderivWithin_eq, ContinuousMultilinearMap.nnnorm_ofSubsingleton, inner_smul_real_left, Ideal.ResidueField.lift_algebraMap, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, Asymptotics.IsTheta.inv, tsum_prod_pow_eq_tsum_sigma, FiniteField.splits_X_pow_card_sub_X, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, IntermediateField.rank_eq_one_iff, ContDiff.continuous_iteratedFDeriv, TangentBundle.symmL_model_space, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, IsGaloisGroup.intermediateField, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, MeasureTheory.integrable_condExpL2_indicator, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, ImplicitFunctionData.range_rightDeriv, tangentCoordChange_self, toSpanSingleton_derivWithin, WeierstrassCurve.Affine.Point.toClass_some, HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub, LinearMap.finrank_range_dualMap_eq_finrank_range, EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, fderiv_norm_smul, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, ContinuousAlternatingMap.isLeast_opNNNorm, ContinuousLinearMap.isEmbedding_restrictScalars, lowerBounds_smul_of_neg, Polynomial.natDegree_preHilbertPoly, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, RCLike.nnnorm_conj, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, HasFiniteFPowerSeriesOnBall.eq_partialSum', VectorField.mlieBracket_const_smul_left, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, CFC.abs_intCast, ValuationSubring.principalUnitGroupEquiv_apply, Module.End.eigenspace_div, LinearIsometry.enorm_toContinuousLinearMap, Unitization.instCStarRing, coe_lpBCFₗᵢ_symm, range_mfderiv_coe_sphere, uniqueMDiffOn_iff_uniqueDiffOn, coe_lpPiLpₗᵢ_symm, AlgEquiv.restrictNormalHom_id, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, Bornology.isVonNBounded_sub, insepDegree_self, differentiable_piLp, ClosedSubmodule.inf_orthogonal_eq_bot, HasFPowerSeriesOnBall.pi, Affine.Triangle.eulerPoint_eq_midpoint, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, FunctionField.inftyValuedFqt.def, Submodule.reflection_eq_self_iff, galRestrict_apply, Polynomial.span_minpoly_eq_annihilator, stereographic_source, ContinuousMultilinearMap.piₗᵢ_symm_apply, RCLike.wInner_one_const_right, Commute.cfc, AlgHom.coe_toContinuousLinearMap, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, ContDiff.iteratedFDeriv_right', Subfield.relrank_top_right, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, NumberField.ComplexEmbedding.IsReal.comp, ContinuousLinearMap.norm_id_le, HasFDerivAt.le_of_lipschitz, AnalyticAt.analyticOrderAt_ne_top, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, LinearEquiv.canLiftContinuousLinearEquiv, Ring.instFiniteDimensionalFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, IsDedekindDomain.selmerGroup.fromUnit_ker, Matrix.ofLp_toEuclideanLin_apply, IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin, Real.one_add_rpow_hasFPowerSeriesAt_zero, spectralNorm.eq_of_normalClosure', mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm', tsum_dirichletSummand, Filter.Tendsto.isVonNBounded_range, NumberField.exists_ideal_in_class_of_norm_le, AffineIndependent.convexHull_inter', Real.hasFDerivAt_fourierIntegral, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isComplex, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left, NumberField.mixedEmbedding.normAtPlace_apply, SchwartzMap.integralCLM_apply, Polynomial.irreducible_factor, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, NumberField.ComplexEmbedding.lift_comp_algebraMap, PolynormableSpace.withSeminorms', Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, hasDerivAt_one, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, HasStrictFDerivAt.hasStrictDerivAt, IsAlgClosure.equivOfEquiv_algebraMap, FormalMultilinearSeries.radius_shift, EuclideanSpace.volume_ball_fin_two, Ideal.instLiesOverBotOfIsPrime, ContinuousLinearEquiv.comp_right_differentiableAt_iff, nnnorm_algebraMap', fderivWithin_sqrt, fderivWithin_natCast, RCLike.norm_sq_re_conj_add, ContinuousMap.spectrum_eq_range, NormedSpace.polar_ball, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, IsZLattice.span_top, innerSLFlip_apply, ContinuousLinearEquiv.differentiableOn, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, ContinuousLinearEquiv.hasStrictFDerivAt, AlgHom.mem_fieldRange, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, fderivWithin_derivWithin, Submodule.ker_starProjection, WeakDual.ker_isMaximal, IntermediateField.finrank_fixedField_eq_card, ContinuousLinearEquiv.mfderiv_eq, hasDerivAt_const_mul, Trivialization.coe_continuousLinearEquivAt_eq, hasLineDerivAt_iff_tendsto_slope_zero, Algebra.normalizedTrace_minpoly, InnerProductSpace.toContinuousLinearMap_toDualMap, HasFDerivAt.list_prod', separableClosure.isSepClosure, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, Real.ceil_logb_natCast, Polynomial.annIdealGenerator_aeval_eq_zero, IntermediateField.finrank_comap, ValuationSubring.mem_nonunits_iff_or, Polynomial.coeff_inv_units, FiniteField.pow_finrank_eq_card, InfiniteGalois.toAlgEquivAux_eq_liftNormal, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', separatingDual_iff_injective, minpoly.eq_X_sub_C', RCLike.normSq_pos, EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center, Polynomial.root_gcd_iff_root_left_right, ContinuousLinearEquiv.comp_contDiffWithinAt_iff, isNilpotent_tensor_residueField_iff, Differential.logDeriv_pow, IsPurelyInseparable.injective_restrictDomain, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable', IsSelfAdjoint.commute_cfcₙHom, primitive_element_iff_minpoly_natDegree_eq, Rat.ringOfIntegersEquiv_apply_coe, ContinuousLinearMap.measurable_coe, HasFDerivAt.fun_neg, ContinuousLinearMap.analyticOn, fderiv_sinh, ContinuousLinearMap.nndist_le_opNNNorm, strictConvex_iff_ordConnected, norm_iteratedFDeriv_prod_le, IntermediateField.normalClosure_def'', inner_eq_ofReal_norm_sq_left_iff, contDiff_nat_iff_continuous_differentiable, hasFDerivAt_pow', ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, absorbent_ball, extremePoints_doublyStochastic, SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv, Valuation.Integers.valuation_pos_iff_ne_zero, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, OrderedFinpartition.compAlongOrderFinpartition_apply, Trivialization.continuousLinearEquivAt_symm_apply, Submodule.topologicalClosure_eq_top_iff, hasDerivAt_abs, DirichletCharacter.LSeries_eulerProduct_exp_log, mdifferentiableOn_coordChangeL, RCLike.conj_im, HasFiniteFPowerSeriesOnBall.add, RatFunc.num_mul_dvd, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, WeierstrassCurve.Projective.addU_smul, iteratedDeriv_comp_const_sub, ContDiffAt.iteratedFDeriv_comp_perm, Polynomial.hasDerivAt, HasFDerivAt.fun_add, Subfield.relrank_eq_rank_of_le, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, WeierstrassCurve.Affine.Point.toClass_injective, Subspace.dualEquivDual_def, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', VectorPrebundle.mk_coordChange, ContinuousLinearMap.opNorm_lsmul_le, PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, Emb.Cardinal.strictMono_filtration, convexHull_eq_union_convexHull_finite_subsets, EuclideanSpace.volume_ball, LinearMap.IsSymmetric.zero, TensorProduct.enorm_assoc, IntermediateField.relfinrank_eq_finrank_of_le, IsIntegralClosure.isFractionRing_of_algebraic, RCLike.conj_I, OrthonormalBasis.repr_symm_single, FiniteField.nonempty_algHom_extension, NumberField.canonicalEmbedding.norm_le_iff, ContinuousMultilinearMap.instUniformContinuousConstSMul, FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal, RootPairing.polarizationEquiv_symm_apply_coroot, WeakDual.CharacterSpace.norm_le_norm_one, IntermediateField.isScalarTower_over_bot, IntermediateField.isSeparable_tower_bot, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, FiniteField.isSquare_iff, Matrix.linfty_opNorm_toMatrix, IntermediateField.minpoly_eq, hasDerivAt_natCast, RatFunc.instExpChar, AdjoinRoot.powerBasis_dim, Seminorm.rescale_to_shell, Mathlib.Meta.NormNum.IsRat.natCeil, Submodule.reflection_bot, RootPairing.linearIndepOn_coroot_iff, ContinuousMultilinearMap.opNNNorm_pi, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, Polynomial.natSepDegree_C, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.fourier_bilin_convolution_eq_integral, closedBall_normSeminorm, Real.hasStrictDerivAt_cos, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left, ContinuousLinearMap.isPositive_def', ContinuousLinearMap.coe_restrictScalarsL, LinearMap.adjoint_inner_left, FractionalIdeal.coe_inv_of_nonzero, IntermediateField.mem_toSubalgebra, legendreSym.eq_pow, IntermediateField.isSplittingField_iff, iter_deriv_inv, HasMFDerivAt.comp_hasMFDerivWithinAt, PowerSeries.coeff_inv, AlgEquiv.restrictNormal_commutes, NumberField.InfinitePlace.comap_mk_lift, Matrix.star_dotProduct_gram_mulVec, exists_integral_multiples, hasStrictFDerivAt_exp_zero, ValuationSubring.coe_comap, ContinuousLinearMap.norm_compL_le, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, NumberField.mixedEmbedding_injective, Matrix.vecMul_injective_iff_isUnit, ContMDiffVectorBundle.contMDiffOn_coordChangeL, IntermediateField.bot_toSubfield, EulerSine.antideriv_cos_comp_const_mul, ZMod.orderOf_dvd_card_sub_one, ContDiff.inv, curveIntegral_eq_intervalIntegral_deriv, Filter.EventuallyEq.fderivWithin', ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, RCLike.inv_def, sepDegree_eq_of_isPurelyInseparable_of_isSeparable, ContinuousLinearMap.inCoordinates_eq, meromorphicOrderAt_smul_of_ne_zero, NumberField.RingOfIntegers.coe_eq_algebraMap, mfderiv_prodMk, NumberField.InfinitePlace.comap_smul, Bornology.isVonNBounded_add, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, Subspace.dualLift_rightInverse, IsPurelyInseparable.pow_mem, NumberField.InfinitePlace.not_isUnramified_iff_card_stabilizer_eq_two, IntermediateField.topEquiv_symm_apply_coe, HasFPowerSeriesAt.sub, RatFunc.liftOn'_div, hasMFDerivWithinAt_snd, Valuation.valuationSubring_not_isField, ContDiffAt.continuousLinearMap_comp, ContinuousMultilinearMap.norm_domDomCongr, FiniteGaloisIntermediateField.adjoin_val, FractionalIdeal.spanFinset_coe, HasStrictFDerivAt.fun_neg, hasDerivWithinAt_zpow, LieAlgebra.rank_le_finrank_engel, Finset.centerMass_segment, HasFDerivWithinAt.arctan, ZSpan.quotientEquiv.symm_apply, OrthogonalFamily.range_linearIsometry, NumberField.mixedEmbedding.convexBodyLT_convex, IsUnramifiedAtInfinitePlaces.id, hasFPowerSeriesOnBall_cuspFunction, HasStrictFDerivAt.sum, MulChar.star_eq_inv, MvPolynomial.vanishingIdeal_empty, ValuationSubring.mem_principalUnitGroup_iff, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, HasCompactSupport.fderiv_apply, Submodule.ker_orthogonalProjection, EuclideanGeometry.oangle_midpoint_rev_right, ConjRootClass.aroots_minpoly_eq_carrier_val, NumberField.mem_span_integralBasis, quadraticCharFun_eq_pow_of_char_ne_two, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, innerSL_real_flip, Lagrange.interpolate_eq_add_interpolate_erase, Submodule.reflection_map_apply, WeierstrassCurve.Projective.add_of_Y_eq, Ideal.coe_smul_primesOver_eq_map_galRestrict, HasDerivAt.real_of_complex, Module.mem_support_iff_nontrivial_residueField_tensorProduct, TensorProduct.dist_tmul_le, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt', SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, IntermediateField.adjoin_eq_range_algebraMap_adjoin, AffineIsometry.map_vadd, Polynomial.mul_mod, ContinuousMultilinearMap.curry0_norm, ContinuousLinearMap.opNNNorm_mul_flip_apply, ContinuousLinearMap.compLeftContinuousBounded_apply, Submodule.sup_orthogonal_of_hasOrthogonalProjection, TensorProduct.norm_lid, MeasureTheory.lpTrimToLpMeas_ae_eq, ContinuousLinearMap.norm_fst, IsFractionRing.fieldEquivOfAlgEquivHom_injective, ContinuousAlternatingMap.nnnorm_toContinuousMultilinearMap, Algebra.discr_isUnit_of_basis, OrderedFinpartition.applyOrderedFinpartition_apply, FractionalIdeal.div_spanSingleton, HasFPowerSeriesOnBall.hasFDerivAt, MeasureTheory.charFun_eq_charFunDual_toDualMap, IntermediateField.rank_top', IntermediateField.isAlgebraic_adjoin_simple, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, NormedAlgebra.Real.nonempty_algEquiv_or, CFC.quasispectrum_abs, ContinuousLinearMap.opNNNorm_comp_le, RatFunc.denom_C, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_iSup_right, TensorProduct.toLinearEquiv_assocIsometry, ContinuousMultilinearMap.analyticOn, FormalMultilinearSeries.changeOriginSeries_summable_aux₂, HasMFDerivAt.prod, MeromorphicNFAt.smul_analytic, fderivWithin_csin, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, RatFunc.num_div_dvd', WeierstrassCurve.Projective.negAddY_eq, Submodule.IsOrtho.disjoint, ContinuousMultilinearMap.curryMid_apply, iteratedDeriv_eq_iteratedFDeriv, norm_cfc_le, OnePoint.smul_infty_def, ZLattice.volume_image_eq_volume_div_covolume', ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq, inv_smul_lt_iff_of_neg, IntermediateField.AdjoinSimple.normal_algebraicClosure, PiTensorProduct.mapL_opNorm, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, FiniteGaloisIntermediateField.adjoin_simple_map_algEquiv, SchwartzMap.compCLM_apply, MonoidAlgebra.Submodule.instIsSemisimpleRingAddMonoidAlgebra, iter_deriv_inv', toMatrix_innerSL_apply, OrthonormalBasis.equiv_apply_basis, ClosedSubmodule.sInf_orthogonal, NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, intervalIntegral.fderivWithin_integral_of_tendsto_ae, NNReal.orderIsoRpow_symm_eq, hasStrictFDerivAt_one, Function.HasTemperateGrowth.smul, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, one_add_rpow_hasFPowerSeriesAt_zero, LaurentSeries.powerSeriesEquivSubring_coe_apply, IntermediateField.normal_iff_forall_map_eq', HasStrictFDerivAt.isBigOTVS_sub, DoubleCentralizer.mul_fst, rescale_to_shell_zpow, Polynomial.isBoundedUnder_abs_atTop_iff, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, BoundedContinuousFunction.toContinuousMapStarₐ_apply_apply, WeierstrassCurve.Jacobian.addX_eq, balanced_closedBall_zero, iteratedFDeriv_zero_fun, Submodule.HasOrthogonalProjection.exists_orthogonal, IntermediateField.intermediateFieldMap_apply_coe, HasFDerivAt.prodMk, IntermediateField.topEquiv_apply, ContinuousLinearEquiv.comp_contDiffOn_iff, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, CFC.spectrum_abs, MDifferentiableAt.coordChangeL, Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two, perfectField_iff_splits_of_natSepDegree_eq_one, WeierstrassCurve.Projective.add_of_X_ne, Manifold.IsImmersionAt.target_subset_preimage_target, RootPairing.eq_baseOf_iff, Submodule.starProjection_top, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, EulerSine.antideriv_sin_comp_const_mul, Subspace.dualCopairing_nondegenerate, hasFDerivAt_sub_const, FixedPoints.toAlgHom_bijective, Lagrange.interpolate_apply, affineCombination_mem_convexHull, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, Submodule.iInf_orthogonal, ContinuousLinearMap.norm_restrictScalars, ContinuousLinearMapWOT.instT3Space, coe_normSeminorm, Algebra.normalizedTrace_algebraMap_apply, IsLocalRing.ResidueField.finite_of_module_finite, ContinuousLinearEquiv.arrowCongrSL_apply, Algebra.normalizedTrace_def, Lagrange.interpolate_eq_iff_values_eq_on, crossProduct_ne_zero_iff_linearIndependent, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, Ideal.FinrankQuotientMap.span_eq_top, Pretrivialization.continuousLinearMap_apply, NormedAlgebra.norm_smul_le, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, NumberField.Units.coe_zpow, NumberField.mem_span_basisOfFractionalIdeal, RatFunc.natDegree_num_mul_right_sub_natDegree_denom_mul_left_eq_intDegree, ContDiffBump.convolution_eq_right, Polynomial.IsSplittingField.instFiniteDimensionalSplittingField, hasFDerivWithinAt_fst, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, FiniteField.minpoly_frobeniusAlgHom, AffineSubspace.sSameSide_iff_exists_right, ValuationSubring.coe_pointwise_smul, ModelWithCorners.transContinuousLinearEquiv_range, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, TensorProduct.nnnorm_assoc, hasFDerivAt_natCast, FormalMultilinearSeries.analyticAt_changeOrigin, mem_convexHull_iff_exists_fintype, IntermediateField.coe_inv, DoubleCentralizer.coe_eq_algebraMap, ContinuousLinearMap.opNorm_mul_apply_le, IsFractionRing.isInteger_of_isUnit_den, hasFDerivAt_intCast, PiTensorProduct.tprodL_apply, CStarMatrix.normedSpaceCore, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt, IntermediateField.AdjoinSimple.isIntegral_gen, HasFPowerSeriesAt.tendsto_partialSum, Differential.logDeriv_algebraMap, Polynomial.aeval_ofReal, Diffeomorph.uniqueDiffOn_preimage, deriv_pow_field, ZSpan.repr_fract_apply, RatFunc.instCharP, ContinuousLinearMap.orthogonal_range, IsGaloisGroup.fixedPoints, contDiff_one_iff_hasFDerivAt, HasFiniteFPowerSeriesAt.add, Submodule.lipschitzWith_starProjection, HasFPowerSeriesAt.hasDerivAt, hasDerivWithinAt_congr_set', Module.End.IsSemisimple_smul, HasFDerivWithinAt.comp_hasFDerivAt_of_eq, LieAlgebra.IsKilling.rootSystem_pairing_apply, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply, LieAlgebra.IsKilling.chainTopCoeff_zero_right, map_mem_algebraicClosure_iff, NormedSpace.norm_smul_le, HasFPowerSeriesAt.eventually_hasSum_sub, Polynomial.mem_roots_map, meromorphicOrderAt_pow, ConjRootClass.carrier_eq_mk_aroots_minpoly, ordinaryHypergeometricSeries_eq_zero_iff, Polynomial.hasDerivAt_aeval, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, ContinuousLinearMap.comp_cpolynomialOn, ZMod.frobenius_zmod, HasFDerivAt.linear_multilinear_comp, Localization.subalgebra.isFractionRing_ofField, ContinuousLinearMap.opNorm_smul_le, Algebra.IsQuadraticExtension.isCyclic, InnerProductSpace.span_gramSchmidt, Asymptotics.isLittleOTVS_congr, FunctionField.ringOfIntegers.instIsFractionRingSubtypeMemSubalgebraPolynomial, hasDerivAt_gronwallBound, fderiv_zero, hasDerivWithinAt_const_add_iff, convexHull_toCone_isLeast, PerfectField.separable_iff_squarefree, NumberField.mixedEmbedding.logMap_apply, IsDedekindDomain.selmerGroup.fromUnitLift_injective, EuclideanGeometry.hasFDerivAt_inversion, fderiv_comp', MeasureTheory.convolutionExistsAt_iff_integrable_swap, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, PiLp.hasFDerivAt_ofLp, deriv_div, torusIntegral_smul, ZLattice.comap_comp, Polynomial.Gal.restrict_surjective, WeierstrassCurve.Projective.baseChange_dblU, LinearEquiv.smulOfNeZero_symm_apply, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, norm_iteratedFDeriv_one, RatFunc.C_injective, VectorField.mpullback_smul, hasDerivAt_ofReal_cpow_const, LinearIsometryEquiv.comp_differentiable_iff, NumberField.InfinitePlace.even_nat_card_aut_of_not_isUnramified, convex_iff_div, hasDerivAt_norm_rpow, hasFDerivAtFilter_id, HasStrictFDerivAt.fun_const_smul, OrthonormalBasis.span_apply, isConformalMap_id, iteratedFDerivWithin_eventually_congr_set', ContinuousMultilinearMap.analyticOnNhd, Module.End.generalized_eigenvec_disjoint_range_ker, instFiniteResidueField, IntermediateField.isPurelyInseparable_bot, NumberField.mixedEmbedding.latticeBasis_apply, ClosedSubmodule.orthogonal_toSubmodule_eq, HasFDerivAt.hasDerivAt, Polynomial.mem_normalizedFactors_iff, Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, IsLocalRing.isLocalHom_residue, FiniteField.sum_pow_units, tendsto_inv_nhdsLT_zero, ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal, convexIndependent_iff_finset, pow_div_pow_eventuallyEq_atTop, differentiableAt_finCons', ContinuousLinearMap.isPositive_iff, LaurentSeries.valuation_coe_ratFunc, TensorProduct.mapIsometry_apply, gal_mul_isSolvable, ContinuousMultilinearMap.compContinuousLinearMapL_apply, Hyperreal.archimedeanClassMk_omega_neg, VectorBundleCore.inCoordinates_eq, Seminorm.smul_closedBall_preimage, HasFDerivWithinAt.unique_on, ValuationSubring.coe_unitGroupMulEquiv_symm_apply, HasStrictFDerivAt.prodMap, MeromorphicOn.extract_zeros_poles, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, VectorField.pullbackWithin_eq, Matrix.IsHermitian.cfcAux_id, WeierstrassCurve.Projective.add_of_Y_ne', cfcₙAux_mem_range_inr, ContinuousLinearMap.norm_bilinearRestrictScalars, NumberField.InfinitePlace.isUnramified_iff_stabilizer_eq_bot, RCLike.inv_pos, ContinuousLinearMap.nhds_zero_eq, WeierstrassCurve.Jacobian.negAddY_of_Z_ne_zero, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, Hyperreal.archimedeanClassMk_coe_nonneg, ContinuousLinearMap.norm_inl, Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable, AlgebraicIndependent.aevalEquivField_apply_coe, LinearMap.IsSymmetric.sub, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, RCLike.real_smul_ofReal, LieAlgebra.IsKilling.orthogonal_span_coroot_eq_ker, ContinuousLinearEquiv.comp_differentiable_iff, cfcₙ_norm_sq_nonneg, HahnSeries.inv_def, SchwartzMap.instFourierSMul, HasFPowerSeriesOnBall.prod, IsGaloisGroup.to_isFractionRing, Unitization.nnnorm_eq_sup, Valuation.Integer.not_isUnit_iff_valuation_lt_one, SchwartzMap.fourierTransformCLM_apply, AffineSubspace.signedInfDist_singleton, HasFPowerSeriesWithinOnBall.neg, norm_deriv_eq_norm_fderiv, IntermediateField.LinearDisjoint.exists_field_of_isDomain, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Trivialization.symm_continuousLinearEquivAt_eq, IsDiscreteValuationRing.TFAE, EuclideanGeometry.angle_midpoint_eq_pi, DoubleCentralizer.zero_toProd, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_right, Ideal.factors_span_eq, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, ContinuousLinearMap.bilinearComp_zero_left, one_add_cpow_hasFPowerSeriesOnBall_zero, ContinuousLinearMap.nnnorm_smulRight_apply, AffineSubspace.wSameSide_iff_exists_right, Subfield.relfinrank_dvd_finrank_top_of_le, hasFPowerSeriesWithinOnBall_pi_iff, hasDerivAt_zero, LinearIsometryEquiv.smul_trans, Ideal.injective_algebraMap_quotient_residueField, SchwartzMap.fderivCLM_fourier_eq, minpoly.natSepDegree_eq_one_iff_pow_mem, ContinuousMultilinearMap.instContinuousSMul, spectralNorm.eq_of_tower, spectrum.scalar_eq, withSeminorms_pi, IsAlgClosed.card_roots_map_eq_natDegree_of_leadingCoeff_ne_zero, ContinuousLinearEquiv.contDiffOn_comp_iff, mellin_const_smul, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, FiniteField.instIsCyclicAlgEquivOfFinite, arithGeom_zero_eq_mul_div, NumberField.norm_embedding_le_house, ContMDiffOn.const_smul_section, FormalMultilinearSeries.ofScalars_smul, SchwartzMap.derivCLM_apply, ContDiffAt.fderiv, Matrix.toLin_finTwoProd_toContinuousLinearMap, HasFPowerSeriesOnBall.eventually_hasSum_sub, minpoly.root, Polynomial.mod_X_sub_C_eq_C_eval, TensorProduct.toLinearMap_mapIsometry, ContinuousMultilinearMap.opNNNorm_le_iff, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, NumberField.FinitePlace.norm_eq_one_iff_notMem, NumberField.canonicalEmbedding_injective, Module.End.IsSemisimple_smul_iff, IntermediateField.restrictScalars_toSubalgebra, Valuation.exists_pow_Uniformizer, PowerSeries.eq_inv_iff_mul_eq_one, VectorBundleCore.continuousOn_coordChange, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, hasDerivWithinAt_inter', Submodule.mem_traceDual, ContinuousAlternatingMap.instCompleteSpace, IntermediateField.finiteDimensional_left, mfderiv_comp_apply, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, NumberField.InfinitePlace.LiesOver.mk_embedding_comp, AffineSubspace.subtypeₐᵢ_linearIsometry, Unitary.inner_map_map, legendreSym.card_sqrts, ContDiffBump.dist_normed_convolution_le, HasFDerivWithinAt.fun_sum, Algebra.normalizedTrace_trans_apply, fderiv_fun_const_smul, Real.hasDerivAt_arctan', TensorProduct.enorm_map, ZMod.gauss_lemma_aux, uniformEquicontinuous_birkhoffAverage, deriv_comp_mul_left, hasDerivAt_neg, LinearMap.IsSymmetric.id, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, RCLike.conj_eq_iff_im, Real.floor_logb_natCast, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, isCompactOperator_iff_image_ball_subset_compact, intervalIntegral.integral_hasDerivAt_right, tsupport_fderiv_apply_subset, hasFTaylorSeriesUpToOn_succ_iff_left, LaurentSeries.valuation_compare, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Padic.isUniformInducing_cast_withVal, HasCompactSupport.hasDerivAt_convolution_left, Polynomial.hasStrictDerivAt, ArchimedeanClass.mk_ratCast_nonneg, isConjRoot_iff_orbitRel, AlgebraicClosure.instIsScalarTower, Hyperreal.tendsto_atBot_iff, IsConformalMap.comp, le_perfectClosure_iff, perfectClosure.isAlgebraic, MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection, ContinuousLinearEquiv.isBigO_comp_rev, smul_inv_le_iff_of_neg, Subspace.map_le_dualAnnihilator_dualAnnihilator, Real.hasStrictDerivAt_arcsin, MvPowerSeries.X_inv, AlgHom.bijective, NumberField.IsCMField.complexConj_eq_self_iff, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, HasFPowerSeriesWithinOnBall.add, Commute.cfcₙ, WeierstrassCurve.Jacobian.isUnit_Y_of_Z_eq_zero, ContinuousLinearMap.add_compLp, IntermediateField.isSeparable_sup, NumberField.mixedEmbedding.logMap_real, curveIntegralFun_restrictScalars, Finset.centerMass_pair, NumberField.mixedEmbedding.commMap_apply_of_isReal, IsFractionRing.num_mul_den_eq_num_iff_eq, FiniteGaloisIntermediateField.finiteDimensional, PowerSeries.ker_coeff_eq_max_ideal, AffineMap.hasStrictDerivAt, MvPolynomial.zeroLocus_span, InnerProductSpace.toLinearMap_rankOne, div_eq_quo_add_rem_div_add_rem_div, instSecondCountableTopologyContinuousLinearMapIdOfFiniteDimensional, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, meromorphicNFAt_smul_iff_right_of_analyticAt, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, Polynomial.natSepDegree_X_sub_C, ContinuousLinearMap.adjointAux_inner_right, hasFDerivWithinAt_ofNat, HasDerivWithinAt.Ioi_iff_Ioo, RatFunc.algebraMap_apply, MeromorphicOn.smul, MaximalSpectrum.iInf_localization_eq_bot, HasMFDerivWithinAt.mul, Filter.Tendsto.inv_tendsto_nhdsLT_zero, OpenPartialHomeomorph.MDifferentiable.symm_comp_deriv, ContinuousLinearEquiv.isOpen, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, HilbertBasis.repr_self, RCLike.conj_re_ax, TensorProduct.commIsometry_apply, ContinuousLinearEquiv.coe_toDiffeomorph, IntermediateField.coe_smul, IsGaloisGroup.fixingSubgroup_bot, Ring.instFaithfulSMulSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, CFC.sqrt_eq_cfc, Algebra.IsAlgebraic.algEquivEquivAlgHom_apply, continuousMultilinearCurryRightEquiv_symm_apply', MeasureTheory.condExpInd_smul', NormedSpace.expSeries_sum_eq_div, ContinuousLinearMap.isBigO_sub, IsSepClosure.isAlgClosure_of_perfectField_top, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, DoubleCentralizer.norm_fst, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq, measurable_smul_const, IntermediateField.relfinrank_dvd_finrank_top_of_le, IntermediateField.set_range_subset, SchwartzMap.smul_apply, ContDiffMapSupportedIn.continuousSMul, ContinuousLinearMap.prodL_apply, Real.hasStrictDerivAt_sin, StrongDual.zero_mem_polar, RCLike.mul_self_norm, TensorProduct.congrIsometry_symm, Subalgebra.frontier_spectrum, BoundedContinuousFunction.coe_toContinuousMapₐ, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, Complex.log_eq_integral, ContinuousAlternatingMap.norm_ofSubsingleton_id, LinearIsometry.contDiff, Trivialization.continuousLinearMapAt_symmL, finSepDegree_dvd_finrank, LinearMap.isStarProjection_toContinuousLinearMap_iff, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, MeromorphicOn.divisor_smul, Manifold.pathELength_eq_lintegral_mfderiv_Icc, HasFDerivAtFilter.isLittleOTVS, Matrix.IsHermitian.roots_charpoly_eq_eigenvalues₀, LinearMap.IsSymmetric.orthogonal_range, exists_linearIndependent_algEquiv_apply, iteratedDerivWithin_eq_equiv_comp, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, Polynomial.roots_C_mul_X_sub_C, HasFDerivAt.const_sub, Polynomial.differentiableAt, ValuativeRel.one_vle_inv, LinearPMap.adjointDomainMkCLMExtend_apply, InfiniteGalois.restrictNormalHom_continuous, exists_pow_btwn, dimH_orthogonalProjection_le, Algebra.IsSeparable.sepDegree_eq, slope_sub_smul, RootPairing.rootForm_restrict_nondegenerate_of_isAnisotropic, fderiv_ccosh, LaurentSeries.tendsto_valuation, Submodule.traceDual_bot, galRestrictHom_symm_apply, AlgHom.restrictNormal_comp, instDiscreteTopologySubtypeMemSubmoduleIntComap, Pretrivialization.continuousOn_continuousLinearMapCoordChange, IsLocalRing.ResidueField.instIsScalarTower, ContDiffMapSupportedIn.seminorm_postcompLM_le, IsGaloisGroup.subgroup, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, ContinuousMultilinearMap.bound, normalClosure_eq_iSup_adjoin, DoubleCentralizer.coe_fst, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_left, instIsScalarTowerQuotientIdealResidueField, left_le_midpoint, Polynomial.natSepDegree_eq_of_isAlgClosed, HasStrictFDerivAt.fun_smul, hasStrictFDerivAt_ofNat, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, NumberField.abs_discr_ge_of_isTotallyComplex, FiniteField.bijective_frobeniusAlgHom_pow, Module.End.genEigenspace_div, smul_inv_lt_iff_of_neg, IntermediateField.fixedField.isScalarTower, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, ContDiffPointwiseHolderAt.fderiv, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, fderiv_fun_mul, curveIntegral_fun_sub, HasFiniteFPowerSeriesOnBall.finite, IntermediateField.coe_equivMap_apply, Submodule.re_inner_starProjection_nonneg, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, Algebra.instIsEpiOfIsDomainOfIsFractionRing, NumberField.mixedEmbedding.latticeBasis_repr_apply, IsGalois.finiteDimensional_of_finite, LocallyConvexSpace.convex_open_basis_zero, Submodule.adjoint_orthogonalProjection, NumberField.FinitePlace.instMonoidWithZeroHomClassReal, Filter.HasBasis.isBigOTVS_iff, IntermediateField.mem_adjoin_simple_iff, Real.sInf_smul_of_nonpos, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, HasFDerivAt.pow', Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField, NumberField.canonicalEmbedding.apply_at, HasStrictFDerivAt.pow', RatFunc.mk_one, LieAlgebra.IsKilling.finrank_rootSpace_eq_one, Complex.IsConservativeOn.hasDerivAt_wedgeIntegral, Asymptotics.IsEquivalent.inv, hasFDerivWithinAt_iff_hasGradientWithinAt, IntermediateField.finrank_le_of_le_left, Real.fourierIntegral_continuousLinearMap_apply', CurveIntegrable.smul, IsPrimitiveRoot.embeddingsEquivPrimitiveRoots_apply_coe, AffineIsometryEquiv.ofEq_rfl, IntermediateField.finInsepDegree_bot, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, Polynomial.isUnit_iff_degree_eq_zero, ContinuousLinearMap.hasFDerivAt_of_bilinear, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, Submodule.isOrtho_bot_right, mfderivWithin_prodMk, LinearMap.adjoint_comp, FormalMultilinearSeries.min_radius_le_radius_add, ContinuousAlternatingMap.opNorm_le_iff, krullTopology_mem_nhds_one_iff, CFC.abs_sq, RatFunc.algebraMap_injective, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, hasStrictDerivAt_one, FormalMultilinearSeries.ofScalars_comp_neg_id, FiniteField.unitsMap_norm_surjective, quadraticChar_sq_one', Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, MonoidAlgebra.Submodule.instIsSemisimpleModule, nonempty_algEquiv_of_range_minpoly_eq, AlgEquiv.fieldRange_eq_top, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, HasStrictFDerivAt.multiset_prod, MvPowerSeries.mul_inv_cancel, OpenPartialHomeomorph.MDifferentiable.mfderiv_injective, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, LinearMap.IsPositive.inner_nonneg_right, strictConvex_iff_div, Matrix.toEuclideanLin_apply_piLp_toLp, Finset.centerMass_eq_of_sum_1, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, pow_div_pow_eventuallyEq_atBot, Lagrange.interpolate_empty, LaurentSeries.coe_range_dense, X_pow_sub_C_irreducible_of_prime_pow, InnerProductSpace.span_gramSchmidt_Iio, Emb.Cardinal.iSup_adjoin_eq_top, ContinuousAlternatingMap.curryLeft_add, NumberField.AdeleRing.algebraMap_fst_apply, WeierstrassCurve.Affine.Point.map_some, HasFPowerSeriesAt.pi, LinearMap.dualMap_surjective_iff, Unitization.quasispectrum_eq_spectrum_inr', smul_ball, ZMod.expand_card, LinearIsometryEquiv.lTensor_def, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', Seminorm.smul_ball_preimage, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', ContDiff.hasStrictDerivAt, LinearIsometry.strictConvexSpace_range_iff, RatFunc.finrank_ratFunc_ratFunc, HasFDerivWithinAt.smul, skewAdjointPart_eq_I_smul_imaginaryPart, NormedSpace.expSeries_eq_expSeries_rat, Matrix.linfty_opNorm_eq_opNorm, WeierstrassCurve.Jacobian.nonsingular_of_Z_ne_zero, ContinuousAlternatingMap.prodLIE_apply, Submodule.mem_orthogonal_singleton_iff_inner_left, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isReal, mfderivWithin_eventually_congr_set, ValueDistribution.logCounting_pow_zero, Padic.rat_dense', JacobsonNoether.exists_separable_and_not_isCentral', LieAlgebra.IsKilling.chainBotCoeff_of_eq_zsmul_add, IntermediateField.toSubalgebra_iSup_of_directed, Manifold.IsImmersionAtOfComplement.writtenInCharts, PowerSeries.intValuation_X, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, LinearIsometry.inl_apply, hasDerivAt_pow, SchwartzMap.decay, span_flip_eq_top_iff_linearIndependent, NumberField.ComplexEmbedding.IsUnmixed.isReal_iff_isReal, ModelWithCorners.uniqueDiffWithinAt_image, LinearIsometryEquiv.comp_hasFDerivAt_iff', Submodule.mem_adjoint_iff, ZMod.pow_card_pow, Matrix.det_eq_prod_roots_charpoly, FormalMultilinearSeries.summable_nnnorm_mul_pow, RCLike.normSq_div, norm_fderiv_le_of_lipschitzOn, RCLike.im_sq_le_normSq, ContinuousLinearMap.isBoundedLinearMap, LinearMap.isSymmetric_iff_isSelfAdjoint, ContinuousLinearMap.opNorm_le_iff_lipschitz, sub_smul_slope, CPolynomialOn.fderiv, IsCyclotomicExtension.Rat.finrank, DirichletCharacter.not_LSeriesSummable_at_one, Submodule.reflection_involutive, SchwartzMap.convolution_flip, LocalSubring.instIsScalarTowerSubtypeMemSubringToSubringOfPrime, toIcoMod_zero_one, ContinuousLinearMap.opNorm_flip, Module.Basis.parallelepiped_map, Hyperreal.stdPart_of_tendsto, IsLocalMaxOn.fderivWithin_eq_zero, Polynomial.cardPowDegree_nonzero, OrderRingHom.subsingleton, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, ContinuousLinearMap.precompCompactConvergenceCLM_apply, VectorPrebundle.continuousOn_coordChange, IsAlgClosed.eval_surjective, VectorField.mpullbackWithin_apply, LinearMap.isSymmetric_iff_sesqForm, FormalMultilinearSeries.radius_compContinuousLinearMap_le, hasDerivWithinAt_derivWithin_iff, hasDerivAt_sub_const_iff, Subspace.dualLift_injective, hasStrictDerivAt_exp, HasStrictFDerivAt.mul_const', ContinuousLinearMap.IsPositive.adjoint_conj, measurable_fderiv_with_param, strictConcaveOn_iff_div, LinearIsometryEquiv.reflections_generate_dim, krullTopology_mem_nhds_one_iff_of_normal, mfderiv_const, IsConformalMap.smul, iteratedFDeriv_prodMk, isCoveringMap_npow, IsAlgClosed.splits, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection, RatFunc.ofFractionRing_eq, IntermediateField.finrank_bot', WeierstrassCurve.Projective.map_addU, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, Algebra.IsAlgebraic.algEquivEquivAlgHom_symm_apply, SchwartzMap.lineDerivOp_apply_eq_fderiv, Real.hasStrictDerivAt_sqrt, Complex.hasDerivAt_Gamma_one, ContinuousLinearMap.exist_extension_of_finiteDimensional_range, ArchimedeanClass.FiniteResidueField.mk_lt_mk, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range, hasFDerivWithinAt_pi, FiniteField.frobeniusAlgEquiv_apply, NumberField.mixedEmbedding.normAtPlace_smul, intervalIntegral.integral_smul_const, galLiftEquiv_algebraMap_apply, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, stdSimplex.barycenter_eq_centerMass, NNRat.Nonneg.coe_ofScientific, Polynomial.deriv, InnerProductSpace.laplacianWithin_smul_nhds, ContinuousLinearMap.differentiableOn, ContinuousMultilinearMap.uncurry0_apply, differentiableWithinAt_apply, ContinuousLinearMap.isPositive_iff', ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, LinearIsometryEquiv.comp_hasFDerivAt_iff, IsGalois.map_fixingSubgroup, Real.hasDerivAt_tan_of_mem_Ioo, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, Submodule.finrank_add_finrank_orthogonal, NumberField.mixedEmbedding.finrank, ContinuousLinearMap.star_eq_adjoint, IsUnramifiedAtInfinitePlaces.card_infinitePlace, CyclotomicRing.instIsTorsionFreeCyclotomicField, Submodule.orthogonal_eq_top_iff, FractionalIdeal.eq_zero_or_one, ContinuousMultilinearMap.curryLeft_apply, ContinuousAlternatingMap.hasFDerivWithinAt, ValuationSubring.mem_smul_pointwise_iff_exists, Finset.centerMass_smul, WeierstrassCurve.Jacobian.Point.toAffineLift_zero, AlgHom.toContinuousLinearMap_norm, instCharPLinearMapSubtypeMemSubringCenterId, Asymptotics.superpolynomialDecay_mul_const_iff, RatFunc.denom_algebraMap, iteratedDeriv_comp_three, IntermediateField.fixingSubgroup_isOpen, AffineSpace.asymptoticNhds_eq_smul, PiLp.hasFDerivAt_apply, Submodule.lipschitzWith_orthogonalProjection, AffineSubspace.direction_smul, ContMDiffWithinAt.coordChangeL, Polynomial.hasFDerivWithinAt_aeval, HasFPowerSeriesWithinAt.neg, CStarAlgebra.isStrictlyPositive_TFAE, continuousOn_cfcₙ_setProd, Real.hasDerivAt_exp, fderiv_sqrt, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, ModularForm.prod_fintype_slash, toIcoDiv_eq_floor, volume_euclideanSpace_eq_dirac, lt_inv_of_neg, FGModuleCat.FGModuleCatDual_coe, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Asymptotics.isThetaTVS_comm, Subfield.lift_rank_comap, hasStrictDerivAt_inv, Asymptotics.superpolynomialDecay_param_mul_iff, GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv, Polynomial.contDiff_aeval, RCLike.wInner_one_const_left, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, ProperCone.hyperplane_separation_of_notMem, OrderedFinpartition.applyOrderedFinpartition_update_left, FractionalIdeal.exists_eq_spanSingleton_mul, LinearMap.continuous_of_isClosed_ker, orthogonalFamily_iff_pairwise, ZSpan.map_fundamentalDomain, tendsto_nat_ceil_mul_div_atTop, RCLike.re_ofReal_pow, FiniteGaloisIntermediateField.adjoin_simple_map_algHom, ContinuousMultilinearMap.norm_compContinuous_linearIsometryEquiv, separableClosure.isSeparable, FormalMultilinearSeries.radius_le_radius_derivSeries, minpoly.natDegree_le, ContinuousAlternatingMap.curryLeftLI_apply, LieAlgebra.IsKilling.chainBotCoeff_le_chainLength, ContinuousLinearMap.norm_single_le_one, Real.nonempty_algEquiv_or, ContMDiffWithinAt.const_smul_section, Padic.coe_withValRingEquiv_symm, RCLike.norm_sq_re_add_conj, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, LinearMap.IsSymmetric.im_inner_apply_self, Submodule.inf_orthogonal_eq_bot, Complex.starConvex_slitPlane, FunctionField.ringOfIntegers.instIsNoetherianPolynomialSubtypeMemSubalgebraOfIsSeparableRatFunc, HasFDerivWithinAt.fun_mul', WeierstrassCurve.Affine.baseChange_slope, uniqueDiffOn_convex_of_isRCLikeNormedField, ContinuousLinearMap.norm_compSL_le, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_left, ContinuousLinearEquiv.uniqueDiffOn_preimage_iff, BoundedContinuousFunction.toContinuousMapₐ_apply, IsAlgClosed.card_aroots_eq_natDegree_of_isUnit_leadingCoeff, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, AdjoinRoot.minpoly_powerBasis_gen, RCLike.nnnorm_nnqsmul, ContDiffMapSupportedIn.withSeminorms, differentiableWithinAt_snd, PrimeSpectrum.isHomeomorph_comap_tensorProductMap_of_isPurelyInseparable, Submodule.isOrtho_sSup_left, Bundle.Trivial.trivialization.coordChangeL, MeasureTheory.withDensityᵥ_smul, xInTermsOfW_vars_aux, wbtw_or_wbtw_smul_vadd_of_nonneg, ContDiffAt.exists_eventually_eq_hasDerivAt, ContinuousMultilinearMap.analyticWithinAt, Bornology.isVonNBounded_vadd, fderiv_star, innerₛₗ_apply, hasFDerivAtFilter_iff_tendsto, InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis, HasFDerivWithinAt.isBigOTVS_sub, CFC.sqrt_algebraMap, Lagrange.sum_basis, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, CFC.posPart_algebraMap, Valued.integer.isUnit_iff_norm_eq_one, trace_eq_sum_embeddings, ContinuousLinearEquiv.hasFDerivAt, hasStrictFDerivAt_list_prod, IntermediateField.adjoin.finiteDimensional, CFC.sqrt_one, IntermediateField.botEquiv_def, spectrum.resolvent_tendsto_cobounded, InnerProductSpace.isIdempotentElem_rankOne_self_iff, le_algebraicClosure_iff, IsCauSeq.geo_series_const, sub_one_div_inv_le_two, Filter.EventuallyEq.iteratedFDeriv, ContinuousMultilinearMap.toUniformOnFun_toFun, ContinuousLinearMap.opNorm_nonneg, IntermediateField.adjoin_adjoin_comm, IntermediateField.adjoin_eq_top_iff, Pretrivialization.continuousLinearMap_symm_apply, Polynomial.abs_isBoundedUnder_iff, div_le_egauge_ball, hasDerivAtFilter_pi, stereographic_apply, MeasureTheory.inner_condExpL2_eq_inner_fun, StrongDual.toLp_apply, inverse_mfderiv_mul_left, OrthogonalFamily.norm_sum, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, AlgebraicIndependent.algebraicClosure, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace, HasFDerivAtFilter.iterate, Valued.integer.isPrincipalIdealRing_of_compactSpace, Submodule.inner_starProjection_left_eq_right, IntermediateField.toSubalgebra_lt_toSubalgebra, FDRep.char_orthonormal, ContinuousLinearMap.normOneClass, MeasureTheory.mem_lpMeas_self, ContinuousLinearMap.opNNNorm_subsingleton, IntermediateField.finSepDegree_bot', ContMDiffAt.mfderiv, ContinuousLinearMap.IsPositive.spectrumRestricts, Module.End.IsSemisimple.minpoly_squarefree, IntermediateField.val_mk, OrthonormalBasis.sum_repr, hasDerivAtFilter_const_add_iff, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, NumberField.InfinitePlace.embedding_injective, Real.iteratedFDeriv_fourierIntegral, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, differentiableAt_snd, NumberField.RingOfIntegers.instIsScalarTower, ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, IsCoercive.ker_eq_bot, NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal, RatFunc.eq_C_iff, Bornology.isVonNBounded_insert, hasDerivWithinAt_abs_neg, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, ContinuousLinearEquiv.analyticOnNhd, NumberField.InfinitePlace.mem_stabilizer_mk_iff, RatFunc.num_mul_eq_mul_denom_iff, StieltjesFunction.ae_hasDerivAt, IsConformalMap.injective, mem_galBasis_iff, InnerProductSpaceable.innerProp, fderivWithin_const_apply, IntermediateField.rank_sup_le, IntermediateField.LinearDisjoint.self_right, LinearIsometry.strictConvexSpace_range, CSA.fin_dim, ContinuousLinearMap.opNorm_neg, WittVector.RecursionBase.solution_pow, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, FormalMultilinearSeries.ofScalars_series_eq_zero, IsLocalRing.CotangentSpace.span_image_eq_top_iff, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, ProbabilityTheory.measure_condCDF_Iic, finSepDegree_eq_finrank_iff, FormalMultilinearSeries.changeOrigin_eval, krullTopology_discreteTopology_of_finiteDimensional, LinearMap.toSeminorm_ball_zero, Lagrange.eval_interpolate_at_node, Valuation.Integers.valuation_irreducible_pos, LinearIsometryEquiv.hasFDerivWithinAt, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, RootPairing.restrictScalars_toLinearMap_apply_apply, LinearMap.finrank_maxGenEigenspace_zero_eq, NumberField.RingOfIntegers.instIsScalarTower_1, AlgHom.normal_bijective, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, Submodule.fstL_comp_coe_orthogonalDecomposition, LaurentSeries.comparePkg_eq_extension, quadraticChar_apply, inner_smul_left_eq_smul, NumberField.toNNReal_valued_eq_adicAbv, iter_deriv_inv_linear_sub, MeromorphicOn.pow, Orientation.kahler_apply_apply, RCLike.re_sq_le_normSq, FiniteDimensional.exists_is_basis_integral, Module.Basis.ofZLatticeBasis_comap, isStarProjection_iff_eq_starProjection_range, ContinuousLinearMap.reApplyInnerSelf_smul, ContinuousLinearMap.add_compLpL, Polynomial.isIntegrallyClosed_iff', NonUnitalCStarAlgebra.toIsScalarTower, convexJoin_left_comm, IntermediateField.coe_pow, FiniteField.frobenius_pow, RCLike.conj_inv, LinearIsometryEquiv.symm_units_smul, IsGaloisGroup.mulEquivAlgEquiv_symm_apply, IsHilbertSum.linearIsometryEquiv_symm_apply_single, WittVector.exists_frobenius_solution_fractionRing_aux, AffineIsometryEquiv.map_vadd, closedAbsConvexHull_eq_closure_absConvexHull, exists_embedding_euclidean_of_compact, Complex.norm_fderiv_le_one_of_mapsTo_ball, UnitAddTorus.mFourierBasis_repr, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, HasFPowerSeriesAt.prod, LinearMap.toSeminorm_apply, AlgEquiv.restrictNormalHom_apply, InfiniteGalois.mk_toAlgEquivAux, hasDerivAt_ofReal_cpow_const', Normal.out, hasStrictDerivAt_natCast, LinearIsometryEquiv.toLinearIsometry_rTensor, Complex.hasDerivAt_Gamma_one_half, VectorPrebundle.contMDiffOn_contMDiffCoordChange, Representation.irreducible_iff_isSimpleModule_asModule, ProbabilityTheory.measurable_measure_condCDF, Real.smul_iSup_of_nonneg, LeftInvariantDerivation.toDerivation_injective, Submodule.starProjection_minimal, MvPolynomial.zeroLocus_top, EuclideanGeometry.orthogonalProjection_linear, instIsAbelianGaloisSubtypeMemIntermediateField, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, ContinuousLinearMap.contMDiffWithinAt, lineDeriv_smul, ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk, PiTensorProduct.mapL_pow, LinearMap.continuous_of_isClosed_graph, IntermediateField.adjoin_simple_comm, algebraicClosure.isAlgClosure, IsAlgebraic.inv_iff, FormalMultilinearSeries.ofScalars_sum_eq, DoubleCentralizer.natCast_toProd, OrthonormalBasis.sum_rankOne_eq_id, NumberField.InfinitePlace.mkComplex_coe, ContinuousLinearMap.dslope_comp, mdifferentiableAt_coordChangeL, hasDerivAt_finCons', MeasureTheory.Lp.toTemperedDistribution_toLp_eq, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, AlgEquiv.liftNormal_commutes, ModP.v_p_lt_val, AlgebraicGeometry.geometrically_iff_of_commRing_of_isClosedUnderIsomorphisms, ContinuousLinearMap.unit_le_opNorm, HasFPowerSeriesWithinAt.add, IntermediateField.inclusion_inclusion, Submodule.starProjection_mem_subspace_eq_self, Emb.Cardinal.adjoin_image_leastExt, MeasureTheory.BoundedContinuousFunction.inner_toLp, ContinuousLinearMap.adjoint_inner_right, exists_extension_norm_eq, LaurentSeries.valuation_def, HasMFDerivAt.prodMk, Subspace.dualAnnihilator_le_dualAnnihilator_iff, FiniteField.X_pow_card_pow_sub_X_natDegree_eq, ContinuousLinearMap.norm_id, FormalMultilinearSeries.id_apply_of_one_lt, hasFDerivAt_integral_of_dominated_of_fderiv_le'', gal_zero_isSolvable, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, HasFDerivWithinAt.fun_pow', FiniteField.bijective_frobeniusAlgEquivOfAlgebraic_pow, sum_Ioc_inv_sq_le_sub, Complex.card_rootsOfUnity, differentiable_pi'', HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, TensorProduct.norm_tmul, ContDiff.contDiff_fderiv_apply, LinearMap.isPositive_iff, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, PowerSeries.C_inv, ContinuousLinearMap.measurable_apply', IntermediateField.le_iff_le, IntermediateField.extendScalars_restrictScalars, NormedSpace.closedBall_inv_subset_polar_closedBall, FiniteField.nonempty_algHom_iff_finrank_dvd, MeasureTheory.convolution_mul_swap, ContDiffMapSupportedIn.postcompLM_apply, minpoly.eq_iff_aeval_minpoly_eq_zero, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, analyticOrderAt_smul, ContinuousLinearMap.norm_smulRightL_le, Real.smul_iSup_of_nonpos, DoubleCentralizer.one_toProd, MeasureTheory.withDensityᵥ_smul', spectralNorm_extends_of_finiteDimensional, Algebra.discr_powerBasis_eq_prod'', convexHull_prod, InfiniteGalois.fixedField_bot, differentiableAt_iff_restrictScalars, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, hasDerivAtFilter_const, smul_mem_asymptoticCone_iff, LinearIsometryEquiv.symm_smul_apply, SchwartzMap.tsupport_derivCLM_subset, CFC.sqrt_rpow_nnreal, RCLike.normSq_zero, hasDerivAt_single, OrthonormalBasis.coe_toBasis_repr_apply, sub_inv_antitoneOn_Icc_right, Algebra.adjoin_eq_top_of_intermediateField, FunctionField.inftyValuation.C, RCLike.enorm_conj, Valued.instFaithfulSMulCompletionOfUniformContinuousConstSMul, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, IntermediateField.adjoin_subset_adjoin_iff, inner_smul_right_eq_smul, IsAlgClosed.roots_eq_zero_iff, differentiableOn_apply, Hyperreal.st_inv, Algebra.map_intTraceAux, LinearIsometryEquiv.star_eq_symm, ContinuousLinearEquiv.dimH_preimage, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, IntermediateField.mem_extendScalars, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, SchwartzMap.integral_smul_laplacian_right_eq_left, differentiableAt_pi, HasFDerivWithinAt.fun_add, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, FormalMultilinearSeries.radius_prod_eq_min, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one, ContinuousLinearMapWOT.add_apply, OrthonormalBasis.coe_equiv_euclideanSpace, NumberField.mixedEmbedding.norm_real, RCLike.conjAe_coe, Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, hasFDerivAt_zero, ZMod.isCyclic_units_two, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, Valuation.Integers.isUnit_iff_valuation_eq_one, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, derivWithin_div, ContDiffOn.inv, NonUnitalCommCStarAlgebra.toSMulCommClass, isAlgClosure_iff, HasFDerivAt.mul_const', ContinuousAlternatingMap.nnnorm_ofSubsingleton, norm_cfcHom, LieAlgebra.IsKilling.traceForm_coroot, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, WeierstrassCurve.Jacobian.addU_smul, InfiniteGalois.proj_of_le, HasFiniteFPowerSeriesOnBall.fderiv', ValuativeRel.inv_vle_one, WittVector.RecursionBase.solution_spec', Submodule.orthogonalProjectionFn_eq, ContinuousMultilinearMap.currySum_apply, TensorProduct.nnnorm_comm, Submodule.IsOrtho.ge, OpenPartialHomeomorph.MDifferentiable.ker_mfderiv_eq_bot, FDRep.char_dual, RootPairing.finrank_rootSpanIn, Valuation.IsUniformizer.is_generator, FiniteField.expand_card, Module.Basis.traceDual_repr_apply, FormalMultilinearSeries.ofScalars_comp_neg, SeminormedSpace.Core.norm_smul, Polynomial.differentiableWithinAt_aeval, Submodule.bot_orthogonal_eq_top, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, ContinuousLinearMap.IsPositive.conj_starProjection, FGModuleCat.FGModuleCatEvaluation_apply', LieModule.traceForm_eq_sum_finrank_nsmul_mul, WeakDual.CharacterSpace.equivAlgHom_coe, HasStrictFDerivAt.fun_pow', convexHull_eq_union, measurable_fderiv, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux, le_egauge_ball_one, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, toPrincipalIdeal_def, Orthonormal.comp_linearIsometryEquiv, ValuationRing.instValuationRingInteger, quadraticChar_eq_pow_of_char_ne_two, Submodule.map_orthogonal, Complex.re_expect, HasStrictFDerivAt.comp, DoubleCentralizer.natCast_snd, ContDiffMapSupportedIn.bounded_iteratedFDeriv, IntermediateField.coe_type_toSubalgebra, IntermediateField.relrank_eq_rank_of_le, CompactConvergenceCLM.continuousSMul, WeierstrassCurve.Projective.map_add, convexHull_eq, inv_antitoneOn_Ioi, HasFiniteFPowerSeriesOnBall.hasFDerivAt, IntermediateField.lift_adjoin, convexJoin_assoc_aux, hasStrictDerivAt_zero, NumberField.basisOfFractionalIdeal_apply, VectorBundleCore.coordChange_linear_comp, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, ContinuousLinearMap.isBigOTVS_fun_comp, Module.Basis.ofZLatticeComap_repr_apply, RCLike.normSq_eq_zero, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, FormalMultilinearSeries.coeff_iterate_fslope, LinearMap.IsSymmetric.conj_inner_sym, HasFPowerSeriesAt.eq_zero, ContinuousLinearMap.coeFn_compLp, ContinuousLinearMap.flip_zero, FiniteField.Extension.exists_frob_pow_eq, FormalMultilinearSeries.leftInv_removeZero, LieAlgebra.IsKilling.chainBotCoeff_zero_right, IsGaloisGroup.fixedPoints_le_of_le, tendsto_pow_div_pow_atTop_atTop, Algebra.norm_smul_one_eq_norm, ContinuousLinearMapWOT.ext_iff, ContinuousAlternatingMap.instT2Space, ContinuousLinearMap.extendTo𝕜'_apply, NumberField.mem_multisetInfinitePlace, ClosedSubmodule.orthogonal_disjoint, fderivWithin_cosh, IsLocalFrameOn.coeff_eq_of_eq, MvPowerSeries.eq_mul_inv_iff_mul_eq, iteratedFDerivWithin_const_of_ne, ContinuousMultilinearMap.norm_ofSubsingleton, ContinuousLinearMap.isAdjointPair_inner, IntermediateField.extendScalars_top, MeromorphicAt.inv, TensorProduct.norm_map, dist_birkhoffAverage_birkhoffAverage_le, analyticOrderNatAt_pow, ContinuousLinearMap.coe_le_coe_iff, AddChar.linearIndependent, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, hasFDerivAtFilter_finCons', ContinuousLinearEquiv.analyticWithinAt, Real.hasFDerivAt_fourierChar_neg_bilinear_right, slope_fun_def_field, IntermediateField.algebraicIndependent_adjoin_iff, IsLocalRing.ResidueField.residue_smul, LinearIsometryEquiv.differentiableAt, Complex.re_nnqsmul, Real.fourier_continuousMultilinearMap_apply, NumberField.InfinitePlace.card_add_two_mul_card_eq_rank, LinearIsometryEquiv.differentiable, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, NumberField.InfinitePlace.mem_orbit_iff, RatFunc.isScalarTower_liftAlgebra, Unitization.splitMul_injective, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_snd, isInvertible_mfderiv_extChartAt, MeromorphicOn.fun_inv, WeierstrassCurve.Jacobian.map_addU, ProbabilityTheory.measure_condCDF_univ, MDifferentiableAt.smul_const_section, NumberField.InfinitePlace.isUnramifiedIn_comap, IntermediateField.rank_eq_rank_subalgebra, Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial, FormalMultilinearSeries.ofScalars_series_injective, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Nonneg.Icc_subset_segment, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousMultilinearMap.norm_map_insertNth_le, quadraticChar_eq_pow_of_char_ne_two', Asymptotics.IsTheta.const_smul_right, HasFPowerSeriesAt.coeff_zero, Submodule.orthogonal_le_orthogonal_iff, DoubleCentralizer.sub_snd, Algebra.normalizedTrace_trans, RingOfIntegers.algebraMap_norm_algebraMap, ModelWithCorners.coe_transContinuousLinearEquiv, IsSimpleRing.exists_algEquiv_matrix_of_isAlgClosed, SeparatingDual.completeSpace_continuousMultilinearMap_iff, Submodule.orthogonal_le_iff_orthogonal_le, ContMDiffOn.smul_section_of_tsupport, WeierstrassCurve.Jacobian.Y_eq_iff, Meromorphic.inv, ContDiffOn.comp_continuousLinearMap, lift_rank_mul_lift_sepDegree_of_isSeparable, ContMDiffWithinAt.smul_section, Polynomial.differentiable, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, Polynomial.rootSet_monomial, ContinuousLinearEquiv.coord_norm', Set.integer_valuation_le_one, Polynomial.separable_cyclotomic, NumberField.InfinitePlace.eq_iff_eq, IntermediateField.fixedField_bot, HasFPowerSeriesOnBall.hasSum_sub, ContinuousLinearMap.nnnorm_id, OrderIso.smulRightDual_symm_apply, smul_mem_asymptoticCone, LieAlgebra.IsKilling.chainTopCoeff_of_eq_zsmul_add, Polynomial.isCoprime_map, absConvexHull_eq_convexHull_balancedHull, FractionRing.isScalarTower_liftAlgebra, Bundle.Trivial.symmₗ_trivialization, ProbabilityTheory.hasDerivAt_mgf, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, DirichletCharacter.delta_mul, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, HasFPowerSeriesAt.eq_zero_of_eventually, hasMFDerivAt_snd, IntermediateField.toSubalgebra_strictMono, Asymptotics.superpolynomialDecay_const_mul_iff, ValuativeRel.inv_vlt_one, ContinuousLinearMap.isPositive_zero, div_le_egauge_closedBall, hasStrictFDerivAt_inv', IntermediateField.lift_sup, spectrum.nonzero_mul_comm, LinearMap.mem_span_iff_bound, Set.Finite.convexHull_eq_image, PowerSeries.inv_eq_inv_aux, Algebra.discr_powerBasis_eq_prod', PadicAlgCl.coe_eq, Polynomial.X_sub_C_mul_removeFactor, uniqueMDiffWithinAt_iff_uniqueDiffWithinAt, Algebra.algebraMap_intTrace, hasFDerivAt_exp_smul_const_of_mem_ball', convexJoin_right_comm, hasDerivAt_mul_const, LieAlgebra.IsKilling.chainBotCoeff_add_chainTopCoeff, SchwartzMap.smulLeftCLM_sub, Submodule.snd_orthogonalDecomposition_apply, NumberField.FinitePlace.isFinitePlace, hasFDerivAtFilter_natCast, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', cfcₙ_apply_mem_elemental, LinearEquiv.det_coe_symm, asymptoticCone_submodule, Module.Basis.ofZLatticeBasis_repr_apply, wbtw_or_wbtw_smul_vadd_of_nonpos, HasMFDerivAt.sum, normalClosure.normal, EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, intervalIntegral.integral_hasStrictDerivAt_right, Ideal.inertiaDeg_le_finrank, iteratedDeriv_fun_pow_zero, CFC.nnrpow_eq_rpow, FixedPoints.toAlgAut_bijective, SchwartzMap.fourier_fderivCLM_eq, SpectrumRestricts.nnreal_iff_spectralRadius_le, right_le_midpoint, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, PadicInt.ker_toZMod, ContinuousLinearMap.integral_comp_id_comm, FiniteField.isSplittingField_sub, hasStrictFDerivAt_exp_smul_const, IsGalois.fixingSubgroup_normal_of_isGalois, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, MDifferentiableOn.smul_section, dist_algebraMap, PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply_coe, AbsoluteValue.isEquiv_iff_exists_rpow_eq, SchwartzMap.fourier_convolution_apply, Seminorm.smul_ball_zero, Complex.hasStrictFDerivAt_log_real, separableClosure.map_eq_of_separableClosure_eq_bot, Polynomial.degree_div_le, Asymptotics.isBigOTVS_map, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, MvPowerSeries.invOfUnit_eq, LinearIsometry.norm_toContinuousLinearMap_le, Real.hasStrictDerivAt_tan, Polynomial.cyclotomic'_splits, AffineSubspace.isometryEquivMap.apply_symm_apply, Submodule.starProjection_le_starProjection_iff, iteratedFDerivWithin_zero_fun, IsCyclotomicExtension.fromZetaAut_spec, IntermediateField.adjoin_adjoin_left, RCLike.wInner_cWeight_const_right, Ideal.exist_integer_multiples_notMem, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, HasStrictFDerivAt.mul, RCLike.inv_eq_conj, intervalIntegral.integral_hasStrictDerivAt_left, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, ContinuousLinearMap.analyticOnNhd, fderiv_fst, iter_deriv_inv_linear, InfiniteGalois.algEquivToLimit_continuous, divRadical_dvd_wronskian_left, instIsPrincipalIdealRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C', LieAlgebra.isRegular_iff_finrank_engel_eq_rank, IntermediateField.normalClosure_mono, NumberField.instFiniteIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, ContinuousAlternatingMap.differentiable, WeakDual.toStrongDual_apply, ContinuousLinearEquiv.uniqueDiffOn_image_iff, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, LinearMap.eq_adjoint_iff_basis_right, IsLocalRing.subsingleton_tensorProduct, CategoryTheory.finrank_endomorphism_simple_eq_one, ContinuousLinearMap.hasMFDerivWithinAt, ContinuousLinearEquiv.nnnorm_symm_pos, InnerProductSpace.laplacian_smul_nhds, convexHull_rangle_single_eq_stdSimplex, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, MeasureTheory.lpNorm_expect_le, Submodule.instOrthogonalCompleteSpace, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, DirichletCharacter.convolution_mul_moebius, WeierstrassCurve.Affine.Point.toClass_eq_zero, IsUltrametricDist.isPowMul_algNormOfAlgEquiv, LaurentSeries.ratfuncAdicComplRingEquiv_apply, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, trace_eq_sum_automorphisms, IsSelfAdjoint.commute_cfcₙ, MvPolynomial.mem_vanishingIdeal_iff, MvPolynomial.mem_vanishingIdeal_singleton_iff, FormalMultilinearSeries.le_radius_pi, Real.hasDerivAt_arctan, AffineSpace.asymptoticNhds_eq_smul_vadd, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, continuousMultilinearCurryLeftEquiv_symm_apply, Polynomial.Monic.dvd_iff_fraction_map_dvd_fraction_map, convexHull_union, WithLp.unitization_mul, FixedPoints.smul, hasDerivAt_exp_smul_const', IsIdempotentElem.quasispectrum_subset, DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, quasispectrum.preimage_algebraMap, convexHull_sub, IsScalarTower.AlgEquiv.restrictNormalHom_comp_apply, VectorBundleCore.localTriv.isLinear, ValuationRing.isInteger_or_isInteger, instOrderIsoClassContinuousLinearMapIdOfNonUnitalAlgEquivClassOfStarHomClassOfContinuousMapClass, hasDerivWithinAt_id, separableClosure_le_iff, solvableByRad.isIntegral, ContinuousMultilinearMap.smulRightL_apply, ContinuousLinearMap.contDiff, Submodule.le_traceDual_mul_iff, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, MvPolynomial.expand_zmod, ContinuousLinearMap.instBorelSpace, LinearMap.isStarProjection_iff_isSymmetricProjection, LinearIsometryEquiv.toLinearEquiv_rTensor, fderiv_mul_const, innerₛₗ_apply_coe, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, fderiv_csinh, exists_pos_left_iff_sameRay_and_ne_zero, RatFunc.intDegree_X, ClassGroup.equiv_mk0, NumberField.RingOfIntegers.map_mk, HasStrictFDerivAt.fun_add, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, Valuation.Uniformizer.is_generator, IsLocalMinOn.fderivWithin_nonneg, instExpCharLinearMapSubtypeMemSubringCenterId, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, ContinuousLinearMap.norm_snd_le, IntermediateField.sup_toSubalgebra_of_right, Submodule.orthogonalDecomposition_apply, iteratedFDeriv_succ_eq_comp_left, IntermediateField.algebraAdjoinAdjoin.instFaithfulSMulSubtypeMemSubalgebraAdjoinAdjoin, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff, Submodule.isOrtho_self, LinearIsometryEquiv.toLinearIsometry_lTensor, WeierstrassCurve.Jacobian.neg_of_Z_ne_zero, fderiv_of_notMem_tsupport, ContinuousLinearMap.smul_compLpL, AddChar.wInner_cWeight_eq_boole, DifferentiableOn.prodMk, Representation.is_simple_module_iff_irreducible_ofModule, IntermediateField.insepDegree_bot, hasStrictFDerivAt_const, FormalMultilinearSeries.summable_norm_mul_pow, ContinuousLinearMap.contMDiffOn, Polynomial.Gal.restrictProd_injective, IsFractionRing.algEquiv_commutes, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv, contMDiffOn_coordChangeL, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, IntermediateField.equivOfEq_apply, ContinuousLinearEquiv.arrowCongrSL_symm_apply, NormedSpace.ext_iff, norm_algebraMap', IntermediateField.rank_bot', OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_univ, krullTopology_t2, NumberField.mixedEmbedding.convexBodySum_convex, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, ContinuousLinearMap.nnbound, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, convexHull_list_sum, range_cfcHom, ContinuousLinearMap.opNorm_mulLeftRight_le, DoubleCentralizer.intCast_fst, convex_halfSpace_im_le, gauge_smul_left, PointwiseConvergenceCLM.evalCLM_apply, Algebra.norm_algebraMap, IsPurelyInseparable.algebraMap_elemReduct_eq, ClosedSubmodule.orthogonal_closure, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, ContDiffPointwiseHolderAt.iteratedFDeriv, IntermediateField.le_sup_toSubalgebra, ContinuousLinearMap.norm_compLpL_le, ZSpan.vadd_mem_fundamentalDomain, LinearMap.toSeminormFamily_apply, perfectClosure.map_eq_of_algEquiv, Polynomial.rootSet_X_pow, algebraicClosure.map_eq_of_algEquiv, AffineSubspace.wOppSide_iff_exists_right, AddChar.map_neg_eq_conj, RatFunc.denom_add_dvd, CFC.abs_one, ringKrullDim_eq_zero_of_field, Module.End.mem_spectrum_iff_isRoot_charpoly, nonempty_algHom_of_minpoly_eq, mfderiv_fst, ContDiffMapSupportedIn.structureMapCLM_zero_injective, ContinuousAlternatingMap.neg_one_pow_smul_map_insertNth, EuclideanSpace.inner_single_right, ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdeal, RCLike.iInter_halfSpaces_eq, mfderivWithin_fst, NumberField.IsCMField.infinitePlace_complexConj, NumberField.prod_archAbsVal_eq, Polynomial.rootSet_prod, Hyperreal.stdPart_omega, IntermediateField.isAlgebraic_adjoin_iff_bot, ContinuousMultilinearMap.piₗᵢ_apply, meromorphicAt_smul_iff_of_ne_zero, nnnorm_cfcHom, Module.Basis.traceDual_powerBasis_eq, NumberField.ComplexEmbedding.isReal_comp_iff, RCLike.normSq_to_complex, Matrix.PosSemidef.sqrt_mul_self, ContDiffAt.continuousAt_iteratedFDeriv, Polynomial.not_irreducible_C, ZSpan.fract_apply, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, Real.deriv_arcsin_aux, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, IsLocalMin.fderiv_eq_zero, continuousOn_cfc, IntermediateField.fieldRange_val, IntermediateField.liftAlgEquiv_apply, ContinuousLinearMap.cpolynomialOn, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, LinearMap.coe_toContinuousLinearMap_symm, NumberField.ComplexEmbedding.IsConj.comp, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable, HasFDerivWithinAt.finset_prod, ContinuousAlternatingMap.nnnorm_constOfIsEmpty, hasStrictFDerivAt_list_prod', IntermediateField.inv_mem, RatFunc.num_div_denom, spectrum.mem_resolventSet_of_norm_lt, ContinuousLinearMap.le_opENorm, continuousMultilinearCurryFin1_symm_apply, IntermediateField.insepDegree_top, ValuationSubring.subtype_apply, Quaternion.hasSum_expSeries_of_imaginary, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, Trivialization.symmL_apply, ContinuousMultilinearMap.opNorm_le_iff, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, FixedPoints.smulCommClass', StrongDual.mem_polar_iff, separableClosure_le_separableClosure_iff, FormalMultilinearSeries.radius_pi_le, MeasureTheory.lpMeasToLpTrim_ae_eq, Submodule.orthogonal_eq_inter, ContinuousLinearMap.mdifferentiableOn, RCLike.normSq_add, AffineSubspace.sOppSide_smul_vsub_vadd_left, MeasureTheory.eLpNorm_condExpL2_le, RCLike.div_re, ContinuousLinearMap.lsmul_flip_apply, IsGaloisGroup.card_eq_finrank, ContinuousAlternatingMap.alternatizeUncurryFin_curryLeft, hasDerivAt_iff_tendsto, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, HasStrictFDerivAt.smul_const, FixedPoints.coe_algebraMap, ContinuousLinearEquiv.coord_self, sub_smul_dslope, ValuationSubring.valuation_eq_one_iff, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, cardinalMk_algHom, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, ContinuousAlternatingMap.unit_le_opNorm, RCLike.geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, IsGalois.tfae, norm_iteratedFDeriv_smul_le, ContDiffAt.differentiableAt_iteratedFDeriv, WeierstrassCurve.Projective.dblX_eq, LinearMap.IsPositive.adjoint_eq, Trivialization.prod_apply', fderivWithin_zero_of_not_differentiableWithinAt, IntermediateField.transcendental_adjoin_iff, Height.logHeight_smul_eq_logHeight, ContinuousLinearMap.sSup_unitClosedBall_eq_norm, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, NumberField.InfinitePlace.isUnramified_iff_mult_le, iteratedDeriv_vcomp_two, ContinuousLinearEquiv.coord_norm, ContinuousAlternatingMap.opNNNorm_le_iff, FiniteDimensional.subalgebra_toSubmodule, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic, ContinuousOn.continuousOn_iteratedFDeriv, inv_le_of_neg, intervalIntegral.integral_hasDerivAt_left, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, Matrix.toEuclideanLin_eq_toLin_orthonormal, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1, MeasureTheory.lpMeasToLpTrim_smul, Real.hasStrictDerivAt_const_rpow, Submodule.starProjection_orthogonal_val, VectorField.lieBracketWithin_eq, minpoly.iterateFrobenius_of_isSeparable, Polynomial.natSepDegree_mul, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, MDifferentiableOn.smul_section_of_tsupport, isStarProjection_iff_eq_starProjection, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, RCLike.geometric_hahn_banach_point_closed, LinearMap.IsSymmetricProjection.le_iff_range_le_range, ContinuousLinearMap.map_add₂, hasDerivWithinAt_intCast, IsFractionRing.associated_den_num_inv, Module.End.hasEigenvalue_iff_mem_spectrum, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, Polynomial.natDegree_mod_lt, IntermediateField.rank_comap, NormedSpace.expSeries_hasSum_exp_of_mem_ball', VectorPrebundle.coordChange_apply, LieAlgebra.IsKilling.chainTopCoeff_le_chainLength, ContinuousMultilinearMap.norm_map_cons_le, LinearMap.not_hasEigenvalue_zero_tfae, NumberField.InfinitePlace.even_card_aut_of_not_isUnramifiedIn, ContinuousMultilinearMap.norm_smulRight, EuclideanGeometry.orthogonalProjection_apply, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, Module.Basis.extendOfIsLattice_apply, hasFDerivAt_exp_zero_of_radius_pos, LSeries_hasDerivAt, separableClosure.separableClosure_eq_bot, Polynomial.div_C_mul, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_right, Hyperreal.infinitesimal_pos_iff_infinitePos_inv, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly, IntermediateField.rank_bot_mul_relrank, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, Real.hasDerivAt_fourierIntegral, IsLocalRing.instFiniteResidueField, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, ContinuousLinearEquiv.strictConvex_preimage, ordinaryHypergeometricSeries_eq_zero_of_neg_nat, NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, ContinuousAlternatingMap.bound, Nat.cast_le_pow_div_sub, IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C, ContinuousLinearMap.hasDerivWithinAt, LeftInvariantDerivation.commutator_coe_derivation, differentiableWithinAt_piLp, IsCyclotomicExtension.Rat.discr_odd_prime', LinearIsometry.rTensor_apply, hasStrictFDerivAt_pow, ValuationSubring.ofPrime_localization, ArchimedeanClass.mk_div, FormalMultilinearSeries.derivSeries_apply_diag, NumberField.InfiniteAdeleRing.denseRange_algebraMap, NormedSpace.polar_closedBall, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, Submodule.norm_orthogonalProjection, AnalyticAt.fderiv, Bundle.Prod.contMDiffVectorBundle, ContinuousLinearEquiv.differentiableWithinAt, IntermediateField.sup_toSubalgebra_of_isAlgebraic_right, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, fderiv_comp_smul, Submodule.instHasOrthogonalProjectionTop, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, ContinuousLinearMap.opNorm_lsmul, LinearIsometry.toLinearMap_lTensor, IntermediateField.toSubalgebra_le_toSubalgebra, convexOn_iff_div, ValuationSubring.ker_unitGroupToResidueFieldUnits, HasFPowerSeriesWithinOnBall.hasSum, Valuation.HasExtension.instIsScalarTower_valuationSubring, coe_innerₛₗ_apply, FormalMultilinearSeries.norm_changeOriginSeriesTerm, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, PiLp.hasStrictFDerivAt_ofLp, fderivWithin_arctan, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, Module.Basis.continuous_coe_repr, ContinuousLinearMap.norm_id_of_nontrivial_seminorm, NumberField.InfinitePlace.comap_id, curveIntegral_add, IsAlgClosed.isAlgClosure_of_transcendence_basis, HasGradientAt.hasDerivAt, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, TensorProduct.nndist_tmul_le, hasDerivAt_exp_zero, GenContFract.sub_convs_eq, HasFTaylorSeriesUpTo.zero_eq', InfiniteGalois.limitToAlgEquiv_symm_apply, AffineSubspace.setOf_sOppSide_eq_image2, NumberField.coe_discr, galRestrict'_comp, ContinuousLinearEquiv.analyticAt, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, LinearMap.finrank_maxGenEigenspace_eq, ProbabilityTheory.gaussianPDFReal_mul, InnerProductSpace.continuousLinearMapOfBilin_apply, Circle.toUnits_apply, ContinuousMultilinearMap.norm_def, Polynomial.degree_mod_lt, NormedSpace.double_dual_bound, instFieldContMDiffRing, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, CStarAlgebra.toStarModule, IntermediateField.adjoin_toSubfield, spectralAlgNorm_isPowMul, inv_smul_le_iff_of_neg, MeasureTheory.convolution_eq_swap, LinearMap.BilinForm.toLin_restrict_range_dualCoannihilator_eq_orthogonal, ContinuousLinearMap.map_zero₂, CFC.isUnit_nnrpow_iff, isInvertible_mfderivWithin_extChartAt_symm, ModelWithCorners.coe_transContinuousLinearEquiv_symm, fderivWithin_def, UniformCauchySeqOnFilter.one_smulRight, mulInvariantVectorField_smul, differentiable_finCons, ContDiff.fderiv_right, hasDerivAt_const_add_iff, HasFDerivAt.prodMap, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, Polynomial.hilbertPoly_mul_one_sub_pow_add, VectorField.mlieBracketWithin_apply, HasFPowerSeriesWithinOnBall.tendsto_partialSum, homothety_inv_two, RCLike.conj_eq_re_sub_im, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, IsTranscendenceBasis.lift_rank_eq_max_lift, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', ContinuousAlternatingMap.opNorm_pi, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, ValuationSubring.smul_mem_pointwise_smul, IntermediateField.finiteDimensional_map, FormalMultilinearSeries.id_apply_one, strictConvexOn_iff_div, ContinuousLinearEquiv.comp_contDiff_iff, RatFunc.toFractionRingRingEquiv_symm_eq, minpoly.degree_dvd, fderiv_csin, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, ContinuousLinearMap.norm_snd, ZSpan.repr_floor_apply, IsPurelyInseparable.isPRadical, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv, MvRatFunc.rank_eq_max_lift, WeakDual.isSeqCompact_polar, separableClosure.map_eq_of_algEquiv, NumberField.Units.finrank_mul_regulator_eq_det, IsPrimitiveRoot.lcm_totient_le_finrank, IsPurelyInseparable.instNonemptyAlgHomOfPerfectField, MeasureTheory.condExpIndSMul_ae_eq_smul, ContinuousAlternatingMap.uniformContinuous_restrictScalars, HasFTaylorSeriesUpTo.fderiv, ContinuousLinearMap.iteratedFDeriv_comp_right, linearIndependent_pow, FractionalIdeal.coe_div, ValuativeRel.one_srel_inv, norm_fderiv_le_of_lip', RatFunc.aeval_X_left_eq_algebraMap, IsSepClosure.isAlgClosure_of_perfectField, LieAlgebra.IsKilling.span_weight_eq_top, ContinuousMultilinearMap.apply_zero_uncurry0, ContinuousMap.idealOf_compl_singleton_isMaximal, Polynomial.residueFieldMapCAlgEquiv_symm_X, IntermediateField.finSepDegree_top, fderiv_cosh, PiTensorProduct.injectiveSeminorm_tprod_le, Polynomial.IsSplittingField.adjoin_rootSet_eq_range, IntermediateField.lift_rank_comap, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, ValuationRing.coe_equivInteger_apply, support_fderiv_subset, HasStrictFDerivAt.fun_mul, IsLocalFrameOn.generating, ContDiff.continuousLinearMap_comp, ContinuousLinearMap.precomp_apply, ContinuousLinearMap.norm_holderL_le, HahnSeries.inv_single, hasFDerivWithinAt_pow, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, Real.compact_inner_le_weight_mul_Lp_of_nonneg, PolynormableSpace.withSeminorms, CSA.isCentral, contDiff_infty_iff_fderiv, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, coe_algEquiv_lpBCF_symm, hasDerivWithinAt_inv, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Asymptotics.isBigOTVS_prodMk_left, MeasureTheory.lpMeas.ae_fin_strongly_measurable', gaugeSeminormFamily_ball, DirichletCharacter.modZero_eq_delta, spectralNorm_eq_of_equiv, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, hasStrictDerivAt_id, Polynomial.splits_iff_splits, curveIntegral_sub, Polynomial.Monic.irreducible_iff_irreducible_map_fraction_map, AlgHom.restrictNormal_commutes, quadraticCharFun_zero, RCLike.sqrt_normSq_eq_norm, WeierstrassCurve.Jacobian.isUnit_X_of_Z_eq_zero, mdifferentiable_smul_section, Matrix.IsHermitian.charpoly_eq, RatFunc.associated_num_inv, IsIntegral.inv_mem_adjoin, HasFDerivWithinAt.mul', IntermediateField.normalClosure_le_iff_of_normal, FiniteField.orderOf_frobeniusAlgHom, RCLike.conj_ofNat, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, HasGradientAt.fderiv_apply, SchwartzMap.instFourierInvSMul, ContinuousAlternatingMap.instContinuousEval, differentiableWithinAt_complex_iff_differentiableWithinAt_real, ContinuousLinearMap.comp_analyticOnNhd, TemperedDistribution.derivCLM_apply_apply, OrthonormalBasis.tensorProduct_apply, ValuationSubring.comap_comap, QuasispectrumRestricts.mul_comm_iff, DirichletCharacter.fourierTransform_eq_gaussSum_mulShift, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, AffineSubspace.setOf_wSameSide_eq_image2, LinearIsometryEquiv.integrable_comp_iff, AlgHom.fieldRange_of_normal, range_derivWithin_subset_closure_span_image, NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, IntermediateField.Lifts.eq_iff, Module.End.genEigenspace_le_genEigenspace_finrank, norm_iteratedFDeriv_zero, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, FiniteField.even_card_iff_char_two, NumberField.FinitePlace.norm_le_one, geom_sum₂_Ico, hasDerivWithinAt_Ici_of_tendsto_deriv, NumberField.Units.sum_mult_mul_log, Polynomial.hasFDerivWithinAt, WeierstrassCurve.Projective.add_of_Y_ne, MeasureTheory.condExpIndSMul_smul', LinearMap.hasDerivAt, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, norm_iteratedFDeriv_eq_norm_iteratedDeriv, MDifferentiableWithinAt.smul, HasMFDerivWithinAt.comp, Complex.isometryOfOrthonormal_symm_apply, WithLp.unitizationAlgEquiv_apply, Real.hasStrictDerivAt_rpow_const, Emb.Cardinal.adjoin_basis_eq_top, ContinuousLinearMap.postcompUniformConvergenceCLM_apply, VectorField.lieBracket_smul_right, NumberField.ComplexEmbedding.IsReal.isConjGal_one, HasFDerivAtFilter.restrictScalars, RCLike.normSq_apply, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, NumberField.ComplexEmbedding.conjugate_coe_eq, NumberField.Embeddings.range_eval_eq_rootSet_minpoly, Ideal.algebraMap_residueField_eq_zero, LinearMap.flip_surjective_iff₂, IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable', CurveIntegrable.sub, HasFiniteFPowerSeriesOnBall.fderiv_eq, smul_closedBall, ContMDiffOn.smul, NumberField.ComplexEmbedding.lift_algebraMap_apply, IntermediateField.iInf_toSubalgebra, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton, Valued.integer.norm_coe_unit, IsGaloisGroup.card_fixingSubgroup_eq_finrank, IntermediateField.normalClosure_map_eq, Complex.hasDerivAt_log_sub_logTaylor, hasStrictDerivAt_iff_hasStrictFDerivAt, UniformConvergenceCLM.instContinuousSemilinearMapClass, ContinuousLinearEquiv.comp_contDiffAt_iff, WeierstrassCurve.j_of_isShortNF, WithSeminorms.isVonNBounded_iff_seminorm_bounded, ContinuousAlternatingMap.hasFDerivAt, WithAbs.instIsSeparable, FormalMultilinearSeries.summable, HasFPowerSeriesAt.locally_zero_iff, hasDerivAt_iff_tendsto_slope, HasStrictDerivAt.complexToReal_fderiv, intervalIntegral.fderiv_integral, MeromorphicNFAt.inv, PiTensorProduct.mapL_add, Lagrange.eval_basis_self, fderiv_fun_const, ContinuousLinearMap.analyticAt_bilinear, inner_gradient_left, eventually_norm_trivializationAt_lt, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_left, TensorProduct.congrIsometry_apply, IntermediateField.relrank_bot_left, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff', Complex.ofReal_nnqsmul, ConvexOn.exists_affine_le_of_lt, HasFPowerSeriesAt.hasStrictFDerivAt, convex_halfSpace_re_gt, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, ModelWithCorners.uniqueDiffOn_preimage_source, MvPowerSeries.mul_inv_rev, MeasureTheory.integral_prod_smul, ContinuousLinearMap.toPointwiseConvergenceCLM_apply, LaurentSeries.mem_integers_of_powerSeries, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, Ideal.bijective_algebraMap_quotient_residueField, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, Polynomial.IsPrimitive.isUnit_iff_isUnit_map, IsConjRoot.sub_algebraMap, algebraMap_galRestrict'_apply, isBoundedLinearMap_continuousMultilinearMap_comp_linear, RingOfIntegers.coe_algebraMap_norm, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, innerSL_apply_coe, differentiableOn_finCons, ValuationSubring.top_coe_inv, Ring.instIsIntegralClosureNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, AffineSubspace.sSameSide_smul_vsub_vadd_left, ContinuousLinearMap.bound, LaurentSeries.instIsFractionRingPowerSeries, MeasureTheory.eLpNorm_le_eLpNorm_fderiv, NumberField.mixedEmbedding.convexBodySum_volume, tendsto_algebraMap_cobounded, Polynomial.IsSplittingField.IsScalarTower.splits, ContMDiff.const_smul_section, ContinuousLinearMap.isPositive_one, Polynomial.monic_annIdealGenerator, AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, LieModule.Weight.toLinear_neg, ContinuousLinearMap.isPositive_sum, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, RatFunc.algebraMap_monomial, Real.hasDerivAt_Gamma_nat, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, Polynomial.hilbertPoly_zero_right, HasStrictFDerivAt.inner, WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero, Height.AdmissibleAbsValues.product_formula, galRestrictHom_apply, RatFunc.denom_dvd, IntermediateField.isPurelyInseparable_tower_top, Algebra.Etale.iff_exists_algEquiv_prod, ZSpan.fract_eq_fract, HasMFDerivAt.comp, hasDerivAt_pi, ContinuousLinearMap.toUniformConvergenceCLM_symm_apply, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, derivWithin_fun_inv', Lagrange.natDegree_basis, dist_algebraMap', Meromorphic.fun_pow, FiniteField.coe_frobeniusAlgHom, hasFDerivAt_inv', LinearMap.toMatrix_adjoint, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Algebra.IsAlgebraic.bijective_of_isScalarTower, MvPolynomial.instIsMaximalVanishingIdealSingletonForallSet, hasDerivWithinAt_finCons, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, IntermediateField.le_normalClosure, CFC.abs_smul, RCLike.conj_smul, Subspace.map_dualCoannihilator, FormalMultilinearSeries.rightInv_coeff, Meromorphic.smul, OpenPartialHomeomorph.unitBallBall_symm_apply, hasDerivAt_zpow, ContinuousLinearMapWOT.instContinuousLinearMapClass, MeasureTheory.AEStronglyMeasurable.convolution_integrand', FormalMultilinearSeries.summable_norm_apply, FDRep.scalar_product_char_eq_finrank_equivariant, ContinuousMultilinearMap.norm_constOfIsEmpty, uniqueDiffOn_extChartAt_target, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, IntermediateField.equivOfEq_trans, spectrum.resolvent_isBigO_inv, WeakDual.CharacterSpace.compContinuousMap_id, mfderiv_neg, VectorBundle.pullback, convexOn_zpow, hasFDerivWithinAt_of_subsingleton, WeierstrassCurve.Jacobian.equation_of_Z_ne_zero, Polynomial.annIdealGenerator_eq_zero_iff, isClosedMap_smul_left, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, ContinuousLinearMap.integral_comp_comm, hasFDerivWithinAt_iff_tendsto, FormalMultilinearSeries.compAlongOrderedFinpartition_apply, IntermediateField.normalClosure_def', TensorProduct.nnnorm_lid, LinearMap.im_inner_adjoint_mul_self_eq_zero, NormedSpace.expSeries_summable_of_mem_ball', Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, Matrix.IsHermitian.mulVec_eigenvectorBasis, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, ValuationSubring.algebraMap_injective, WittVector.isocrystal_classification, fderiv_pi, ContinuousLinearMapWOT.sub_apply, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', autAdjoinRootXPowSubC_root, ContinuousLinearMap.map_neg₂, Matrix.l2_opNorm_def, IsAlgClosed.surjective_restrictDomain_of_isAlgebraic, EuclideanGeometry.Sphere.secondInter_map, PowerSeries.Inv_divided_by_X_pow_order_rightInv, AddCircle.equivAddCircle_symm_apply_mk, OrthogonalFamily.linearIsometry_apply, ContinuousMultilinearMap.le_opNNNorm, HasFiniteFPowerSeriesOnBall.sub, Ideal.ResidueField.liftₐ_algebraMap, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Bornology.isVonNBounded_singleton, Matrix.toEuclideanLin_toLp, ModuleCat.isScalarTower_of_algebra_moduleCat, IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers, IntermediateField.mem_bot, nnnorm_cfcₙ_le, ZMod.euler_criterion, NumberField.hermiteTheorem.rank_le_rankOfDiscrBdd, ContinuousLinearMapWOT.continuous_dual_apply, continuous_stereoInvFun, ContinuousLinearMap.iteratedFDeriv_comp_left, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center, Submodule.orthogonalProjection_eq_zero_iff, ContinuousLinearMap.holderL_apply_apply, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, StrongDual.mem_polar_singleton, FormalMultilinearSeries.comp_rightInv_aux2, ZSpan.coe_fract_self, RatFunc.single_inv, AddChar.expect_apply_eq_ite, IntermediateField.adjoin_algebraic_toSubalgebra, LeftInvariantDerivation.toFun_eq_coe, sepDegree_le_rank, ContinuousMultilinearMap.opNorm_prod, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, Asymptotics.isLittleOTVS_insert, Real.hasDerivAt_sinh, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction, isClosedEmbedding_smul_left, MeasureTheory.condExpL1CLM_smul, isConformalMap_const_smul, wbtw_midpoint, hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, Complex.norm_fderiv_le_div_of_mapsTo_ball, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1, norm_innerSL_le, MeromorphicAt.smul, Algebra.QuasiFinite.instIsArtinianRingFiber, AffineSubspace.subtypeₐᵢ_toAffineMap, IsFractionRing.num_mul_den_eq_num_iff_eq', DirichletCharacter.LSeries_eulerProduct, IntermediateField.mem_restrict, Valuation.HasExtension.instLiesOverSubtypeMemValuationSubringValuationSubringMaximalIdeal, HasStrictFDerivAt.sub, OrthonormalBasis.measurePreserving_measurableEquiv, IsDedekindDomain.integer_univ, Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, ContinuousLinearMap.isLeast_opNorm, fderiv_const_smul_of_field, perfectClosure.perfectRing, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, ContinuousLinearMap.IsPositive.isSelfAdjoint, CStarAlgebra.exists_sum_four_unitary, ValuationRing.of_field, spectrum.map_pow_of_pos, HasLineDerivAt.smul, OrthonormalBasis.sum_repr', continuousMultilinearCurryRightEquiv_apply, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, Seminorm.convex_closedBall, RCLike.real_smul_eq_coe_mul, hasStrictFDerivAt_intCast, algebraMap.coe_ratCast, Submodule.coe_orthogonalProjection_apply, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, NumberField.Units.dirichletUnitTheorem.exists_unit, Submodule.starProjection_coe_eq_isCompl_projection, IsLocalDiffeomorphAt.mfderivToContinuousLinearEquiv_coe, HasFDerivAt.neg, RCLike.ofReal_inv, normal_self, ContDiffMapSupportedIn.structureMapLM_zero_apply, ContinuousMap.idealOfSet_ofIdeal_isClosed, RCLike.ofRealAm_coe, Matrix.linearIndependent_cols_of_invertible, RCLike.normSq_one, LinearMap.injective_iff_antilipschitz, PerfectClosure.mk_inv, AffineIndependent.convexHull_inter, ContinuousAlternatingMap.prodLIE_symm_apply, analyticOrderAt_smul_eq_top_of_right, fderiv_comp_deriv_of_eq, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_apply, Polynomial.monic_normalize, Polynomial.map_dvd_map', DifferentiableOn.hasDerivAt, ContinuousLinearMapWOT.instContinuousNeg, Bornology.sUnion_isVonNBounded_eq_univ, ArchimedeanClass.FiniteElement.mk_natCast, SchwartzMap.integral_smul_deriv_right_eq_neg_left, inv_lt_of_neg, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, NumberField.ComplexEmbedding.isConj_one_iff, PowerSeries.smul_inv, LinearIsometryEquiv.norm_iteratedFDeriv_comp_left, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, IntermediateField.LinearDisjoint.isDomain, LinearMap.posSemidef_toMatrix_iff, tendsto_pow_atTop_nhds_zero_iff, ContDiff.fderiv, Submodule.starProjection_apply_eq_zero_iff, ContMDiffAt.smul_section, fderiv_list_prod', SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, Complex.log_inv_eq_integral, AnalyticOnNhd.eval_continuousLinearMap', instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, Module.Basis.norm_repr_le_norm, PadicInt.coe_dpow_eq, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, IntermediateField.finrank_dvd_of_le_right, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, Orthonormal.inner_right_fintype, HasMFDerivAt.mul', ContinuousLinearMap.flipₗᵢ_symm, ImplicitFunctionData.rightDeriv_fderiv_implicitFunction, Asymptotics.IsBigOTVS.refl, two_mul_le_add_mul_sq, NumberField.InfinitePlace.comap_surjective, WeierstrassCurve.Jacobian.add_of_Z_eq_zero, Asymptotics.isTheta_const_smul_right, HasFDerivAt.star_star, ContinuousLinearMap.postcomp_uniformConvergenceCLM_apply, ZMod.orderOf_units_dvd_card_sub_one, IsGalois.splits, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, hasDerivAt_of_tendsto_locally_uniformly_on', Polynomial.resultant_eq_zero_iff, NumberField.InfinitePlace.card_complex_embeddings, HasGradientWithinAt.hasFDerivWithinAt, ContinuousLinearMap.dist_le_opNorm, FormalMultilinearSeries.rightInv_coeff_one, IntermediateField.fixingSubgroup_bot, hasFDerivAt_exp, ContinuousAlternatingMap.opNNNorm_prod, IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar, IsAlgClosed.splits_domain, mfderivWithin_id, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Pi.orthonormalBasis_repr, RCLike.hasSum_conj', CyclotomicRing.eq_adjoin_primitive_root, Polynomial.hasDerivWithinAt, ZSpan.mem_fundamentalDomain, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, uniqueDiffWithinAt_extChartAt_target, IntermediateField.finrank_le_of_le_right, NumberField.RingOfIntegers.instIsIntegralClosure, InnerProductSpace.conj_inner_symm, ApproximatesLinearOn.lipschitzOnWith, Polynomial.mod_def, Orthonormal.tmul, norm_fderiv_norm_id_rpow, ContinuousLinearMap.isBigOTVS_id, LinearMap.isAdjointPair_inner, MeasureTheory.condExpIndL1Fin_smul', LinearMap.IsPositive.adjoint_conj, ContinuousLinearMap.norm_holder_apply_apply_le, upperHemicontinuous_spectrum, LinearMap.isPositive_one, Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iff, mfderivWithin_sumSwap, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, AnalyticOnNhd.eval_mvPolynomial, Affine.Simplex.affineSpan_pair_eq_altitude_iff, LinearMap.orthogonal_span_singleton_eq_to_lin_ker, Polynomial.pairwise_coprime_X_sub_C, Matrix.sub_scalar_sq_eq_discr, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, absorbent_ball_zero, ContinuousAlternatingMap.continuous_toContinuousMultilinearMap, Submodule.norm_subtypeL_le, range_cfc, RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_u, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, IsUltrametricDist.isPowMul_invariantExtension, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, isGalois_bot, hasDerivWithinAt_iff_tendsto_slope, fderiv_const_smul, hasFDerivAtFilter_pi', measurable_fderiv_apply_const_with_param, constFormalMultilinearSeries_apply_succ, IntermediateField.mem_fixingSubgroup_iff, FormalMultilinearSeries.continuousOn, Polynomial.natSepDegree_X_pow, hasFDerivAt_inv, IntermediateField.intermediateFieldMap_symm_apply_coe, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, mfderiv_prod_left, IntermediateField.finrank_dvd_of_le_left, Affine.Simplex.direction_altitude, LinearIsometryEquiv.symm_lTensor, ContinuousLinearMap.coe_ofIsClosedGraph, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, DoubleCentralizer.toProdHom_apply, ContinuousAlternatingMap.enorm_toContinuousMultilinearMap, Submodule.isOrtho_bot_left, ContinuousMultilinearMap.isUniformInducing_toUniformOnFun, LieAlgebra.IsKilling.mem_sl2SubalgebraOfRoot_iff, NumberField.mixedEmbedding.norm_unit, inv_nonpos', algebraMap_galRestrictHom_apply, Algebra.prod_embeddings_eq_finrank_pow, DoubleCentralizer.mul_snd, HasFDerivWithinAt.comp_hasFDerivAt, hasMFDerivWithinAt_inl, ContinuousLinearMap.fpowerSeries_apply_one, IntermediateField.map_id, fderiv_continuousLinearEquiv_comp', ContinuousLinearMap.smulRightL_apply_apply, continuousOn_clm_apply, logDeriv_pow, Set.Finite.convexHull_eq, Real.hasDerivAt_sqrt, ContinuousLinearMapWOT.ContinuousLinearMap.continuous_toWOT, SchwartzMap.one_add_le_sup_seminorm_apply, HahnSeries.cardSupp_inv_le, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, HasFDerivAt.fun_mul', Seminorm.continuous_iff_continuous_comp, Hyperreal.stdPart_epsilon, minpoly.eq_X_sub_C, spectrum.mem_resolventSet_of_spectralRadius_lt, constFormalMultilinearSeries_zero, Polynomial.SplittingField.adjoin_rootSet, OpenPartialHomeomorph.unitBallBall_apply, isSplittingField_iff_intermediateField, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, ValueDistribution.logCounting_inv, ContinuousMultilinearMap.instIsTopologicalAddGroup, Asymptotics.IsBigO.isBigOTVS, IsSepClosure.self_of_isSepClosed, LinearPMap.adjointAux_inner, HasStrictFDerivAt.mul_const, Asymptotics.isLittleOTVS_neg_left, Real.hasDerivWithinAt_arccos_Iic, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, ContDiffBump.convolution_tendsto_right_of_continuous, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, FractionalIdeal.den_mem_inv, NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iff, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, Lagrange.nodal_erase_eq_nodal_div, ContinuousLinearMap.opNNNorm_mul_apply, AbsoluteValue.isEquiv_iff_isHomeomorph, isGalois_iff_isGalois_bot, eventually_norm_mfderiv_extChartAt_lt, spectrum.zero_eq, ContinuousMultilinearMap.curryFinFinset_apply, InfiniteGalois.fixingSubgroup_isClosed, IsSepClosed.surjective_restrictDomain_of_isSeparable, EuclideanGeometry.orthogonalProjection_eq_iff_mem, NormedField.nhdsWithin_isUnit_neBot, RootPairing.ker_corootForm_eq_dualAnnihilator, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, Submodule.le_traceDual_iff_map_le_one, exists_integral_inj_algHom_of_fg, MeromorphicAt.fun_inv, Subspace.dualAnnihilator_inf_eq, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, FunctionField.inftyValuation_apply, OrderedFinpartition.applyOrderedFinpartition_update_right, ConjRootClass.irreducible_minpoly, FiniteField.algebraMap_norm_eq_pow_sum, eq_midpoint_of_dist_eq_half, insepDegree_le_of_left_le, IntermediateField.finiteDimensional_adjoin_pair, IsLocalRing.instIsScalarTowerResidueField, IsLocalRing.ResidueField.lift_residue_apply, MvPowerSeries.smul_inv, spectrum.subset_circle_of_unitary, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, VectorBundleCore.coordChange_comp, spectrum.subset_closedBall_norm, SchwartzMap.denseRange_toLpCLM, IntermediateField.normal_sup, IsAlgClosed.associated_iff_roots_eq_roots, ValuationSubring.primeSpectrumEquiv_apply, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, hasFDerivAt_fst, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, Asymptotics.isLittleOTVS_sup, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, IntermediateField.coe_algebraMap_apply, mfderiv_comp_mfderivWithin_of_eq, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, LinearMap.IsSymmetric.coe_re_inner_apply_self, SchwartzMap.integrable_pow_mul_iteratedFDeriv, FormalMultilinearSeries.radius_eq_liminf, UniformSpace.Completion.hatInv_extends, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, NumberField.IsCMField.complexConj_torsion, Polynomial.residueFieldMapCAlgEquiv_algebraMap, HasFTaylorSeriesUpToOn.restrictScalars, isConformalMap_iff_is_complex_or_conj_linear, Subspace.dualAnnihilator_dualCoannihilator_eq, starConvex_iff_div, ContinuousLinearMap.apply_apply, ContinuousLinearEquiv.comp_differentiableWithinAt_iff, Submodule.traceDual_top, Asymptotics.isThetaTVS_iff_isTheta, hasFDerivAt_pi', ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk, RatFunc.toFractionRingAlgEquiv_apply, OrthogonalFamily.summable_iff_norm_sq_summable, ContinuousLinearMap.norm_map_removeNth_le, Module.End.exists_isNilpotent_isSemisimple, Polynomial.isCoprime_iff_aeval_ne_zero, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, LieModule.range_traceForm_le_span_weight, algebraMap_cobounded_le_cobounded, iteratedFDeriv_neg, sub_inv_antitoneOn_Iio, separableClosure.isGalois, Real.fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, IsSymmSndFDerivWithinAt.eq, ContinuousLinearMap.map_smulₛₗ₂, CurveIntegrable.add, Asymptotics.superpolynomialDecay_param_pow_mul_iff, PiTensorProduct.mapLMultilinear_opNorm, hasDerivWithinAt_inter, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, ContinuousMultilinearMap.norm_image_sub_le', hasFPowerSeriesAt_iff', NumberField.InfinitePlace.apply, LinearMap.canLiftContinuousLinearMap, LinearIsometryEquiv.differentiableOn, RCLike.geometric_hahn_banach_closed_compact, FDRep.dualTensorIsoLinHom_hom_hom, WeierstrassCurve.Jacobian.isUnit_addZ_of_X_ne, MeasureTheory.eLpNorm_conj, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, inner_gradient_right, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, LaurentSeries.exists_ratFunc_eq_v, IntermediateField.restrictScalars_adjoin, ax_grothendieck_zeroLocus, hasStrictDerivAt_exp_zero, Transcendental.linearIndependent_sub_inv, NonUnitalCStarAlgebra.toSMulCommClass, Submodule.orthogonalProjection_norm_le, HasFDerivAt.mul', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, DoubleCentralizer.intCast_toProd, Matrix.PosDef.posDef_sqrt, CauSeq.lim_inv, IntermediateField.finrank_adjoin_simple_eq_one_iff, Function.HasTemperateGrowth.isBigO_uniform, LinearMap.BilinForm.le_flip_dualSubmodule, differentiableOn_snd, ArchimedeanClass.stdPart_inv, iteratedFDerivWithin_zero_apply, EuclideanSpace.volume_closedBall, FiniteField.natCard_algEquiv_extension, ClassGroup.mk_def, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, WeierstrassCurve.Projective.dblXYZ_of_Y_eq, fderiv_single, IsSepClosed.exists_aeval_eq_zero, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, Submodule.orthogonalProjection_orthogonal, Set.Finite.isVonNBounded, IntermediateField.isSeparable_tower_top, slope_def_module, Real.hasStrictDerivAt_exp, inv_antitoneOn_Icc_left, coe_algEquiv_lpBCF, openSegment_subset_union, inner_conj_symm, LinearMap.finrank_eigenspace_le, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_symm_apply, Algebra.finite_of_essFiniteType_of_isAlgebraic, inv_eq_of_aeval_divX_ne_zero, Height.logHeight_pow, MvPolynomial.vanishingIdeal_zeroLocus_eq_radical, le_egauge_closedBall_one, hasFDerivAt_list_prod_attach', Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mul, instSubsingletonAlgHomOfIsPurelyInseparable, one_add_rpow_hasFPowerSeriesOnBall_zero, Polynomial.IsSplittingField.map, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, LinearIsometryEquiv.rTensor_def, MeasureTheory.norm_condExpL2_le_one, ContinuousLinearEquiv.mdifferentiableAt, HasCompactSupport.convolution_integrand_bound_right, ValuationSubring.coe_subtype, MeromorphicAt.meromorphicTrailingCoeffAt_pow, bddAbove_smul_iff_of_neg, LinearMap.mem_span_iff_continuous, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, fderivWithin_mem_iff, Padic.isDenseInducing_cast_withVal, Ideal.Fiber.exists_smul_eq_one_tmul, UniqueMDiffOn.uniqueDiffWithinAt_range_inter, AddChar.inv_apply_eq_conj, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, Asymptotics.isBigOTVS_comm, DifferentiableAt.lineDeriv_eq_fderiv, OrthonormalBasis.repr_reindex, Ideal.ResidueField.mapₐ_apply, normalClosure.is_finiteDimensional, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, MeasureTheory.condExpL2_comp_continuousLinearMap, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, Subspace.isCompl_dualAnnihilator, FormalMultilinearSeries.ofScalars_norm_eq_mul, isBoundedBilinearMap_smulRight, CFC.log_smul, inCoordinates_tangent_bundle_core_model_space, isOpen_setOf_linearIndependent, NormedSpace.expSeries_hasSum_exp_of_mem_ball, LinearIsometryEquiv.differentiableWithinAt, Polynomial.separable_map, IntermediateField.finiteDimensional_sup, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, IntermediateField.Lifts.le_iff, Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin, VectorBundle.prod, Algebra.normalizedTrace_self_apply, AnalyticOnNhd.eval_continuousLinearMap, hasStrictFDerivAt_pi, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, WeierstrassCurve.Affine.Point.toClass_apply, Submodule.isOrtho_sup_left, Polynomial.normalizedFactors_cyclotomic_card, ContinuousLinearMap.adjoint_innerSL_apply, NumberField.InfinitePlace.comap_embedding_of_isReal, ZLattice.coe_comap, LSeries.hasDerivAt_term, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, Valuation.Integers.bijective_algebraMap_of_subsingleton_units_mrange, Submodule.IsOrtho.comap, hasFDerivAt_iff_isLittleO_nhds_zero, MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton, OrthogonalFamily.inner_right_fintype, geom_sum_Ico_le_of_lt_one, Asymptotics.isLittleO_pow_pow_atTop_of_lt, Valuation.coeff_zero_minpoly, ContDiffMapSupportedIn.structureMapLM_apply, RatFunc.map_apply_div_ne_zero, RCLike.normSq_sub, trace_adjoinSimpleGen, IntermediateField.fixingSubgroup_sup, ContinuousLinearMap.coprodEquivL_symm_apply, VectorPrebundle.contMDiffCoordChange_apply, isBoundedLinearMap_prod_multilinear, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Orthonormal.inner_sum, differentiableWithinAt_fst, IntermediateField.normal_iff_normalClosure_eq, EuclideanGeometry.reflection_apply, continuousOn_coordChange, HasCompactSupport.convolution_integrand_bound_right_of_subset, LinearIsometryEquiv.comp_fderiv', IntermediateField.rank_adjoin_simple_eq_one_iff, Polynomial.coeff_preHilbertPoly_self, LinearPMap.adjoint_apply_of_dense, PadicInt.val_toZMod_eq_zmodRepr, HasStrictDerivAt_ofNat, Filter.IsBoundedUnder.isLittleO_sub_self_inv, le_iff_norm_sqrt_mul_rpow, Real.fourier_smul_convolution_eq, IsSepClosed.exists_eval₂_eq_zero, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, DoubleCentralizer.smul_snd, RCLike.wInner_cWeight_eq_smul_wInner_one, inverse_mfderiv_add_left, postcomp_compactConvergenceCLM_apply, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, HasFiniteFPowerSeriesAt.comp, Subspace.comap_dualAnnihilator_dualAnnihilator, NumberField.ComplexEmbedding.orderOf_isConj_two_of_ne_one, ContinuousMap.idealOfSet_isMaximal_iff, IntermediateField.AdjoinPair.algebraMap_gen₂, ContinuousLinearMap.integral_id_map, hasDerivWithinAt_iff_tendsto, PrimeSpectrum.nontrivial_iff_mem_rangeComap, MeasureTheory.condExpL2_const_inner, NumberField.house.basis_repr_norm_le_const_mul_house, balancedHull_convexHull_subseteq_absConvexHull, Unitary.path_apply, curveIntegrable_restrictScalars_iff, LinearMap.IsSymmetric.intCast, SpectrumRestricts.nnreal_iff_nnnorm, cyclotomicCharacter.continuous, IsCoercive.isClosed_range, Submodule.mem_traceDual_iff_isIntegral, LieAlgebra.IsKilling.rootSystem_root_apply, NumberField.IsCMField.Units.complexConj_eq_self_iff, ContinuousLinearMap.toWOT_apply, Unitary.spectrum_subset_circle, Polynomial.IsPrimitive.dvd_iff_fraction_map_dvd_fraction_map, IntermediateField.isIntegral_iff, Subfield.toIsStrictOrderedRing, TensorProduct.ext_iff_inner_right_threefold, mem_contMDiffFiberwiseLinear_iff, RatFunc.denom_zero, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, curveIntegralFun_def, ArchimedeanClass.FiniteResidueField.instIsOrderedRing, Submodule.coe_prodEquivOfClosedCompl, InnerProductSpaceable.inner_.conj_symm, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, ContinuousLinearMap.intervalIntegral_comp_comm, hasDerivAt_finCons, Asymptotics.IsThetaTVS.rfl, inner_eq_ofReal_norm_sq_right_iff, HasFDerivAt.smul, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, homothety_one_half, RatFunc.associated_denom_inv, ContinuousLinearMap.contMDiffAt, IsLocalRing.residue_surjective, isOpen_setOf_nat_le_rank, FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin, SchwartzMap.smulLeftCLM_smul, CurveIntegrable.neg, PadicInt.toZMod_spec, isClosed_setOf_isCompactOperator, DoubleCentralizer.coe_snd, ContinuousMultilinearMap.fin0_apply_norm, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, Algebra.botEquiv_symm_apply, WeierstrassCurve.Projective.isUnit_addZ_of_X_ne, MeasureTheory.integral_convolution, ValuationSubring.principalUnitGroup_injective, contractLeft_assoc_coevaluation', ContinuousLinearMap.le_opNorm_enorm, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum, fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, IsSelfAdjoint.commute_cfc, separableClosure.normalClosure_eq_self, fderiv_sin, ArchimedeanClass.mk_inv, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, cfcHom_apply_mem_elemental, hasStrictDerivAt_pow, Projectivization.Subspace.mem_submodule_iff, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, IsAlgClosed.dvd_iff_roots_le_roots, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, IntermediateField.coe_map, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, TrivSqZeroExt.snd_expSeries_of_smul_comm, RCLike.conj_neg_I, ContinuousMultilinearMap.norm_curryMid, ConvexOn.univ_sSup_of_nat_affine_eq, ContinuousLinearEquiv.comp_right_differentiable_iff, convexHull_range_eq_exists_affineCombination, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, LinearMap.trace_map, ContinuousAlternatingMap.ratio_le_opNorm, WeierstrassCurve.j_of_isCharThreeJNeZeroNF_of_char_three, ContinuousMultilinearMap.norm_mkPiAlgebraFin, wbtw_iff_sameRay_vsub, RCLike.inv_I, IntermediateField.adjoin.powerBasis_dim, TensorProduct.assocIsometry_symm_apply, hasFDerivAt_exp_of_mem_ball, LaurentSeries.valuation_X_pow, InnerProductSpace.Core.inner_conj_symm, InnerProductSpace.gramSchmidt_mem_span, isConjRoot_iff_eq_algebraMap', SimpContFract.determinant_aux, IsCyclotomicExtension.autEquivPow_symm_apply, ModelWithCorners.uniqueDiffOn, norm_iteratedFDeriv_fderiv, NormedSpace.dual_def, LinearMap.IsSymmetric.add, HasFDerivAtFilter.hasDerivAtFilter, NumberField.house_eq_sup', TensorProduct.inner_map_map, IsGalois.of_fixedField_normal_subgroup, RCLike.geometric_hahn_banach_open_open, IntermediateField.Lifts.nonempty_algHom_of_exist_lifts_finset, Polynomial.residueFieldMapCAlgEquiv_symm_C, const_smul_mfderiv, fderiv_norm_sq, Filter.EventuallyEq.hasDerivAtFilter_iff, instProperSpaceSubtypeMemSubmoduleOfCompleteSpaceOfLocallyCompactSpace, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, IntermediateField.essFiniteType_iff, Emb.cardinal_separableClosure, HasMFDerivAt.const_smul, IntermediateField.AdjoinSimple.algebraMap_gen, Valuation.Integers.dvd_iff_le, Subspace.finrank_add_finrank_dualAnnihilator_eq, Lagrange.interpolate_singleton, Complex.ofReal_choose, IntermediateField.isPurelyInseparable_sup, Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosed, TensorProduct.toLinearMap_mapInclIsometry, NonUnitalCommCStarAlgebra.toIsScalarTower, inv_antitoneOn_Iio, mfderivWithin_snd, Function.HasTemperateGrowth.isBigO, Polynomial.eventually_no_roots, NumberField.FinitePlace.norm_def, FormalMultilinearSeries.hasFPowerSeriesOnBall, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, ContinuousLinearMap.coe_mulₗᵢ, Rat.ringOfIntegersWithValEquiv_apply, OrthogonalFamily.inner_right_dfinsupp, spectrum.mem_resolventSet_of_norm_lt_mul, ContinuousLinearMap.isUnit_iff_bijective, NumberField.mixedEmbedding.convexBodySum_mem, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', ClassGroup.equiv_mk, PowerSeries.X_eq_normalizeX, Real.smul_iInf_of_nonneg, UniqueDiffWithinAt.of_real, orthonormal_span, norm_cfc_lt, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, ContinuousLinearMap.innerSL_apply_comp, conformalAt_iff', TensorProduct.lidIsometry_symm_apply, ContinuousLinearMap.instStarOrderedRingRCLike, surjective_stereographic, Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModule, ContinuousLinearMap.mdifferentiableAt, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, Matrix.mulVec_injective_iff_isUnit, hasDerivAt_abs_pos, ContinuousAlternatingMap.instContinuousEvalConst, PiTensorProduct.injectiveSeminorm_def, ContinuousLinearMap.coeFn_holder, ContDiffMapSupportedIn.structureMapLM_eq, hasStrictFDerivAt_id, IsIntegralClosure.isLocalization_of_isSeparable, HilbertBasis.hasSum_repr_symm, ContinuousAlternatingMap.norm_image_sub_le, IsGalois.mem_bot_iff_fixed, hasStrictFDerivAt_sub_const, ContinuousLinearMap.coe_deriv₂, IsDedekindDomain.selmerGroup.valuation_ker_eq, IsMIntegralCurveAt.eventually_hasDerivAt, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, IsAlgClosed.exists_aeval_eq_zero, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, hasFDerivAt_stereoInvFunAux_comp_coe, LinearIsometryEquiv.comp_hasStrictFDerivAt_iff, LinearMap.adjoint_id, inner_smul_left, contDiff_succ_iff_hasFDerivAt, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, mfderiv_prod_eq_add_apply, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, FiniteField.finrank_extension, Matrix.linearIndependent_rows_iff_isUnit, ValuationSubring.principalUnitGroup_symm_apply, MeasureTheory.condExpL2_indicator_nonneg, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, PadicInt.coe_pow, NumberField.mixedEmbedding.convexBodyLT'_convex, Submodule.coe_prodEquivOfClosedCompl_symm, selfAdjoint.expUnitary_coe, DoubleCentralizer.add_toProd, PowerSeries.inv_mul_cancel, Filter.Tendsto.inv_tendsto_atBot, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, Valuation.HasExtension.algebraMap_injective, ValuationRing.instIsFractionRingInteger, IntermediateField.algebra_adjoin_le_adjoin, HasFDerivWithinAt.sum, TemperedDistribution.smulLeftCLM_apply_apply, X_pow_sub_C_irreducible_iff_of_prime, IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, selfAdjoint.val_nnqsmul, Subspace.dualPairing_eq, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Complex.continuousOn_one_add_mul_inv, hasFDerivAt_pi, NumberField.InfinitePlace.IsUnramified.comap, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, mfderivWithin_comp, Polynomial.map_normalize, fderiv_inner_apply, RatFunc.algebraMap_comp_C, differentiableOn_fst, AffineIsometryEquiv.pointReflection_midpoint_right, hasFDerivWithinAt_snd, IsFractionRing.isUnit_den_iff, Icc_subset_segment, IsBoundedLinearMap.isLinearMap_and_continuous_iff_isBoundedLinearMap, FractionalIdeal.spanSingleton_inv, ContMDiff.coordChangeL, RatFunc.ofFractionRing_algebraMap, IsCyclotomicExtension.Rat.discr_prime_pow_eq_unit_mul_pow', FractionalIdeal.inv_of_ne_zero, RatFunc.eval_algebraMap, Module.Basis.traceDual_injective, AddCircle.homeomorphAddCircle_symm_apply_mk, differentiableWithinAt_finCons, fderiv_const_apply, Real.hasStrictDerivAt_log_of_pos, FormalMultilinearSeries.ofScalars_norm, IsCyclotomicExtension.autEquivPow_apply, ContinuousMultilinearMap.norm_ofSubsingleton_id, IsPurelyInseparable.elemExponent_def, HasFDerivWithinAt.fun_mul, hasFTaylorSeriesUpToOn_pi, RCLike.normSq_conj, IsCyclotomicExtension.discr_prime_pow, separableClosure.isPurelyInseparable, HasStrictFDerivAt.smul, ContinuousLinearMap.orthogonal_ker, AnalyticAt.hasStrictDerivAt, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, Nonneg.segment_eq_Icc, iter_deriv_pow, Asymptotics.IsThetaTVS.refl, ContinuousLinearMap.continuousAt_uncurry_of_multilinear, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, HasStrictFDerivAt.finset_prod, ContMDiff.smul_section, contDiffWithinAt_succ_iff_hasFDerivWithinAt, Filter.EventuallyEq.hasDerivWithinAt_iff, instIsFractionRingQuotientIdealResidueField, ProbabilityTheory.instIsProbabilityMeasurecdf, Asymptotics.IsBigO.hasFDerivAt, WeierstrassCurve.Jacobian.isUnit_addU_of_Y_ne, hasFDerivWithinAt_apply, SeminormFamily.basisSets_smul_left, ArchimedeanClass.stdPart_eq_sSup, InnerProductSpace.norm_rankOne, FixedPoints.minpoly.of_eval₂, Urysohns.CU.lim_eq_midpoint, HasFDerivAt.fun_sub, Complex.hasDerivAt_Gamma_nat, Subspace.dualEquivDual_apply, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two, ContMDiffMap.coeFnLinearMap_apply, Submodule.isHilbertSumOrthogonal, Polynomial.SplittingField.instNormal, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, RCLike.inv_re, DoubleCentralizer.neg_fst, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, PiTensorProduct.mapLMultilinear_toFun_apply, FunctionField.ringOfIntegers.not_isField, IsAlgClosed.ringHom_bijective_of_isIntegral, CFC.isUnit_sqrt_iff, HasFiniteFPowerSeriesOnBall.fderiv, CompletableTopField.nice, ContinuousLinearEquiv.norm_pos, HasFDerivAt.comp, FormalMultilinearSeries.ofScalarsSum_unop, real_inner_I_smul_self, LinearIsometry.lTensor_def, Hyperreal.archimedeanClassMk_epsilon_pos, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, Orthonormal.inner_right_sum, circleEquivGen_apply, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff, IntermediateField.finite_of_fg_of_isAlgebraic, minpoly.isIntegrallyClosed_eq_field_fractions', ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, TensorProduct.edist_tmul_le, Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans, quasispectrum.instCompactSpace, fderiv_eq_smul_deriv, unitary.inner_map_map, LinearMap.IsPositive.conj_adjoint, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Polynomial.IsSplittingField.finiteDimensional, LinearMap.ker_toContinuousLinearMap, Lagrange.nodalWeight_eq_eval_derivative_nodal, IntermediateField.isScalarTower_mid, IntermediateField.finSepDegree_bot, ZLattice.comap_refl, hasStrictFDerivAt_exp_smul_const_of_mem_ball, exists_pos_right_iff_sameRay_and_ne_zero, Hyperreal.tendsto_atTop_iff, RCLike.norm_nnqsmul, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, LinearMap.IsSymmetric.pow, hasFDerivAt_prodMk_right, Padic.valuation_inv, DoubleCentralizer.toProdMulOppositeHom_apply, IsGalois.ofDual_intermediateFieldEquivSubgroup_apply, ContinuousLinearMap.coeFn_compLp', gal_X_isSolvable, LinearMap.withSeminorms_induced, Valuation.HasExtension.algebraMap_mem_maximalIdeal_iff, RatFunc.num_denom_neg, IsCyclotomicExtension.discr_prime_pow_ne_two', ContinuousLinearEquiv.mfderivWithin_eq, Finpartition.IsEquipartition.card_interedges_sparsePairs_le', MDifferentiableWithinAt.smul_section, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, degree_radical_le, ContMDiffOn.smul_section, curveIntegralFun_zero, perfectClosure.isPurelyInseparable, AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn, iteratedFDeriv_add_apply', hasFDerivAtFilter_intCast, iteratedFDeriv_succ_apply_left, UniformSpace.Completion.coe_inv, Polynomial.valuation_X_eq_neg_one, IsSymmSndFDerivAt.eq, hasFDerivAtFilter_one, le_iff_norm_sqrt_mul_sqrt_inv, Submodule.orthogonalProjectionFn_mem, LinearMap.IsPositive.re_inner_nonneg_left, iteratedFDeriv_const_of_ne, IntermediateField.isSeparable_adjoin_iff_isSeparable, hasDerivWithinAt_sub_const_iff, AbsoluteValue.eq_trivial_of_isEquiv_trivial, Lagrange.eval_basis_not_at_node, ContinuousLinearMapWOT.zero_apply, Asymptotics.superpolynomialDecay_mul_param_iff, LinearMap.range_lt_top_of_det_eq_zero, FDRep.finrank_hom_simple_simple, AffineSubspace.sOppSide_smul_vsub_vadd_right, HasFDerivWithinAt.list_prod', NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, QuadraticMap.hasLineDerivAt, prod_galRestrict_eq_norm, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', fderiv_inv', IntermediateField.sepDegree_top, Module.Basis.traceDual_eq_iff, ContinuousLinearEquiv.contDiff, ContinuousLinearMapWOT.ext_inner_iff, IsGaloisGroup.fixedPoints_eq_bot, ContinuousLinearMap.coeFn_ofIsClosedGraph, RatFunc.monic_denom, NormedSpace.exp_eq_expSeries_sum, ZMod.pow_div_two_eq_neg_one_or_one, Trivialization.localFrame_apply_of_mem_baseSet, Continuous.fderiv_one, GaloisField.splits_zmod_X_pow_sub_X, VectorField.mlieBracket_const_smul_right, norm_inner_div_norm_mul_norm_eq_one_iff, MeasureTheory.lpMeas.aestronglyMeasurable, IsLocalMinOn.fderivWithin_eq_zero, tendsto_zero_geometric_tsum_pnat, RCLike.geometric_hahn_banach_open_point, WeierstrassCurve.Affine.Point.map_id, CFC.rpow_sqrt, FormalMultilinearSeries.comp_assoc, PiTensorProduct.tprodL_coe, ModelWithCorners.extChartAt_transContinuousLinearEquiv_target, HasFPowerSeriesWithinAt.comp, Submodule.mem_iff_norm_starProjection, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, Real.hasDerivAt_negMulLog, Localization.subalgebra.instIsFractionRingSubtypeMemSubalgebra, continuousMultilinearCurryFin1_apply, IsCoercive.antilipschitz, PiLp.hasStrictFDerivAt_toLp, IsAlgClosed.perfectRing, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, LineDifferentiableAt.smul, hasFDerivWithinAt_id, Orthonormal.comp_linearIsometry, hasStrictFDerivAt_euclidean, LinearMap.dualAnnihilator_ker_eq_range_flip, hasFDerivAt_finset_prod, Hyperreal.coeRingHom_toFun, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm, unitary.linearIsometryEquiv_coe_apply, HilbertBasis.finite_spans_dense, nnnorm_cfcₙ_lt, Trivialization.coordChangeL_prod, mfderiv_id, IntermediateField.extendScalars_le_extendScalars_iff, NormedSpace.exp_eq_ofScalarsSum, RatFunc.toFractionRing_eq, IntermediateField.coe_one, Finset.centerMass_mem_convexHull_of_nonpos, Polynomial.int_cyclotomic_spec, mfderivWithin_comp_of_eq
zpow 📖	CompOp	3 math math: zpow_neg', zpow_zero', zpow_succ'

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
div_eq_mul_inv 📖	mathematical	—	toDiv NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring CommRing.toRing toCommRing toInv	—	—
inv_zero 📖	mathematical	—	toInv AddMonoid.toZero AddCommMonoid.toAddMonoid NonUnitalNonAssocSemiring.toAddCommMonoid NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring CommRing.toRing toCommRing	—	—
mul_inv_cancel 📖	mathematical	—	NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring CommRing.toRing toCommRing toInv Semiring.toOne	—	—
nnqsmul_def 📖	mathematical	—	nnqsmul NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring CommRing.toRing toCommRing NNRat.cast toNNRatCast	—	—
nnratCast_def 📖	mathematical	—	NNRat.cast toNNRatCast toDiv Semiring.toNatCast Ring.toSemiring CommRing.toRing toCommRing NNRat.num NNRat.den	—	—
qsmul_def 📖	mathematical	—	qsmul NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring CommRing.toRing toCommRing toRatCast	—	—
ratCast_def 📖	mathematical	—	toRatCast toDiv Ring.toIntCast CommRing.toRing toCommRing Semiring.toNatCast Ring.toSemiring	—	—
toNontrivial 📖	mathematical	—	Nontrivial	—	—
zpow_neg' 📖	mathematical	—	zpow toInv	—	—
zpow_succ' 📖	mathematical	—	zpow NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring Ring.toSemiring CommRing.toRing toCommRing	—	—
zpow_zero' 📖	mathematical	—	zpow Semiring.toOne Ring.toSemiring CommRing.toRing toCommRing	—	—

NNRat

Definitions

Name	Category	Theorems
castRec 📖	CompOp	—
smulDivisionSemiring 📖	CompOp	9 math math: SubfieldClass.nnqsmul_mem, SubfieldClass.coe_nnqsmul, Nonneg.coe_nnqsmul, LinearOrderedSemifield.toPosSMulStrictMono_rat, Nonneg.mk_nnqsmul, smul_one_eq_cast, smul_def, nnqsmul_nonneg, selfAdjoint.val_nnqsmul

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cast_def 📖	mathematical	—	cast DivisionSemiring.toNNRatCast DivInvMonoid.toDiv GroupWithZero.toDivInvMonoid DivisionSemiring.toGroupWithZero AddMonoidWithOne.toNatCast AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne Semiring.toNonAssocSemiring DivisionSemiring.toSemiring num den	—	DivisionSemiring.nnratCast_def
smul_def 📖	mathematical	—	NNRat smulDivisionSemiring Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring DivisionSemiring.toSemiring cast DivisionSemiring.toNNRatCast	—	DivisionSemiring.nnqsmul_def
smul_one_eq_cast 📖	mathematical	—	NNRat smulDivisionSemiring AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne Semiring.toNonAssocSemiring DivisionSemiring.toSemiring cast DivisionSemiring.toNNRatCast	—	smul_def mul_one

Rat

Definitions

Name	Category	Theorems
castRec 📖	CompOp	—
smulDivisionRing 📖	CompOp	6 math math: SubfieldClass.coe_qsmul, SubfieldClass.qsmul_mem, selfAdjoint.val_qsmul, smul_one_eq_cast, smul_def, LinearOrderedField.toPosSMulStrictMono_rat

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cast_def 📖	mathematical	—	DivisionRing.toRatCast DivInvMonoid.toDiv DivisionRing.toDivInvMonoid AddGroupWithOne.toIntCast Ring.toAddGroupWithOne DivisionRing.toRing AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne	—	DivisionRing.ratCast_def
cast_mk' 📖	mathematical	—	DivisionRing.toRatCast DivInvMonoid.toDiv DivisionRing.toDivInvMonoid AddGroupWithOne.toIntCast Ring.toAddGroupWithOne DivisionRing.toRing AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne	—	cast_def
ofScientific_eq_ofScientific 📖	—	—	—	—	—
smul_def 📖	mathematical	—	smulDivisionRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing DivisionRing.toRing DivisionRing.toRatCast	—	DivisionRing.qsmul_def
smul_one_eq_cast 📖	mathematical	—	smulDivisionRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne DivisionRing.toRing DivisionRing.toRatCast	—	smul_def mul_one

Semifield

Definitions

Name	Category	Theorems
nnqsmul 📖	CompOp	1 math math: nnqsmul_def
toCommGroupWithZero 📖	CompOp	419 math math: ArithmeticFunction.vonMangoldt.residueClass_eq, Polynomial.degree_normalize, ordinaryHypergeometric_sum_eq, Polynomial.coe_normUnit_of_ne_zero, monovaryOn_inv₀, HasStrictDerivAt.to_localInverse, tendsto_inv_atTop_zero, RatFunc.num_div, NormedSpace.expSeries_eq_ofScalars, inv_atBot₀, Lagrange.eval_interpolate_not_at_node', Lagrange.nodalWeight_eq_eval_nodal_erase_inv, AdjoinRoot.minpoly_root, round_neg_two_inv, Algebra.normalizedTrace_eq_of_finiteDimensional, Int.log_inv, DirichletCharacter.LSeries_eulerProduct_tprod, Meromorphic.fun_inv, Polynomial.div_def, Asymptotics.SuperpolynomialDecay.param_inv_mul, ValuationSubring.mem_or_inv_mem, OpenPartialHomeomorph.hasDerivAt_symm, spectrum.inv₀_mem_iff, norm_smul_inv_norm', Lagrange.leadingCoeff_basis, Int.ceil_div_ceil_inv_sub_one, DirichletCharacter.LSeries_modOne_eq, Quaternion.coe_inv, round_two_inv, DirichletCharacter.LSeriesSummable_of_one_lt_re, minpoly.eq_of_irreducible, HasStrictDerivAt.of_local_left_inverse, inv_atTop₀, ValuativeRel.inv_srel_one, IsStrictOrderedRing.toContinuousInv₀, NormedSpace.exp_series_hasSum_exp', Lagrange.eval_interpolate_not_at_node, DiffContOnCl.inv, DirichletCharacter.LSeries_twist_vonMangoldt_eq, Polynomial.abc, AddCircle.homeomorphAddCircle_apply_mk, Subring.center.coe_inv, sub_inv_antitoneOn_Ioi, two_inv_lt_one, DirichletCharacter.LFunction_eq_LSeries, difference_quotients_converge_uniformly, AntivaryOn.inv_left₀, hasFDerivWithinAt_inv, DirichletCharacter.norm_LSeries_product_ge_one, Ring.choose_eq_smul, norm_smul_inv_norm, inv_pow_le_inv_pow_of_le, inv_pow_anti, Polynomial.roots_degree_eq_one, deriv_fun_inv'', Asymptotics.isTheta_inv, Set.inv_Iio₀, Set.inv_Ioo_0_right, inv_le_inv_of_neg, inv_pow_strictAnti, antivary_inv₀, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, DirichletCharacter.LFunction_changeLevel, MeromorphicAt.inv_iff, inv_strictAntiOn, inv_lt_zero', HasLineDerivAt.tendsto_slope_zero_right, ContDiffAt.inv, Hyperreal.infinitesimal_inv_of_infinite, le_inv_of_neg, antivaryOn_inv_left₀, DirichletCharacter.norm_le_one, Derivation.leibniz_div, NormedSpace.exp_eq_tsum, DirichletCharacter.mul_delta, Nonneg.inv_mk, EulerProduct.eulerProduct_completely_multiplicative, Quaternion.inv_def, Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField, IsAlgebraic.inv, Hyperreal.inv_omega, Hyperreal.infinite_iff_infinitesimal_inv, abs_inv, DirichletCharacter.unit_norm_eq_one, ValuationRing.iff_isInteger_or_isInteger, Int.clog_of_right_le_one, ArithmeticFunction.vonMangoldt.residueClass_apply, MeromorphicOn.divisor_inv, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, divRadical_dvd_derivative, Polynomial.leadingCoeff_mul_prod_normalizedFactors, inv_pow_lt_inv_pow_of_lt, NormedSpace.expSeries_sum_eq, IsLocalization.AtPrime.equivQuotientMapOfIsMaximal_symm_apply_mk, NormedSpace.smul_mem_polar, FractionalIdeal.one_div_spanSingleton, monovary_inv_right₀, DirichletCharacter.LSeriesSummable_mul, ValuativeRel.one_rel_inv, IntermediateField.inv_mem', TrivSqZeroExt.eq_smul_exp_of_ne_zero, Derivation.leibniz_inv, RingPreordering.inv_mem, Antivary.inv_right₀, DirichletCharacter.LSeries_changeLevel, MvPowerSeries.constantCoeff_inv, derivWithin_inv, FractionalIdeal.count_ne_zero, RCLike.normSq_inv, RatFunc.numDenom_div, MvPowerSeries.coeff_inv, geom_sum_lt, sub_inv_antitoneOn_Icc_left, NormedSpace.norm_expSeries_summable_of_mem_ball', tendsto_inv_nhdsGT_zero, HasLineDerivAt.tendsto_slope_zero, HasStrictDerivAt.to_local_left_inverse, ordinaryHypergeometricSeries_apply_eq', differentiableAt_inv_iff, MonovaryOn.inv_left₀, PowerSeries.normalized_count_X_eq_of_coe, ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier, Hyperreal.infinitePos_iff_infinitesimal_inv_pos, traceForm_dualSubmodule_adjoin, Antivary.inv_left₀, Polynomial.roots_C_mul_X_add_C, AddCircle.equivAddCircle_apply_mk, DirichletCharacter.LSeries.mul_mu_eq_one, meromorphicNFAt_inv, HasLineDerivAt.tendsto_slope_zero_left, ValuationRing.isFractionRing_iff, EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers, antivary_inv_right₀, deriv_inv, Char.card_pow_card, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, tendsto_inv_atBot_nhdsLT_zero, Algebra.norm_inv, NormedSpace.expSeries_summable', HasDerivAt.tendsto_slope_zero_left, Subalgebra.inv_mem_of_root_of_coeff_zero_ne_zero, EulerProduct.eulerProduct_completely_multiplicative_tprod, Quaternion.normSq_inv, meromorphicOrderAt_inv, Algebra.normalizedTrace_eq_of_fininteDimensional, inv_nhdsGT_zero, FractionalIdeal.mul_generator_self_inv, RCLike.inv_im, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, MonovaryOn.inv_right₀, NormedSpace.expSeries_apply_eq, MvPowerSeries.C_inv, ContDiffWithinAt.inv, tendsto_inv_atTop_nhdsGT_zero, hasDerivAt_inv, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, tendsto_inv_atBot_zero, PowerSeries.constantCoeff_inv, spectrum.inv₀_mem_inv_iff, MeromorphicOn.inv_iff, Hyperreal.inv_epsilon, inv_lt_inv_of_neg, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, sum_Ioo_inv_sq_le, meromorphicTrailingCoeffAt_inv, EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers, CancelDenoms.inv_subst, ordinaryHypergeometric_eq_tsum, gauge_smul_left_of_nonneg, meromorphicNFOn_inv, GenContFract.convs_succ, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, cfc_inv, antivaryOn_inv₀, InnerProductSpace.gramSchmidtOrthonormalBasis_apply_of_orthogonal, Field.isSeparable_inv, contDiffAt_inv, Mathlib.Tactic.Ring.inv_zero, EulerProduct.eulerProduct_completely_multiplicative_hasProd, jacobiSum_eq_gaussSum_mul_gaussSum_div_gaussSum, Hyperreal.IsSt.inv, DirichletCharacter.LSeriesSummable_twist_vonMangoldt, Monovary.inv_right₀, Antivary.inv₀, DirichletCharacter.convolution_twist_vonMangoldt, Height.mulHeight₁_inv, Hyperreal.coe_inv, NormedField.continuousAt_inv, ValuativeRel.inv_rel_one, Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv, MeromorphicOn.inv, hasDerivAt_iff_tendsto_slope_zero, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, spectrum.inv₀_mem, ordinaryHypergeometricSeries_apply_eq, Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zero, hasStrictFDerivAt_inv, IsFractionRing.associated_num_den_inv, fderiv_inv, inv_sub_inv, Monovary.inv_left₀, Nonneg.coe_inv, slope_fun_def, Height.logHeight₁_inv, natDegree_radical_le, DirichletCharacter.LSeriesSummable_iff, deriv_inv'', selfAdjoint.val_inv, HasFDerivAt.lim, cfc_inv_id, NormedSpace.norm_expSeries_summable', ValuativeRel.one_vlt_inv, SimpleGraph.FarFromTriangleFree.lt_half, NormedSpace.expSeries_apply_eq', contDiffOn_inv, DirichletCharacter.absicssaOfAbsConv_eq_one, RatFunc.denom_div, val_inv_cfcUnits, MulChar.star_apply', Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap, divRadical_dvd_wronskian_right, Monovary.inv₀, inv_antitoneOn_Icc_right, stdSimplex.barycenter_apply, ContinuousLinearEquiv.det_coe_symm, Polynomial.div_C, MeromorphicOn.divisor_fun_inv, inv_nhdsLT_zero, Polynomial.leadingCoeff_preHilbertPoly, Hyperreal.infinitesimal_iff_infinite_inv, ValuationSubring.mem_or_inv_mem', instContMDiffInv₀ModelWithCornersSelf, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, DirichletCharacter.norm_LFunction_product_ge_one, spectrum.map_inv, derivWithin_inv', Polynomial.normalize_eq_self_iff_monic, Positive.coe_inv, HasDerivWithinAt.inv, DirichletCharacter.LSeries_eulerProduct_hasProd, RCLike.inv_pos_of_pos, ValuationSubring.inv_mem_nonunits_iff, logDeriv_inv, MonovaryOn.inv₀, Asymptotics.IsTheta.inv, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, tsum_dirichletSummand, IsStrictOrderedRing.toHasContinuousInv₀, hasLineDerivAt_iff_tendsto_slope_zero, Algebra.normalizedTrace_minpoly, ValuationSubring.mem_nonunits_iff_or, Polynomial.coeff_inv_units, DirichletCharacter.LSeries_eulerProduct_exp_log, monovaryOn_inv_left₀, iter_deriv_inv, PowerSeries.coeff_inv, ContDiff.inv, RCLike.inv_def, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, MulChar.star_eq_inv, fderivWithin_inv, FractionalIdeal.div_spanSingleton, RatFunc.num_div_dvd', ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq, inv_smul_lt_iff_of_neg, iter_deriv_inv', Asymptotics.IsLittleOTVS.tendsto_inv_smul, Algebra.normalizedTrace_def, Units.continuousOn_inv₀_spectrum, IsAbsoluteValue.abv_inv, IntermediateField.coe_inv, Polynomial.mem_normalizedFactors_iff, Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg, tendsto_inv_nhdsLT_zero, Seminorm.smul_closedBall_preimage, RCLike.inv_pos, IsLocalMin.inv, HahnSeries.inv_def, smul_inv_le_iff_of_neg, Asymptotics.SuperpolynomialDecay.inv_param_mul, Filter.Tendsto.inv_tendsto_nhdsLT_zero, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, Polynomial.roots_C_mul_X_sub_C, ValuativeRel.one_vle_inv, smul_inv_lt_iff_of_neg, Asymptotics.IsEquivalent.inv, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, Seminorm.smul_ball_preimage, DirichletCharacter.not_LSeriesSummable_at_one, lt_inv_of_neg, hasStrictDerivAt_inv, GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv, FractionalIdeal.exists_eq_spanSingleton_mul, AdjoinRoot.minpoly_powerBasis_gen, HasDerivAt.tendsto_slope_zero, sub_one_div_inv_le_two, Filter.Tendsto.inv_tendsto_nhdsGT_zero, iter_deriv_inv_linear_sub, RCLike.conj_inv, IsAlgebraic.inv_iff, monovary_inv₀, AntivaryOn.inv_right₀, sum_Ioc_inv_sq_le_sub, PowerSeries.C_inv, sub_inv_antitoneOn_Icc_right, Hyperreal.st_inv, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, ContDiffOn.inv, LieAlgebra.IsKilling.traceForm_coroot, ValuativeRel.inv_vle_one, toPrincipalIdeal_def, inv_antitoneOn_Ioi, MeromorphicAt.inv, MeromorphicOn.fun_inv, spectrum.inv₀_mem_inv, Meromorphic.inv, HasDerivAt.fun_inv, DirichletCharacter.delta_mul, ValuativeRel.inv_vlt_one, PowerSeries.inv_eq_inv_aux, deriv_inv', LinearEquiv.det_coe_symm, Filter.Tendsto.inv_tendsto_atTop, RCLike.inv_eq_conj, iter_deriv_inv_linear, divRadical_dvd_wronskian_left, DirichletCharacter.convolution_mul_moebius, ValuationRing.isInteger_or_isInteger, monovary_inv_left₀, Nat.inv_pos_of_nat, gauge_smul_left, Derivation.leibniz_div_const, IntermediateField.inv_mem, inv_le_of_neg, IsFractionRing.associated_den_num_inv, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, NormedSpace.expSeries_hasSum_exp_of_mem_ball', Polynomial.div_C_mul, Hyperreal.infinitesimal_pos_iff_infinitePos_inv, Int.log_of_right_le_one, AntivaryOn.inv₀, GenContFract.sub_convs_eq, inv_smul_le_iff_of_neg, homothety_inv_two, IsLocalization.AtPrime.equivQuotMaximalIdeal_symm_apply_mk, ValuativeRel.one_srel_inv, HahnSeries.inv_single, hasDerivWithinAt_inv, DirichletCharacter.modZero_eq_delta, DirichletCharacter.fourierTransform_eq_gaussSum_mulShift, OpenPartialHomeomorph.hasStrictDerivAt_symm, MeromorphicNFAt.inv, algebraMap.coe_inv, ValuationSubring.top_coe_inv, tendsto_algebraMap_inv_atTop_nhds_zero_nat, derivWithin_fun_inv', Subalgebra.inv_mem_of_algebraic, spectrum.resolvent_isBigO_inv, NormedSpace.expSeries_summable_of_mem_ball', Int.neg_log_inv_eq_clog, AddCircle.equivAddCircle_symm_apply_mk, RatFunc.single_inv, DirichletCharacter.LSeries_eulerProduct, RCLike.ofReal_inv, PerfectClosure.mk_inv, Polynomial.monic_normalize, antivaryOn_inv_right₀, inv_lt_of_neg, PowerSeries.smul_inv, two_mul_le_add_mul_sq, Polynomial.mod_def, Int.neg_clog_inv_eq_log, hasFDerivAt_inv, inv_nonpos', HahnSeries.cardSupp_inv_le, ValueDistribution.logCounting_inv, MeromorphicAt.fun_inv, MvPowerSeries.smul_inv, UniformSpace.Completion.hatInv_extends, NumberField.IsCMField.complexConj_torsion, sub_inv_antitoneOn_Iio, Transcendental.linearIndependent_sub_inv, CauSeq.lim_inv, ArchimedeanClass.stdPart_inv, slope_def_module, inv_antitoneOn_Icc_left, Nat.cast_inv_le_one, inv_eq_of_aeval_divX_ne_zero, AddChar.inv_apply_eq_conj, Polynomial.normalizedFactors_cyclotomic_card, antivary_inv_left₀, HasDerivAt.of_local_left_inverse, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, Polynomial.coeff_preHilbertPoly_self, Filter.IsBoundedUnder.isLittleO_sub_self_inv, monovaryOn_inv_right₀, Int.clog_inv, ArchimedeanClass.mk_inv, RCLike.inv_I, HasDerivAt.inv, inv_antitoneOn_Iio, HasDerivWithinAt.fun_inv, Filter.Tendsto.inv_tendsto_atBot, inv_eq_of_root_of_coeff_zero_ne_zero, HasDerivAt.tendsto_slope_zero_right, Polynomial.map_normalize, FractionalIdeal.spanSingleton_inv, AddCircle.homeomorphAddCircle_symm_apply_mk, inv_add_inv, RCLike.inv_re, CompletableTopField.nice, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Lagrange.nodalWeight_eq_eval_derivative_nodal, Padic.valuation_inv, degree_radical_le, UniformSpace.Completion.coe_inv, Lagrange.eval_basis_not_at_node, NormedSpace.exp_eq_ofScalarsSum
toCommSemiring 📖	CompOp	2804 math math: Field.FiniteDimensional.of_exists_primitive_element, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, Pi.comul_eq_adjoint, FiniteField.Extension.frob_apply, RatFunc.instFaithfulSMulPolynomialLaurentSeries, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, TensorProduct.mapInclIsometry_apply, MvPolynomial.vanishingIdeal_anti_mono, LinearMap.IsSymmetric.clm_adjoint_eq, Polynomial.Gal.galActionHom_restrict, AffineSubspace.sOppSide_iff_exists_right, RCLike.conj_re, Polynomial.degree_normalize, TemperedDistribution.lineDerivOpCLM_eq, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', PiTensorProduct.mapL_id, Algebra.IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, Algebra.normalizedTrace_map, AlgEquiv.restrictNormal_trans, IntermediateField.extendScalars_toSubfield, ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, MeasureTheory.lpNorm_conj, Algebra.normalizedTrace_algebraMap_eq_id, TensorProduct.enorm_lid, IntermediateField.finInsepDegree_top, InfiniteGalois.normal_iff_isGalois, LinearMap.BilinForm.dualSubmoduleParing_spec, LinearMap.IsSymmetric.conj_eigenvalue_eq_self, RatFunc.ofFractionRing_mk', HasStrictFDerivAt.fun_mul', unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, TensorProduct.inner_tmul, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, HasMFDerivAt.mul, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, LinearMap.ortho_smul_right, Orthonormal.inner_left_finsupp, ordinaryHypergeometric_sum_eq, LeftInvariantDerivation.lift_zero, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, norm_cfcₙHom, IntermediateField.aeval_gen_minpoly, OrthonormalBasis.orthogonalProjection_eq_sum, IntermediateField.adjoin_eq_top_iff_of_isAlgebraic, IsIntegralClosure.rank, MvPolynomial.radical_le_vanishingIdeal_zeroLocus, strictConvexOn_iff_slope_strict_mono_adjacent, ValuationSubring.coe_mem_principalUnitGroup_iff, ValuationSubring.valuation_lt_one_iff, IsLocalRing.ResidueField.algebraMap_residue, IntermediateField.fieldRange_le, LinearMap.adjoint_adjoint, IntermediateField.LinearDisjoint.iff_inf_eq_bot, IntermediateField.normal_inf, TensorProduct.ext_iff_inner_left, Valuation.FiniteField.algebraMap_le_one, binomialSeries_eq_ordinaryHypergeometricSeries, InnerProductSpace.toLinearIsometry_toDual, IsUltrametricDist.algNormOfAlgEquiv_extends, Valuation.FiniteField.algebraMap_eq_one, AlgEquiv.coe_adjoinSingletonEquivAdjoinRootMinpoly_symm, galRestrict_symm_algebraMap_apply, Subspace.dualAnnihilator_dualAnnihilator_eq_map, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, RatFunc.num_div, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal, IsSelfAdjoint.commute_cfcHom, Real.hasFDerivAt_fourierChar_neg_bilinear_left, QuadraticMap.lineDeriv, cfcₙ_norm_nonneg, IsGalois.tower_top_intermediateField, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, hasStrictFDerivAt_exp_of_mem_ball, hasFDerivAt_iff_hasGradientAt, Orientation.ne_iff_eq_neg, cfcₙHom_apply_mem_elemental, SimpleGraph.lapMatrix_toLinearMap₂', FormalMultilinearSeries.ofScalars_apply_eq', ValuationSubring.image_maximalIdeal, Ideal.exists_comap_galRestrict_eq, NumberField.canonicalEmbedding.mem_span_latticeBasis, hasStrictFDerivAt_list_prod_finRange', NumberField.integralBasis_apply, InnerProductSpace.rankOne_one_left_eq_innerSL, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow, FormalMultilinearSeries.ofScalars_eq_zero_of_scalar_zero, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, IntermediateField.adjoin.finrank, Subalgebra.spectrum_sUnion_connectedComponentIn, ValuationSubring.integralClosure_algebraMap_injective, ContMDiffMap.coeFnAlgHom_apply, IntermediateField.algebraMap_mem, NormedSpace.expSeries_summable_of_mem_ball, LinearMap.IsSymmetric.restrictScalars, PrimeSpectrum.residueField_specComap, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, PiTensorProduct.mapLMonoidHom_apply, NumberField.prod_nonarchAbsVal_eq, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, ContinuousAlternatingMap.isEmbedding_restrictScalars, HasFDerivWithinAt.pow, Valuation.mem_maximalIdeal_iff, convex_iff_ordConnected, WeakDual.isCompact_polar, nnnorm_cfc_lt, Representation.IsIrreducible.instIsSimpleModuleMonoidAlgebraAsModule, fderivWithin_fun_smul, IsGalois.card_aut_eq_finrank, IntermediateField.extendScalars_sup, NumberField.IsCMField.zpowers_complexConj_eq_top, IntermediateField.coe_algebraMap_over_bot, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, Matrix.IsHermitian.det_abs, Algebra.normalizedTrace_surjective, ModularForm.mul_slash, Subspace.instModuleDualFiniteDimensional, Algebra.normalizedTrace_eq_of_finiteDimensional, hasFDerivAt_multiset_prod, NumberField.FinitePlace.mk_apply, LinearMap.isPositive_adjoint_comp_self, autAdjoinRootXPowSubCEquiv_root, BoundedContinuousFunction.algebraMap_apply, spectrum.subset_closedBall_norm_mul, spectrumRestricts_iff, spectrum.instCompactSpace, NumberField.instFreeIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, concaveOn_iff_slope_anti_adjacent, SeparableClosure.isSepClosed, MeasureTheory.convolution_mul, Matrix.spectrum_toEuclideanLin, RatFunc.num_div_dvd, mem_subalgebraEquivIntermediateField, Submodule.instStrictConvexSpace, InnerProductSpace.isIdempotentElem_rankOne_self, Matrix.cstar_nnnorm_def, minpoly.algEquiv_apply, Algebra.isInvariant_of_isGalois, IsPurelyInseparable.elemExponent_min', IntermediateField.isScalarTower_mid', ConjRootClass.aeval_minpoly_iff, Polynomial.Gal.restrict_smul, StrongDual.polarSubmodule_eq_setOf, NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd, ContinuousLinearMap.isUniformEmbedding_restrictScalars, RCLike.star_def, Asymptotics.isLittleOTVS_one, finrank_quotient_span_eq_natDegree_norm, AlgebraicGeometry.functionField_isFractionRing_of_isAffineOpen, HasDerivAtFilter.comp_hasFDerivAtFilter, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, NumberField.InfinitePlace.nat_card_stabilizer_eq_one_or_two, NumberField.RingOfIntegers.instSMulDistribClass, Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, IsGaloisGroup.iff_isFractionRing, NumberField.InfinitePlace.isUnramified_iff_card_stabilizer_eq_one, WeakDual.isClosed_image_polar_of_mem_nhds, one_add_cpow_hasFPowerSeriesAt_zero, NumberField.IsCMField.equivInfinitePlace_symm_apply, spectrum.inv₀_mem_iff, IsIntegralClosure.isFractionRing_of_finite_extension, NumberField.InfinitePlace.IsUnramified.comap_algHom, RCLike.inner_apply', Polynomial.fiberEquivQuotient_tmul, quasispectrumRestricts_iff_spectrumRestricts_inr', LinearMap.IsSymmetric.diagonalization_apply_self_apply, IntermediateField.coe_bot, Subspace.dualLift_of_subtype, Ideal.ramificationIdx_le_finrank, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, fderivWithin_fun_pow', flip_innerSL_real, AffineIsometryEquiv.ofTop_apply, LieAlgebra.finrank_engel, PadicComplex.coe_eq, RCLike.sub_conj, OrthonormalBasis.toBasis_tensorProduct, TensorProduct.congrIsometry_refl_refl, Field.Emb.Cardinal.directed_filtration, Subspace.dualRestrict_comp_dualLift, isClosedEmbedding_cfcₙAux, LieModule.traceForm_eq_sum_finrank_nsmul', IntermediateField.lift_insepDegree_bot', Ring.ordFrac_eq_div, LeftInvariantDerivation.coe_derivation, TensorProduct.enorm_comm, innerSL_apply_apply, fderiv_multiset_prod, HasFPowerSeriesWithinOnBall.restrictScalars, CFC.abs_eq_cfcₙ_coe_norm, AlgebraicGeometry.ValuativeCommSq.isFractionRing, IsDedekindDomain.HeightOneSpectrum.instFaithfulSMulSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, LinearMap.adjoint_innerₛₗ_apply, EuclideanSpace.inner_single_left, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, Valuation.HasExtension.instIsLocalHomSubtypeMemValuationSubringValuationSubringRingHomAlgebraMap, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, Unitization.splitMul_apply, ContinuousLinearMap.toBilinForm_apply, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, LinearMap.adjoint_eq_toCLM_adjoint, HasFDerivAt.fun_mul, minpoly.eq_iff_aeval_eq_zero, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_apply, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, IsPurelyInseparable.insepDegree_eq, MvPolynomial.le_vanishingIdeal_zeroLocus, LeftInvariantDerivation.left_invariant', Field.insepDegree_le_rank, selfAdjoint.expUnitaryPathToOne_apply, algebraMap.coe_logDeriv, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Field.Emb.Cardinal.filtration_succ, LieAlgebra.IsKilling.rootSystem_coroot_apply, Irreducible.natSepDegree_eq_one_iff_of_monic', algebraicClosure.algebraicClosure_eq_bot, NumberField.FinitePlace.norm_def', Matrix.spectrum_toLpLin, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_right, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, NumberField.mixedEmbedding.mem_idealLattice, IsFractionRing.fieldEquivOfAlgEquivHom_apply, InnerProductSpace.Core.inner_smul_left, Polynomial.int_coeff_eq, HasDerivAt.comp_hasFDerivAt_of_eq, InnerProductSpace.toDual_symm_apply, IsConformalMap.is_complex_or_conj_linear, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, NumberField.Units.regOfFamily_eq_det, FiniteField.frobeniusAlgEquivOfAlgebraic_apply, InfiniteGalois.normalAutEquivQuotient_apply, IsPurelyInseparable.elemExponent_min, RCLike.conj_nat_cast, Polynomial.Monic.natSepDegree_eq_one_iff_of_irreducible', instIsFractionRing, LeftInvariantDerivation.left_invariant, PerfectField.separable_of_irreducible, PowerSeries.maximalIdeal_eq_span_X, FractionalIdeal.isFractional_div_of_ne_zero, WeierstrassCurve.Projective.dblU_smul, NumberField.FinitePlace.embedding_apply, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, IntermediateField.isAlgebraic_tower_bot, ConjRootClass.separable_minpoly, Subspace.dualCoannihilator_dualAnnihilator_eq, MeasureTheory.charFun_toDual_symm_eq_charFunDual, IsGaloisGroup.fixedPoints_top, Normal.splits', IntermediateField.mem_adjoin_iff, IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply, isConjRoot_iff_exists_algEquiv, IsPurelyInseparable.finInsepDegree_eq, PreInnerProductSpace.Core.smul_left, Matrix.PosSemidef.sqrt_eq_zero_iff, IntermediateField.mem_carrier, IsPurelyInseparable.elemExponent_def', Differentiable.fderiv_norm_rpow, NumberField.InfiniteAdeleRing.algebraMap_apply, IntermediateField.botEquiv_symm, Normal.minpoly_eq_iff_mem_orbit, TensorProduct.ext_iff_inner_right_threefold', Field.finSepDegree_eq_of_isAlgClosed, RCLike.is_real_TFAE, ValuationSubring.ofPrime_valuation_eq_one_iff_mem_primeCompl, TensorProduct.toLinearEquiv_lidIsometry, NormedSpace.exp_series_hasSum_exp', HasFPowerSeriesOnBall.restrictScalars, contractLeft_assoc_coevaluation, Field.FiniteDimensional.of_finite_intermediateField, FiniteField.frobeniusAlgHom_apply, WeierstrassCurve.Projective.Point.toAffine_smul, Orientation.eq_or_eq_neg, IsIntegralClosure.isLocalization, HasStrictFDerivAt.mul', NumberField.RingOfIntegers.instIsFractionRing, inner_gradientWithin_right, fderiv_fun_pow, ValuationSubring.valuation_unit, IsGalois.card_fixingSubgroup_eq_finrank, Subfield.relfinrank_eq_finrank_of_le, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, InnerProductSpace.smul_left, Polynomial.SplittingFieldAux.algebraMap_succ, isGalois_iff_isGalois_top, ModularForm.prod_slash, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, Polynomial.hilbertPoly_smul, hasStrictFDerivAt_exp_smul_const_of_mem_ball', ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Matrix.mem_spectrum_iff_isRoot_charpoly, Field.localization_map_bijective, fderiv_fun_smul, Field.finSepDegree_mul_finInsepDegree, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, IsPurelyInseparable.finrank_eq_pow, starConvex_iff_ordConnected, FractionalIdeal.coe_extendedHomₐ_eq_span, LinearMap.toMatrixOrthonormal_reindex, AlgebraicGeometry.functionField_isFractionRing_of_affine, HasStrictFDerivAt.pow, InfiniteGalois.mem_bot_iff_fixed, exists_pos_right_iff_sameRay, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, RCLike.mul_conj, RCLike.norm_conj, CyclotomicRing.instIsFractionRingCyclotomicFieldOfIsDomainOfNeZeroCast, LinearMap.ortho_smul_left, HasStrictFDerivAt.const_mul, Field.isSeparable_algebraMap, Algebra.normalizedTrace_comp_algHom, Polynomial.Monic.eq_X_pow_char_pow_sub_C_pow_of_natSepDegree_eq_one, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, InnerProductSpace.inner_left_rankOne_apply, Polynomial.IsSplittingField.splits_iff, cfcₙHom_nnreal_eq_restrict, AlgebraicClosure.maxIdeal.isMaximal, IsFractionRing.mk'_eq_one_iff_eq, HasFDerivAt.finset_prod, IntermediateField.normal_iff_forall_map_eq, Subspace.dualAnnihilator_dualAnnihilator_eq, PowerSeries.derivative_inv', NumberField.InfinitePlace.IsUnramified.stabilizer_eq_bot, HasFDerivAt.norm_sq, IntermediateField.extendScalars_injective, polynomialFunctions.starClosure_topologicalClosure, ConjRootClass.minpoly.map_eq_prod, innerₛₗ_apply_apply, NumberField.Units.pos_at_place, fderiv_fun_pow', minpoly.aux_inj_roots_of_min_poly, autAdjoinRootXPowSubCEquiv_symm_smul, Ring.choose_eq_smul, ContinuousLinearMap.eq_adjoint_iff, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, RCLike.smul_re, IsFractionRing.mk'_eq_div, IntermediateField.LinearDisjoint.map', spectrum.nonempty_of_isAlgClosed_of_finiteDimensional, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, Algebra.instFiniteResidueFieldOfQuasiFiniteAt, segment_eq_uIcc, ModularForm.prod_slash_sum_weights, WeierstrassCurve.Projective.add_of_Z_eq_zero, NumberField.InfinitePlace.card_stabilizer, gelfandStarTransform_apply_apply, IntermediateField.restrictScalars_normal, RCLike.nonUnitalContinuousFunctionalCalculus, HasDerivAt.hasGradientAt, IntermediateField.isScalarTower, IsFractionRing.fieldEquivOfAlgEquiv_trans, FormalMultilinearSeries.ofScalars_apply_eq, NormedSpace.Dual.toWeakDual_continuous, HasFDerivWithinAt.const_mul, ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator, IsGalois.mem_range_algebraMap_iff_fixed, Algebra.FormallySmooth.adjoin_of_algebraicIndependent, ContinuousMultilinearMap.norm_smulRightL_le, tensorIteratedFDerivTwo_eq_iteratedFDeriv, IntermediateField.algebraAdjoinAdjoin.instIsAlgebraicSubtypeMemSubalgebraAdjoinAdjoin, Algebra.normalizedTrace_algebraMap, IsSelfAdjoint.adjoint_eq, isPurelyInseparable_iff_fd_isPurelyInseparable, Algebra.WeaklyQuasiFiniteAt.finite_residueField, HasStrictFDerivAt.star, openSegment_eq_Ioo, ContinuousMultilinearMap.norm_mkPiAlgebra_le, AlgEquiv.restrictNormalHom_surjective, spectrum_diagonal, Field.finInsepDegree_self, zpow_zero', TensorProduct.adjoint_map, IsUltrametricDist.invariantExtension_apply, exists_nonneg_left_iff_sameRay, LinearIsometryEquiv.lTensor_apply, PowerBasis.equivAdjoinSimple_symm_aeval, FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal, Orientation.map_eq_neg_iff_det_neg, HasFDerivAt.star, NumberField.instFiniteDimensional, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, ContinuousLinearMap.isPositive_self_comp_adjoint, LinearMap.adjoint_toContinuousLinearMap, FunctionField.ringOfIntegers.instIsIntegralClosureSubtypeMemSubalgebraPolynomial, IntermediateField.lift_adjoin_simple, spectrum.isOpen_resolventSet, NumberField.InfinitePlace.smul_apply, algebraicClosure.normalClosure_eq_self, LDL.lowerInv_eq_gramSchmidtBasis, IntermediateField.AdjoinDouble.normal_algebraicClosure, algebraicClosure.map_eq_of_algebraicClosure_eq_bot, ContinuousLinearMap.toSesqForm_apply_coe, IsPurelyInseparable.exists_pow_mem_range_tensorProduct, finrank_algHom, FiniteField.orderOf_frobeniusAlgEquivOfAlgebraic, NormedSpace.expSeries_apply_eq_div', Polynomial.mem_iff_eq_smul_annIdealGenerator, LinearMap.rank_diagonal, NumberField.RingOfIntegers.withValEquiv_symm_apply, LinearIsometryEquiv.adjoint_eq_symm, TensorProduct.mapIsometry_id_id, galRestrict'_id, ContinuousAlternatingMap.toAlternatingMap_curryLeft, Matrix.toEuclideanLin_apply, InfiniteGalois.krullTopology_mem_nhds_one_iff_of_isGalois, FiniteField.coe_frobeniusAlgEquivOfAlgebraic, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, HasFDerivWithinAt.mul, Polynomial.IsSplittingField.adjoin_rootSet, VectorFourier.fourierPowSMulRight_eq_comp, AffineSubspace.sSameSide_iff_exists_left, RootPairing.restrictScalars_pairing, fderivWithin_const_mul, HasFDerivWithinAt.multiset_prod, Algebra.instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced, IntermediateField.isAlgebraic_adjoin_iff_top, Algebra.isGeometricallyReduced_iff, Field.sepDegree_self, FiniteField.card_algEquiv_extension, Orthonormal.basisTensorProduct, IntermediateField.inf_toSubalgebra, algebraicClosure.isAlgebraic, NumberField.ComplexEmbedding.IsConj.coe_stabilizer_mk, fderivWithin_star, PiTensorProduct.mapL_one, NumberField.Units.coe_mul, IsFractionRing.exists_reduced_fraction, RCLike.conjCLE_apply, IsGalois.normalClosure, ValuationSubring.subtype_injective, AlgEquiv.adjoinSingletonEquivAdjoinRootMinpoly_symm_toAlgHom, Unitization.nnnorm_def, RatFunc.coe_X, UpperHalfPlane.coe_pos_real_smul, IsPurelyInseparable.iterateFrobenius_algebraMap, IsUltrametricDist.invariantExtension_extends, HasFDerivAt.fun_smul, FiniteDimensional.mem_span_of_iInf_ker_le_ker, SpectrumRestricts.compactSpace, Orthonormal.inner_left_fintype, RatFunc.isCoprime_num_denom, FunctionField.inftyValuation.polynomial, NormedSpace.expSeries_eq_expSeries, NormedSpace.expSeries_summable, compactOperator_topologicalClosure, IsFractionRing.algHom_commutes, IntermediateField.isAlgebraic_iff, Complex.starConvex_ofReal_slitPlane, PiTensorProduct.mapL_smul, BoundedContinuousFunction.coe_toContinuousMapStarₐ, ContinuousLinearMap.adjointAux_norm, RCLike.toIsStrictOrderedModule, IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower', LeftInvariantDerivation.lift_add, FormalMultilinearSeries.ofScalarsSum_op, LinearMap.flip_injective_iff₁, FormalMultilinearSeries.ofScalars_eq_zero, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, FormalMultilinearSeries.ofScalars_apply_zero, HasDerivAt.comp_hasFDerivWithinAt, LinearMap.ker_smul', LinearMap.toMatrixOrthonormal_apply_apply, FractionalIdeal.inv_nonzero, HasFDerivAt.restrictScalars, IntermediateField.instSMulMemClass, nnratCast_def, IntermediateField.coe_inclusion, PiTensorProduct.projectiveSeminorm_apply, Nonneg.segment_eq_uIcc, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, AffineSubspace.coe_subtypeₐᵢ, Polynomial.separable_X_pow_sub_C_of_irreducible, RatFunc.coe_coe, Field.finSepDegree_self, HasStrictFDerivAt.list_prod', PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, Complex.starConvex_one_slitPlane, AffineSubspace.sOppSide_iff_exists_left, Basis.linearEquiv_dual_iff_finiteDimensional, NumberField.FinitePlace.norm_embedding_eq, hasStrictDerivAt_exp_smul_const, Derivation.leibniz_div, Polynomial.separable_X_pow_sub_C, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, Polynomial.span_singleton_annIdealGenerator, NormedSpace.exp_eq_tsum, NumberField.IsCMField.isQuadraticExtension, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, Subspace.finrank_dualCoannihilator_eq, Field.Emb.Cardinal.two_le_deg, NumberField.ComplexEmbedding.Extension.not_isReal_of_not_isReal, Polynomial.Gal.restrictDvd_def, LeftInvariantDerivation.lift_smul, Rat.IsIntegralClosure.intEquiv_apply_eq_ringOfIntegersEquiv, IsPrimitiveRoot.powerBasis_gen_mem_adjoin_zeta_sub_one, FractionalIdeal.div_of_ne_zero, hasStrictDerivAt_exp_smul_const', InfiniteGalois.fixingSubgroup_fixedField, Real.fourier_iteratedFDeriv, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, SchwartzMap.smulLeftCLM_real_smul, InnerProductSpace.toDualMap_apply_apply, WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, IntermediateField.finInsepDegree_le_of_left_le, LinearMap.eq_adjoint_iff_basis_left, Quaternion.inv_def, Matrix.ker_mulVecLin_conjTranspose_mul_self, Subspace.finiteDimensional_quot_dualCoannihilator_iff, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, IntermediateField.isAlgebraic_adjoin_iff, IntermediateField.minpoly_gen, Field.Emb.Cardinal.isLeast_leastExt, Algebra.IsQuadraticExtension.isMulCommutative_galoisGroup, LaurentSeries.inducing_coe, NonUnitalSubalgebra.unitization_injective, WeakDual.toStrongDual_inj, TrivSqZeroExt.fst_expSeries, ContinuousLinearMap.uniformContinuous_restrictScalars, isSeparable_algebraMap, PrimeSpectrum.coe_preimageOrderIsoFiber_symm_apply_coe_asIdeal, IsGalois.self, NumberField.mixedEmbedding.fundamentalCone.smul_mem_of_mem, ContinuousLinearMap.holderₗ_apply_apply, LaurentSeries.continuous_coe, isCyclic_of_isSplittingField_X_pow_sub_C, Polynomial.SplittingFieldAux.adjoin_rootSet, openSegment_eq_Ioo', hasStrictFDerivAt_multiset_prod, NumberField.IsCMField.orderOf_complexConj, Normal.algHomEquivAut_symm_apply, IsIdempotentElem.spectrum_subset, coe_innerSL_apply, fderivWithin_finset_prod, IntermediateField.map_map, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, PowerSeries.normUnit_X, IsPrimitiveRoot.adjoinEquivRingOfIntegers_symm_apply, LinearMap.dualMap_surjective_of_injective, IntermediateField.fixingSubgroup_top, IntermediateField.coe_toSubalgebra, instIsAbelianGalois, Matrix.PosSemidef.det_sqrt, AlgebraicGeometry.pointEquivClosedPoint_apply_coe, range_cfcₙHom, Field.Emb.Cardinal.succEquiv_coherence, IntermediateField.bot_toSubalgebra, IntermediateField.isScalarTower_bot, Algebra.discr_powerBasis_eq_norm, TensorProduct.lidIsometry_apply, IsSepClosed.lift_def, Normal.splits, NumberField.InfinitePlace.smul_eq_comap, Orientation.map_eq_iff_det_pos, IsPrimitiveRoot.norm_eq_neg_one_pow, convex_halfSpace_re_le, Submodule.comap_smul, LinearMap.flip_surjective_iff₁, coeSubmodule_differentIdeal, coe_galRestrict_apply, minpoly.sub_algebraMap, IntermediateField.sup_toSubalgebra_of_isAlgebraic_left, hasFDerivAt_ringInverse, tensorIteratedFDerivWithinTwo_eq_iteratedFDerivWithin, norm_cfcₙ_lt, Polynomial.separable_or, NumberField.InfinitePlace.smul_mk, WeierstrassCurve.Projective.addXYZ_of_X_eq, WeakDual.coe_toStrongDual, fermatLastTheoremWith'_polynomial, Matrix.linfty_opNNNorm_eq_opNNNorm, Ideal.Fiber.lift_residueField_surjective, isConjRoot_iff_aeval_eq_zero, InnerProductSpace.nnnorm_rankOne, RatFunc.mk_eq_mk', Field.rank_mul_sepDegree_of_isSeparable, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, PreInnerProductSpace.Core.conj_inner_symm, ProbabilityTheory.isPosSemidef_covarianceBilin, fderiv_smul, OrthonormalBasis.orthogonalProjection_apply_eq_sum, ValuationRing.iff_isInteger_or_isInteger, FiniteField.algebraMap_trace_eq_sum_pow, IsLocalRing.maximalIdeal_eq_bot, HasFDerivWithinAt.star, LinearMap.trace_eq_sum_inner, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, FormalMultilinearSeries.ofScalars_series_of_subsingleton, solvableByRad.isSolvable, exists_basis_of_pairing_ne_zero, ContinuousMap.spectrum_eq_preimage_range, Unitization.quasispectrum_inr_eq, IntermediateField.linearDisjoint_comm, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, InnerProductSpace.isSymmetricProjection_rankOne_self, Subspace.dualPairing_nondegenerate, Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRing, Polynomial.leadingCoeff_mul_prod_normalizedFactors, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, NormedSpace.norm_expSeries_summable, NormedSpace.expSeries_sum_eq, hasGradientWithinAt_iff_hasFDerivWithinAt, spectrum.isCompact, FiniteField.instIsScalarTowerZModExtension, Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, FormalMultilinearSeries.ofScalars_add, Polynomial.monic_mapAlg_iff, IntermediateField.equivOfEq_symm, ValuationSubring.isLocalRing, Polynomial.X_pow_sub_C_separable_iff, NormedSpace.smul_mem_polar, IntermediateField.restrictRestrictAlgEquivMapHom_apply, Algebra.norm_eq_prod_embeddings, NNRat.cast_multisetProd, MonomialOrder.isUnit_leadingCoeff, SeparatingDual.dualMap_surjective_iff, Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed, WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, IsGalois.intermediateFieldEquivSubgroup_apply, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, SpectrumRestricts.algebraMap_image, AlgHom.fieldRange_toSubalgebra, Ideal.sum_ramification_inertia, PadicAlgCl.norm_extends, minpoly.degree_le, NormedSpace.inclusionInDoubleDual_norm_eq, IntermediateField.fieldRange_comp_val, PiTensorProduct.projectiveSeminorm_tprod_le, IntermediateField.linearDisjoint_iff, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, FractionRing.instIsScalarTower_1, IntermediateField.adjoin.powerBasis_gen, NumberField.ComplexEmbedding.IsConj.eq, FractionalIdeal.fractional_div_of_nonzero, Ideal.card_primesOverFinset_le_finrank, NumberField.Units.regulator_eq_det, logDeriv_eqOn_iff, Matrix.PosSemidef.posSemidef_sqrt, PiTensorProduct.tprodL_toFun, IntermediateField.toSubalgebra_map, IntermediateField.equivOfEq_rfl, continuousOn_cfc_setProd, IntermediateField.map_fixingSubgroup, fderiv_mul_const', LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, RCLike.conj_ofReal, IntermediateField.normal_iff_normalClosure_le, TrivSqZeroExt.eq_smul_exp_of_ne_zero, Derivation.leibniz_inv, ContinuousAlternatingMap.norm_restrictScalars, mem_perfectClosure_iff_pow_mem, Submodule.adjoint_subtypeL, ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, hasStrictFDerivAt_exp, NumberField.AdeleRing.algebraMap_snd_apply, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, Module.Basis.trace_traceDual_mul, coevaluation_apply_one, Field.Emb.Cardinal.noMaxOrder_rank_toType, MvPolynomial.vanishingIdeal_pointToPoint, LinearMap.isSymmetric_adjoint_mul_self, ValuationSubring.idealOfLE_le_of_le, gelfandStarTransform_symm_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, ContinuousLinearMap.norm_smulRightL, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1, Algebra.instFiniteResidueFieldOfFormallyUnramified, IsPurelyInseparable.bijective_comp_algebraMap, RCLike.conjLIE_apply, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, HasFDerivWithinAt.fun_smul, GaloisField.finrank, RCLike.conj_mul, RatFunc.instIsFractionRingPolynomial, NormedAlgebra.exists_isMinOn_norm_sub_smul, InnerProductSpace.trace_rankOne, NumberField.Units.coe_coe, minpoly.natSepDegree_eq_one_iff_eq_X_sub_C_pow, FunctionField.algebraMap_injective, MvPolynomial.instIsPrimeVanishingIdealSingletonForallSet, Algebra.IsCentral.baseField_essentially_unique, PrimeSpectrum.isOpenMap_comap_algebraMap_tensorProduct_of_field, continuousOn_cfcₙ, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', ContinuousLinearMap.continuous_restrictScalars, Real.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, hasFDerivAt_norm_rpow, Matrix.finite_spectrum, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime, IsNormalClosure.splits, top_fixedByFinite, Field.absoluteGaloisGroup.commutator_closure_isNormal, LaurentSeries.algebraMap_apply, DualNumber.maximalIdeal_eq_span_singleton_eps, IntermediateField.relfinrank_dvd_finrank_bot, UniqueFactorizationMonoid.integer_of_integral, IsGalois.sup_right, NumberField.Units.finrank_mul_regOfFamily_eq_det, Matrix.linfty_opNNNorm_toMatrix, RCLike.instContinuousMapUniqueHom, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, FormalMultilinearSeries.ofScalars_sub, NormedSpace.expSeries_hasSum_exp, isConjRoot_iff_eq_algebraMap, ContinuousLinearMap.IsPositive.conj_adjoint, algebraMap_galRestrict_apply, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, minpoly.map_eq_of_isSeparable_of_isPurelyInseparable, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, IntermediateField.adjoin_simple_adjoin_simple, IntermediateField.adjoin_simple_toSubalgebra_of_integral, normalClosure.restrictScalars_eq, Module.End.hasUnifEigenvalue_iff_mem_spectrum, NumberField.InfinitePlace.isUnramified_self, contDiffOn_stereoToFun, LeftInvariantDerivation.evalAt_coe, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_right, IsPrimitiveRoot.adjoinEquivRingOfIntegers_apply, range_cfcₙ, LinearMap.adjoint_rTensor, NumberField.det_basisOfFractionalIdeal_eq_absNorm, convex_halfSpace_im_gt, Matrix.PosSemidef.sqrt_eq_one_iff, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, NumberField.InfinitePlace.isUnramified_smul_iff, Field.Emb.cardinal_eq_of_isSeparable, IntermediateField.AdjoinSimple.norm_gen_eq_one, HilbertBasis.hasSum_orthogonalProjection, NumberField.InfinitePlace.orbitRelEquiv_apply_mk'', LinearMap.adjoint_inner_right, IsAbelianGalois.toIsMulCommutative, InnerProductSpace.adjoint_rankOne, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, IntermediateField.range_val, PiTensorProduct.mapL_coe, IntermediateField.instFiniteSubtypeMemBot, IntermediateField.isCyclotomicExtension_lcm_sup, fderiv_pow, InnerProductSpace.rankOne_eq_zero, Ideal.image_subset_nonunits_valuationSubring, map_mem_perfectClosure_iff, AlgEquiv.card_le, Matrix.PosSemidef.sqrt_sq, finrank_quotient_span_eq_natDegree, Unitization.splitMul_injective_of_clm_mul_injective, TensorProduct.ext_iff_inner_left_threefold', Convex.toWeakSpace_closure, Module.Basis.trace_mul_traceDual, LinearIsometry.lTensor_apply, minpoly.frobenius_of_isSeparable, RatFunc.numDenom_div, IntermediateField.linearDisjoint_iff', RCLike.re_eq_norm_of_mul_conj, Algebra.IsGeometricallyReduced.isReduced_algebraicClosure_tensorProduct, IsGaloisGroup.fixedPoints_fixingSubgroup, integralClosure.isFractionRing_of_finite_extension, InnerProductSpace.inner_right_rankOne_apply, IsLiouville.rfl, HasFDerivWithinAt.hasGradientWithinAt, HasFDerivAt.pow, IsSimpleModule.algebraMap_end_bijective_of_isAlgClosed, spectrum.eventually_isUnit_resolvent, NumberField.RingOfIntegers.coe_eq_zero_iff, innerSL_inj, AffineIsometryEquiv.coe_ofEq_apply, fderivWithin_inv', IntermediateField.extendScalars.orderIso_apply, RatFunc.instIsScalarTowerOfPolynomial_1, AffineSubspace.wOppSide_iff_exists_left, NumberField.InfinitePlace.IsRamified.comap_embedding_conjugate, TensorProduct.ext_iff_inner_left_threefold, RCLike.conj_eq_iff_re, IsPurelyInseparable.injective_comp_algebraMap, StrongDual.toLp_of_not_memLp, AffineSubspace.isometryEquivMap.toAffineMap_eq, algebraicClosure.isIntegralClosure, Quaternion.expSeries_odd_of_imaginary, AlgebraicClosure.instIsAlgClosureOfIsAlgebraic, quasispectrum.isCompact, Algebra.normalizedTrace_intermediateField, TensorProduct.inner_lid_lid, NumberField.InfinitePlace.even_card_aut_of_not_isUnramified, NormedSpace.norm_expSeries_summable_of_mem_ball', Matrix.piLp_ofLp_toEuclideanLin, cfcₙAux_id, minpoly.dvd_iff, PiTensorProduct.liftIsometry_tprodL, HasStrictFDerivAt.cexp, TensorProduct.norm_comm, NormedSpace.inclusionInDoubleDual_norm_le, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, isStrictlyPositive_algebraMap, IsFractionRing.fieldEquivOfAlgEquiv_refl, galLift_algebraMap_apply, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, WeakDual.isCompact_closedBall, NumberField.Units.norm, PiTensorProduct.injectiveSeminorm_le_projectiveSeminorm, isNormalClosure_normalClosure, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, Asymptotics.superpolynomialDecay_iff_zpow_tendsto_zero, IsScalarTower.AlgEquiv.restrictNormalHom_comp, PiTensorProduct.bddBelow_projectiveSemiNormAux, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply', IntermediateField.mem_fixedField_iff, NumberField.IsCMField.complexConj_apply_apply, IntermediateField.finrank_eq_one_iff, IntermediateField.lift_top, LaurentSeries.exists_ratFunc_val_lt, Algebra.IsCentral.right_of_tensor_of_field, mul_inv_cancel, RatFunc.num_algebraMap, IntermediateField.sInf_toSubalgebra, HasFDerivWithinAt.mul_const, Derivation.leibniz_zpow, ordinaryHypergeometricSeries_apply_eq', fderiv_pow', spectrum.one_eq, NumberField.RingOfIntegers.instIsLocalizationAlgebraMapSubmonoidIntNonZeroDivisors, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, fderiv_mul, FormalMultilinearSeries.coeff_ofScalars, IntermediateField.adjoin_map, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Algebra.WeaklyQuasiFiniteAt.finite_locoalization, NumberField.mixedEmbedding.span_idealLatticeBasis, Valuation.HasExtension.maximalIdeal_comap_algebraMap_eq_maximalIdeal, Matrix.instFiniteSpectrum, NumberField.ComplexEmbedding.IsConj.symm, Orthonormal.inner_left_right_finset, map_mem_separableClosure_iff, IntermediateField.insepDegree_bot', IntermediateField.fixedField_antitone, AlgebraicIndependent.lift_reprField, RCLike.conj_I_ax, cfcₙHom_eq_cfcₙHom_of_cfcHom, Polynomial.hilbertPoly_succ, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, TensorProduct.norm_assoc, TensorProduct.nnnorm_tmul, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, IntermediateField.isAlgebraic_adjoin, galLift_comp, IsCyclotomicExtension.splits_cyclotomic, IsLocalRing.ResidueField.instIsScalarTower_1, mem_subalgebraEquivIntermediateField_symm, InnerProductSpace.toDualMap_apply, FDRep.average_char_eq_finrank_invariants, instIsLiouvilleSubtypeMemIntermediateField, Algebra.adjoin.powerBasis_dim, NumberField.mixedEmbedding.convexBodySumFun_smul, NumberField.IsCMField.coe_ringOfIntegersComplexConj, DifferentiableAt.conj_conj, AffineIsometryEquiv.ofTop_symm_apply_coe, InfiniteGalois.mulEquivToLimit_symm_continuous, NumberField.mixedEmbedding.logMap_real_smul, ContinuousLinearMap.adjoint_inner_left, PowerSeries.normalized_count_X_eq_of_coe, ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrier, TensorProduct.inner_mapIncl_mapIncl, ContDiffWithinAt.restrictScalars_iteratedFDerivWithin_eventuallyEq, Valuation.FiniteField.instIsTrivialOn, FractionalIdeal.div_nonzero, nnnorm_algebraMap, fdifferential_apply, instTotallySeparatedSpaceAlgEquivOfIsIntegral, InnerProductSpace.AlgebraOfCoalgebra.mul_def, SeparableClosure.hasEnoughRootsOfUnity_pow, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, IsTranscendenceBasis.isAlgebraic_field, LinearMap.range_dualMap_eq_dualAnnihilator_ker, RatFunc.num_dvd, Ring.instIsFractionRingNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, FiniteField.frobeniusAlgEquiv_symm_apply, isPurelyInseparable_iff_pow_mem, NNRat.cast_prod, Real.one_div_sub_hasFPowerSeriesOnBall_zero, RCLike.uniqueNonUnitalContinuousFunctionalCalculus, IntermediateField.toSubfield_map, PowerBasis.equivAdjoinSimple_aeval, IntermediateField.extendScalars_adjoin, fderiv_pow_ring, FiniteDimensional.of_subalgebra_toSubmodule, IntermediateField.isPurelyInseparable_tower_bot, le_separableClosure_iff, DifferentiableAt.fderiv_restrictScalars, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, Normal.algHomEquivAut_apply, IsCyclotomicExtension.finrank, selfAdjoint.unitarySelfAddISMul_coe, AffineIsometryEquiv.ofEq_symm, HasDerivWithinAt.complexToReal_fderiv, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, Valuation.Integers.isFractionRing, integral_conj, NumberField.FinitePlace.norm_lt_one_iff_mem, IntermediateField.extendScalars_inf, Polynomial.Gal.instIsScalarTowerSplittingField, IsGaloisGroup.of_isGalois, InnerProductSpace.rank_rankOne, IntermediateField.botContinuousSMul, NumberField.IsCMField.equivInfinitePlace_apply, IsometricContinuousFunctionalCalculus.toNonUnital, LinearMap.flip_bijective_iff₁, InnerProductSpace.toDual_apply_apply, LinearMap.flip_bijective_iff₂, WittVector.frobeniusPoly_zmod, ContinuousLinearMap.adjointAux_apply, eq_separableClosure_iff, LinearMap.BilinForm.mem_dualSubmodule, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, fderivWithin_fun_mul', MvPolynomial.map_restrict_dom_evalₗ, LocalSubring.instAtPrimeSubtypeMemSubringToSubringOfPrime, ValuationSubring.coe_unitGroupMulEquiv_apply, ProperCone.innerDual_singleton, algebraMap_isometry, RCLike.add_conj, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, Polynomial.isPrimitive_iff_ne_zero, RingOfIntegers.norm_algebraMap, CFC.exp_eq_normedSpace_exp, NumberField.InfinitePlace.smul_coe_apply, IsFractionRing.of_field, LinearMap.minpoly_dvd_charpoly, RCLike.im_eq_conj_sub, spectrum.pow_image_subset, ValuationRing.isFractionRing_iff, hasFDerivAt_list_prod', segment_eq_Icc', InnerProductSpace.rankOne_def, TensorProduct.nnnorm_map, RCLike.conj_im_ax, NumberField.IsCMField.is_quadratic, PiTensorProduct.norm_eval_le_injectiveSeminorm, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, IntermediateField.normal_iff_forall_fieldRange_le, PointwiseConvergenceCLM.equivWeakDual_apply, Polynomial.fderiv_aeval, inner_self_conj, Valuation.pow_Uniformizer_is_pow_generator, Algebra.bijective_algebraMap_iff, FiniteField.finrank_zmod_extension, FGModuleCat.FGModuleCatDual_obj, fderiv_mul', IsGalois.normalAutEquivQuotient_apply, IsGalois.normalBasis_apply, Units.continuousOn_zpow₀_spectrum, NumberField.IsCMField.complexConj_apply_eq_self, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, instSMulDistribClassAlgEquiv, ContinuousFunctionalCalculus.toNonUnital, ClosedSubmodule.orthogonal_eq_inter, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, IntermediateField.adjoin_simple_eq_top_iff_of_isAlgebraic, HasFDerivWithinAt.cexp, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, PowerSeries.instUniqueFactorizationMonoid, QuadraticForm.equivalent_weightedSumSquares, LeftInvariantDerivation.left_invariant'', ordinaryHypergeometricSeries_apply_zero, Polynomial.SplittingFieldAux.scalar_tower', FiniteField.algebraMap_norm_eq_pow, NormedSpace.expSeries_summable', NormedSpace.norm_expSeries_summable_of_mem_ball, Field.Emb.Cardinal.strictMono_leastExt, IntermediateField.rank_adjoin_eq_one_iff, mem_segment_iff_sameRay, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, binomialSeries_apply, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure_1, RCLike.conj_div, galLiftEquiv_apply, Orientation.map_eq_det_inv_smul, HasDerivAtFilter.hasGradientAtFilter, ContinuousLinearMap.coe_restrict_scalarsL', HasDerivAt.complexToReal_fderiv, NumberField.InfinitePlace.LiesOver.comap_eq, IntermediateField.isAlgebraic_tower_top, StrongDual.polarSubmodule_eq_polar, Polynomial.separable_X_pow_sub_C', NumberField.InfinitePlace.even_finrank_of_not_isUnramifiedIn, PiTensorProduct.liftEquiv_symm_apply, Subfield.algebraMap_ofSubfield, RCLike.summable_conj, IsCyclotomicExtension.splits_X_pow_sub_one, Algebra.TensorProduct.isField_of_isAlgebraic, transcendental_aeval_iff, Valuation.ideal_isPrincipal, LinearMap.dualMap_injective_iff, inner_smul_real_right, Algebra.normalizedTrace_eq_of_fininteDimensional, TensorProduct.toLinearEquiv_congrIsometry, hasFDerivAt_exp_smul_const', ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, Complex.one_add_cpow_hasFPowerSeriesAt_zero, FormalMultilinearSeries.ofScalars_norm_le, NumberField.mixedEmbedding.covolume_idealLattice, Representation.isSemisimpleRepresentation_iff_isSemisimpleModule_asModule, IntermediateField.finrank_eq_fixingSubgroup_index, Commute.cfcₙHom, LinearMap.dualPairing_nondegenerate, Submodule.norm_subtypeL, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, FGModuleCat.FGModuleCatCoevaluation_apply_one, LinearMap.toMatrixOrthonormal_symm_apply, segment_eq_Icc, Subspace.dualRestrict_leftInverse, FiniteField.algebraMap_norm_eq_prod_pow, Subfield.bot_eq_of_zMod_algebra, trace_eq_trace_adjoin, Polynomial.eval_homogenize, LinearMap.toMatrix_innerₛₗ_apply, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Valuation.associated_of_isUniformizer, PointwiseConvergenceCLM.equivWeakDual_symm_apply, PadicAlgCl.instUniformContinuousConstSMulPadic, TensorProduct.toLinearEquiv_commIsometry, div_eq_mul_inv, MonomialOrder.span_leadingTerm_eq_span_monomial', IntermediateField.adjoin_root_eq_top, Matrix.ker_mulVecLin_transpose_mul_self, IsDedekindDomain.HeightOneSpectrum.instIsTorsionFreeSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, hasFDerivWithinAt_pow', IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_right, IsGaloisGroup.fixingSubgroup_fixedPoints, IsGaloisGroup.mulEquivAlgEquiv_apply_apply, IsFractionRing.stabilizerHom_surjective, InfiniteGalois.proj_adjoin_singleton_val, normalClosure_def, IntermediateField.lift_inf, Matrix.PosSemidef.toLinearMap₂'_zero_iff, convex_halfSpace_im_lt, Algebra.QuasiFinite.instFiniteResidueField, WeakDual.isSeqCompact_closedBall, IsFractional.div_of_nonzero, PiTensorProduct.liftEquiv_apply, HasFDerivAt.cexp, NumberField.InfinitePlace.isRamified_iff, NumberField.InfinitePlace.card_isUnramified, NormedSpace.expSeries_apply_eq, Field.rank_mul_insepDegree_of_isPurelyInseparable, IntermediateField.linearDisjoint_comm', LocalSubring.map_maximalIdeal_eq_top_of_isMax, IsFractionRing.fieldEquivOfAlgEquiv_algebraMap, WeakDual.exists_countable_separating, Polynomial.natSepDegree_eq_natDegree_iff, LinearMap.isSelfAdjoint_iff', Subspace.dual_finrank_eq, NumberField.IsCMField.complexEmbedding_complexConj, sum_embeddings_eq_finrank_mul, mem_perfectClosure_iff, IntermediateField.smul_mem, NumberField.InfinitePlace.isComplex_smul_iff, AlgHom.map_fieldRange, innerSLFlip_apply_apply, Polynomial.annIdealGenerator_mem, PadicAlgCl.spectralNorm_eq, Polynomial.hasFDerivAt, FiniteField.instFiniteExtension_1, strictConvex_iff_convex, IntermediateField.extendScalars_self, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, Subalgebra.isField_of_algebraic, Polynomial.IsSplittingField.splits, PowerBasis.equivAdjoinSimple_gen, Field.Emb.Cardinal.equivSucc_coherence, FiniteField.frobeniusAlgEquivOfAlgebraic_symm_apply, Polynomial.IsSplittingField.splits', LinearMap.mem_span_iff_continuous_of_finite, Module.AEval.isTorsion_of_finiteDimensional, NumberField.InfinitePlace.IsRamified.isReal, NumberField.CMExtension.equivMaximalRealSubfield_apply, minpoly.ker_aeval_eq_span_minpoly, IsDedekindDomain.FiniteAdeleRing.instIsScalarTower, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, IntermediateField.restrictScalars_adjoin_eq_sup, NumberField.Units.mem_torsion, FiniteGaloisIntermediateField.isGalois, LinearMap.finiteDimensional', TensorProduct.ext_iff_inner_right, fderivWithin_mul_const', NonUnitalStarSubalgebra.unitization_injective, IntermediateField.mem_adjoin_iff_div, IsGalois.is_separable_splitting_field, fderivWithin_smul, InnerProductSpace.enorm_rankOne, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, PiTensorProduct.mapL_mul, cfcHom_real_eq_restrict, IntermediateField.Lifts.lt_iff, ContinuousLinearMap.toLinearMap_innerSL_apply, NumberField.ComplexEmbedding.IsConj.isReal_comp, spectrum.inv₀_mem_inv_iff, AlgebraicGeometry.FormallyUnramified.instIsSeparableCarrierResidueFieldCoeContinuousMapCarrierCarrierCommRingCatHomTopCatBaseOfLocallyOfFiniteType, IntermediateField.top_toSubalgebra, IntermediateField.extendScalars_le_iff, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, finrank_of_isSplittingField_X_pow_sub_C, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', Representation.isSimpleModule_iff_irreducible_ofModule, hasFDerivAt_list_prod_finRange', NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, LinearMap.IsSymmetric.adjoint_eq, HasGradientAt.hasFDerivAt, Polynomial.prime_of_degree_eq_one, Real.fourier_fderiv, IsStrictlyPositive.smul, Localization.subalgebra.isLocalization_ofField, ContinuousMap.adjoin_id_eq_span_one_union, IsGaloisGroup.fixedPoints_bot, PowerBasis.equivAdjoinSimple_symm_gen, SeparableClosure.hasEnoughRootsOfUnity, HasFDerivWithinAt.norm_sq, minpoly.prime, CFC.abs_algebraMap, IntermediateField.coe_val, Complex.restrictScalars_one_smulRight, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Polynomial.SplittingField.splits, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, Module.End.IsSemisimple.aeval, AlgHom.fieldRange_toSubfield, SpectrumRestricts.subset_preimage, groupCohomology.norm_ofAlgebraAutOnUnits_eq, IntermediateField.fixingSubgroup_le, Matrix.IsHermitian.cfcAux_apply, RatFunc.valuation_eq_LaurentSeries_valuation, NumberField.Units.coe_neg_one, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, Unitization.norm_eq_sup, Irreducible.hasSeparableContraction, Matrix.ofLp_toEuclideanCLM, Quaternion.expSeries_even_of_imaginary, Polynomial.IsSplittingField.instIsTorsionFreeSplittingField, AlgebraicClosure.instIsAlgClosure, PrimeSpectrum.residueField_comap, HasStrictFDerivAt.restrictScalars, NumberField.InfinitePlace.card_isUnramified_compl, PiTensorProduct.mapL_comp, PadicInt.coe_adicCompletionIntegersEquiv_apply, IntermediateField.finrank_eq_finrank_subalgebra, FractionalIdeal.coe_inv_of_ne_zero, Algebra.Transcendental.rank_eq_cardinalMk, ordinaryHypergeometric_eq_tsum, Algebra.instFiniteResidueFieldOfIsUnramifiedAt, hasDerivAt_exp_smul_const, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', NormedSpace.algebraMap_exp_comm, NormedSpace.expSeries_apply_eq_div, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, NumberField.mixedEmbedding.logMap_eq_logEmbedding, IntermediateField.restrictRestrictAlgEquivMapHom_injective, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDual, Algebra.IsCentral.left_of_tensor_of_field, Algebra.adjoin_eq_top_of_primitive_element, fderivWithin_fun_pow, exists_nonneg_right_iff_sameRay, Height.mulHeight_smul_eq_mulHeight, isCoprime_iff, FiniteField.coe_frobeniusAlgEquivOfAlgebraic_iterate, NumberField.isFinitePlace_iff, Transcendental.algebraicClosure, Polynomial.int_eval₂_eq, RCLike.inner_tmul_eq, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, Algebra.normalizedTrace_algebraMap_apply_eq_self, RCLike.smul_im, LinearMap.dualMap_bijective_iff, NumberField.InfinitePlace.IsUnramified.eq, HasFDerivAt.multiset_prod, LinearMap.star_eq_adjoint, MvPolynomial.pointToPoint_zeroLocus_le, HasFDerivAt.mul_const, unitary.spectrum_subset_circle, IntermediateField.finrank_adjoin_eq_one_iff, Ring.instIsSeparableFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, exists_integral_inj_algHom_of_quotient, FDRep.char_linHom, IsGaloisGroup.finiteDimensional, IntermediateField.normal_iff_forall_map_le', Matrix.isPositive_toEuclideanLin_iff, ContinuousLinearMap.coe_restrictScalarsIsometry, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, TensorProduct.enorm_tmul, PadicInt.isFractionRing, IntermediateField.normal_iff_forall_fieldRange_eq, Polynomial.aeval_conj, ProbabilityTheory.hasFPowerSeriesAt_mgf, IsPrimitiveRoot.separable_minpoly_mod, RCLike.re_eq_add_conj, instIsAbelianGaloisSubtypeMemIntermediateField_1, NumberField.integralBasis_repr_apply, exists_finite_inj_algHom_of_fg, IsLocalRing.PrimeSpectrum.comap_residue, Polynomial.separable_prod_X_sub_C_iff', Field.finSepDegree_le_finrank, PiTensorProduct.dualSeminorms_bounded, ValuationSubring.instIsDomainSubtypeMem, LinearMap.hasBasis_weakBilin, CommCStarAlgebra.toStarModule, Field.nonempty_algHom_of_range_minpoly_subset, FiniteField.splits_X_pow_nat_card_sub_X, HasFDerivWithinAt.mul_const', HasDerivAt.comp_hasFDerivWithinAt_of_eq, spectrum.isClosed, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, WeakBilin.locallyConvexSpace, MvPolynomial.zeroLocus_bot, IsSelfAdjoint.conj_adjoint, TensorProduct.inner_assoc_assoc, fderiv_const_mul, zpow_succ', IntermediateField.finrank_bot, ConjRootClass.splits_minpoly, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, DoubleCentralizer.algebraMap_snd, NormedSpace.expSeries_apply_zero, WeakDual.polar_def, IntermediateField.fixingSubgroup_antitone, RCLike.wInner_const_left, RCLike.wInner_cWeight_const_left, InfiniteGalois.restrict_fixedField, FormalMultilinearSeries.ofScalarsSum_zero, hasStrictFDerivAt_norm_sq, LinearMap.adjoint_toSpanSingleton, Polynomial.IsSplittingField.adjoin_rootSet', AlgebraicGeometry.instIsFractionRingCarrierStalkCommRingCatPresheafFunctionField, IntermediateField.sepDegree_bot, ContinuousMultilinearMap.norm_mkPiAlgebra, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, mem_quasispectrum_iff, Asymptotics.superpolynomialDecay_iff_isLittleO, Algebra.normalizedTrace_self, RatFunc.algebraMap_apply_div, algebraMap_memℓp_infty, galLiftEquiv_symm_apply, fderiv_pow_ring', IntermediateField.algebraMap_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, InfiniteGalois.instCompactSpaceAlgEquivOfIsGalois, IsConjRoot.exists_algEquiv, IntermediateField.finInsepDegree_bot', NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, RCLike.inner_apply, Algebra.norm_eq_norm_adjoin, upperHemicontinuous_quasispectrum, spectrum.isBounded, NumberField.FinitePlace.coe_apply, Subspace.quotAnnihilatorEquiv_apply, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, WeakDual.CharacterSpace.compContinuousMap_apply, Subalgebra.frontier_subset_frontier, LinearMap.re_inner_adjoint_mul_self_nonneg, IntermediateField.restrictScalars_bot_eq_self, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, functionField_iff, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, ValuationSubring.instIsFractionRingSubtypeMem, LinearMap.isPositive_self_comp_adjoint, RCLike.hasSum_conj, Field.finSepDegree_eq_finrank_of_isSeparable, PowerBasis.toMatrix_isIntegral, HasFPowerSeriesAt.restrictScalars, AlgebraicClosure.Monics.splits_finsetProd, MvPolynomial.le_zeroLocus_iff_le_vanishingIdeal, Polynomial.hasFDerivAt_aeval, IntermediateField.adjoin.range_algebraMap_subset, LinearIsometryEquiv.toLinearEquiv_lTensor, spectrum.isUnit_one_sub_smul_of_lt_inv_radius, ContDiffAt.restrictScalars_iteratedFDeriv, PiTensorProduct.injectiveSeminorm_apply, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, LinearIsometryEquiv.toLinearEquiv_smul, Valuation.HasExtension.instIsScalarTower_valuationSubring', Algebra.adjoin.powerBasis_gen, rank_dual_eq_card_dual_of_aleph0_le_rank, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, InfiniteGalois.limitToAlgEquiv_apply, hasFDerivAt_pow, IsFractionRing.mk'_num_den, ValuationSubring.algebraMap_apply, Matrix.l2_opNNNorm_def, NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConj, IntermediateField.mem_lift, IntermediateField.isAlgebraic_adjoin_pair, RatFunc.faithfulSMul, ContinuousLinearMap.adjointAux_adjointAux, Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder, LinearMap.hasEigenvalue_zero_tfae, AffineSubspace.wSameSide_iff_exists_left, Ideal.finrank_quotient_map, lift_rank_lt_rank_dual, LinearMap.eq_adjoint_iff, NumberField.mixedEmbedding.norm_smul, Algebra.discr_mul_isIntegral_mem_adjoin, IntermediateField.finrank_sup_le, ConvexOn.convex_re_epigraph, Differential.instDifferentialAlgebraSubtypeMemIntermediateField_1, ValuationSubring.valuation_eq_iff, NumberField.InfinitePlace.IsRamified.comap_embedding, ordinaryHypergeometricSeries_apply_eq, LinearMap.norm_extendTo𝕜'_apply_sq, OrthonormalBasis.tensorProduct_apply', NumberField.InfinitePlace.LiesOver.embedding_comp_eq_or_conjugate_embedding_comp_eq, galRestrictHom_symm_algebraMap_apply, exists_pos_left_iff_sameRay, IntermediateField.adjoinRootEquivAdjoin_apply_root, IntermediateField.normalClosureOperator_apply, IntermediateField.fixingSubgroup_isClosed, AffineSubspace.isometryEquivMap.coe_apply, ContinuousLinearMap.isSelfAdjoint_iff', HasFDerivWithinAt.restrictScalars, IsConjRoot.add_algebraMap, krullTopology_isTotallySeparated, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, IntermediateField.rank_bot, NumberField.FinitePlace.norm_def_int, differentiableWithinAt_iff_restrictScalars, derivWithin_comp_mul_left, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, Valuation.valuationSubring_isPrincipalIdealRing, RCLike.ofReal_alg, HasFDerivAt.fun_pow', le_restrictScalars_separableClosure, algebraMap.coe_div, NumberField.InfinitePlace.isRamified_iff_card_stabilizer_eq_two, HasMFDerivWithinAt.mul', WeierstrassCurve.Projective.neg_of_Z_ne_zero, PointedContMDiffMap.instIsScalarTowerSomeENatTop, FormalMultilinearSeries.ofScalarsSum_eq_tsum, IntermediateField.adjoin.algebraMap_mem, IsLocalRing.exists_factor_valuationRing, IntermediateField.instIsScalarTowerSubtypeMem_1, MvPolynomial.mem_zeroLocus_iff, Matrix.PosSemidef.isUnit_sqrt_iff, cfc_zpow, spectralNorm_smul, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, RCLike.conj_tsum, IsSemisimpleRing.exists_algEquiv_pi_matrix_of_isAlgClosed, Polynomial.separable_prod_X_sub_C_iff, LinearMap.weakBilin_withSeminorms, NumberField.ComplexEmbedding.isConj_apply_apply, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, isSolvable_of_isScalarTower, WeakDual.isClosed_closedBall, MvPolynomial.eval_indicator_apply_eq_zero, NumberField.RingOfIntegers.withValEquiv_apply, IntermediateField.finrank_bot_mul_relfinrank, Asymptotics.superpolynomialDecay_mul_param_pow_iff, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, fdifferential_comp, WeierstrassCurve.Projective.negDblY_eq, Algebra.norm_eq_prod_automorphisms, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, RCLike.wInner_const_right, Field.lift_rank_mul_lift_insepDegree_of_isPurelyInseparable, InnerProductSpace.rankOne_def', IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_right, natDegree_radical_le, IsCyclotomicExtension.finiteDimensional, IsUltrametricDist.algNormOfAlgEquiv_apply, IntermediateField.bot_eq_top_iff_finrank_eq_one, ContinuousAlternatingMap.continuous_restrictScalars, IntermediateField.finiteDimensional_adjoin, IntermediateField.isTranscendenceBasis_adjoin_iff, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_left, LinearMap.adjoint_lTensor, LinearEquiv.smulOfNeZero_apply, IntermediateField.lift_injective, PadicComplex.instIsScalarTowerPadicPadicAlgCl, RCLike.conj_eq_iff_real, HasFDerivAtFilter.star, LinearMap.toMatrixOrthonormal_apply, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, FiniteGaloisIntermediateField.adjoin_map, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, convex_halfSpace_re_ge, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux, Subspace.finrank_add_finrank_dualCoannihilator_eq, Matrix.IsHermitian.spectrum_eq_image_range, IsFractionRing.mk'_mk_eq_div, IntermediateField.coe_extendScalars, Polynomial.X_pow_sub_one_separable_iff, NumberField.RingOfIntegers.coe_injective, HasFDerivAt.const_mul, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, MvPolynomial.frobenius_zmod, StrongDual.toLpₗ_apply, DifferentiableWithinAt.restrictScalars_fderivWithin, IntermediateField.AdjoinSimple.trace_gen_eq_zero, integralClosure.isFractionRing_of_algebraic, Orthonormal.inner_left_sum, IntermediateField.lift_sepDegree_bot', Valued.integer.coe_span_singleton_eq_closedBall, IntermediateField.mem_adjoin_range_iff, cfc_inv_id, Orientation.inner_mul_areaForm_sub', NormedSpace.norm_expSeries_summable', instIsTopologicalGroupAlgEquiv, fderivWithin_multiset_prod, HasFDerivAt.mul, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, InnerProductSpace.innerSL_norm, Ioo_subset_openSegment, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, toWeakSpace_closedConvexHull_eq, Unitization.norm_def, Polynomial.int_leadingCoeff_eq, AlgebraicClosure.le_maxIdeal, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, selfAdjoint.star_coe_unitarySelfAddISMul, IsSepClosed.algebraMap_surjective, IntermediateField.finSepDegree_adjoin_simple_le_finrank, Matrix.ker_diagonal_toLin', TensorProduct.inner_comm_comm, ValuationSubring.coe_mem_nonunits_iff, NormedSpace.expSeries_apply_eq', Polynomial.IsSplittingField.splittingField, convex_halfSpace_im_ge, Subspace.dualAnnihilator_inj, Field.Emb.Cardinal.filtration_apply, Polynomial.natSepDegree_mul_eq_iff, AffineSubspace.subtypeₐᵢ_linear, AlgebraicClosure.toSplittingField_coeff, LieModule.traceForm_eq_sum_finrank_nsmul, NumberField.RingOfIntegers.isIntegral_coe, IntermediateField.relrank_dvd_rank_bot, hasStrictFDerivAt_pow', LinearMap.flip_injective_iff₂, Asymptotics.superpolynomialDecay_iff_isBigO, ValuationSubring.mem_nonunits_iff_exists_mem_maximalIdeal, AlgHom.liftNormal_commutes, NormedAlgebra.instRegularNormedAlgebra, NumberField.Units.complexEmbedding_apply, convex_halfSpace_re_lt, Polynomial.natSepDegree_smul_nonzero, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, IntermediateField.AdjoinPair.algebraMap_gen₁, NumberField.fractionalIdeal_rank, hasGradientAt_iff_hasFDerivAt, RatFunc.denom_div, NumberField.InfinitePlace.not_isUnramified_iff, quasispectrum.algebraMap_mem_iff, hasFDerivAt_exp_smul_const_of_mem_ball, fderiv_fun_mul', NumberField.InfinitePlace.isUnramified_iff, NormedSpace.expSeries_sum_eq_rat, Valuation.HasExtension.algebraMap_mem_valuationSubring, Module.End.finite_spectrum, IsGalois.intermediateFieldEquivSubgroup_symm_apply, Polynomial.natSepDegree_expand, NumberField.InfinitePlace.denseRange_algebraMap_pi, TensorProduct.assocIsometry_apply, Matrix.toLin_conjTranspose, RCLike.instStarModuleReal, FixedPoints.toAlgAut_surjective, Orthonormal.inner_finsupp_eq_sum_left, cfcHom_nnreal_eq_restrict, Matrix.IsHermitian.spectral_theorem, WithLp.unitizationAlgEquiv_symm_apply_ofLp, PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable, Module.Basis.continuous_toMatrix, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_apply, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, IntermediateField.LinearDisjoint.of_inf_eq_bot, RatFunc.intDegree_polynomial, norm_cfcₙ_le, NumberField.InfinitePlace.isReal_smul_iff, AlgHom.coe_fieldRange, IntermediateField.adjoin_simple_toSubalgebra_of_isAlgebraic, Polynomial.int_monic_iff, RCLike.continuous_conj, minpoly.add_algebraMap, NormedSpace.exp_def, Matrix.PosSemidef.sq_sqrt, LinearIsometryEquiv.rTensor_apply, norm_algebraMap, NumberField.Units.coe_pow, IsPurelyInseparable.algebraMap_elemReduct_eq', Subspace.dualLift_of_mem, InnerProductSpace.isStarProjection_rankOne_self, coord_norm', NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, LaurentSeries.LaurentSeries_coe, WeakDual.isClosed_polar, spec_cfcₙAux, AlgebraicIndependent.liftAlgHom_comp_reprField, QuadraticMap.lineDifferentiableAt, Subalgebra.finiteDimensional_toSubmodule, hasFDerivAt_exp_smul_const, Field.Algebra.IsSeparable.finSepDegree_eq, IntermediateField.finrank_top', IntermediateField.inclusion_self, NumberField.Units.abs_det_eq_abs_det, IntermediateField.lift_bot, IsPurelyInseparable.algebraMap_iterateFrobenius, PerfectField.toPerfectRing, RootPairing.ker_rootForm_eq_dualAnnihilator, fderiv_finset_prod, IsGalois.fixedField_top, hasStrictFDerivAt_list_prod_attach', IntermediateField.normalClosure_of_normal, StrongDual.norm_toLpₗ_le, HasFPowerSeriesWithinAt.restrictScalars, Algebra.discr_powerBasis_eq_prod, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular, Polynomial.mem_iff_annIdealGenerator_dvd, spectrum.subset_polynomial_aeval, nnnorm_cfc_le, IsFractionRing.restrictScalars_fieldEquivOfAlgEquiv, stabilizer_isOpen_of_isIntegral, Algebra.IsAlgebraic.isNormalClosure_iff, PiTensorProduct.mapLMultilinear_apply_apply, IntermediateField.sup_toSubalgebra_of_left, spectralNorm_extends, InfiniteGalois.isOpen_iff_finite, galLift_id, InfiniteGalois.mem_range_algebraMap_iff_fixed, isSplittingField_AdjoinRoot_X_pow_sub_C, Matrix.IsHermitian.eigenvectorUnitary_coe, hasStrictFDerivAt_ringInverse, Subspace.dualAnnihilator_iInf_eq, NumberField.InfinitePlace.even_finrank_of_not_isUnramified, AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_fromSpecResidueField, Field.Emb.Cardinal.deg_lt_aleph0, isInteger_of_is_root_of_monic, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, NumberField.inverse_basisMatrix_mulVec_eq_repr, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, RatFunc.denom_div_dvd, InnerProductSpace.rankOne_comp_rankOne, HasStrictDerivAt.comp_hasStrictFDerivAt, fermatLastTheoremWith'_of_semifield, HasDerivWithinAt.comp_hasFDerivWithinAt, IntermediateField.relfinrank_bot_left, NumberField.RingOfIntegers.instIsIntegralClosureInt, Module.Basis.traceDual_involutive, SpectrumRestricts.starAlgHom_apply, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, AnalyticAt.hasFPowerSeriesAt, LinearMap.BilinForm.orthogonal_span_singleton_eq_toLin_ker, Polynomial.Gal.splits_in_splittingField_of_comp, LinearIsometry.toLinearMap_rTensor, Matrix.toEuclideanLin_eq_toLin, NumberField.Units.coe_injective, CFC.log_smul', RatFunc.rank_ratFunc_ratFunc, IntermediateField.toSubalgebra_injective, StrongDual.toLpₗ_of_not_memLp, PiTensorProduct.mapL_apply, Matrix.isHermitian_iff_isSymmetric, Subspace.dualRestrict_surjective, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, hasStrictFDerivAt_finset_prod, NumberField.Units.coe_one, spectralAlgNorm_extends, Valued.integer.norm_unit, IntermediateField.le_extendScalars_iff, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, InnerProductSpace.rankOne_comp, spectrum.map_inv, HasDerivWithinAt.comp_hasFDerivAt, ValuationSubring.prime_idealOfLE, StrongDual.mem_polarSubmodule, RatFunc.instIsScalarTowerOfPolynomial, minpoly.ofSubring, hasDerivWithinAt_comp_mul_left_smul_iff, Polynomial.normalize_eq_self_iff_monic, Real.fourierIntegral_fderiv, IntermediateField.extendScalars.orderIso_symm_apply_coe, exists_isTranscendenceBasis_and_isSeparable_of_perfectField, InnerProductSpace.toMatrix_rankOne, cfcₙHom_real_eq_restrict, normal_iff, AlgHom.card, PiTensorProduct.liftIsometry_comp_mapL, Submodule.map_smul', RCLike.conj_wInner_symm, InnerProductSpace.isSymmetric_rankOne_self, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, FiniteDimensional.finiteDimensional_subalgebra, inv_zero, FractionalIdeal.smul_mem_dual_one, Commute.cfcHom, IsPurelyInseparable.bijective_restrictDomain, LinearIsometryEquiv.symm_rTensor, IntermediateField.sepDegree_bot', Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, cfc_apply_mem_elemental, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, TensorProduct.commIsometry_symm, NumberField.mixedEmbedding.unitSMul_smul, IntermediateField.inclusion_injective, Differential.instDifferentialAlgebraSubtypeMemIntermediateField, ContinuousAlternatingMap.restrictScalarsCLM_apply, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_left, hfdifferential_apply, IntermediateField.LinearDisjoint.bot_right, MvPolynomial.quotient_mk_comp_C_injective, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, Irreducible.separable, Polynomial.isSplittingField_C, LinearMap.range_smul', AlgebraicClosure.Monics.map_eq_prod, Field.primitive_element_iff_minpoly_degree_eq, LindemannWeierstrass.integral_exp_mul_eval, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcₙHom, IntermediateField.map_fixingSubgroup_index, AlgHom.fieldRange_eq_top, IntermediateField.normal_iff_forall_map_le, NumberField.AdeleRing.algebraMap_injective, spectrum.differentiableOn_inverse_one_sub_smul, ValuationSubring.ofPrime_scalar_tower, IsAlgClosed.algebraMap_bijective_of_isIntegral, separableClosure.isAlgebraic, IntermediateField.adjoin_toSubalgebra, FunctionField.ringOfIntegers.algebraMap_injective, Field.sepDegree_mul_insepDegree, IsFractionRing.mk'_eq_zero_iff_eq_zero, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, DoubleCentralizer.algebraMap_fst, NumberField.ComplexEmbedding.isConj_symm, Real.hasFPowerSeriesOnBall_linear_zero, NumberField.ComplexEmbedding.Extension.comp_eq, ContinuousLinearMap.adjoint_toSpanSingleton, ContinuousLinearMap.toBilinForm_injective, quasispectrumRestricts_iff_spectrumRestricts_inr, Ideal.ramificationIdx_mul_inertiaDeg_of_isLocalRing, rootOfSplitsXPowSubC_pow, AlgHom.card_le, inner_smul_real_left, FiniteField.splits_X_pow_card_sub_X, IntermediateField.rank_eq_one_iff, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, HasDerivAtFilter.comp_hasFDerivAtFilter_of_eq, IsGaloisGroup.intermediateField, ProbabilityTheory.isPosSemidef_covarianceBilinDual, LinearMap.finrank_range_dualMap_eq_finrank_range, ContinuousLinearMap.isEmbedding_restrictScalars, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, RCLike.nnnorm_conj, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, ValuationSubring.principalUnitGroupEquiv_apply, Module.End.eigenspace_div, Unitization.instCStarRing, AlgEquiv.restrictNormalHom_id, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, Field.insepDegree_self, galRestrict_apply, Polynomial.span_minpoly_eq_annihilator, RCLike.wInner_one_const_right, Commute.cfc, AlgHom.coe_toContinuousLinearMap, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, HasFDerivWithinAt.pow', Ring.instFiniteDimensionalFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Matrix.ofLp_toEuclideanLin_apply, IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin, Real.one_add_rpow_hasFPowerSeriesAt_zero, spectralNorm.eq_of_normalClosure', InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, NumberField.ComplexEmbedding.lift_comp_algebraMap, Ideal.instLiesOverBotOfIsPrime, nnnorm_algebraMap', mem_span_of_iInf_ker_le_ker, isClosedEmbedding_cfcₙHom_of_cfcHom, RCLike.norm_sq_re_conj_add, spectrum.map_polynomial_aeval_of_degree_pos, ContinuousMap.spectrum_eq_range, innerSLFlip_apply, AlgHom.mem_fieldRange, WeakDual.ker_isMaximal, IntermediateField.finrank_fixedField_eq_card, Algebra.normalizedTrace_minpoly, InnerProductSpace.toContinuousLinearMap_toDualMap, HasFDerivAt.list_prod', separableClosure.isSepClosure, Polynomial.annIdealGenerator_aeval_eq_zero, InfiniteGalois.toAlgEquivAux_eq_liftNormal, separatingDual_iff_injective, IsPurelyInseparable.injective_restrictDomain, IsSelfAdjoint.commute_cfcₙHom, Field.primitive_element_iff_minpoly_natDegree_eq, Rat.ringOfIntegersEquiv_apply_coe, Polynomial.fderivWithin_aeval, strictConvex_iff_ordConnected, IntermediateField.normalClosure_def'', hasFDerivAt_pow', extremePoints_doublyStochastic, RCLike.conj_im, Polynomial.fderivWithin, WeierstrassCurve.Projective.addU_smul, Subfield.relrank_eq_rank_of_le, Subspace.dualEquivDual_def, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, Field.Emb.Cardinal.strictMono_filtration, TensorProduct.enorm_assoc, IntermediateField.relfinrank_eq_finrank_of_le, IsIntegralClosure.isFractionRing_of_algebraic, RCLike.conj_I, FiniteField.nonempty_algHom_extension, FractionalIdeal.spanSingleton_mul_coeIdeal_eq_coeIdeal, WeakDual.CharacterSpace.norm_le_norm_one, IntermediateField.isScalarTower_over_bot, IntermediateField.isSeparable_tower_bot, Matrix.linfty_opNorm_toMatrix, IntermediateField.minpoly_eq, innerSL_apply_norm, InnerProductSpace.toDual_apply_eq_toDualMap_apply, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left, nnqsmul_def, ContinuousLinearMap.coe_restrictScalarsL, LinearMap.adjoint_inner_left, FractionalIdeal.coe_inv_of_nonzero, IntermediateField.mem_toSubalgebra, IntermediateField.isSplittingField_iff, AlgEquiv.restrictNormal_commutes, NumberField.InfinitePlace.comap_mk_lift, IntermediateField.bot_toSubfield, RCLike.inv_def, Field.sepDegree_eq_of_isPurelyInseparable_of_isSeparable, NumberField.RingOfIntegers.coe_eq_algebraMap, NumberField.InfinitePlace.comap_smul, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, Subspace.dualLift_rightInverse, IsPurelyInseparable.pow_mem, NumberField.InfinitePlace.not_isUnramified_iff_card_stabilizer_eq_two, IntermediateField.topEquiv_symm_apply_coe, HasStrictDerivAt.comp_hasStrictFDerivAt_of_eq, Valuation.valuationSubring_not_isField, FiniteGaloisIntermediateField.adjoin_val, LieAlgebra.rank_le_finrank_engel, NumberField.mixedEmbedding.convexBodyLT_convex, IsUnramifiedAtInfinitePlaces.id, hasFPowerSeriesOnBall_cuspFunction, MvPolynomial.vanishingIdeal_empty, NumberField.mem_span_integralBasis, innerSL_real_flip, WeierstrassCurve.Projective.add_of_Y_eq, Ideal.coe_smul_primesOver_eq_map_galRestrict, TensorProduct.dist_tmul_le, IntermediateField.adjoin_eq_range_algebraMap_adjoin, TensorProduct.norm_lid, IsFractionRing.fieldEquivOfAlgEquivHom_injective, Algebra.discr_isUnit_of_basis, MeasureTheory.charFun_eq_charFunDual_toDualMap, IntermediateField.rank_top', IntermediateField.isAlgebraic_adjoin_simple, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, CFC.quasispectrum_abs, TensorProduct.toLinearEquiv_assocIsometry, HasMFDerivAt.prod, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, RatFunc.num_div_dvd', norm_cfc_le, IntermediateField.AdjoinSimple.normal_algebraicClosure, PiTensorProduct.mapL_opNorm, FiniteGaloisIntermediateField.adjoin_simple_map_algEquiv, toMatrix_innerSL_apply, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, one_add_rpow_hasFPowerSeriesAt_zero, IntermediateField.normal_iff_forall_map_eq', BoundedContinuousFunction.toContinuousMapStarₐ_apply_apply, IntermediateField.intermediateFieldMap_apply_coe, IntermediateField.topEquiv_apply, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, CFC.spectrum_abs, Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two, WeierstrassCurve.Projective.add_of_X_ne, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, Subspace.dualCopairing_nondegenerate, FixedPoints.toAlgHom_bijective, Polynomial.SplittingFieldAux.splits, ContinuousLinearMap.norm_restrictScalars, Algebra.normalizedTrace_algebraMap_apply, IsLocalRing.ResidueField.finite_of_module_finite, Algebra.normalizedTrace_def, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, Ideal.FinrankQuotientMap.span_eq_top, NormedAlgebra.norm_smul_le, NumberField.Units.coe_zpow, NumberField.mem_span_basisOfFractionalIdeal, Units.continuousOn_inv₀_spectrum, Polynomial.IsSplittingField.instFiniteDimensionalSplittingField, FiniteField.minpoly_frobeniusAlgHom, AffineSubspace.sSameSide_iff_exists_right, TensorProduct.nnnorm_assoc, DoubleCentralizer.coe_eq_algebraMap, IsFractionRing.isInteger_of_isUnit_den, PiTensorProduct.tprodL_apply, IntermediateField.AdjoinSimple.isIntegral_gen, Differential.logDeriv_algebraMap, ContinuousLinearMap.orthogonal_range, IsGaloisGroup.fixedPoints, SpectrumRestricts.image, LieAlgebra.IsKilling.rootSystem_pairing_apply, map_mem_algebraicClosure_iff, ordinaryHypergeometricSeries_eq_zero_iff, ZMod.frobenius_zmod, Localization.subalgebra.isFractionRing_ofField, Algebra.IsQuadraticExtension.isCyclic, FunctionField.ringOfIntegers.instIsFractionRingSubtypeMemSubalgebraPolynomial, PerfectField.separable_iff_squarefree, Polynomial.Gal.restrict_surjective, LinearEquiv.smulOfNeZero_symm_apply, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, NumberField.InfinitePlace.even_nat_card_aut_of_not_isUnramified, IntermediateField.isPurelyInseparable_bot, Polynomial.mem_normalizedFactors_iff, LaurentSeries.valuation_coe_ratFunc, TensorProduct.mapIsometry_apply, ValuationSubring.coe_unitGroupMulEquiv_symm_apply, WeierstrassCurve.Projective.add_of_Y_ne', cfcₙAux_mem_range_inr, NumberField.InfinitePlace.isUnramified_iff_stabilizer_eq_bot, PiTensorProduct.liftIsometry_apply_apply, ContinuousMap.adjoin_id_eq_span_one_add, Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable, AlgebraicIndependent.aevalEquivField_apply_coe, ProbabilityTheory.covarianceBilin_map, RCLike.real_smul_ofReal, cfcₙ_norm_sq_nonneg, IsGaloisGroup.to_isFractionRing, Unitization.nnnorm_eq_sup, Valuation.Integer.not_isUnit_iff_valuation_lt_one, IntermediateField.LinearDisjoint.exists_field_of_isDomain, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_right, Ideal.factors_span_eq, one_add_cpow_hasFPowerSeriesOnBall_zero, AffineSubspace.wSameSide_iff_exists_right, minpoly.natSepDegree_eq_one_iff_pow_mem, spectralNorm.eq_of_tower, spectrum.scalar_eq, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, FiniteField.instIsCyclicAlgEquivOfFinite, FormalMultilinearSeries.ofScalars_smul, Matrix.toLin_finTwoProd_toContinuousLinearMap, minpoly.root, TensorProduct.toLinearMap_mapIsometry, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, NumberField.FinitePlace.norm_eq_one_iff_notMem, IntermediateField.restrictScalars_toSubalgebra, Valuation.exists_pow_Uniformizer, IntermediateField.finiteDimensional_left, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, NumberField.InfinitePlace.LiesOver.mk_embedding_comp, AffineSubspace.subtypeₐᵢ_linearIsometry, Algebra.normalizedTrace_trans_apply, TensorProduct.enorm_map, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, RCLike.conj_eq_iff_im, ContinuousLinearMap.adjoint_comp, PiTensorProduct.norm_eval_le_projectiveSeminorm, isConjRoot_iff_orbitRel, le_perfectClosure_iff, perfectClosure.isAlgebraic, MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection, Subspace.map_le_dualAnnihilator_dualAnnihilator, AlgHom.bijective, NumberField.IsCMField.complexConj_eq_self_iff, Commute.cfcₙ, IntermediateField.isSeparable_sup, NumberField.mixedEmbedding.logMap_real, FiniteGaloisIntermediateField.finiteDimensional, PowerSeries.ker_coeff_eq_max_ideal, MvPolynomial.zeroLocus_span, InnerProductSpace.toLinearMap_rankOne, ContinuousLinearMap.adjointAux_inner_right, HasMFDerivWithinAt.mul, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, RCLike.conj_re_ax, TensorProduct.commIsometry_apply, IntermediateField.coe_smul, Ring.instFaithfulSMulSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, NormedSpace.expSeries_sum_eq_div, IntermediateField.set_range_subset, TensorProduct.congrIsometry_symm, Subalgebra.frontier_spectrum, BoundedContinuousFunction.coe_toContinuousMapₐ, Complex.log_eq_integral, Field.finSepDegree_dvd_finrank, exists_linearIndependent_algEquiv_apply, InfiniteGalois.restrictNormalHom_continuous, Algebra.IsSeparable.sepDegree_eq, RootPairing.rootForm_restrict_nondegenerate_of_isAnisotropic, galRestrictHom_symm_apply, AlgHom.restrictNormal_comp, IsLocalRing.ResidueField.instIsScalarTower, IsGaloisGroup.subgroup, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_left, HasStrictFDerivAt.fun_smul, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, FiniteField.bijective_frobeniusAlgHom_pow, IntermediateField.fixedField.isScalarTower, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, fderiv_fun_mul, IntermediateField.coe_equivMap_apply, IsGalois.finiteDimensional_of_finite, Submodule.adjoint_orthogonalProjection, IntermediateField.mem_adjoin_simple_iff, HasFDerivAt.pow', Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField, HasStrictFDerivAt.pow', hasFDerivWithinAt_iff_hasGradientWithinAt, IsPrimitiveRoot.embeddingsEquivPrimitiveRoots_apply_coe, AffineIsometryEquiv.ofEq_rfl, IntermediateField.finInsepDegree_bot, LinearMap.IsSymmetric.trace_eq_sum_eigenvalues, LinearMap.adjoint_comp, krullTopology_mem_nhds_one_iff, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, FormalMultilinearSeries.ofScalars_comp_neg_id, Field.nonempty_algEquiv_of_range_minpoly_eq, AlgEquiv.fieldRange_eq_top, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, HasStrictFDerivAt.multiset_prod, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, Matrix.toEuclideanLin_apply_piLp_toLp, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, LaurentSeries.coe_range_dense, Field.Emb.Cardinal.iSup_adjoin_eq_top, NumberField.AdeleRing.algebraMap_fst_apply, LinearMap.dualMap_surjective_iff, Unitization.quasispectrum_eq_spectrum_inr', ZMod.expand_card, LinearIsometry.strictConvexSpace_range_iff, RatFunc.finrank_ratFunc_ratFunc, HasFDerivWithinAt.smul, NormedSpace.expSeries_eq_expSeries_rat, Matrix.linfty_opNorm_eq_opNorm, JacobsonNoether.exists_separable_and_not_isCentral', IntermediateField.toSubalgebra_iSup_of_directed, NumberField.ComplexEmbedding.IsUnmixed.isReal_iff_isReal, Polynomial.separable_iff_derivative_ne_zero, LocalSubring.instIsScalarTowerSubtypeMemSubringToSubringOfPrime, Polynomial.Monic.eq_X_pow_char_pow_sub_C_of_natSepDegree_eq_one_of_irreducible, LinearMap.isSymmetric_iff_sesqForm, Subspace.dualLift_injective, HasStrictFDerivAt.mul_const', ContinuousLinearMap.IsPositive.adjoint_conj, krullTopology_mem_nhds_one_iff_of_normal, RatFunc.ofFractionRing_eq, IntermediateField.finrank_bot', FiniteField.frobeniusAlgEquiv_apply, NumberField.mixedEmbedding.normAtPlace_smul, galLiftEquiv_algebraMap_apply, IsGalois.map_fixingSubgroup, ContinuousLinearMap.star_eq_adjoint, IsUnramifiedAtInfinitePlaces.card_infinitePlace, Asymptotics.superpolynomialDecay_mul_const_iff, RatFunc.denom_algebraMap, IntermediateField.fixingSubgroup_isOpen, Polynomial.hasFDerivWithinAt_aeval, continuousOn_cfcₙ_setProd, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, ModularForm.prod_fintype_slash, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Asymptotics.superpolynomialDecay_param_mul_iff, RCLike.wInner_one_const_left, fderivWithin_list_prod', ProperCone.hyperplane_separation_of_notMem, Module.ker_algebraMap_end, FiniteGaloisIntermediateField.adjoin_simple_map_algHom, separableClosure.isSeparable, minpoly.natDegree_le, RCLike.norm_sq_re_add_conj, Complex.starConvex_slitPlane, HasFDerivWithinAt.fun_mul', IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_left, BoundedContinuousFunction.toContinuousMapₐ_apply, PrimeSpectrum.isHomeomorph_comap_tensorProductMap_of_isPurelyInseparable, fderiv_star, innerₛₗ_apply, innerSL_apply, Valued.integer.isUnit_iff_norm_eq_one, trace_eq_sum_embeddings, hasStrictFDerivAt_list_prod, IntermediateField.adjoin.finiteDimensional, IntermediateField.botEquiv_def, spectrum.resolvent_tendsto_cobounded, InnerProductSpace.isIdempotentElem_rankOne_self_iff, le_algebraicClosure_iff, IntermediateField.adjoin_adjoin_comm, IntermediateField.adjoin_eq_top_iff, StrongDual.toLp_apply, AlgebraicIndependent.algebraicClosure, Valued.integer.isPrincipalIdealRing_of_compactSpace, IntermediateField.toSubalgebra_lt_toSubalgebra, FDRep.char_orthonormal, IntermediateField.finSepDegree_bot', Polynomial.exists_separable_of_irreducible, Module.End.IsSemisimple.minpoly_squarefree, IntermediateField.val_mk, NumberField.RingOfIntegers.instIsScalarTower, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, NumberField.InfinitePlace.mem_stabilizer_mk_iff, RatFunc.num_mul_eq_mul_denom_iff, mem_galBasis_iff, InnerProductSpaceable.innerProp, IntermediateField.rank_sup_le, IntermediateField.LinearDisjoint.self_right, LinearIsometry.strictConvexSpace_range, CSA.fin_dim, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, FormalMultilinearSeries.ofScalars_series_eq_zero, fderivWithin_pow_ring', Field.finSepDegree_eq_finrank_iff, krullTopology_discreteTopology_of_finiteDimensional, RootPairing.restrictScalars_toLinearMap_apply_apply, NumberField.RingOfIntegers.instIsScalarTower_1, AlgHom.normal_bijective, NumberField.toNNReal_valued_eq_adicAbv, Orientation.kahler_apply_apply, FiniteDimensional.exists_is_basis_integral, FiniteField.frobenius_pow, RCLike.conj_inv, IsGaloisGroup.mulEquivAlgEquiv_symm_apply, IsSelfAdjoint.adjoint_conj, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, IsIntegral.mem_range_algebraMap_of_minpoly_splits, AlgEquiv.restrictNormalHom_apply, InfiniteGalois.mk_toAlgEquivAux, Normal.out, LinearIsometryEquiv.toLinearIsometry_rTensor, Representation.irreducible_iff_isSimpleModule_asModule, LeftInvariantDerivation.toDerivation_injective, MvPolynomial.zeroLocus_top, instIsAbelianGaloisSubtypeMemIntermediateField, PiTensorProduct.mapL_pow, IntermediateField.adjoin_simple_comm, algebraicClosure.isAlgClosure, FormalMultilinearSeries.ofScalars_sum_eq, OrthonormalBasis.sum_rankOne_eq_id, LeftInvariantDerivation.evalAt_mul, AlgEquiv.liftNormal_commutes, IntermediateField.inclusion_inclusion, Field.Emb.Cardinal.adjoin_image_leastExt, MeasureTheory.BoundedContinuousFunction.inner_toLp, ContinuousLinearMap.adjoint_inner_right, exists_extension_norm_eq, LaurentSeries.valuation_def, Subspace.dualAnnihilator_le_dualAnnihilator_iff, HasFDerivWithinAt.fun_pow', FiniteField.bijective_frobeniusAlgEquivOfAlgebraic_pow, TensorProduct.norm_tmul, IntermediateField.le_iff_le, IntermediateField.extendScalars_restrictScalars, NonnegSpectrumClass.of_spectrum_nonneg, FiniteField.nonempty_algHom_iff_finrank_dvd, MeasureTheory.convolution_mul_swap, minpoly.eq_iff_aeval_minpoly_eq_zero, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, ContinuousLinearMap.norm_smulRightL_le, quasispectrumRestricts_iff_spectrumRestricts, spectralNorm_extends_of_finiteDimensional, Algebra.discr_powerBasis_eq_prod'', InfiniteGalois.fixedField_bot, differentiableAt_iff_restrictScalars, Algebra.adjoin_eq_top_of_intermediateField, RCLike.enorm_conj, IntermediateField.adjoin_subset_adjoin_iff, IntermediateField.mem_extendScalars, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, Polynomial.coeff_eq_esymm_roots_of_splits, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.isUnit_iff_valued_eq_one, RCLike.conjAe_coe, fderivWithin_mul_const, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, HasFDerivAt.mul_const', norm_cfcHom, LieAlgebra.IsKilling.traceForm_coroot, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, InfiniteGalois.proj_of_le, Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective, TensorProduct.nnnorm_comm, FDRep.char_dual, Valuation.IsUniformizer.is_generator, FiniteField.expand_card, Module.Basis.traceDual_repr_apply, FormalMultilinearSeries.ofScalars_comp_neg, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, FGModuleCat.FGModuleCatEvaluation_apply', WeakDual.CharacterSpace.equivAlgHom_coe, HasStrictFDerivAt.fun_pow', IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, Polynomial.nodup_roots_iff_of_splits, IntermediateField.coe_type_toSubalgebra, IntermediateField.relrank_eq_rank_of_le, IntermediateField.lift_adjoin, HasFDerivAt.hasGradientAt, NumberField.basisOfFractionalIdeal_apply, LinearMap.IsSymmetric.conj_inner_sym, FiniteField.Extension.exists_frob_pow_eq, IsGaloisGroup.fixedPoints_le_of_le, Algebra.norm_smul_one_eq_norm, ContinuousLinearMap.isAdjointPair_inner, IntermediateField.extendScalars_top, TensorProduct.norm_map, Real.hasFDerivAt_fourierChar_neg_bilinear_right, IntermediateField.algebraicIndependent_adjoin_iff, NumberField.InfinitePlace.mem_orbit_iff, RatFunc.isScalarTower_liftAlgebra, Unitization.splitMul_injective, NumberField.InfinitePlace.isUnramifiedIn_comap, IntermediateField.rank_eq_rank_subalgebra, FormalMultilinearSeries.ofScalars_series_injective, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Nonneg.Icc_subset_segment, Algebra.normalizedTrace_trans, RingOfIntegers.algebraMap_norm_algebraMap, IsSimpleRing.exists_algEquiv_matrix_of_isAlgClosed, Field.lift_rank_mul_lift_sepDegree_of_isSeparable, autEquivRootsOfUnity_apply_rootOfSplit, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, ContinuousLinearEquiv.coord_norm', Polynomial.separable_cyclotomic, IntermediateField.fixedField_bot, Polynomial.isCoprime_map, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, IntermediateField.toSubalgebra_strictMono, Asymptotics.superpolynomialDecay_const_mul_iff, hasStrictFDerivAt_inv', IntermediateField.lift_sup, spectrum.nonzero_mul_comm, LinearMap.mem_span_iff_bound, Algebra.discr_powerBasis_eq_prod', PadicAlgCl.coe_eq, hasFDerivAt_exp_smul_const_of_mem_ball', NumberField.FinitePlace.isFinitePlace, cfcₙ_apply_mem_elemental, normalClosure.normal, quasispectrum_eq_spectrum_union_zero, Ideal.inertiaDeg_le_finrank, FixedPoints.toAlgAut_bijective, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, hasStrictFDerivAt_exp_smul_const, IsGalois.fixingSubgroup_normal_of_isGalois, dist_algebraMap, PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply_coe, Complex.hasStrictFDerivAt_log_real, separableClosure.map_eq_of_separableClosure_eq_bot, AffineSubspace.isometryEquivMap.apply_symm_apply, IsCyclotomicExtension.fromZetaAut_spec, IntermediateField.adjoin_adjoin_left, RCLike.wInner_cWeight_const_right, Ideal.exist_integer_multiples_notMem, HasStrictFDerivAt.mul, RCLike.inv_eq_conj, InfiniteGalois.algEquivToLimit_continuous, instIsPrincipalIdealRingSubtypeAdicCompletionMemValuationSubringAdicCompletionIntegers, LieAlgebra.isRegular_iff_finrank_engel_eq_rank, IntermediateField.normalClosure_mono, NumberField.instFiniteIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmodule, WeakDual.toStrongDual_apply, ContinuousMap.elemental_id_eq_top, LinearMap.eq_adjoint_iff_basis_right, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, trace_eq_sum_automorphisms, IsSelfAdjoint.commute_cfcₙ, MvPolynomial.mem_vanishingIdeal_iff, MvPolynomial.mem_vanishingIdeal_singleton_iff, hasDerivAt_exp_smul_const', IsIdempotentElem.quasispectrum_subset, WeakDual.CharacterSpace.compContinuousMap_comp, quasispectrum.preimage_algebraMap, IsScalarTower.AlgEquiv.restrictNormalHom_comp_apply, ValuationRing.isInteger_or_isInteger, separableClosure_le_iff, solvableByRad.isIntegral, ContinuousMultilinearMap.smulRightL_apply, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, MvPolynomial.expand_zmod, LinearIsometryEquiv.toLinearEquiv_rTensor, HasDerivAt.comp_hasFDerivAt, fderiv_mul_const, innerₛₗ_apply_coe, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, exists_pos_left_iff_sameRay_and_ne_zero, NumberField.RingOfIntegers.map_mk, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, Valuation.Uniformizer.is_generator, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, IntermediateField.sup_toSubalgebra_of_right, IntermediateField.algebraAdjoinAdjoin.instFaithfulSMulSubtypeMemSubalgebraAdjoinAdjoin, LinearIsometryEquiv.toLinearIsometry_lTensor, Representation.is_simple_module_iff_irreducible_ofModule, IntermediateField.insepDegree_bot, IsFractionRing.algEquiv_commutes, IntermediateField.equivOfEq_apply, SpectrumRestricts.rightInvOn, norm_algebraMap', IntermediateField.rank_bot', krullTopology_t2, NumberField.mixedEmbedding.convexBodySum_convex, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, range_cfcHom, convex_halfSpace_im_le, Algebra.norm_algebraMap, IsPurelyInseparable.algebraMap_elemReduct_eq, IntermediateField.le_sup_toSubalgebra, LinearMap.toSeminormFamily_apply, perfectClosure.map_eq_of_algEquiv, algebraicClosure.map_eq_of_algEquiv, AffineSubspace.wOppSide_iff_exists_right, AddChar.map_neg_eq_conj, ringKrullDim_eq_zero_of_field, Module.End.mem_spectrum_iff_isRoot_charpoly, Field.nonempty_algHom_of_minpoly_eq, EuclideanSpace.inner_single_right, ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdeal, NumberField.IsCMField.infinitePlace_complexConj, IntermediateField.isAlgebraic_adjoin_iff_bot, nnnorm_cfcHom, Module.Basis.traceDual_powerBasis_eq, Matrix.PosSemidef.sqrt_mul_self, WeakDual.CharacterSpace.equivAlgHom_symm_coe, continuousOn_cfc, IntermediateField.fieldRange_val, IntermediateField.liftAlgEquiv_apply, Matrix.range_diagonal, NumberField.ComplexEmbedding.IsConj.comp, HasFDerivWithinAt.finset_prod, hasStrictFDerivAt_list_prod', RatFunc.num_div_denom, spectrum.mem_resolventSet_of_norm_lt, IntermediateField.insepDegree_top, ValuationSubring.subtype_apply, Quaternion.hasSum_expSeries_of_imaginary, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, FixedPoints.smulCommClass', separableClosure_le_separableClosure_iff, Submodule.orthogonal_eq_inter, RCLike.normSq_add, IsGaloisGroup.card_eq_finrank, FixedPoints.coe_algebraMap, UniformOnFun.continuousSMul_submodule_of_image_bounded, ValuationSubring.valuation_eq_one_iff, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, cardinalMk_algHom, IsGalois.tfae, WeierstrassCurve.Projective.dblX_eq, LinearMap.IsPositive.adjoint_eq, IntermediateField.transcendental_adjoin_iff, Height.logHeight_smul_eq_logHeight, NumberField.InfinitePlace.isUnramified_iff_mult_le, ContinuousLinearEquiv.coord_norm, FiniteDimensional.subalgebra_toSubmodule, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, Matrix.toEuclideanLin_eq_toLin_orthonormal, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1, MeasureTheory.lpMeasToLpTrim_smul, minpoly.iterateFrobenius_of_isSeparable, LinearEquiv.conjAlgEquiv_surjective, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, Module.End.hasEigenvalue_iff_mem_spectrum, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, NormedSpace.expSeries_hasSum_exp_of_mem_ball', fderivWithin_pow, LinearMap.not_hasEigenvalue_zero_tfae, NumberField.InfinitePlace.even_card_aut_of_not_isUnramifiedIn, ContinuousMultilinearMap.norm_smulRight, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, separableClosure.separableClosure_eq_bot, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_right, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly, IntermediateField.rank_bot_mul_relrank, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, ordinaryHypergeometricSeries_eq_zero_of_neg_nat, LeftInvariantDerivation.commutator_coe_derivation, LinearIsometry.rTensor_apply, hasStrictFDerivAt_pow, ValuationSubring.ofPrime_localization, NumberField.InfiniteAdeleRing.denseRange_algebraMap, NumberField.mixedEmbedding.fundamentalCone.smul_mem_iff_mem, Submodule.norm_orthogonalProjection, HasDerivAt.conj_conj, IntermediateField.sup_toSubalgebra_of_isAlgebraic_right, LinearIsometry.toLinearMap_lTensor, Submodule.comap_smul', IntermediateField.toSubalgebra_le_toSubalgebra, Valuation.HasExtension.instIsScalarTower_valuationSubring, coe_innerₛₗ_apply, IsAlgClosed.isAlgClosure_of_transcendence_basis, HasGradientAt.hasDerivAt, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, TensorProduct.nndist_tmul_le, InfiniteGalois.limitToAlgEquiv_symm_apply, galRestrict'_comp, InnerProductSpace.continuousLinearMapOfBilin_apply, NormedSpace.double_dual_bound, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, CStarAlgebra.toStarModule, IntermediateField.adjoin_toSubfield, LinearMap.BilinForm.toLin_restrict_range_dualCoannihilator_eq_orthogonal, RCLike.conj_eq_re_sub_im, IsTranscendenceBasis.lift_rank_eq_max_lift, IntermediateField.finiteDimensional_map, RatFunc.toFractionRingRingEquiv_symm_eq, minpoly.degree_dvd, IsPurelyInseparable.isPRadical, MvRatFunc.rank_eq_max_lift, WeakDual.isSeqCompact_polar, separableClosure.map_eq_of_algEquiv, NumberField.Units.finrank_mul_regulator_eq_det, IsPrimitiveRoot.lcm_totient_le_finrank, IsPurelyInseparable.instNonemptyAlgHomOfPerfectField, ContinuousAlternatingMap.uniformContinuous_restrictScalars, linearIndependent_pow, FractionalIdeal.coe_div, rank_lt_rank_dual, LieAlgebra.IsKilling.span_weight_eq_top, Polynomial.residueFieldMapCAlgEquiv_symm_X, IntermediateField.finSepDegree_top, PiTensorProduct.injectiveSeminorm_tprod_le, Polynomial.IsSplittingField.adjoin_rootSet_eq_range, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, HasStrictFDerivAt.fun_mul, hasFDerivWithinAt_pow, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, CSA.isCentral, coe_algEquiv_lpBCF_symm, spectralNorm_eq_of_equiv, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, AlgHom.restrictNormal_commutes, IsIntegral.inv_mem_adjoin, HasFDerivWithinAt.mul', IntermediateField.normalClosure_le_iff_of_normal, FiniteField.orderOf_frobeniusAlgHom, RCLike.conj_ofNat, OrthonormalBasis.tensorProduct_apply, QuasispectrumRestricts.mul_comm_iff, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, AlgHom.fieldRange_of_normal, NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype, IntermediateField.Lifts.eq_iff, algebraMap.coe_expect, NumberField.FinitePlace.norm_le_one, NumberField.Units.sum_mult_mul_log, Polynomial.hasFDerivWithinAt, WeierstrassCurve.Projective.add_of_Y_ne, WithLp.unitizationAlgEquiv_apply, Field.Emb.Cardinal.adjoin_basis_eq_top, NumberField.ComplexEmbedding.IsReal.isConjGal_one, HasFDerivAtFilter.restrictScalars, LinearMap.flip_surjective_iff₂, NumberField.ComplexEmbedding.lift_algebraMap_apply, IntermediateField.iInf_toSubalgebra, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton, Valued.integer.norm_coe_unit, IntermediateField.normalClosure_map_eq, WithAbs.instIsSeparable, HasStrictDerivAt.complexToReal_fderiv, PiTensorProduct.mapL_add, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_left, TensorProduct.congrIsometry_apply, IntermediateField.relrank_bot_left, convex_halfSpace_re_gt, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, IsConjRoot.sub_algebraMap, algebraMap_galRestrict'_apply, algebraMap.coe_inv, RingOfIntegers.coe_algebraMap_norm, innerSL_apply_coe, Ring.instIsIntegralClosureNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, fderivWithin_mul', LaurentSeries.instIsFractionRingPowerSeries, HasDerivWithinAt.comp_hasFDerivWithinAt_of_eq, tendsto_algebraMap_cobounded, Polynomial.IsSplittingField.IsScalarTower.splits, tendsto_algebraMap_inv_atTop_nhds_zero_nat, AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField_apply, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, galRestrictHom_apply, RatFunc.denom_dvd, IntermediateField.isPurelyInseparable_tower_top, Algebra.Etale.iff_exists_algEquiv_prod, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, dist_algebraMap', FiniteField.coe_frobeniusAlgHom, hasFDerivAt_inv', LinearMap.toMatrix_adjoint, MvPolynomial.instIsMaximalVanishingIdealSingletonForallSet, IntermediateField.le_normalClosure, RCLike.conj_smul, Subspace.map_dualCoannihilator, FDRep.scalar_product_char_eq_finrank_equivariant, cfcₙHom_of_cfcHom_map_quasispectrum, IntermediateField.equivOfEq_trans, spectrum.resolvent_isBigO_inv, WeakDual.CharacterSpace.compContinuousMap_id, convexOn_zpow, Polynomial.annIdealGenerator_eq_zero_iff, ContinuousLinearMap.isPositive_adjoint_comp_self, IntermediateField.normalClosure_def', TensorProduct.nnnorm_lid, LinearMap.im_inner_adjoint_mul_self_eq_zero, NormedSpace.expSeries_summable_of_mem_ball', Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, Matrix.IsHermitian.mulVec_eigenvectorBasis, ValuationSubring.algebraMap_injective, autAdjoinRootXPowSubC_root, Matrix.l2_opNorm_def, IsAlgClosed.surjective_restrictDomain_of_isAlgebraic, Matrix.toEuclideanLin_toLp, ModuleCat.isScalarTower_of_algebra_moduleCat, IntermediateField.mem_bot, nnnorm_cfcₙ_le, IntermediateField.adjoin_algebraic_toSubalgebra, LeftInvariantDerivation.toFun_eq_coe, Field.sepDegree_le_rank, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1, norm_innerSL_le, AffineSubspace.subtypeₐᵢ_toAffineMap, IntermediateField.mem_restrict, Valuation.HasExtension.instLiesOverSubtypeMemValuationSubringValuationSubringMaximalIdeal, Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, perfectClosure.perfectRing, CStarAlgebra.exists_sum_four_unitary, spectrum.map_pow_of_pos, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, RCLike.real_smul_eq_coe_mul, algebraMap.coe_ratCast, NumberField.Units.dirichletUnitTheorem.exists_unit, normal_self, isFractionRing_of_exists_eq_algebraMap_or_inv_eq_algebraMap_of_injective, Polynomial.monic_normalize, NumberField.ComplexEmbedding.isConj_one_iff, PowerSeries.smul_inv, IntermediateField.LinearDisjoint.isDomain, LinearMap.posSemidef_toMatrix_iff, fderiv_list_prod', HasMFDerivWithinAt.prod, Complex.log_inv_eq_integral, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Module.Basis.norm_repr_le_norm, IntermediateField.finrank_dvd_of_le_right, HasMFDerivAt.mul', NumberField.InfinitePlace.comap_surjective, HasFDerivAt.star_star, IsGalois.splits, Polynomial.resultant_eq_zero_iff, HasGradientWithinAt.hasFDerivWithinAt, IntermediateField.fixingSubgroup_bot, hasFDerivAt_exp, IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar, RCLike.hasSum_conj', IntermediateField.finrank_le_of_le_right, NumberField.RingOfIntegers.instIsIntegralClosure, InnerProductSpace.conj_inner_symm, Orthonormal.tmul, LinearMap.isAdjointPair_inner, LinearMap.IsPositive.adjoint_conj, upperHemicontinuous_spectrum, AnalyticOnNhd.eval_mvPolynomial, Polynomial.pairwise_coprime_X_sub_C, IsIntegral.minpoly_splits_tower_top, Submodule.norm_subtypeL_le, range_cfc, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, fderivWithin_pow_ring, isGalois_bot, IntermediateField.mem_fixingSubgroup_iff, IntermediateField.intermediateFieldMap_symm_apply_coe, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, LinearIsometryEquiv.symm_lTensor, NumberField.mixedEmbedding.norm_unit, algebraMap_galRestrictHom_apply, Algebra.prod_embeddings_eq_finrank_pow, IntermediateField.map_id, ContinuousLinearMap.smulRightL_apply_apply, LinearMap.range_smul, HasFDerivAt.fun_mul', minpoly.eq_X_sub_C, spectrum.mem_resolventSet_of_spectralRadius_lt, Polynomial.SplittingField.adjoin_rootSet, isSplittingField_iff_intermediateField, IsSepClosure.self_of_isSepClosed, HasStrictFDerivAt.mul_const, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, LinearIsometryEquiv.toContinuousLinearEquiv_smul, NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iff, isGalois_iff_isGalois_bot, spectrum.zero_eq, InfiniteGalois.fixingSubgroup_isClosed, IsSepClosed.surjective_restrictDomain_of_isSeparable, RootPairing.ker_corootForm_eq_dualAnnihilator, exists_integral_inj_algHom_of_fg, Subspace.dualAnnihilator_inf_eq, FiniteField.algebraMap_norm_eq_pow_sum, Field.insepDegree_le_of_left_le, IntermediateField.finiteDimensional_adjoin_pair, MvPowerSeries.smul_inv, spectrum.subset_circle_of_unitary, spectrum.subset_closedBall_norm, IntermediateField.normal_sup, ValuationSubring.primeSpectrumEquiv_apply, IntermediateField.coe_algebraMap_apply, NumberField.IsCMField.complexConj_torsion, Polynomial.residueFieldMapCAlgEquiv_algebraMap, HasFTaylorSeriesUpToOn.restrictScalars, isConformalMap_iff_is_complex_or_conj_linear, Subspace.dualAnnihilator_dualCoannihilator_eq, Module.End.exists_isNilpotent_isSemisimple, Polynomial.isCoprime_iff_aeval_ne_zero, LieModule.range_traceForm_le_span_weight, algebraMap_cobounded_le_cobounded, separableClosure.isGalois, HasGradientAtFilter.hasDerivAtFilter, Asymptotics.superpolynomialDecay_param_pow_mul_iff, PiTensorProduct.mapLMultilinear_opNorm, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, fderivWithin_restrictScalars_comp, FDRep.dualTensorIsoLinHom_hom_hom, MeasureTheory.eLpNorm_conj, inner_gradient_right, Real.fourierIntegral_iteratedFDeriv, IntermediateField.restrictScalars_adjoin, ax_grothendieck_zeroLocus, Transcendental.linearIndependent_sub_inv, Submodule.orthogonalProjection_norm_le, HasFDerivAt.mul', Matrix.PosDef.posDef_sqrt, IntermediateField.finrank_adjoin_simple_eq_one_iff, LinearMap.BilinForm.le_flip_dualSubmodule, FiniteField.natCard_algEquiv_extension, WeierstrassCurve.Projective.dblXYZ_of_Y_eq, integralClosure.mem_lifts_of_monic_of_dvd_map, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, IntermediateField.isSeparable_tower_top, coe_algEquiv_lpBCF, inner_conj_symm, Algebra.finite_of_essFiniteType_of_isAlgebraic, Module.End.eigenspace_aeval_polynomial_degree_1, algebraMap.coe_zpow, inv_eq_of_aeval_divX_ne_zero, MvPolynomial.vanishingIdeal_zeroLocus_eq_radical, exists_eq_sum_perm_of_mem_doublyStochastic, hasFDerivAt_list_prod_attach', instSubsingletonAlgHomOfIsPurelyInseparable, one_add_rpow_hasFPowerSeriesOnBall_zero, Polynomial.IsSplittingField.map, MeasureTheory.norm_condExpL2_le_one, ValuationSubring.coe_subtype, LinearMap.mem_span_iff_continuous, AddChar.inv_apply_eq_conj, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, IsFractionRing.ideal_span_singleton_map_subset, normalClosure.is_finiteDimensional, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, Subspace.isCompl_dualAnnihilator, FormalMultilinearSeries.ofScalars_norm_eq_mul, isBoundedBilinearMap_smulRight, CFC.log_smul, NormedSpace.expSeries_hasSum_exp_of_mem_ball, Polynomial.separable_map, IntermediateField.finiteDimensional_sup, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, IntermediateField.Lifts.le_iff, Algebra.normalizedTrace_self_apply, Polynomial.normalizedFactors_cyclotomic_card, HasDerivWithinAt.comp_hasFDerivAt_of_eq, ContinuousLinearMap.adjoint_innerSL_apply, MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton, Valuation.coeff_zero_minpoly, RCLike.normSq_sub, trace_adjoinSimpleGen, IntermediateField.fixingSubgroup_sup, fderivWithin_fun_mul, AlgEquiv.eq_linearEquivConjAlgEquiv, Orthonormal.inner_sum, IntermediateField.normal_iff_normalClosure_eq, IntermediateField.rank_adjoin_simple_eq_one_iff, le_iff_norm_sqrt_mul_rpow, Subspace.comap_dualAnnihilator_dualAnnihilator, NumberField.ComplexEmbedding.orderOf_isConj_two_of_ne_one, IntermediateField.AdjoinPair.algebraMap_gen₂, NumberField.house.basis_repr_norm_le_const_mul_house, Unitary.path_apply, cyclotomicCharacter.continuous, LieAlgebra.IsKilling.rootSystem_root_apply, NumberField.IsCMField.Units.complexConj_eq_self_iff, Unitary.spectrum_subset_circle, IntermediateField.isIntegral_iff, HasDerivAt.star_conj, TensorProduct.ext_iff_inner_right_threefold, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, InnerProductSpaceable.inner_.conj_symm, Polynomial.int_natDegree, ContinuousLinearMap.norm_smulRightL_apply, HasFDerivAt.smul, SchwartzMap.smulLeftCLM_smul, Algebra.botEquiv_symm_apply, contractLeft_assoc_coevaluation', fderiv_norm_sq_apply, IsSelfAdjoint.commute_cfc, separableClosure.normalClosure_eq_self, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, cfcHom_apply_mem_elemental, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, IntermediateField.coe_map, IsFractionRing.lift_mk', TrivSqZeroExt.snd_expSeries_of_smul_comm, RCLike.conj_neg_I, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, LinearMap.trace_map, ContinuousMultilinearMap.norm_mkPiAlgebraFin, wbtw_iff_sameRay_vsub, IntermediateField.adjoin.powerBasis_dim, TensorProduct.assocIsometry_symm_apply, hasFDerivAt_exp_of_mem_ball, InnerProductSpace.Core.inner_conj_symm, isConjRoot_iff_eq_algebraMap', IsCyclotomicExtension.autEquivPow_symm_apply, NormedSpace.dual_def, TensorProduct.inner_map_map, IsGalois.of_fixedField_normal_subgroup, IntermediateField.Lifts.nonempty_algHom_of_exist_lifts_finset, Polynomial.residueFieldMapCAlgEquiv_symm_C, fderiv_norm_sq, exists_mem_doublyStochastic_eq_smul_iff, IntermediateField.essFiniteType_iff, Field.Emb.cardinal_separableClosure, IntermediateField.AdjoinSimple.algebraMap_gen, Subspace.finrank_add_finrank_dualAnnihilator_eq, IntermediateField.isPurelyInseparable_sup, Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosed, TensorProduct.toLinearMap_mapInclIsometry, NumberField.FinitePlace.norm_def, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, Rat.ringOfIntegersWithValEquiv_apply, spectrum.mem_resolventSet_of_norm_lt_mul, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', PowerSeries.X_eq_normalizeX, norm_cfc_lt, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModule, NonnegSpectrumClass.iff_spectrum_nonneg, ContinuousLinearMap.toSesqForm_apply_norm_le, PiTensorProduct.injectiveSeminorm_def, IsIntegralClosure.isLocalization_of_isSeparable, IsGalois.mem_bot_iff_fixed, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, LinearMap.adjoint_id, inner_smul_left, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, FiniteField.finrank_extension, ValuationSubring.principalUnitGroup_symm_apply, ContinuousLinearMap.adjoint_adjoint, NumberField.mixedEmbedding.convexBodyLT'_convex, selfAdjoint.expUnitary_coe, fderivWithin_mul, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, Valuation.HasExtension.algebraMap_injective, ValuationRing.instIsFractionRingInteger, IntermediateField.algebra_adjoin_le_adjoin, IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, Subspace.dualPairing_eq, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Complex.continuousOn_one_add_mul_inv, NumberField.InfinitePlace.IsUnramified.comap, Polynomial.map_normalize, IsFractionRing.isUnit_den_iff, Icc_subset_segment, FractionalIdeal.inv_of_ne_zero, Module.Basis.traceDual_injective, Submodule.map_smul, FormalMultilinearSeries.ofScalars_norm, IsCyclotomicExtension.autEquivPow_apply, IsPurelyInseparable.elemExponent_def, HasFDerivWithinAt.fun_mul, RCLike.normSq_conj, separableClosure.isPurelyInseparable, HasStrictFDerivAt.smul, ContinuousLinearMap.orthogonal_ker, LinearMap.ker_smul, Nonneg.segment_eq_Icc, HasStrictFDerivAt.finset_prod, instIsFractionRingQuotientIdealResidueField, InnerProductSpace.norm_rankOne, Subspace.dualEquivDual_apply, Polynomial.SplittingField.instNormal, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, PiTensorProduct.mapLMultilinear_toFun_apply, FormalMultilinearSeries.ofScalarsSum_unop, IntermediateField.finite_of_fg_of_isAlgebraic, TensorProduct.edist_tmul_le, Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, quasispectrum.instCompactSpace, LinearMap.IsPositive.conj_adjoint, Polynomial.IsSplittingField.finiteDimensional, IntermediateField.isScalarTower_mid, IntermediateField.finSepDegree_bot, hasStrictFDerivAt_exp_smul_const_of_mem_ball, exists_pos_right_iff_sameRay_and_ne_zero, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, IsGalois.ofDual_intermediateFieldEquivSubgroup_apply, Valuation.HasExtension.algebraMap_mem_maximalIdeal_iff, Unitization.cfcₙ_eq_cfc_inr, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, degree_radical_le, perfectClosure.isPurelyInseparable, le_iff_norm_sqrt_mul_sqrt_inv, IntermediateField.isSeparable_adjoin_iff_isSeparable, Asymptotics.superpolynomialDecay_mul_param_iff, HasFDerivWithinAt.list_prod', QuadraticMap.hasLineDerivAt, prod_galRestrict_eq_norm, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', fderiv_inv', IntermediateField.sepDegree_top, Module.Basis.traceDual_eq_iff, IsGaloisGroup.fixedPoints_eq_bot, NormedSpace.exp_eq_expSeries_sum, WeierstrassCurve.Affine.Point.map_id, PiTensorProduct.tprodL_coe, convexOn_iff_slope_mono_adjacent, fderivWithin_pow', Localization.subalgebra.instIsFractionRingSubtypeMemSubalgebra, IsAlgClosed.perfectRing, LeftInvariantDerivation.evalAt_apply, LinearMap.dualAnnihilator_ker_eq_range_flip, hasFDerivAt_finset_prod, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm, nnnorm_cfcₙ_lt, IntermediateField.extendScalars_le_extendScalars_iff, RatFunc.toFractionRing_eq
toDiv 📖	CompOp	2 math math: nnratCast_def, div_eq_mul_inv
toDivisionSemiring 📖	CompOp	7377 math math: withSeminorms_iff_mem_nhds_isVonNBounded, Field.FiniteDimensional.of_exists_primitive_element, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, IsLocalMaxOn.fderivWithin_nonpos, Polynomial.mul_div_eq_iff_isRoot, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, FiniteField.Extension.frob_apply, LinearMap.det_toContinuousLinearMap, RatFunc.instFaithfulSMulPolynomialLaurentSeries, mfderiv_sumSwap, TangentBundle.continuousLinearMapAt_model_space, hasFDerivAt_iff_hasDerivAt, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, ContinuousLinearEquiv.antilipschitz, VectorBundleCore.toFiberBundleCore_coordChange, ContMDiffAt.coordChangeL, iteratedDeriv_scomp_two, TensorProduct.mapInclIsometry_apply, Finset.expect_ite_mem, ContinuousLinearMap.rayleigh_smul, Polynomial.Gal.galActionHom_restrict, mfderiv_prod_eq_add, Real.hasDerivAt_arccos, Real.hasDerivAt_fourier, InnerProductSpace.Core.inner_smul_right, AffineSpace.asymptoticNhds_smul, NumberField.basisMatrix_eq_embeddingsMatrixReindex, LinearIsometryEquiv.strictConvex_preimage, WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero, Polynomial.degree_normalize, TemperedDistribution.lineDerivOpCLM_eq, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', PiTensorProduct.mapL_id, Algebra.IsUnramifiedAt.exists_primesOver_under_adjoin_eq_singleton_and_residueField_bijective, ContinuousLinearMap.instT2Space, Submodule.starProjection_apply_eq_isComplProjection, Lagrange.interpolate_one, DiffContOnCl.smul, nhds_hasBasis_absConvex_open, fderiv_iteratedFDeriv, Polynomial.differentiableWithinAt, MeasureTheory.convolution_flip, Trivialization.pullback_linear, Algebra.normalizedTrace_map, FormalMultilinearSeries.comp_rightInv_aux1, ContinuousLinearMap.hasFPowerSeriesOnBall, MDifferentiable.coordChangeL, AlgEquiv.restrictNormal_trans, RatFunc.laurent_injective, IsAlgClosed.roots_eq_zero_iff_degree_nonpos, IntermediateField.extendScalars_toSubfield, exists_rat_pow_btwn, ContinuousLinearEquiv.conjContinuousAlgEquiv_refl, AddCircle.coe_equivIco_mk_apply, hasStrictFDerivAt_apply, differentiableWithinAt_finCons', NumberField.InfinitePlace.Completion.isometry_extensionEmbeddingOfIsReal, Orthonormal.linearIndependent, fderiv_snd, LinearIsometryEquiv.hasStrictFDerivAt, Bundle.Trivial.continuousLinearEquivAt_trivialization, ContinuousLinearMap.derivWithin_of_bilinear, HasStrictFDerivAt.isLittleOTVS, ValuationRing.mem_integer_iff, Finset.dens_union_of_disjoint, SchwartzMap.lineDerivOpCLM_eq, NumberField.InfinitePlace.isNontrivial, Algebra.normalizedTrace_algebraMap_eq_id, AddChar.card_addChar_le, NumberField.InfinitePlace.eq_iff_isEquiv, IntermediateField.finInsepDegree_top, LieAlgebra.IsKilling.iInf_ker_weight_eq_bot, InfiniteGalois.normal_iff_isGalois, LinearMap.BilinForm.dualSubmoduleParing_spec, Height.logHeight₁_pow, continuous_cfcₙHomSuperset_left, SpectrumRestricts.nnreal_of_nonneg, hasDerivWithinAt_Iio_iff_Iic, HasStrictFDerivAt.fun_mul', fderivWithin_ofNat, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, HasMFDerivAt.mul, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, Submodule.coe_continuous_linearProjOfClosedCompl', InnerProductSpace.isPositive_rankOne_self, LinearIsometryEquiv.comp_fderiv, Polynomial.natSepDegree_le_natDegree, MeasureTheory.condExpL1_smul, Seminorm.absorbent_closedBall_zero, ContinuousLinearMap.isBigO_comp, Lagrange.interpolate_eq_of_values_eq_on, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, ContinuousAlternatingMap.opNorm_prod, LinearMap.ortho_smul_right, Orthonormal.inner_left_finsupp, ordinaryHypergeometric_sum_eq, ArchimedeanClass.FiniteResidueField.mk_ratCast, Polynomial.coe_normUnit_of_ne_zero, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, NNRat.coe_floor, norm_cfcₙHom, IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', IntermediateField.aeval_gen_minpoly, OrthonormalBasis.orthogonalProjection_eq_sum, IntermediateField.adjoin_eq_top_iff_of_isAlgebraic, hasDerivWithinAt_ofNat, ContinuousLinearMap.analyticWithinAt_bilinear, ValuationSubring.mem_comap, IsIntegralClosure.rank, strictConvexOn_iff_slope_strict_mono_adjacent, HasCompactSupport.convolution_integrand_bound_left, Subfield.rank_comap, ContinuousLinearMap.compSL_apply, ContinuousLinearMap.continuous₂, LinearMap.IsSymmetric.inner_map_polarization, RCLike.geometric_hahn_banach_point_open, Polynomial.IsSplittingField.mul, NNRat.cast_strictMono, ValuationSubring.coe_mem_principalUnitGroup_iff, fderivWithin_comp_derivWithin_of_eq, ContinuousLinearEquiv.differentiable, ContinuousLinearMap.opNorm_prod, hasDerivWithinAt_add_const_iff, IsLocalRing.ResidueField.algebraMap_residue, LinearMap.coe_toSeminorm, ContinuousLinearMap.integral_compLp, FormalMultilinearSeries.comp_partialSum, Real.sSup_smul_of_nonpos, IntermediateField.fieldRange_le, tendsto_birkhoffAverage_apply_sub_birkhoffAverage', LinearMap.adjoint_adjoint, DoubleCentralizer.star_snd, ContinuousLinearMap.norm_inr_le_one, quadraticChar_card_sqrts, IntermediateField.LinearDisjoint.iff_inf_eq_bot, LinearMap.BilinForm.symmCompOfNondegenerate_left_apply, IntermediateField.normal_inf, FixedPoints.finrank_eq_card, binomialSeries_eq_ordinaryHypergeometricSeries, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, Matrix.IsHermitian.isClosedEmbedding_cfcAux, StarAddMonoid.toStarModuleNNRat, InnerProductSpace.toLinearIsometry_toDual, IsUltrametricDist.algNormOfAlgEquiv_extends, RCLike.normSq_to_real, ZMod.pow_card_sub_one, Polynomial.cardPowDegree_zero, Seminorm.continuous_of_continuous_comp, HasMFDerivAt.add, tendsto_inv_atTop_zero, galRestrict_symm_algebraMap_apply, NumberField.InfinitePlace.norm_embedding_of_isReal, WithSeminorms.image_isVonNBounded_iff_seminorm_bounded, Filter.IsBoundedUnder.smul_tendsto_zero, tendsto_const_mul_pow_nhds_iff', RatFunc.num_div, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal, Real.hasFDerivAt_fourierChar_neg_bilinear_left, InnerProductSpace.span_gramSchmidtNormed, LinearIsometryEquiv.analyticOnNhd, hasStrictDerivAt_intCast, ContinuousAlternatingMap.uniformContinuous_eval_const, cfcₙ_norm_nonneg, ContinuousWithinAt.cfcₙ, IsGalois.tower_top_intermediateField, LeftInvariantDerivation.leibniz, MeasureTheory.convolution_eq_right', hasStrictFDerivAt_exp_of_mem_ball, quasispectrum.algebraMap_mem, hasFDerivAt_iff_hasGradientAt, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, FixedPoints.minpoly.monic, cfcₙHom_apply_mem_elemental, ContinuousMultilinearMap.cpolynomialOn, LinearIsometry.norm_compContinuousAlternatingMap, ClassGroup.mk0_integralRep, IsHilbertSum.surjective_isometry, SimpleGraph.lapMatrix_toLinearMap₂', curveIntegral_smul, FormalMultilinearSeries.ofScalars_apply_eq', ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, Submodule.reflection_trans_reflection, AddDissociated.randomisation, NumberField.InfinitePlace.sum_mult_eq, FixedPoints.minpoly.irreducible, extDeriv_constOfIsEmpty, RCLike.separate_convex_open_set, RootPairing.coroot_eq_polarizationEquiv_apply_root, Bundle.Trivial.symmL_trivialization, Ideal.exists_comap_galRestrict_eq, NumberField.canonicalEmbedding.mem_span_latticeBasis, Real.fderiv_fourierIntegral, Submodule.orthogonalDecomposition_symm_apply, hasStrictFDerivAt_list_prod_finRange', RatFunc.coe_mapAlgHom_eq_coe_map, OrthogonalFamily.linearIsometry_apply_single, NumberField.integralBasis_apply, AbsoluteValue.isEquiv_trivial_iff_eq_trivial, ContinuousLinearMapWOT.neg_apply, LinearIsometry.nnnorm_toContinuousLinearMap, ContinuousLinearMap.isStarProjection_iff_isSymmetricProjection, InnerProductSpace.rankOne_one_left_eq_innerSL, ContDiff.fderiv_succ, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow, Submodule.IsOrtho.starProjection_comp_starProjection, FormalMultilinearSeries.ofScalars_eq_zero_of_scalar_zero, convexHull_insert, fderiv_intCast, PrimeSpectrum.preimageEquivFiber_symm_apply_coe, IntermediateField.adjoin.finrank, IsPurelyInseparable.minpoly_eq', IntermediateField.algebraMap_mem, NonUnitalCStarAlgebra.toStarModule, Finset.card_mul_cast_addConst, NormedSpace.expSeries_summable_of_mem_ball, hasDerivAt_sqrt_mul_log, Filter.EventuallyEq.fderivWithin, IsLocalRing.finrank_CotangentSpace_eq_one_iff, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, LinearMap.IsSymmetric.restrictScalars, bddBelow_smul_iff_of_neg, Matrix.GeneralLinearGroup.val_mkOfDetNeZero, PrimeSpectrum.residueField_specComap, fderivWithin_one, ContinuousLinearMap.continuous_det, HasFiniteFPowerSeriesAt.neg, Polynomial.isEquivalent_atBot_div, FormalMultilinearSeries.ofScalars_series_eq_zero_of_scalar_zero, NumberField.mixedEmbedding.convexBodyLT'_mem, NumberField.InfinitePlace.comap_mk, PiTensorProduct.mapLMonoidHom_apply, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv, ClosedSubmodule.toSubmodule_orthogonal_eq, RootPairing.instIsRootSystemSubtypeMemSubmoduleSpanRangeCoeEmbeddingRootCorootRestrictScalars', ContinuousLinearMap.map_add_add, NumberField.prod_nonarchAbsVal_eq, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, ContinuousAlternatingMap.isEmbedding_restrictScalars, ContinuousAlternatingMap.norm_constOfIsEmpty, HasFDerivWithinAt.pow, ContinuousLinearMap.sSup_unit_ball_eq_norm, Lagrange.eval_interpolate_not_at_node', ContinuousAlternatingMap.norm_ofSubsingleton_id_le, convex_iff_ordConnected, hasFDerivWithinAt_const, MeromorphicOn.divisor_fun_smul, ContinuousAlternatingMap.isClosedEmbedding_toContinuousMultilinearMap, hasFDerivAt_one, Representation.IsIrreducible.instIsSimpleModuleMonoidAlgebraAsModule, Real.hasDerivAt_sigmoid, taylorWithinEval_hasDerivAt_Ioo, Manifold.IsImmersionAtOfComplement.target_subset_preimage_target, convexHull_multiset_sum, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center, WeierstrassCurve.Jacobian.baseChange_add, IsGalois.card_aut_eq_finrank, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, NormedSpace.Dual.isClosed_image_polar_of_mem_nhds, ContinuousLinearMap.analyticWithinAt, AdjoinRoot.minpoly_root, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, HasFDerivWithinAt.add, IntermediateField.extendScalars_sup, NumberField.IsCMField.zpowers_complexConj_eq_top, IntermediateField.coe_algebraMap_over_bot, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, Matrix.IsHermitian.det_abs, MDifferentiableAt.mfderiv_prod, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, Algebra.normalizedTrace_surjective, LinearMap.IsPositive.ne_zero_iff, Submodule.iUnion_ssubset_of_forall_ne_top_of_card_lt, hasFDerivAtFilter_pi, ContinuousLinearMap.toLinearMap₁₂_injective, Height.mulHeight₁_eq, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, Subspace.instModuleDualFiniteDimensional, Finset.dens_cons, curveIntegrable_segment, Algebra.normalizedTrace_eq_of_finiteDimensional, hasFDerivAt_multiset_prod, IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot, NumberField.FinitePlace.mk_apply, LinearMap.isPositive_adjoint_comp_self, Matrix.GeneralLinearGroup.IsParabolic.parabolicFixedPoint_pow, Manifold.IsImmersionAt.map_target_subset_target, Submodule.toLinearEquiv_orthogonalDecomposition_symm, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, OrthonormalBasis.repr_injective, spectrumRestricts_iff, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', ContinuousLinearMap.continuousSMul, hasFTaylorSeriesUpToOn_top_iff_right, NNRat.not_cast_lt_zero, ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, concaveOn_iff_slope_anti_adjacent, arithGeom_eq', IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable', expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, HasFPowerSeriesWithinOnBall.hasSum_sub, AffineSubspace.setOf_sSameSide_eq_image2, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, intervalIntegral.integral_hasDerivWithinAt_right, Matrix.spectrum_toEuclideanLin, ContDiff.iteratedFDeriv_right, Bornology.isVonNBounded_add_of_nonempty, NumberField.canonicalEmbedding.latticeBasis_apply, IsLocalRing.ker_residue, FormalMultilinearSeries.radius_pi_eq_iInf, ContinuousLinearMap.norm_inl_le_one, MeasureTheory.norm_condExpL2_le, RatFunc.num_div_dvd, ContinuousLinearEquiv.contDiff_comp_iff, Ideal.exists_mem_span_singleton_map_residueField_eq, mem_subalgebraEquivIntermediateField, SchwartzMap.pairing_apply_apply, Submodule.instStrictConvexSpace, InnerProductSpace.isIdempotentElem_rankOne_self, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, minpoly.algEquiv_apply, Algebra.isInvariant_of_isGalois, ContinuousMultilinearMap.norm_map_snoc_le, MonoidAlgebra.Submodule.exists_isCompl, NumberField.InfinitePlace.le_iff_le, LineDifferentiableWithinAt.smul, MeasureTheory.Measure.MapLinearEquiv.isAddHaarMeasure, IsPurelyInseparable.elemExponent_min', ImplicitFunctionData.isInvertible_fderiv_prodFun, Trivialization.continuousLinearMapAt_apply, iteratedFDerivWithin_eventually_congr_set, ApproximatesLinearOn.lipschitz, NumberField.norm_norm_le_norm_mul_house_pow, IntermediateField.isScalarTower_mid', Real.hasStrictDerivAt_rpow_const_of_ne, FractionalIdeal.map_one_div, ConjRootClass.aeval_minpoly_iff, Polynomial.Gal.restrict_smul, ContinuousAlternatingMap.isUniformEmbedding_toContinuousMultilinearMap, StrongDual.polarSubmodule_eq_setOf, ContinuousLinearMap.continuous_integral_comp_L1, ContinuousLinearMap.isBigOWith_sub, IsAbsoluteValue.abv_div, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, NumberField.hermiteTheorem.minkowskiBound_lt_boundOfDiscBdd, one_le_pow_mul_abs_eval_div, ContinuousLinearMap.isUniformEmbedding_restrictScalars, ConvexCone.canLift, hasDerivWithinAt_taylorWithinEval, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, Asymptotics.isLittleOTVS_one, Polynomial.div_def, one_div_add_one_div, NNRat.cast_eq_zero, HasFTaylorSeriesUpTo.cont, ImplicitFunctionData.isCompl_ker, CategoryTheory.finrank_hom_simple_simple_le_one, ContinuousLinearMap.hasDerivAtFilter, finrank_quotient_span_eq_natDegree_norm, fderivWithin_csinh, DoubleCentralizer.intCast_snd, FractionRing.instIsScalarTower, toIcoMod_eq_fract_mul, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, DoubleCentralizer.range_toProdMulOpposite, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, ContinuousLinearMapWOT.withSeminorms, hasFDerivAt_integral_of_dominated_loc_of_lip_interval, intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_right, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, NumberField.InfinitePlace.nat_card_stabilizer_eq_one_or_two, Submodule.re_inner_starProjection_eq_normSq, HasFPowerSeriesOnBall.add, differentiableWithinAt_pi'', Ideal.ker_algebraMap_residueField, RatFunc.laurent_X, Lagrange.degree_basisDivisor_self, VectorField.fderiv_apply_lieBracket, NumberField.RingOfIntegers.instSMulDistribClass, MeasureTheory.inner_condExpL2_left_eq_right, Polynomial.idealX_span, QuadraticForm.posDef_toMatrix', RootPairing.restrictScalars_coe_coroot, Ideal.coe_smul_primesOver_mk_eq_map_galRestrict, NumberField.isInfinitePlace_iff, AnalyticOnNhd.compContinuousLinearMap, AffineIsometryEquiv.linear_eq_linear_isometry, ClassGroup.Quot_mk_eq_mk, IsGaloisGroup.iff_isFractionRing, NumberField.InfinitePlace.isUnramified_iff_card_stabilizer_eq_one, Bornology.isVonNBounded_add_self, Polynomial.exists_partition_polynomial, fderiv_id, ZLattice.covolume_eq_det_inv, RCLike.algebraMap_eq_ofReal, NumberField.IsCMField.equivInfinitePlace_symm_apply, Module.Basis.constrL_basis, IsPrimitiveRoot.minpoly_dvd_pow_mod, Submodule.reflection_orthogonal_apply, NumberField.InfinitePlace.IsUnramified.comap_algHom, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, convex_iff_sum_mem, Polynomial.fiberEquivQuotient_tmul, ContinuousLinearMap.comp_memLp, ZMod.units_pow_card_sub_one_eq_one, OrderRingHom.eq_id, MeasureTheory.integral_fintype_prod_volume_eq_pow, Real.fderiv_fourierChar_neg_bilinear_right_apply, NumberField.InfinitePlace.isometry_embedding, LinearMap.IsSymmetric.diagonalization_apply_self_apply, Matrix.isParabolic_iff_exists, Module.rankAtStalk_eq, IntermediateField.coe_bot, Subspace.dualLift_of_subtype, LinearMap.IsPositive.re_inner_nonneg_right, ContinuousAlternatingMap.instIsUniformAddGroup, WeierstrassCurve.Projective.comp_equiv_comp, Real.fourier_continuousLinearMap_apply, Ideal.ramificationIdx_le_finrank, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, LieAlgebra.IsKilling.isCompl_ker_weight_span_coroot, norm_iteratedFDeriv_mul_le, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, Padic.complete', intervalIntegral.fderiv_integral_of_tendsto_ae, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isComplex, ContDiffAt.fderiv_right_succ, flip_innerSL_real, WeierstrassCurve.Jacobian.Point.toAffine_of_Z_ne_zero, Submodule.starProjection_orthogonal', RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, NormedSpace.isBounded_iff_subset_smul_ball, AffineIsometryEquiv.ofTop_apply, cfc_map_div, LieAlgebra.finrank_engel, DoubleCentralizer.natCast_fst, hasFPowerSeriesOnBall_pi_iff, LinearMap.IsSymmetric.im_inner_self_apply, RatFunc.num_one, DifferentiableAt.prodMap, ContinuousLinearMap.IsPositive.toLinearMap, AnalyticOnNhd.iteratedFDeriv_of_isOpen, Polynomial.natSepDegree_pow, ZMod.charpoly_pow_card, ContinuousLinearMap.norm_compLp_le, Submodule.toLinearEquiv_orthogonalDecomposition, Continuous.convolution_integrand_fst, PadicComplex.coe_eq, MDifferentiableOn.smul_const_section, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, ContinuousLinearEquiv.symm_toDiffeomorph, ContDiffMapSupportedIn.structureMapCLM_apply, OrthonormalBasis.toBasis_tensorProduct, TensorProduct.congrIsometry_refl_refl, eventually_enorm_mfderivWithin_symm_extChartAt_lt, ContinuousAlternatingMap.opNNNorm_pi, NumberField.mem_maximalRealSubfield_iff, HasFPowerSeriesWithinAt.const_smul, norm_smul_inv_norm', MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, tangentMap_snd, LaurentSeries.LaurentSeriesRingEquiv_def, Field.Emb.Cardinal.directed_filtration, SchwartzMap.lineDerivOp_fourier_eq, FirstOrder.Field.realize_genericMonicPolyHasRoot, Subspace.dualRestrict_comp_dualLift, AddChar.expect_ne_zero_iff_eq_zero, isClosedEmbedding_cfcₙAux, Lagrange.leadingCoeff_basis, AddChar.wInner_cWeight_self, LieModule.traceForm_eq_sum_finrank_nsmul', IntermediateField.lift_insepDegree_bot', Ring.ordFrac_eq_div, innerSL_apply_apply, ContinuousLinearMapWOT.instIsUniformAddGroup, Submodule.isOrtho_sup_right, RCLike.norm_expect_le, fderiv_multiset_prod, Polynomial.eventually_atBot_not_isRoot, HasFPowerSeriesWithinOnBall.restrictScalars, NormedSpace.isVonNBounded_iff, CFC.abs_eq_cfcₙ_coe_norm, ContinuousLinearEquiv.subsingleton_or_norm_symm_pos, Finset.dens_inter_add_dens_sdiff, aemeasurable_smul_const, LinearIsometry.rTensor_def, LinearMap.adjoint_innerₛₗ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, VectorField.fderiv_apply_lieBracket_of_isSymmSndFDerivAt, HasFTaylorSeriesUpTo.hasFDerivAt, HasFDerivAtFilter.fun_sum, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, LinearMap.continuousLinearMapClassOfFiniteDimensional, hasDerivAt_neg', ContMDiffWithinAt.mfderivWithin_const, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, HasFDerivAtFilter.sub, Finset.mulConst_mul_card, Unitization.splitMul_apply, geom₂_sum, inner_eq_norm_mul_iff, ContinuousLinearMap.toBilinForm_apply, NumberField.CMExtension.algebraMap_equivMaximalRealSubfield_symm_apply, DoubleCentralizer.nnnorm_def', ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, LinearMap.adjoint_eq_toCLM_adjoint, HasFDerivAt.fun_mul, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, ClosedSubmodule.orthogonal_gc, LinearMap.isPositive_id, IsCyclotomicExtension.discr_odd_prime, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Seminorm.bddAbove_range_iff, fderivWithin_zero_of_not_accPt, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, Finset.card_mul_divConst, Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero, NormedSpace.image_isVonNBounded_iff, VectorField.mpullbackWithin_smul, nnnorm_cfcₙ_lt_iff, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_apply, eqOn_dslope_sub_smul, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, Submodule.orthogonalProjection_mem_subspace_eq_self, IsPurelyInseparable.insepDegree_eq, Finset.card_mul_dens, ContinuousLinearMap.nnnorm_def, ContinuousLinearMap.IsPositive.inner_nonneg_right, gauge_smul_of_nonneg, DoubleCentralizer.zero_snd, LeftInvariantDerivation.left_invariant', Field.insepDegree_le_rank, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, hasDerivAt_bernoulliFun, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, FormalMultilinearSeries.le_changeOriginSeries_radius, algebraMap.coe_logDeriv, ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff, derivWithin_fderivWithin, HasFDerivWithinAt.prodMap, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Field.Emb.Cardinal.filtration_succ, RatFunc.denom_one, Set.unit_eq, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, NumberField.mixedEmbedding.norm_eq_norm, IntermediateField.relfinrank_mul_finrank_top, Polynomial.map_div, LieAlgebra.IsKilling.rootSystem_coroot_apply, instLiesOverFiberOfIsPrime, PowerSeries.eq_divided_by_X_pow_order_Iff_Unit, mfderiv_comp, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, X_pow_sub_C_irreducible_iff_of_odd, IsLocalRing.finrank_cotangentSpace_eq_zero, WittVector.RecursionMain.succNthVal_spec', InnerProductSpace.span_gramSchmidtNormed_range, HasFDerivWithinAt.hasLineDerivWithinAt, ContinuousLinearMap.opNorm_comp_linearIsometryEquiv, Submodule.orthogonal_disjoint, algebraicClosure.algebraicClosure_eq_bot, ApproximatesLinearOn.surjOn_closedBall_of_nonlinearRightInverse, ContDiffPointwiseHolderAt.isBigO, Finset.card_mul_subConst, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, NumberField.FinitePlace.norm_def', SchwartzMap.decay', Module.Basis.ofZLatticeBasis_apply, Seminorm.smul_inf, ContinuousAlternatingMap.map_insertNth, PowerSeries.Inv_divided_by_X_pow_order_leftInv, FormalMultilinearSeries.derivSeries_coeff_one, instIsTorsionFreeCyclotomicFieldOfIsDomainOfIsFractionRing, Polynomial.isCoveringMapOn_eval, Submodule.starProjection_add_starProjection_orthogonal, Matrix.spectrum_toLpLin, HasDerivAt.comp_ofReal, OrderedFinpartition.norm_compAlongOrderedFinpartition_le, tangentConeAt_nonempty_of_properSpace, instIsZLatticeComap, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_right, ContinuousOn.cfcₙ', mdifferentiableOn_symm_coordChangeL, X_pow_sub_C_irreducible_of_odd, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, ContinuousLinearMap.opNorm_lsmul_apply_le, sum_div_card_sq_le_sum_sq_div_card, Continuous.integral_hasStrictDerivAt, Polynomial.mod_eq_self_iff, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Submodule.mem_orthogonal_singleton_iff_inner_right, NumberField.mixedEmbedding.mem_idealLattice, RatFunc.denom_mul_dvd, IsFractionRing.fieldEquivOfAlgEquivHom_apply, Complex.re_balance, mdifferentiableWithinAt_smul_const_section, InnerProductSpace.Core.inner_smul_left, SchwartzMap.bilinLeftCLM_apply, ContinuousMap.setOfIdeal_ofSet_eq_interior, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, NumberField.Units.regOfFamily_eq_det, Submodule.IsLattice.rank', Filter.tendsto_const_mul_atTop_iff_pos, FiniteField.frobeniusAlgEquivOfAlgebraic_apply, ContinuousLinearMap.nhds_zero_eq_of_basis, HasGradientAt.hasDerivAt', IsHilbertSum.linearIsometryEquiv_symm_apply, SmoothBumpCovering.exists_immersion_euclidean, Fintype.expect_dite_eq, PowerSeries.Unit_of_divided_by_X_pow_order_zero, OrderedFinpartition.norm_applyOrderedFinpartition_le, iteratedDeriv_pow, ContinuousLinearMap.cpolynomialAt, HasMFDerivWithinAt.prodMk, differentiableOn_pi, InfiniteGalois.normalAutEquivQuotient_apply, IsPurelyInseparable.elemExponent_min, AffineMap.hasDerivWithinAt, Submodule.starProjection_singleton, IsGaloisGroup.fixingSubgroup_top, HasFPowerSeriesAt.eventually_hasSum, LeftInvariantDerivation.left_invariant, mfderiv_comp_apply_of_eq, Nat.floor_div_natCast, PowerSeries.degree_weierstrassMod_lt, PowerSeries.maximalIdeal_eq_span_X, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, hasStrictFDerivAt_snd, WeierstrassCurve.Projective.dblU_smul, IsGreatest.nnnorm_cfcₙ, NumberField.FinitePlace.embedding_apply, NormedSpace.toIsBoundedSMul, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, WeierstrassCurve.Jacobian.negAddY_eq, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, ContinuousAlternatingMap.isClosed_range_toContinuousMultilinearMap, CategoryTheory.finrank_hom_simple_simple_eq_one_iff, NNRat.cast_one, Valuation.Integers.isPrincipal_iff_exists_isGreatest, curveIntegralFun_smul, addInvariantVectorField_smul, IntermediateField.isAlgebraic_tower_bot, hasDerivAt_exp_zero_of_radius_pos, Module.Basis.exists_opNorm_le, ClosedSubmodule.mem_orthogonal', Finset.one_le_mulConst_self, egauge_ball_le_of_one_lt_norm, MeasureTheory.charFun_toDual_symm_eq_charFunDual, IsGaloisGroup.fixedPoints_top, inv_atTop₀, hasDerivWithinAt_iff_isLittleO, hasStrictFDerivAt_iff_isLittleOTVS, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, Normal.splits', IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply, RatFunc.laurent_algebraMap, isConjRoot_iff_exists_algEquiv, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, IsStrictOrderedRing.toContinuousInv₀, OrthogonalFamily.orthonormal_sigma_orthonormal, Set.unitEquivUnitsInteger_symm_apply_coe, IsPurelyInseparable.finInsepDegree_eq, Field.isDomain, ContinuousAlternatingMap.piLIE_apply_apply, PreInnerProductSpace.Core.smul_left, Matrix.PosSemidef.sqrt_eq_zero_iff, IntermediateField.mem_carrier, IsPurelyInseparable.elemExponent_def', Differentiable.fderiv_norm_rpow, UniqueMDiffOn.uniqueDiffOn, FDerivMeasurableAux.le_of_mem_A, lintegral_fderiv_lineMap_eq_edist, NumberField.InfiniteAdeleRing.algebraMap_apply, RCLike.normSq_neg, ContinuousLinearMap.isBigOWith_id, ContinuousLinearMap.integrable_of_bilin_of_bdd_left, curveIntegrable_fun_neg_iff, hasDerivWithinAt_zero, IntermediateField.botEquiv_symm, ContDiffAt.hasStrictDerivAt, NNRat.cast_listProd, ContinuousLinearEquiv.coe_toDiffeomorph_symm, Submodule.reflection_symm, Normal.minpoly_eq_iff_mem_orbit, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', Subfield.relfinrank_mul_finrank_top, padicNormE.nonarchimedean', CurveIntegrable.zero, fderiv_comp_deriv, ContinuousMultilinearMap.contDiffAt, Field.finSepDegree_eq_of_isAlgClosed, hasDerivAtFilter_ofNat, iteratedDeriv_comp_const_mul, sbtw_midpoint_of_ne, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, curveIntegrable_smul_iff, TensorProduct.toLinearEquiv_lidIsometry, HasFPowerSeriesOnBall.restrictScalars, contractLeft_assoc_coevaluation, Field.FiniteDimensional.of_finite_intermediateField, LinearMap.BilinForm.restrict_nondegenerate_iff_isCompl_orthogonal, Complex.im_expect, Lagrange.eval_interpolate_not_at_node, ContinuousLinearMap.opNNNorm_le_iff, ContinuousLinearMap.isometry_mul_flip, OrthonormalBasis.toBasis_singleton, ZSpan.smul, AnalyticOnNhd.eval_linearMap', HasStrictFDerivAt.mul', isPowMul_spectralNorm_of_finiteDimensional_normal, fderiv_fun_pow, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, Module.Basis.ofZLatticeComap_apply, IntermediateField.relrank_mul_rank_top, IsGalois.card_fixingSubgroup_eq_finrank, NNRat.cast_add_of_ne_zero, Subfield.relfinrank_eq_finrank_of_le, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, InnerProductSpace.smul_left, ClosedSubmodule.inf_orthogonal, HasFDerivAtFilter.const_sub, LinearMap.coe_toContinuousLinearMap', balanced_ball_zero, HasFDerivWithinAt.linear_multilinear_comp, Polynomial.SplittingFieldAux.algebraMap_succ, iteratedFDerivWithin_succ_eq_comp_left, ContinuousLinearMap.isPositive_natCast, tendsto_birkhoffAverage_apply_sub_birkhoffAverage, isGalois_iff_isGalois_top, minpoly_algHom_toLinearMap, ContinuousMultilinearMap.opNorm_zero_iff, NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, Polynomial.hilbertPoly_smul, LinearMap.linearIndependent_of_isOrthoᵢ, hasStrictFDerivAt_exp_smul_const_of_mem_ball', ArchimedeanClass.FiniteResidueField.mk_eq_zero, NumberField.abs_discr_ge', hasFDerivWithinAt_comp_smul_iff_smul, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, convexJoin_segments, Submodule.starProjection_comp_starProjection_eq_zero_iff, FDerivMeasurableAux.differentiable_set_subset_D, Submodule.one_le_traceDual_one, Ideal.algebraMap_quotient_residueField_mk, SchwartzMap.laplacianCLM_eq, fderiv_fun_smul, MeromorphicOn.fun_smul, monomial_has_deriv_aux, Field.finSepDegree_mul_finInsepDegree, continuous_equivFun_basis, exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensional, LinearEquiv.toLinearEquiv_toContinuousLinearEquiv_symm, LinearIsometryEquiv.conjStarAlgEquiv_apply, MeasureTheory.smul_convolution, LinearMap.BilinForm.restrict_nondegenerate_orthogonal_spanSingleton, IsLocalRing.ResidueField.map_comp, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, IsPurelyInseparable.finrank_eq_pow, VectorField.mlieBracketWithin_const_smul_right, starConvex_iff_ordConnected, FractionalIdeal.coe_extendedHomₐ_eq_span, HasFDerivAt.le_of_lipschitzOn, Lagrange.interpolate_eq_nodalWeight_mul_nodal_div_X_sub_C, mem_principal_ideals_iff, LinearMap.toMatrixOrthonormal_reindex, contDiff_one_iff_fderiv, MeasureTheory.ConvolutionExistsAt.integrable, HasStrictFDerivAt.pow, InfiniteGalois.mem_bot_iff_fixed, Real.hasDerivAt_mul_log, exists_pos_right_iff_sameRay, NNRat.cast_le, Lagrange.interpolate_eq_sum_interpolate_insert_sdiff, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, Filter.tendsto_div_const_atTop_iff_pos, Polynomial.natSepDegree_X_sub_C_pow, Asymptotics.isLittleOTVS_prodMk_left, inner_smul_left_eq_star_smul, fderivWithin_sinh, RCLike.mul_conj, ValueDistribution.logCounting_pow_top, NNRat.floor_coe, OnePoint.smul_infty_eq_self_iff, WithSeminorms.continuousSMul, LinearMap.ortho_smul_left, hasLineDerivAt_iff_isLittleO_nhds_zero, deriv.scomp_of_eq, HasFDerivWithinAt.comp_of_tendsto, smul_unitClosedBall, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, Finset.subConst_le_addConst_sq, Real.hasStrictDerivAt_sinh, TestFunction.continuous_iff_continuous_comp, Polynomial.exists_partition_polynomial_aux, HasFiniteFPowerSeriesOnBall.sum, HasStrictFDerivAt.const_mul, Algebra.normalizedTrace_comp_algHom, Finset.dens_sdiff_add_dens_inter, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, LinearMap.IsSymmetricProjection.ext_iff, ConvexOn.univ_sSup_of_countable_affine_eq, FractionalIdeal.count_finsuppProd, ContinuousLinearMap.ebound, RatFunc.laurent_div, Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff, InnerProductSpace.inner_left_rankOne_apply, Polynomial.IsSplittingField.splits_iff, cfcₙHom_nnreal_eq_restrict, TestFunction.toBoundedContinuousFunctionCLM_apply, minpoly.natSepDegree_eq_one_iff_eq_X_pow_sub_C, RCLike.continuous_normSq, two_inv_lt_one, IsLocalFrameOn.coeff_apply_of_mem, ClosedSubmodule.orthogonal_injective, ContinuousAlternatingMap.norm_def, HasFDerivAt.finset_prod, ENNReal.orderIsoRpow_symm_apply, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, IntermediateField.normal_iff_forall_map_eq, ContinuousLinearMap.smul_compLp, PowerSeries.derivative_inv', hasDerivWithinAt_abs_pos, Submodule.norm_starProjection_apply_le, instIsLocalRingTensorProductResidueFieldOfIsLocalHomRingHomAlgebraMap, ContinuousLinearMap.norm_extendTo𝕜, IsLocalMax.fderiv_eq_zero, ContinuousLinearMap.contMDiff, ContinuousLinearMap.mdifferentiable, NumberField.InfinitePlace.IsUnramified.stabilizer_eq_bot, HasStrictFDerivAt.fun_sum, LieModule.exists_nontrivial_weightSpace_of_lieIdeal, HasSum.hasSum_at_zero, Pretrivialization.continuousLinearMap_symm_apply', HasFPowerSeriesAt.add, WeierstrassCurve.Jacobian.negY_of_Z_ne_zero, HasFDerivAt.norm_sq, VectorBundleCore.coordChange_self, lineDifferentiableAt_smul_iff, differentiable_fst, ContinuousAlternatingMap.curryLeft_smul, derivWithin.scomp_of_eq, fderiv_const_smul_field, IntermediateField.extendScalars_injective, HasFTaylorSeriesUpToOn.comp_continuousAffineMap, LinearIsometry.map_starProjection', ContinuousLinearMap.hasBasis_nhds_zero, HasFDerivAtFilter.isBigOTVS_sub, antideriv_bernoulliFun, DifferentiableAt.fderiv_prodMk, ConjRootClass.minpoly.map_eq_prod, NumberField.mixedEmbedding.commMap_apply_of_isComplex, Valuation.Integers.valuation_irreducible_lt_one, innerₛₗ_apply_apply, hasFDerivWithinAt_inv, eventually_nhds_norm_smul_sub_lt, LinearIsometryEquiv.coe_toAffineIsometryEquiv, NumberField.Units.pos_at_place, DoubleCentralizer.pow_snd, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, finite_of_finite_type_of_isJacobsonRing, OrthonormalBasis.repr_self, NumberField.InfinitePlace.Completion.norm_coe, RCLike.ofReal_balance, Submodule.symmetric_isOrtho, SpectrumRestricts.nnreal_iff, iteratedDeriv_scomp_three, padicNormE.image', ContDiffAt.continuousAt_fderiv, fderiv_fun_pow', Polynomial.hilbertPoly_eq_zero_of_le_rootMultiplicity_one, hasDerivWithinAt_pi, IsometryEquiv.midpoint_fixed, NNRat.cast_add, Real.integrable_prod_sub, NormedSpace.isVonNBounded_ball, OrthogonalFamily.norm_sq_diff_sum, MDifferentiable.smul, IsAlgClosed.card_roots_eq_natDegree, Nonneg.mk_nnratCast, Ring.choose_eq_smul, norm_smul_inv_norm, ContinuousLinearEquiv.comp_hasFDerivAt_iff, ContinuousLinearMap.eq_adjoint_iff, hasMFDerivAt_sumSwap, ContinuousLinearMap.hasFDerivAt, fderivWithin_intCast, IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable, NumberField.InfinitePlace.comap_apply, ContDiffAt.fderiv_succ, ContMDiffVectorBundle.pullback, toMatrix_rotation, ContinuousLinearMap.topologicalAddGroup, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, IsFractionRing.mk'_eq_div, SchwartzMap.toLpCLM_apply, Polynomial.Separable.natSepDegree_eq_natDegree, Polynomial.div_tendsto_zero_iff_degree_lt, LinearMap.IsSymmetric.directSum_decompose_apply, derivWithin.scomp, IntermediateField.LinearDisjoint.map', ZMod.trace_pow_card, gal_X_pow_isSolvable, Subfield.splits_bot, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, HasFPowerSeriesAt.comp, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, ContinuousLinearMap.IsPositive.smul_of_nonneg, Finset.divConst_mul_card, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, InnerProductSpace.rankOne_apply, Algebra.instFiniteResidueFieldOfQuasiFiniteAt, Unitary.coe_linearIsometryEquiv_apply, segment_eq_uIcc, MeromorphicOn.divisor_pow, WeierstrassCurve.Projective.add_of_Z_eq_zero, MeasureTheory.convolution_tendsto_right, Nat.one_div_le_one_div, NumberField.InfinitePlace.card_stabilizer, ContinuousLinearMap.coe_toContinuousLinearEquivOfDetNeZero, IntermediateField.restrictScalars_normal, Submodule.reflection_singleton_apply, RCLike.nonUnitalContinuousFunctionalCalculus, IntermediateField.isScalarTower, HasFDerivAt.of_notMem_tsupport, HasFTaylorSeriesUpToOn.zero_eq', IsFractionRing.fieldEquivOfAlgEquiv_trans, fderiv_sum, Fintype.expect_ite_eq, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, AffineIsometryEquiv.pointReflection_midpoint_left, HarmonicAt.analyticAt_complex_partial, FormalMultilinearSeries.ofScalars_apply_eq, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, MvPolynomial.schwartz_zippel_totalDegree, Nat.ceil_le_two_mul, Polynomial.splits_map_iff, Ring.ordFrac_eq_ord, NormedSpace.Dual.toWeakDual_continuous, PowerSeries.inv_eq_iff_mul_eq_one, HasFiniteFPowerSeriesAt.finite, HasFDerivWithinAt.const_mul, isClosed_setOf_tendsto_birkhoffAverage, IsGalois.mem_range_algebraMap_iff_fixed, deriv_fun_inv'', fderiv_ofNat, Algebra.FormallySmooth.adjoin_of_algebraicIndependent, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ValuationSubring.mem_inv_pointwise_smul_iff, FormalMultilinearSeries.id_apply_one', ContinuousMultilinearMap.norm_smulRightL_le, tensorIteratedFDerivTwo_eq_iteratedFDeriv, AnalyticOnNhd.iteratedFDeriv, ContinuousLinearEquiv.contDiffAt_comp_iff, IntermediateField.algebraAdjoinAdjoin.instIsAlgebraicSubtypeMemSubalgebraAdjoinAdjoin, IsAlgClosed.instIsAlgClosure, FixedPoints.rank_le_card, ContinuousLinearMap.precompL_apply, cfcₙ_integral, DoubleCentralizer.nnnorm_snd, Algebra.normalizedTrace_algebraMap, ContinuousLinearEquiv.isBigO_comp, isPurelyInseparable_iff_fd_isPurelyInseparable, Algebra.WeaklyQuasiFiniteAt.finite_residueField, HasStrictFDerivAt.star, OrderRingHom.apply_eq_self, OrthonormalBasis.measurePreserving_repr, Submodule.reflection_apply, openSegment_eq_Ioo, RCLike.ofReal_comp_balance, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, curveIntegralFun_segment, DifferentiableAt.hasDerivAt, Finpartition.IsEquipartition.card_biUnion_offDiag_le, fderivWithin_zero, AlgEquiv.restrictNormalHom_surjective, LieAlgebra.IsKilling.le_chainBotCoeff_of_rootSpace_ne_top, RCLike.geometric_hahn_banach_closed_point, differentiable_finCons', Submodule.orthogonal_eq_bot_iff, TensorProduct.adjoint_map, IsUltrametricDist.invariantExtension_apply, spectrum.pow_mem_pow, Real.hasDerivAt_arcosh, curveIntegral_neg, exists_nonneg_left_iff_sameRay, ConjRootClass.minpoly_injective, cfcₙ_setIntegral, Polynomial.add_mod, Matrix.linearIndependent_rows_of_invertible, HasFDerivAt.sub, VectorBundleCore.contMDiffOn_coordChange, FormalMultilinearSeries.radius_le_smul, LinearIsometryEquiv.lTensor_apply, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, mfderiv_comp_of_eq, PowerBasis.equivAdjoinSimple_symm_aeval, InnerProductSpace.gramSchmidt_def, HasFDerivAt.star, NumberField.instFiniteDimensional, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_right, Finset.mulConst_le_card, InfiniteGalois.toAlgEquivAux_eq_proj_of_mem, iteratedFDerivWithin_succ_const, enorm_fderiv_norm_rpow_le, ContinuousLinearMap.isPositive_self_comp_adjoint, Lagrange.basis_singleton, iteratedDeriv_scomp_eq_sum_orderedFinpartition, trivialization_linear, NNRat.toNNRat_sum_of_nonneg, formalMultilinearSeries_geometric_apply_norm_le, ContinuousLinearMap.hasFPowerSeriesAt, Bundle.Trivial.continuousLinearMapAt_trivialization, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, LinearMap.adjoint_toContinuousLinearMap, WeierstrassCurve.integralModel_Δ_eq, FunctionField.ringOfIntegers.instIsIntegralClosureSubtypeMemSubalgebraPolynomial, X_pow_sub_C_irreducible_iff_forall_prime_of_odd, hasDerivAt_iff_isLittleO, IntermediateField.lift_adjoin_simple, NumberField.InfinitePlace.smul_apply, HasDerivWithinAt.hasFDerivWithinAt, Algebra.algebraMap_intNorm, Unitary.linearIsometryEquiv_coe_apply, algebraicClosure.normalClosure_eq_self, NormedSpace.isBounded_iff_subset_smul_closedBall, LDL.lowerInv_eq_gramSchmidtBasis, SeparatingDual.exists_eq_one, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, hasFPowerSeriesAt_const, hasStrictFDerivAt_pi', IntermediateField.AdjoinDouble.normal_algebraicClosure, Polynomial.natSepDegree_eq_zero_iff, HasFDerivAtFilter.neg, fderiv_eq_deriv_mul, algebraicClosure.map_eq_of_algebraicClosure_eq_bot, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, HasFPowerSeriesOnBall.const_smul, ContinuousLinearMap.toSesqForm_apply_coe, IsPurelyInseparable.exists_pow_mem_range_tensorProduct, finrank_algHom, FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius, ContinuousMultilinearMap.curry0_apply, HasFDerivWithinAt.fun_const_smul, norm_iteratedFDerivWithin_zero, iteratedFDerivWithin_of_isOpen, HasStrictFDerivAt.const_smul, hasStrictFDerivAt_natCast, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, inTangentCoordinates_eq_mfderiv_comp, FormalMultilinearSeries.radius_compNeg, Fintype.expect_ite_zero, hasFDerivAtFilter_ofNat, FiniteField.orderOf_frobeniusAlgEquivOfAlgebraic, LieAlgebra.IsKilling.apply_coroot_eq_cast', hasFDerivAtFilter_zero, NNRat.cast_mono, HasFDerivAt.multilinear_comp, Polynomial.differentiableOn_aeval, NormedSpace.expSeries_apply_eq_div', IsLocalRing.residue_eq_zero_iff, Polynomial.mem_iff_eq_smul_annIdealGenerator, Real.fourierIntegral_continuousMultilinearMap_apply, EuclideanGeometry.oangle_midpoint_right, NumberField.IsTotallyComplex.finrank, Finset.dens_union_add_dens_inter, LinearIsometryEquiv.adjoint_eq_symm, Polynomial.natDegree_hilbertPoly_of_ne_zero_of_rootMultiplicity_lt, extDeriv_fun_smul, RatFunc.liftMonoidWithZeroHom_apply_div', fderivWithin_ccosh, TensorProduct.mapIsometry_id_id, galRestrict'_id, ContinuousAlternatingMap.toAlternatingMap_curryLeft, inv_strictAntiOn, Matrix.toEuclideanLin_apply, inner_self_eq_norm_sq_to_K, InfiniteGalois.krullTopology_mem_nhds_one_iff_of_isGalois, IsContDiffImplicitAt.hasFDerivAt, Finset.expect_ite_zero, LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, AffineBasis.convexHull_eq_nonneg_coord, Complex.im_nnqsmul, iteratedDerivWithin_eq_iteratedFDerivWithin, ContinuousLinearMap.toLinearMap₁₂_apply, FiniteField.coe_frobeniusAlgEquivOfAlgebraic, HasFDerivWithinAt.mul, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, LinearMap.IsPositive.isPositive_smul_iff, ContinuousLinearMap.sSup_sphere_eq_nnnorm, analyticOrderAt_smul_eq_top_of_left, Polynomial.IsSplittingField.adjoin_rootSet, VectorFourier.fourierPowSMulRight_eq_comp, ContinuousLinearMap.finiteDimensional, ContinuousAlternatingMap.le_opNNNorm, LinearIsometryEquiv.trans_smul, IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparable, Finset.dens_eq_sum_dens_image, Polynomial.isUnit_map, HasFPowerSeriesOnBall.tendsto_partialSum_prod, RootPairing.restrictScalars_pairing, ContinuousLinearMap.hasFDerivWithinAt_of_bilinear, hasFDerivWithinAt_pi', HasFDerivWithinAt.multiset_prod, IsHilbertSum.hasSum_linearIsometryEquiv_symm, Algebra.instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced, IntermediateField.isAlgebraic_adjoin_iff_top, WeierstrassCurve.Projective.dblU_eq, ContinuousLinearMap.opNorm_mul, Algebra.isGeometricallyReduced_iff, Submodule.IsOrtho.map_iff, MeasureTheory.integral_fintype_prod_eq_pow, DoubleCentralizer.smul_toProd, mfderivWithin_projIcc_one, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, FiniteField.card_algEquiv_extension, FGModuleCat.instFiniteHomModuleCatObjIsFG, NumberField.mixedEmbedding.convexBodyLT_mem, NumberField.InfinitePlace.coe_apply, Real.sInf_smul_of_nonneg, Algebra.IsAlgebraic.algHom_bijective, InnerProductSpace.Core.inner_smul_ofReal_right, NumberField.IsTotallyReal.finrank, IntermediateField.inf_toSubalgebra, algebraicClosure.isAlgebraic, HasFDerivAt.arctan, NumberField.ComplexEmbedding.IsConj.coe_stabilizer_mk, PiTensorProduct.mapL_one, NumberField.Units.coe_mul, Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg, Real.hasStrictDerivAt_arccos, DoubleCentralizer.toProdMulOpposite_injective, ContinuousLinearMap.norm_fst_le, PowerSeries.eq_mul_inv_iff_mul_eq, PointwiseConvergenceCLM.postcomp_apply, ContMDiffAt.mfderiv_apply, hasFDerivAt_snd, Finset.card_mul_addConst, PowerSeries.isUnit_divided_by_X_pow_order, IsGalois.normalClosure, ValuationSubring.subtype_injective, DoubleCentralizer.norm_fst_eq_snd, Unitization.nnnorm_def, RatFunc.coe_X, NumberField.InfinitePlace.comp_of_comap_eq, MvPowerSeries.eq_inv_iff_mul_eq_one, IsPurelyInseparable.iterateFrobenius_algebraMap, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, ContinuousLinearMap.le_opNorm, IsUltrametricDist.invariantExtension_extends, convexHull_toCone_eq_sInf, ImplicitFunctionData.range_leftDeriv, HasFDerivAt.fun_smul, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, Orthonormal.inner_left_fintype, Height.mulHeight₁_pow, IntermediateField.finiteDimensional_right, HasLineDerivAt.tendsto_slope_zero_right, RatFunc.isCoprime_num_denom, ZLattice.comap_toAddSubgroup, ValuationRing.range_algebraMap_eq, FunctionField.inftyValuation.polynomial, Complex.hasDerivAt_GammaIntegral, NormedSpace.expSeries_eq_expSeries, NormedSpace.expSeries_summable, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, compactOperator_topologicalClosure, RCLike.wInner_cWeight_eq_expect, IsFractionRing.algHom_commutes, Submodule.coe_orthogonalDecomposition_symm, IntermediateField.isAlgebraic_iff, NumberField.ComplexEmbedding.conjugate_comp, PiTensorProduct.mapL_smul, Subfield.relrank_mul_rank_top, MeasureTheory.aestronglyMeasurable_condExpL2, Lagrange.basisDivisor_self, Submodule.orthogonalProjection_bot, Real.fderiv_fourier, DoubleCentralizer.norm_def', ContinuousLinearMap.adjointAux_norm, IsDedekindDomain.HeightOneSpectrum.adicCompletion.instIsScalarTower', differentiable_apply, NNRat.coe_indicator, Submodule.range_starProjection, Fintype.expect_dite_eq', ContinuousLinearMap.fderiv, fderiv_neg, RCLike.toIsStrictOrderedRing, LinearIsometryEquiv.inner_map_eq_flip, MeasureTheory.convolution_smul, hasDerivAtFilter_natCast, Matrix.PosSemidef.sq_eq_sq_iff, Int.self_le_zpow_clog, padicNormE.eq_padic_norm', Polynomial.isEquivalent_atTop_lead, LinearMap.flip_injective_iff₁, FormalMultilinearSeries.ofScalars_eq_zero, EuclideanGeometry.orthogonalProjection_apply_mem, meromorphicOrderAt_ne_top_iff, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, FormalMultilinearSeries.ofScalars_apply_zero, ContinuousAlternatingMap.instContinuousSMul, LinearMap.ker_smul', LinearMap.toMatrixOrthonormal_apply_apply, Finset.card_div_choose_le_card_shadow_div_choose, HasFDerivAt.restrictScalars, ContinuousLinearMap.hasStrictFDerivAt_of_bilinear, ContinuousLinearMap.fpowerSeries_apply_zero, IntermediateField.instSMulMemClass, SameRay.exists_eq_smul_add, VectorPrebundle.mk_contMDiffCoordChange, IntermediateField.coe_inclusion, Submodule.exists_add_mem_mem_orthogonal, PadicInt.algebraMap_apply, Nonneg.segment_eq_uIcc, VectorFourier.fourierIntegral_continuousLinearMap_apply, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply, AffineSubspace.coe_subtypeₐᵢ, Polynomial.contraction_degree_eq_or_insep, FractionRing.algebraMap_liftAlgebra, FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop, closedConvexHull_eq_closure_convexHull, Finset.mem_convexHull', LinearMap.IsSymmetric.coe_re_inner_self_apply, Lagrange.eq_interpolate_iff, RatFunc.coe_coe, ContinuousLinearMap.comp_memLp', HasStrictFDerivAt.list_prod', PrimeSpectrum.coe_preimageHomeomorphFiber_apply_asIdeal, FiniteField.sum_pow_lt_card_sub_one, SchwartzMap.fourier_lineDerivOp_eq, Manifold.IsImmersionAtOfComplement.map_target_subset_target, LinearMap.BilinForm.span_singleton_inf_orthogonal_eq_bot, Real.sSup_smul_of_nonneg, LinearMap.BilinForm.apply_dualBasis_left, AddChar.wInner_cWeight_eq_zero_iff_ne, ContinuousLinearMapWOT.inducingFn_apply, TemperedDistribution.instLineDerivLeftSMulReal, Basis.linearEquiv_dual_iff_finiteDimensional, ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, NumberField.FinitePlace.norm_embedding_eq, hasStrictDerivAt_exp_smul_const, Derivation.leibniz_div, ContinuousMap.setOfIdeal_ofSet_of_isOpen, Polynomial.separable_X_pow_sub_C, isBoundedBilinearMap_comp, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, Polynomial.span_singleton_annIdealGenerator, fderivWithin_sin, set_smul_sphere_zero, NumberField.IsCMField.isQuadraticExtension, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, Polynomial.valuation_of_mk, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, Module.Basis.mulOpposite_is_orthonormal_iff, Subspace.finrank_dualCoannihilator_eq, ContMDiff.smul, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, one_div_strictAntiOn, FormalMultilinearSeries.nnnorm_changeOrigin_le, hasStrictDerivAt_add_const_iff, Trivialization.continuousLinearEquivAt_apply, hasLineDerivWithinAt_smul_iff, Field.Emb.Cardinal.two_le_deg, NumberField.ComplexEmbedding.Extension.not_isReal_of_not_isReal, Asymptotics.IsTheta.smul, MDifferentiable.const_smul, hasMFDerivAt_fst, MeasureTheory.condExpL2_indicator_ae_eq_smul, AbsoluteValue.isEquiv_iff_lt_one_iff, fderiv_fun_sub, mfderivWithin_comp_projIcc_one, NumberField.InfinitePlace.comap_comp, RootPairing.finrank_corootSpanIn_int, LeftInvariantDerivation.lift_smul, IsMIntegralCurveOn.hasDerivWithinAt, FormalMultilinearSeries.rightInv_removeZero, Polynomial.X_pow_sub_one_splits, arithGeom_zero_eq_mul_div', tendsto_zpow_atTop_zero, isCompactOperator_iff_isCompact_closure_image_ball, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, DoubleCentralizer.norm_def, ClosedSubmodule.orthogonal_closure'', Finset.local_lubell_yamamoto_meshalkin_inequality_div, hasStrictDerivAt_exp_smul_const', InfiniteGalois.fixingSubgroup_fixedField, HasCompactSupport.fderiv, OrderIso.smulRightDual_apply, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_complexPlane, LinearIsometry.toAffineIsometry_toAffineMap, MeromorphicAt.fun_smul, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, SchwartzMap.smulLeftCLM_real_smul, InnerProductSpace.toDualMap_apply_apply, WeierstrassCurve.Jacobian.eval_polynomialX_of_Z_ne_zero, Submodule.le_orthogonal_orthogonal, hasFDerivWithinAt_intCast, IntermediateField.finInsepDegree_le_of_left_le, LinearMap.eq_adjoint_iff_basis_left, contDiff_succ_iff_fderiv, ContinuousLinearMap.opNNNorm_prod, ContinuousLinearEquiv.comp_differentiableOn_iff, Nat.ceil_lt_two_mul, Lagrange.basisDivisor_add_symm, MDifferentiableOn.smul, ZLattice.rank, hasDerivAtFilter_zero, Subspace.finiteDimensional_quot_dualCoannihilator_iff, HasMFDerivAt.neg, smul_closedBall', ZSpan.quotientEquiv_apply_mk, Polynomial.map_mod, LinearMap.IsSymmetricProjection.isIdempotentElem, HasFDerivAt.fun_const_smul, Polynomial.cardPowDegree_isEuclidean, IntermediateField.isAlgebraic_adjoin_iff, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, IntermediateField.minpoly_gen, Field.Emb.Cardinal.isLeast_leastExt, Filter.EventuallyEq.hasDerivWithinAt_iff_of_mem, Finset.divConst_le_card, Matrix.PosSemidef.posDef_iff_isUnit, Finset.one_le_mulConst, Algebra.IsQuadraticExtension.isMulCommutative_galoisGroup, LaurentSeries.inducing_coe, SeparatingDual.exists_continuousLinearEquiv_apply_eq, Manifold.pathELength_def, PowerSeries.IsWeierstrassFactorization.isWeierstrassDivision, WeakDual.toStrongDual_inj, TrivSqZeroExt.fst_expSeries, EuclideanSpace.volume_closedBall_fin_three, NumberField.exists_conjugate_one_le_norm, NumberField.InfinitePlace.conjugate_embedding_injective, ContinuousLinearMap.uniformContinuous_restrictScalars, Cubic.splits_iff_card_roots, Real.hasDerivAt_arsinh, ContinuousLinearMap.mulLeftRight_apply, NumberField.InfinitePlace.norm_embedding_eq, isModuleTopologyOfFiniteDimensional, LinearMap.extendTo𝕜'_apply, IntermediateField.aeval_coe, LinearIsometryEquiv.fderiv, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, PrimeSpectrum.coe_preimageOrderIsoFiber_symm_apply_coe_asIdeal, ContinuousLinearMap.holderₗ_apply_apply, Localization.subalgebra.mem_range_mapToFractionRing_iff_ofField, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, dslope_sub_smul, hasDerivAt_id', rescale_to_shell_semi_normed_zpow, ContinuousMultilinearMap.unit_le_opNorm, LaurentSeries.continuous_coe, IsLocalRing.instIsLocalHomResidueFieldRingHomResidue, convexJoin_segment_singleton, SameRay.exists_eq_smul, ContinuousMultilinearMap.curryRight_norm, hasDerivWithinAt_Iic_of_tendsto_deriv, mellin_hasDerivAt_of_isBigO_rpow, ContinuousLinearMap.analyticOn_bilinear, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, Submodule.instHasOrthogonalProjectionOfCompleteSpace, fderiv.log, openSegment_eq_Ioo', FDerivMeasurableAux.norm_sub_le_of_mem_A, HasFDerivAt.add, ContinuousLinearMap.deriv, hasStrictFDerivAt_multiset_prod, IsSepClosed.roots_eq_zero_iff, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, MeasureTheory.convolution_lsmul, NumberField.IsCMField.orderOf_complexConj, ContinuousAlternatingMap.instContinuousConstSMul, Normal.algHomEquivAut_symm_apply, abs_nnqsmul, curveIntegral_fun_zero, gal_X_pow_sub_C_isSolvable, meromorphicNFOn_smul_iff_right_of_analyticOnNhd, ModelWithCorners.uniqueDiffOn_preimage, LinearMap.nonneg_iff_isPositive, Lagrange.interpolate_eq_sum, Nat.floor_div_ofNat, Bornology.isVonNBounded_covers, hasDerivAt_abs_neg, coe_innerSL_apply, MvPolynomial.rank_R, HasFDerivWithinAt.const_sub, IsAlgClosed.splits_codomain, LinearMap.IsSymmetric.inner_map_self_eq_zero, ContinuousLinearMap.isCompact_image_coe_closedBall, IntermediateField.map_map, Real.deriv_sqrt_aux, OrthonormalBasis.prod_apply, iteratedFDeriv_add_apply, deriv_fderiv, PowerSeries.normUnit_X, RegularNormedAlgebra.isometry_mul', convexJoin_singleton_segment, ContDiffWithinAt.hasFDerivWithinAt_nhds, IsPrimitiveRoot.adjoinEquivRingOfIntegers_symm_apply, FiniteDimensional.nonempty_continuousLinearEquiv_iff_finrank_eq, IntermediateField.fixingSubgroup_top, HasFDerivAt.sum, HasStrictDerivAt.real_of_complex, ContinuousLinearMap.isClosed_image_coe_closedBall, IntermediateField.coe_toSubalgebra, DoubleCentralizer.central, RootPairing.Base.exists_mem_span_pairingIn_ne_zero_and_pairwise_ne, ModelWithCorners.hasMFDerivAt, WeierstrassCurve.Projective.isUnit_dblU_of_Y_eq, Matrix.PosSemidef.det_sqrt, Hyperreal.archimdeanClassMk_coe, MeasureTheory.integral_condExpL2_eq, FiniteField.roots_X_pow_card_sub_X, HasFPowerSeriesOnBall.coeff_zero, IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_one, integral_smul_const, FormalMultilinearSeries.norm_apply_eq_norm_coef, quadraticCharFun_eq_zero_iff, hasFDerivAtFilter_const, VectorBundleCore.localTriv_symm_fst, range_cfcₙHom, Field.Emb.Cardinal.succEquiv_coherence, IntermediateField.bot_toSubalgebra, HasMFDerivWithinAt.prodMap, Algebra.discr_powerBasis_eq_norm, hasDerivWithinAt_abs, hasFPowerSeriesOnBall_const, NNRat.floor_cast, hasFDerivAtFilter_iff_isLittleO, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, TensorProduct.lidIsometry_apply, IsSepClosed.lift_def, ContDiffMapSupportedIn.seminorm_le_iff, eventually_norm_mfderivWithin_symm_extChartAt_lt, QuasispectrumRestricts.map_zero, NumberField.InfinitePlace.mkReal_coe, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, Normal.splits, ContinuousLinearMap.hasDerivAt, hasDerivAt_of_tendstoUniformly, NumberField.InfinitePlace.smul_eq_comap, Submodule.exists_forall_notMem_of_forall_ne_top, Trivialization.comp_continuousLinearEquivAt_eq_coord_change, Subfield.mem_bot_iff_pow_eq_self, UniqueMDiffOn.uniqueDiffOn_target_inter, IsPrimitiveRoot.norm_eq_neg_one_pow, VectorFourier.hasFDerivAt_fourierIntegral, Polynomial.factor_dvd_of_natDegree_ne_zero, Finset.cast_subConst_mul_card, Finset.centerMass_id_mem_convexHull, Submodule.comap_smul, LinearMap.flip_surjective_iff₁, Seminorm.ball_norm_mul_subset, coeSubmodule_differentIdeal, coe_galRestrict_apply, WeierstrassCurve.Projective.Point.toAffineLift_zero, minpoly.sub_algebraMap, IntermediateField.sup_toSubalgebra_of_isAlgebraic_left, iteratedFDeriv_sum, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding, hasFDerivAt_ringInverse, LinearMap.IsPositive.inner_nonneg_left, IntermediateField.relfinrank_top_right, norm_cfcₙ_lt, ContinuousMultilinearMap.opNorm_smul_le, contDiffAt_one_iff, Function.HasTemperateGrowth.fun_smul, Filter.HasBasis.isLittleOTVS_iff, NumberField.InfinitePlace.smul_mk, HasFDerivWithinAt.of_notMem_tsupport, ContinuousLinearMap.instCStarRingId, WeakDual.coe_toStrongDual, fermatLastTheoremWith'_polynomial, NormedSpace.eq_zero_iff_forall_dual_eq_zero, hasFDerivAt_finCons, PowerSeries.intValuation_eq_of_coe, HasMFDerivWithinAt.neg, Algebra.FormallySmooth.iff_injective_lTensor_residueField, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, AffineIsometryEquiv.map_vsub, Finset.centerMass_id_mem_convexHull_of_nonpos, hasFDerivWithinAt_finCons, coeSubmodule_differentIdeal_fractionRing, Ideal.Fiber.lift_residueField_surjective, InformationTheory.hasDerivAt_klFun, MeasureTheory.setIntegral_condExpL2_indicator, InnerProductSpace.nnnorm_rankOne, Field.rank_mul_sepDegree_of_isSeparable, ContinuousMultilinearMap.norm_restr, WeierstrassCurve.Jacobian.comp_equiv_comp, ContinuousMultilinearMap.norm_image_sub_le, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, convexHull_add, fderiv_smul, Finset.divConst_le_mulConst_sq, stereographic_apply_neg, LinearIsometry.norm_toContinuousLinearMap, OrthonormalBasis.orthogonalProjection_apply_eq_sum, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_left, FiniteField.instIsSplittingFieldExtensionHSubPolynomialHPowNatXCard, hasMFDerivAt_inr, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, ContinuousLinearEquiv.arrowCongr_apply, differentiable_snd, FiniteField.algebraMap_trace_eq_sum_pow, HasFDerivWithinAt.star, hasDerivAt_of_tendstoLocallyUniformlyOn, hasDerivAtFilter_iff_tendsto_slope, ContinuousLinearMap.norm_toSpanSingleton, NumberField.ComplexEmbedding.involutive_conjugate, fderivWithin_eventually_congr_set', intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left, ContinuousLinearMap.setIntegral_compLp, LinearMap.trace_eq_sum_inner, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, ContinuousLinearMap.toUniformConvergenceCLM_apply, FormalMultilinearSeries.ofScalars_series_of_subsingleton, ContinuousAlternatingMap.curryLeft_apply_apply, NormedSpace.isVonNBounded_closedBall, ContinuousLinearMap.flip_smul, logDeriv_fun_pow, Representation.IsIrreducible.finrank_eq_one_of_isMulCommutative, solvableByRad.isSolvable, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, mfderivWithin_sumInr, exists_basis_of_pairing_ne_zero, Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos, WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero, LinearMap.BilinForm.isCompl_orthogonal_iff_disjoint, FractionalIdeal.count_finprod_coprime, ContinuousLinearEquiv.isBigO_sub, HasFDerivAt.isBigOTVS_sub, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, Unitization.quasispectrum_inr_eq, IntermediateField.linearDisjoint_comm, ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem, HasCompactSupport.hasDerivAt_convolution_right, NumberField.InfiniteAdeleRing.mixedEmbedding_eq_algebraMap_comp, InnerProductSpace.isSymmetricProjection_rankOne_self, hasDerivWithinAt_neg, HasFTaylorSeriesUpToOn.eventually_hasFDerivAt, divRadical_dvd_derivative, Polynomial.leadingCoeff_mul_prod_normalizedFactors, Module.Basis.constrL_apply, MeromorphicOn.divisor_fun_pow, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, Bundle.ContinuousRiemannianMetric.continuous, IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbv, hasMFDerivAt_neg, HasFDerivWithinAt.const_smul, Matrix.IsHermitian.charpoly_cfc_eq, NormedSpace.norm_expSeries_summable, ContinuousLinearEquiv.hasMFDerivAt, MeasureTheory.ConvolutionExistsAt.integrable_swap, isPowMul_spectralNorm, NormedSpace.expSeries_sum_eq, IsGreatest.norm_cfcₙ, Polynomial.deriv_aeval, VectorBundleCore.trivializationAt_coordChange_eq, hasGradientWithinAt_iff_hasFDerivWithinAt, DoubleCentralizer.nnnorm_def, norm_inner_eq_norm_iff, HasFiniteFPowerSeriesOnBall.eq_partialSum, FiniteField.instIsScalarTowerZModExtension, Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, LinearMap.BilinForm.dualSubmodule_span_of_basis, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, NumberField.RingOfIntegers.instIsTorsionFree_2, ContinuousLinearMap.measurable_apply₂, IsLocalFrameOn.coeff_congr, FormalMultilinearSeries.ofScalars_add, DifferentiableAt.fderiv_norm_self, continuousOn_tangentCoordChange, ContinuousAlternatingMap.isEmbedding_toContinuousMultilinearMap, RootPairing.finrank_rootSpanIn_int, Polynomial.monic_mapAlg_iff, RCLike.im_ofReal_pow, FloorSemiring.tendsto_pow_div_factorial_atTop, IntermediateField.equivOfEq_symm, LinearIsometryEquiv.smul_apply, LaurentSeries.val_le_one_iff_eq_coe, Matrix.card_GL_field, inner_eq_norm_mul_iff_div, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, LinearIsometryEquiv.contDiff, OnePoint.smul_some_eq_ite, HasFDerivAt.comp_hasFDerivWithinAt, ContDiff.continuous_fderiv_apply, FiniteDimensional.RCLike.properSpace_submodule, AffineMap.hasDerivAt_lineMap, Polynomial.dvd_C_mul, Function.hasTemperateGrowth_iff_isBigO, range_stereographic_symm, cfcₙ_comp_norm, Seminorm.convexOn, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, Polynomial.X_pow_sub_C_separable_iff, Submodule.traceDual_top', HasGradientAtFilter.hasDerivAtFilter', IntermediateField.restrictRestrictAlgEquivMapHom_apply, Algebra.norm_eq_prod_embeddings, NNRat.cast_multisetProd, DifferentiableWithinAt.prodMk, PiLp.volume_preserving_toLp, MonomialOrder.isUnit_leadingCoeff, IsPurelyInseparable.minpoly_eq, SeparatingDual.dualMap_surjective_iff, NumberField.canonicalEmbedding.integralBasis_repr_apply, Finset.pluennecke_ruzsa_inequality_nsmul_add, ValuationSubring.smul_mem_pointwise_smul_iff, IsLocalExtr.fderiv_eq_zero, EuclideanGeometry.orthogonalProjection_apply', WeierstrassCurve.Jacobian.eval_polynomialY_of_Z_ne_zero, IsGalois.intermediateFieldEquivSubgroup_apply, ContMDiffAt.smul, isOpenEmbedding_stereographic_symm, Polynomial.natSepDegree_zero, intervalIntegral.integral_hasDerivWithinAt_left, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, Polynomial.ofReal_eval, HasFPowerSeriesOnBall.fderiv_eq, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, strictConvex_closedBall, SpectrumRestricts.algebraMap_image, Continuous.cfcₙ_of_mem_nhdsSet, NormedSpace.toNormSMulClass, Ideal.algebraMap_residueField_surjective, mfderivWithin_comp_of_preimage_mem_nhdsWithin_of_eq, AlgHom.fieldRange_toSubalgebra, ContinuousMultilinearMap.nnnorm_constOfIsEmpty, ContinuousLinearMapWOT.instLocallyConvexSpace, ContinuousLinearMap.instLocallyConvexSpace, Ideal.sum_ramification_inertia, PadicAlgCl.norm_extends, FunctionField.classNumber_eq_one_iff, Asymptotics.IsLittleOTVS.zero, ContinuousLinearMap.flip_mul, minpoly.degree_le, IsAlgClosed.card_roots_map_eq_natDegree_of_isUnit_leadingCoeff, NormedSpace.inclusionInDoubleDual_norm_eq, IsFractionRing.integerNormalization_eq_zero_iff, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, WeierstrassCurve.Projective.isUnit_Y_of_Z_eq_zero, IntermediateField.fieldRange_comp_val, VectorBundle.trivialization_linear', SchwartzMap.smulLeftCLM_sum, NNRat.den_mul_den_eq_den_mul_gcd, IsRealClosed.exists_eq_pow_of_nonneg, IntermediateField.linearDisjoint_iff, ContinuousLinearEquiv.conjContinuousAlgEquiv_trans, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff', FractionRing.instIsScalarTower_1, AffineMap.hasDerivWithinAt_lineMap, IntermediateField.adjoin.powerBasis_gen, WeierstrassCurve.Affine.slope_of_Y_ne, NumberField.ComplexEmbedding.IsConj.eq, mfderiv_prod_eq_add_comp, ContinuousLinearMap.fderiv_of_bilinear, IsDedekindDomain.integer_empty, Ideal.card_primesOverFinset_le_finrank, NumberField.Units.regulator_eq_det, Matrix.PosSemidef.posSemidef_sqrt, hasFDerivAt_of_subsingleton, Real.hasDerivWithinAt_arccos_Ici, unitary.linearIsometryEquiv_coe_symm_apply, PiTensorProduct.tprodL_toFun, IntermediateField.toSubalgebra_map, ContinuousLinearMap.isPositive_def, IntermediateField.equivOfEq_rfl, Seminorm.gaugeSeminorm_ball, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, Continuous.cfcₙ, ContinuousLinearMap.nnnorm_toSpanSingleton, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, EuclideanGeometry.oangle_midpoint_rev_left, IntermediateField.map_fixingSubgroup, Polynomial.abs_tendsto_atTop_iff, IsLocalRing.finrank_CotangentSpace_eq_one, ContinuousLinearEquiv.hasMFDerivWithinAt, ContinuousAlternatingMap.alternatizeUncurryFin_smul, contDiffAt_map_inverse, fderiv_mul_const', LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, FGModuleCat.FGModuleCatEvaluation_apply, Complex.hasDerivAt_Gammaℝ_one, SchwartzMap.toBoundedContinuousFunctionCLM_apply, curveIntegral_segment, Asymptotics.isLittleOTVS_fun_neg_left, TestFunction.postcompCLM_apply, Module.End.map_genEigenrange_le, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, IntermediateField.normal_iff_normalClosure_le, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, IsLocalRing.finrank_cotangentSpace_eq_zero_iff, TrivSqZeroExt.eq_smul_exp_of_ne_zero, Asymptotics.isBigOTVS_iff_smallSets, Derivation.leibniz_inv, ContinuousAlternatingMap.norm_restrictScalars, Real.fourierIntegral_continuousLinearMap_apply, OrthonormalBasis.coe_ofRepr, Submodule.starProjection_top', ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, MvPowerSeries.inv_eq_iff_mul_eq_one, mem_perfectClosure_iff_pow_mem, OrthonormalBasis.toBasis_mulOpposite, Submodule.adjoint_subtypeL, LinearMap.BilinForm.orthogonal_eq_bot_iff, MeasureTheory.convolutionExistsAt_flip, ContinuousAlternatingMap.isUniformEmbedding_restrictScalars, hasStrictFDerivAt_exp, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, convexHull_basis_eq_stdSimplex, Module.Basis.trace_traceDual_mul, IntermediateField.relrank_top_right, IsCoercive.range_eq_top, coevaluation_apply_one, Field.Emb.Cardinal.noMaxOrder_rank_toType, LinearMap.isSymmetric_adjoint_mul_self, InnerProductSpace.Core.cauchy_schwarz_aux, ContinuousLinearMap.opNorm_mul_apply, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply, ContinuousLinearMap.norm_smulRightL, wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg, NumberField.InfinitePlace.card_filter_mk_eq, RatFunc.num_denom_add, Convex.radon_partition, Submodule.le_traceDual_traceDual, Subfield.finrank_comap, mfderiv_comp_mfderivWithin, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1, Algebra.instFiniteResidueFieldOfFormallyUnramified, IsPurelyInseparable.bijective_comp_algebraMap, NNRat.one_le_cast, Submodule.reflection_orthogonalComplement_singleton_eq_neg, deriv_fun_div, LieAlgebra.IsKilling.invtSubmoduleToLieIdeal_top, ContinuousLinearEquiv.comp_fderiv, PosSMulMono.nnrat_of_rat, IsLocalRing.map_tensorProduct_mk_eq_top, HasFDerivWithinAt.fun_smul, Complex.orthonormalBasisOneI_repr_apply, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, ContinuousLinearMap.isBigO_id, GaloisField.finrank, IsLocalRing.residue_def, RCLike.conj_mul, ContDiffAt.fderiv_right, AnalyticOn.compContinuousLinearMap, hasStrictFDerivAt_iff_isLittleO, MeasureTheory.convolution_def, WeierstrassCurve.Affine.slope_of_Y_ne', Affine.Triangle.dist_circumcenter_reflection_orthocenter, HasStrictFDerivAt.prodMk, MeasureTheory.norm_condExpL2_coe_le, Pretrivialization.continuousLinearMapCoordChange_apply, ContinuousMultilinearMap.curryLeft_norm, HasStrictFDerivAt.of_notMem_tsupport, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, HasDerivAt.hasFDerivAt, MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable, InnerProductSpace.trace_rankOne, coe_toPrincipalIdeal, AdjoinRoot.mul_div_root_cancel, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, IntermediateField.continuousSMul, NumberField.Units.coe_coe, ContinuousMultilinearMap.uncurry0_norm, hasMFDerivWithinAt_inr, FunctionField.algebraMap_injective, HasFPowerSeriesWithinOnBall.prod, Nonneg.coe_nnratCast, NormedSpace.eq_iff_forall_dual_eq, Set.coe_unit, ContinuousLinearEquiv.integral_comp_comm, Algebra.IsCentral.baseField_essentially_unique, Algebra.map_intNormAux, ContinuousMultilinearMap.le_opNorm, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, ContDiffOn.fderiv_of_isOpen, Bundle.Trivial.linearMapAt_trivialization, Matrix.PosDef.isUnit, continuousOn_cfcₙ, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton', ContinuousLinearMap.continuous_restrictScalars, HasFDerivWithinAt.neg, hasStrictDerivAt_const_add_iff, iteratedFDeriv_const_smul_apply, Finset.centerMass_insert, isBoundedBilinearMap_compMultilinear, ContinuousLinearEquiv.comp_right_fderiv, hasLineDerivAt_smul_iff, Submodule.isIdempotentElem_starProjection, differentiableOn_finCons', VectorField.lieBracket_const_smul_left, RCLike.div_im, SimpContFract.determinant, hasFDerivAt_norm_rpow, Complex.re_comp_balance, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletionIntegers, dist_birkhoffAverage_apply_birkhoffAverage, IsGaloisGroup.mulEquivCongr_apply_smul, Algebra.ringChar_eq, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, ZSpan.repr_ceil_apply, Asymptotics.isEquivalent_nat_ceil, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime, IsDedekindDomain.HeightOneSpectrum.coe_algebraMap_mem, Ideal.ResidueField.ringHom_ext_iff, HasFPowerSeriesOnBall.uniform_geometric_approx, LinearIsometry.inner_map_map, DoubleCentralizer.neg_snd, IsNormalClosure.splits, FiniteField.forall_pow_eq_one_iff, top_fixedByFinite, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ZLattice.comap_equiv_apply, ConvexOn.hasDerivWithinAt_rightDeriv_of_mem_interior, ContinuousAlternatingMap.instIsTopologicalAddGroup, ContinuousLinearMap.analyticAt, iteratedFDeriv_succ_const, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, LaurentSeries.algebraMap_apply, IntermediateField.relfinrank_dvd_finrank_bot, Asymptotics.isBigOTVS_fun_neg_left, WeierstrassCurve.Projective.isUnit_addU_of_Y_ne, IsGalois.sup_right, ContDiffAt.iteratedFDeriv_right, NumberField.Units.finrank_mul_regOfFamily_eq_det, ContDiffBump.convolution_tendsto_right, isCoveringMap_zpow, Matrix.linfty_opNNNorm_toMatrix, HasFTaylorSeriesUpToOn.cont, RatFunc.laurent_at_zero, Asymptotics.isBigOTVS_fun_neg_right, Trivialization.symm_apply_eq_mk_continuousLinearEquivAt_symm, IsLocalRing.ResidueField.map_comp_residue, AnalyticOnNhd.fderiv_of_isOpen, Module.Basis.coe_constrL, ContinuousAlternatingMap.le_opNorm, MvPowerSeries.constantCoeff_inv, Seminorm.rescale_to_shell_zpow, IsDedekindDomain.selmerGroup.monotone, FormalMultilinearSeries.ofScalars_sub, Valuation.mem_unitGroup_iff, Asymptotics.IsEquivalent.smul, differentiableAt_apply, ConjRootClass.monic_minpoly, NormedSpace.expSeries_hasSum_exp, midpoint_le_right, ContinuousMultilinearMap.range_toUniformOnFun, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, derivWithin_fun_div, tangentMapWithin_snd, algebraMap_galRestrict_apply, Matrix.toEuclideanCLM_toLp, Seminorm.smul_closedBall_zero, WeakDual.CharacterSpace.homeoEval_naturality, minpoly.map_eq_of_isSeparable_of_isPurelyInseparable, DifferentiableWithinAt.hasDerivWithinAt, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, CPolynomialOn.iteratedFDeriv, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, LinearMap.BilinForm.dualSubmodule_dualSubmodule_flip_of_basis, ContinuousLinearMap.isPositive_id, IntermediateField.adjoin_simple_adjoin_simple, FormalMultilinearSeries.coeff_eq_zero, analyticOrderAt_centeredMonomial, IntermediateField.adjoin_simple_toSubalgebra_of_integral, normalClosure.restrictScalars_eq, differentiableAt_pi'', RCLike.conjCLE_coe, Height.mulHeight_pow, HasFPowerSeriesOnBall.sum, Module.End.hasUnifEigenvalue_iff_mem_spectrum, contDiffOn_stereoToFun, Real.hasFDerivAt_fourier, ContinuousLinearMap.isUniformAddGroup, LeftInvariantDerivation.evalAt_coe, Unitary.coe_symm_linearIsometryEquiv_apply, mfderivWithin_sumInl, fderiv_inverse, smul_sphere', hasStrictFDerivAt_exp_smul_const', FractionalIdeal.count_finprod, SchwartzMap.smulLeftCLM_fun_neg, FractionalIdeal.count_ne_zero, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_right, IsRealClosed.exists_eq_pow_of_odd, IsPrimitiveRoot.adjoinEquivRingOfIntegers_apply, HasFPowerSeriesOnBall.fderiv, range_cfcₙ, LinearMap.adjoint_rTensor, NumberField.det_basisOfFractionalIdeal_eq_absNorm, dist_midpoint_midpoint_le, RCLike.normSq_inv, Matrix.PosSemidef.sqrt_eq_one_iff, Algebra.traceMatrix_eq_embeddingsMatrix_mul_trans, LinearMap.IsPositive.add, IntermediateField.restrictRestrictAlgEquivMapHom_surjective, NumberField.InfinitePlace.isUnramified_smul_iff, ImplicitFunctionData.leftDeriv_fderiv_implicitFunction, Field.Emb.cardinal_eq_of_isSeparable, IntermediateField.AdjoinSimple.norm_gen_eq_one, FixedPoints.finrank_le_card, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, NumberField.InfinitePlace.orbitRelEquiv_apply_mk'', LinearMap.adjoint_inner_right, padicNormE.defn, MeasureTheory.mem_lpMeas_indicatorConstLp, iteratedFDeriv_const_smul_apply', IsAbelianGalois.toIsMulCommutative, InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, map_nnrat_smul, PiLp.hasFDerivAt_toLp, stereoInvFun_apply, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, IntermediateField.range_val, PiTensorProduct.mapL_coe, Finset.dens_le_one, IntermediateField.instFiniteSubtypeMemBot, ArchimedeanClass.FiniteElement.mk_intCast, NumberField.InfinitePlace.Completion.locallyCompactSpace, IntermediateField.isCyclotomicExtension_lcm_sup, Filter.EventuallyEq.hasDerivAt_iff, Manifold.IsImmersionAt.writtenInCharts, fderiv_pow, InnerProductSpace.rankOne_eq_zero, ContinuousLinearMap.lipschitz, Polynomial.differentiable_aeval, DoubleCentralizer.range_toProd, map_mem_perfectClosure_iff, fderiv_one, AlgEquiv.card_le, Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, finrank_quotient_span_eq_natDegree, RCLike.mul_wInner_left, padicNormE.add_eq_max_of_ne', Polynomial.natSepDegree_eq_natDegree_of_separable, Module.Basis.trace_mul_traceDual, Submodule.isOrtho_sSup_right, LinearIsometry.lTensor_apply, AddChar.expect_apply_eq_zero_iff_ne_zero, ClosedSubmodule.bot_orthogonal_eq_top, LinearIsometry.norm_compContinuousMultilinearMap, ContinuousAlternatingMap.norm_curryLeft, hasDerivAtFilter_neg, RatFunc.numDenom_div, Complex.ofReal_balance, tsum_pow_div_one_sub_eq_tsum_sigma, IntermediateField.linearDisjoint_iff', Real.hasDerivAt_binEntropy, Submodule.norm_sq_eq_add_norm_sq_starProjection, hasDerivAt_gronwallBound_shift, AffineIsometry.linear_eq_linearIsometry, Algebra.IsGeometricallyReduced.isReduced_algebraicClosure_tensorProduct, UniqueDiffOn.of_real, ContMDiffOn.coordChangeL, IsGaloisGroup.fixedPoints_fixingSubgroup, gal_X_pow_sub_one_isSolvable, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, HasFDerivAt.pow, ContinuousLinearMapWOT.smul_apply, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, Asymptotics.isBigOTVS_iff_isBigO, ContinuousMultilinearMap.isLeast_opNorm, Polynomial.existsUnique_hilbertPoly, fderivWithin_comp_derivWithin, ContDiff.continuous_fderiv, ContinuousAlternatingMap.apply_apply, Finpartition.IsEquipartition.sum_nonUniforms_lt', hasFDerivAt_id, Bornology.isVonNBounded_sub_of_nonempty, Real.hasDerivAt_qaryEntropy, NumberField.RingOfIntegers.coe_eq_zero_iff, Filter.tendsto_zpow_atTop_atTop, innerSL_inj, AffineIsometryEquiv.coe_ofEq_apply, WithSeminorms.isVonNBounded_iff_seminorm_bddAbove, MeasureTheory.condExpIndSMul_smul, hasDerivAt_add_const_iff, IntermediateField.extendScalars.orderIso_apply, hasDerivWithinAt_pow, Submodule.closed_of_finiteDimensional, hasDerivWithinAt_iff_hasFDerivWithinAt, Polynomial.natDegree_removeFactor, RatFunc.instIsScalarTowerOfPolynomial_1, Padic.norm_p_pow, MeasureTheory.ae_ae_add_linearMap_mem_iff, NumberField.InfinitePlace.IsRamified.comap_embedding_conjugate, MeasureTheory.lintegral_nnnorm_condExpL2_le, MvPowerSeries.coeff_inv, Monotone.ae_hasDerivAt, IsPurelyInseparable.injective_comp_algebraMap, StrongDual.toLp_of_not_memLp, AffineSubspace.isometryEquivMap.toAffineMap_eq, Ideal.surjectiveOnStalks_residueField, DoubleCentralizer.add_fst, Quaternion.expSeries_odd_of_imaginary, deriv_pi, LinearMap.IsSymmetric.coe_toSelfAdjoint, Polynomial.natSepDegree_C_mul_X_sub_C_pow, Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_map, AlgebraicClosure.instIsAlgClosureOfIsAlgebraic, HasFPowerSeriesWithinAt.coeff_zero, Algebra.normalizedTrace_intermediateField, NumberField.InfinitePlace.even_card_aut_of_not_isUnramified, EuclideanSpace.volume_closedBall_fin_two, OrthonormalBasis.toBasis_map, ContDiffMapSupportedIn.uniformSpace_eq_iInf, hasFDerivAt_apply, RatFunc.num_C, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, Matrix.piLp_ofLp_toEuclideanLin, LinearMap.finrank_genEigenspace_le, cfcₙAux_id, LinearMap.IsSymmetric.diagonalization_symm_apply, PiTensorProduct.liftIsometry_tprodL, HasStrictFDerivAt.cexp, WeierstrassCurve.Jacobian.map_add, maximal_orthonormal_iff_basis_of_finiteDimensional, Matrix.projVandermonde_apply_of_ne_zero, VectorField.mpullback_smul_apply, OnePoint.map_smul, contDiffWithinAt_iff_of_ne_infty, NormedSpace.inclusionInDoubleDual_norm_le, mfderiv_sumInl, ValuationSubring.principalUnitGroup_le_principalUnitGroup, RatFunc.smul_eq_C_mul, SeparatingDual.instNontrivialContinuousLinearMapIdOfContinuousSMul, PrimeSpectrum.preimageEquivFiber_apply_asIdeal, AnalyticOnNhd.eval_linearMap, LinearEquiv.coe_toContinuousLinearEquiv_symm, hasFTaylorSeriesUpToOn_pi', curveIntegral_segment_const, IsFractionRing.fieldEquivOfAlgEquiv_refl, hasDerivWithinAt_one, mfderiv_sub, sub_smul_slope_vadd, tendsto_inv_nhdsGT_zero, galLift_algebraMap_apply, VectorBundleCore.localTriv_symm_apply, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, WeakDual.isCompact_closedBall, ArchimedeanClass.stdPart_eq_sInf, AffineSubspace.setOf_wOppSide_eq_image2, ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv, NumberField.Units.norm, ContinuousLinearMap.isPositive_toLinearMap_iff, instPolynormableSpaceProd, TangentBundle.trivializationAt_apply, ConvexOn.sSup_of_countable_affine_eq, isNormalClosure_normalClosure, VectorFourier.iteratedFDeriv_fourierIntegral, TestFunction.coe_ofSupportedInCLM, Real.differentiableAt_rpow_of_ne, PointedContMDiffMap.smul_def, Hyperreal.stdPart_coe, Polynomial.natSepDegree_X, FGModuleCat.instFiniteHom, ContDiffBump.normed_convolution_eq_right, IsScalarTower.AlgEquiv.restrictNormalHom_comp, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, Finset.card_mul_mulConst, ContinuousLinearMap.uniformContinuousConstSMul, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContDiffMapSupportedIn.continuous_iff_comp_withOrder, HasLineDerivAt.tendsto_slope_zero, IntermediateField.mem_fixedField_iff, NumberField.IsCMField.complexConj_apply_apply, ContinuousAlternatingMap.instUniformContinuousConstSMul, IntermediateField.finrank_eq_one_iff, ContinuousLinearMap.holder_smul_left, RatFunc.laurent_laurent, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, IntermediateField.lift_top, ContinuousLinearMap.precompR_apply, HarmonicAt.differentiableAt_complex_partial, LaurentSeries.exists_ratFunc_val_lt, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, WeierstrassCurve.Affine.addPolynomial_slope, IsGaloisGroup.fixingSubgroup_le_of_le, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Field.instIsLocalRing, isSymmSndFDerivAt_iff_iteratedFDeriv, RatFunc.num_algebraMap, IntermediateField.sInf_toSubalgebra, HasFDerivWithinAt.mul_const, absorbent_nhds_zero, ContMDiffAt.const_smul_section, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd', hasDerivAtFilter_one, Polynomial.natSepDegree_map, Matrix.GeneralLinearGroup.IsParabolic.pow, Derivation.leibniz_zpow, ordinaryHypergeometricSeries_apply_eq', MeasureTheory.hasFDerivAt_convolution_right_with_param, ContinuousLinearEquiv.differentiableAt, fderiv_pow', ContMDiffAt.mfderiv_const, AnalyticOn.domDomCongr_iteratedFDeriv, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, ContMDiffSection.coe_smul, fderiv_mul, IntermediateField.adjoin_map, Finset.addConst_le_subConst_sq, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, Asymptotics.IsLittleO.isLittleOTVS, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, hasDerivAt_ofNat, LinearIsometry.isConformalMap, LinearIsometryEquiv.reflections_generate, ContinuousLinearMap.ratio_le_opNorm, IntermediateField.finrank_lt_of_gt, Submodule.map_orthogonal_equiv, mfderiv_prodMap, iteratedFDerivWithin_eq_equiv_comp, Algebra.WeaklyQuasiFiniteAt.finite_locoalization, DifferentiableAt.isBigOTVS_sub, Matrix.l2_opNNNorm_mulVec, AddCommGroup.mul_modEq_mul_left, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, hasFDerivAt_prodMk_left, Lagrange.degree_interpolate_erase_lt, NumberField.ComplexEmbedding.IsConj.symm, map_mem_separableClosure_iff, HasStrictFDerivAt.isLittleO, IntermediateField.insepDegree_bot', HasCompactSupport.hasFDerivAt_convolution_right, Set.coe_integer, instOrderedSMulProd, IntermediateField.fixedField_antitone, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, ClosedSubmodule.top_orthogonal_eq_bot, PrimeSpectrum.mem_image_comap_basicOpen, ZMod.card_units, ArchimedeanClass.FiniteResidueField.ofArchimedean_inj, differentialIdeal_le_iff, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, SchwartzMap.norm_iteratedFDeriv_le_seminorm, Submodule.norm_orthogonalProjection_apply_le, Filter.tendsto_neg_const_mul_pow_atTop, instPolynormableSpaceSubtypeMemSubmodule, LinearMap.deriv, VectorPrebundle.linear_trivializationOfMemPretrivializationAtlas, AlgebraicIndependent.lift_reprField, uniqueDiffWithinAt_convex_of_isRCLikeNormedField, cfcₙHom_eq_cfcₙHom_of_cfcHom, Continuous.fderiv, Polynomial.hilbertPoly_succ, X_pow_sub_C_irreducible_iff_of_prime_pow, Lagrange.basis_eq_prod_sub_inv_mul_nodal_div, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, HasFDerivWithinAt.inner, NormedSpace.polar_ball_subset_closedBall_div, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, IntermediateField.isAlgebraic_adjoin, galLift_comp, SameRay.exists_pos_right, DoubleCentralizer.smul_fst, Finset.card_mul_cast_subConst, norm_fderiv_le_of_lipschitz, IsCyclotomicExtension.splits_cyclotomic, IsLocalRing.ResidueField.instIsScalarTower_1, mem_subalgebraEquivIntermediateField_symm, InnerProductSpace.toDualMap_apply, FDRep.average_char_eq_finrank_invariants, TotallyBounded.isVonNBounded, instIsLiouvilleSubtypeMemIntermediateField, Polynomial.factor_dvd_of_degree_ne_zero, RCLike.normSq_nonneg, Nat.one_div_cast_pos, CategoryTheory.finrank_endomorphism_eq_one, hasFDerivWithinAt_finCons', IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two, NumberField.InfinitePlace.instMonoidWithZeroHomClassReal, NumberField.IsCMField.coe_ringOfIntegersComplexConj, Subalgebra.LinearDisjoint.exists_field_of_isDomain_of_injective, AffineIsometryEquiv.ofTop_symm_apply_coe, InfiniteGalois.mulEquivToLimit_symm_continuous, TangentBundle.coordChange_model_space, ZMod.pow_card, ContinuousLinearMap.adjoint_inner_left, PowerSeries.normalized_count_X_eq_of_coe, fderivWithin_cos, WeierstrassCurve.Jacobian.addX_of_Z_ne_zero, PointwiseConvergenceCLM.isInducing_inducingFn, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, TensorProduct.inner_mapIncl_mapIncl, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, WeierstrassCurve.Affine.addX_eq_addX_negY_sub, Field.DirectLimit.nontrivial, ContinuousLinearEquiv.arrowCongr_symm, ContinuousLinearMap.isBoundedBilinearMap, ArchimedeanClass.stdPart_map_real, fdifferential_apply, ContinuousMultilinearMap.opNorm_nonneg, ContinuousMultilinearMap.hasBasis_nhds_zero, ContinuousMultilinearMap.instIsUniformAddGroup, ball_normSeminorm, HasFPowerSeriesWithinOnBall.sum, instTotallySeparatedSpaceAlgEquivOfIsIntegral, InnerProductSpace.AlgebraOfCoalgebra.mul_def, Real.hasStrictDerivAt_arcosh, Field.toIsField, LinearMap.extendTo𝕜_apply, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq, Filter.EventuallyEq.iteratedFDerivWithin, RatFunc.liftMonoidWithZeroHom_apply_div, MeromorphicAt.fun_pow, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, NNRat.cast_nonneg, compContinuousLinearMap_zero, HasLineDerivWithinAt.smul, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, LinearMap.range_dualMap_eq_dualAnnihilator_ker, mdifferentiable_smul_const_section, Finset.expect_eq_single_of_mem, FormalMultilinearSeries.apply_eq_pow_smul_coeff, RatFunc.num_dvd, hasDerivAtFilter_id, FormalMultilinearSeries.le_radius_compContinuousLinearMap, Ideal.ResidueField.liftₐ_comp_toAlgHom, Filter.Tendsto.atTop_smul_nhds_tendsto_asymptoticNhds, Differentiable.fderiv_two, continuousMultilinearCurryFin0_symm_apply, minpoly.isIntegrallyClosed_eq_field_fractions, ContinuousLinearEquiv.integrable_comp_iff, Asymptotics.isBigOTVS_congr, ContinuousLinearMap.instContinuousEvalConst, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, fderivWithin_ccos, Asymptotics.isBigOTVS_neg_right, MDifferentiableOn.coordChangeL, hasDerivAt_update, quadraticCharFun_one, VectorField.mlieBracketWithin_const_smul_left, Lagrange.degree_interpolate_lt, ContinuousLinearMap.IsPositive.isSymmetric, ContinuousAlternatingMap.ofSubsingletonLIE_apply, add_thirds, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, nnnorm_apply_le_nnnorm_cfcₙ, NNRat.cast_prod, fderiv_fun_add, MeromorphicOn.fun_pow, FormalMultilinearSeries.compAlongComposition_bound, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_fst, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, NNRat.coe_castHom, IntermediateField.toSubfield_map, FractionalIdeal.canonicalEquiv_mk0, ContinuousLinearMap.lipschitz_apply, PowerBasis.equivAdjoinSimple_aeval, Trivialization.prod.isLinear, inner_eq_sum_norm_sq_div_four, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, IntermediateField.extendScalars_adjoin, NumberField.InfinitePlace.isInfinitePlace, IsAlgClosed.exists_pow_nat_eq, fderiv_pow_ring, constFormalMultilinearSeries_apply_zero, IntermediateField.isPurelyInseparable_tower_bot, le_separableClosure_iff, DifferentiableAt.fderiv_restrictScalars, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, Normal.algHomEquivAut_apply, inTangentCoordinates_eq, LinearIsometryEquiv.conjStarAlgEquiv_trans, IsCyclotomicExtension.finrank, FormalMultilinearSeries.radius_smul_eq, Polynomial.preHilbertPoly_eq_choose_sub_add, DifferentiableAt.comp_ringHom, AffineIsometryEquiv.ofEq_symm, RatFunc.laurentAux_div, Polynomial.abs_tendsto_atBot_iff, ContinuousLinearMap.bilinearComp_zero_right, FractionalIdeal.coe_dual_one, RootPairing.finrank_corootSpanIn, tendsto_nat_floor_mul_div_atTop, Polynomial.roots_C_mul_X_add_C, ZMod.instIsDomain, DivisibleHull.instIsStrictOrderedModuleNNRat, LinearMap.IsSymmetric.continuous, IsContMDiffRiemannianBundle.exists_contMDiff, Filter.tendsto_const_mul_pow_atTop_iff, Module.End.IsSemisimple.pow, ContinuousMap.ideal_isMaximal_iff, PrimeSpectrum.iInf_localization_eq_bot, InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup, BaireSpace.instBarrelledSpace, hasDerivAtFilter_add_const_iff, LinearIsometry.extend_apply, NumberField.FinitePlace.norm_lt_one_iff_mem, IntermediateField.extendScalars_inf, Polynomial.Gal.instIsScalarTowerSplittingField, hasDerivAt_jacobiTheta₂_fst, AdjoinRoot.span_maximal_of_irreducible, IsGaloisGroup.of_isGalois, uniform_continuous_npow_on_bounded, InnerProductSpace.rank_rankOne, LinearMap.isSymmetric_sum, FiniteField.pow_finrank_eq_natCard, MDifferentiableAt.const_smul, LinearMap.toSeminorm_comp, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, Submodule.isOrtho_top_left, NumberField.mixedEmbedding.unit_smul_eq_iff_mul_eq, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq_inner, IntermediateField.botContinuousSMul, NumberField.IsCMField.equivInfinitePlace_apply, IsometricContinuousFunctionalCalculus.toNonUnital, Finset.dens_eq_card_div_card, RatFunc.mk_eq_div, contMDiffAt_coordChangeL, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isReal, HasFDerivWithinAt.fun_sub, LinearMap.flip_bijective_iff₁, InnerProductSpace.toDual_apply_apply, LinearMap.flip_bijective_iff₂, NumberField.InfinitePlace.ComplexEmbedding.conjugate_sign, AlgHom.instContinuousLinearMapClassOfAlgHomClass, ContinuousLinearMap.adjointAux_apply, ContinuousLinearMap.nonneg_iff_isPositive, Real.hasDerivAt_arcsin, RCLike.real_smul_eq_coe_smul, eq_separableClosure_iff, Int.log_one_right, WeierstrassCurve.Affine.C_addPolynomial_slope, LinearMap.BilinForm.mem_dualSubmodule, coe_lpBCFₗᵢ, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, Submodule.linearEquiv_det_reflection, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, LinearMap.isSymmetric_linearIsometryEquiv_conj_iff, Trivialization.symmL_continuousLinearMapAt, Nat.floor_div_eq_div, ValuationSubring.coe_unitGroupMulEquiv_apply, ProperCone.innerDual_singleton, quadraticCharFun_mul, Finset.dens_disjiUnion, Submodule.IsOrtho.map, spectralNorm.spectralNorm_pow_natDegree_eq_prod_roots, LinearIsometryEquiv.comp_differentiableOn_iff, RingOfIntegers.norm_algebraMap, LinearIsometryEquiv.comp_differentiableAt_iff, differentiable_inner, HasFPowerSeriesWithinOnBall.sub, HasLineDerivAt.tendsto_slope_zero_left, Submodule.mk_mem_projectivization_iff, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, ContDiffWithinAt.continuousLinearMap_comp, NumberField.InfinitePlace.smul_coe_apply, LinearMap.minpoly_dvd_charpoly, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, spectrum.pow_image_subset, ValuationRing.isFractionRing_iff, HasFDerivWithinAt.prodMk, ContinuousAlternatingMap.norm_ofSubsingleton, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_list_prod', segment_eq_Icc', Submodule.toLinearMap_starProjection_eq_isComplProjection, Matrix.cRank_diagonal, FunctionField.ringOfIntegers.instIsDomainSubtypeMemSubalgebraPolynomial, hasStrictFDerivAt_finCons, InnerProductSpace.rankOne_def, MDifferentiableWithinAt.coordChangeL, minpoly.degree_le_of_ne_zero, Diffeomorph.mfderivToContinuousLinearEquiv_coe, TensorProduct.nnnorm_map, Module.Basis.ofZLatticeBasis_span, arithGeom_same_eq_mul_div', MvPowerSeries.inv_mul_cancel, ContinuousLinearMap.coe_flipₗᵢ', HasMFDerivAt.prodMap, ValuationSubring.unitGroup_injective, NumberField.IsCMField.is_quadratic, div_eq_quo_add_sum_rem_div, star_nnrat_smul, PiTensorProduct.norm_eval_le_injectiveSeminorm, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, IsFractionRing.mk'_num_den', deriv_inv, IntermediateField.normal_iff_forall_fieldRange_le, Submodule.sub_starProjection_mem_orthogonal, ContinuousLinearMap.fpowerSeriesBilinear_apply_add_three, contDiffOn_succ_iff_fderiv_of_isOpen, PointwiseConvergenceCLM.equivWeakDual_apply, Polynomial.fderiv_aeval, one_half_lt_one, fderivWithin_fderivWithin_eq_of_mem_nhds, Char.card_pow_card, ContinuousLinearMap.norm_smulRight_apply, Valuation.pow_Uniformizer_is_pow_generator, Real.hasStrictDerivAt_cosh, Module.End.maxUnifEigenspaceIndex_le_finrank, contDiff_iff_continuous_differentiable, tendsto_pow_div_pow_atTop_zero, dist_birkhoffAverage_birkhoffAverage, hasDerivAt_const, dslope_sub_smul_of_ne, FiniteField.finrank_zmod_extension, FGModuleCat.FGModuleCatDual_obj, Finset.centerMass_smul_left, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', NNRat.preimage_cast_Iic, Module.Basis.equivFunL_symm_apply_repr, ArchimedeanClass.FiniteResidueField.ofArchimedean_injective, PrincipalIdeals.normal, IsometryEquiv.map_midpoint, fderiv_mul', LinearIsometryEquiv.conjStarAlgEquiv_ext_iff, OrthonormalBasis.repr_apply_apply, IsGalois.normalAutEquivQuotient_apply, IsGalois.normalBasis_apply, UniformSpace.Completion.norm_toComplL, Units.continuousOn_zpow₀_spectrum, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, NumberField.IsCMField.complexConj_apply_eq_self, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, instSMulDistribClassAlgEquiv, Complex.hasDerivAt_Gammaℂ_one, VectorField.lieBracket_fmul_left, integrable_cfcₙ, HasFDerivAtFilter.sum, RatFunc.num_zero, ContinuousFunctionalCalculus.toNonUnital, toIcoMod_eq_add_fract_mul, intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_right, ContinuousMultilinearMap.analyticAt, hasMFDerivAt_id, ClosedSubmodule.orthogonal_eq_inter, Valuation.Integers.le_iff_dvd, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, IntermediateField.adjoin_simple_eq_top_iff_of_isAlgebraic, ContinuousMultilinearMap.prodL_apply, toIocMod_eq_sub_fract_mul, FormalMultilinearSeries.radius_inv_eq_limsup, Real.hasStrictDerivAt_log, Polynomial.hilbertPoly_zero_left, HasFDerivWithinAt.cexp, IsCyclotomicExtension.isSplittingField_X_pow_sub_one, hasFDerivWithinAt_iff_hasDerivWithinAt, IsAlgClosed.card_roots_map_eq_natDegree_from_simpleRing, IsFractionRing.div_surjective, NumberField.Units.dirichletUnitTheorem.sum_logEmbedding_component, NumberField.mixedEmbedding.fundamentalCone.existsUnique_preimage_of_mem_integerSet, hasFTaylorSeriesUpToOn_succ_iff_right, ContinuousLinearMap.coe_flipMultilinearEquiv, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, Seminorm.bddAbove_iff, LaurentSeries.exists_Polynomial_intValuation_lt, NonUnitalAlgHom.coe_Lmul, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, QuadraticForm.equivalent_weightedSumSquares, ContinuousMultilinearMap.norm_map_init_le, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, hasMFDerivWithinAt_id, LeftInvariantDerivation.left_invariant'', ordinaryHypergeometricSeries_apply_zero, Lagrange.basis_empty, SchwartzMap.compCLMOfAntilipschitz_apply, Polynomial.SplittingFieldAux.scalar_tower', ContinuousAlternatingMap.hasStrictFDerivAt, FiniteField.algebraMap_norm_eq_pow, SchwartzMap.fourierInv_apply_eq, trace_eq_finrank_mul_minpoly_nextCoeff, SchwartzMap.smulRightCLM_apply_apply, LinearOrderedField.inducedOrderRingHom_toFun, NormedSpace.norm_expSeries_summable_of_mem_ball, gal_prod_isSolvable, LinearIsometryEquiv.conjStarAlgEquiv_refl, CurveIntegrable.fun_zero, Field.Emb.Cardinal.strictMono_leastExt, IntermediateField.rank_adjoin_eq_one_iff, InnerProductSpace.laplacian_smul, NNRat.natCast_le_cast, hasStrictFDerivAt_iff_hasStrictDerivAt, RCLike.tendsto_add_mul_div_add_mul_atTop_nhds, ValuationSubring.mem_unitGroup_iff, mem_segment_iff_sameRay, NNRat.instContinuousInv₀, binomialSeries_apply, eventually_singleton_add_smul_subset, VectorField.mpullback_apply, LinearMap.IsSymmetric.toSelfAdjoint_apply, RatFunc.liftOn_div, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure_1, Submodule.coe_continuous_linearProjOfClosedCompl, ContinuousLinearMapWOT.instIsTopologicalAddGroup, fderiv_mem_iff, galLiftEquiv_apply, iteratedFDeriv_neg_apply, Submodule.coe_orthogonalDecomposition, VectorField.lieBracket_eq, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, hasMFDerivWithinAt_fst, ContinuousLinearMap.coe_restrict_scalarsL', differentiableAt_fst, ContinuousLinearMapWOT.isInducing_inducingFn, fderivWithin_fderivWithin_eq_of_eventuallyEq, NumberField.InfinitePlace.LiesOver.comap_eq, DoubleCentralizer.star_fst, NNRat.coe_ceil, differentiableOn_pi'', NNRat.preimage_cast_Ioi, InnerProductSpace.laplacianWithin_smul, StrongDual.polarSubmodule_eq_polar, Polynomial.separable_X_pow_sub_C', StrictConvex.affinity, NumberField.InfinitePlace.even_finrank_of_not_isUnramifiedIn, Submodule.finrank_orthogonal_span_singleton, summable_prod_mul_pow, IsAlgClosed.factors, instIsScalarTowerAtPrimeFractionRing, PiTensorProduct.liftEquiv_symm_apply, Finset.nonneg_addConst, IsLocalRing.ResidueField.lift_comp_residue, Subfield.algebraMap_ofSubfield, Polynomial.fact_irreducible_factor, RCLike.geometric_hahn_banach_point_point, IsCyclotomicExtension.splits_X_pow_sub_one, norm_cfcₙ_lt_iff, Algebra.TensorProduct.isField_of_isAlgebraic, ContinuousLinearMap.fpowerSeries_apply_add_two, TestFunction.coe_ofSupportedInLM, IntermediateField.rank_top, mfderivWithin_eventually_congr_set', transcendental_aeval_iff, toIcoDiv_zero_one, LinearMap.span_singleton_sup_ker_eq_top, LinearMap.dualMap_injective_iff, concaveOn_iff_div, LinearMap.isPositive_natCast, inner_smul_real_right, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Algebra.normalizedTrace_eq_of_fininteDimensional, TensorProduct.toLinearEquiv_congrIsometry, Asymptotics.isLittleOTVS_fun_neg_right, ContinuousMultilinearMap.opNorm_zero, hasFDerivAt_exp_smul_const', Finset.mulConst_empty_left, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, PowerSeries.IsWeierstrassFactorization.natDegree_eq_toNat_order_map, FormalMultilinearSeries.ofScalars_norm_le, Submodule.isOrtho_iSup_left, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall, IsCoercive.bounded_below, IsLocalFrameOn.toBasisAt_coe, LinearMap.BilinForm.exists_orthogonal_basis, NumberField.mixedEmbedding.covolume_idealLattice, inv_nhdsGT_zero, Representation.isSemisimpleRepresentation_iff_isSemisimpleModule_asModule, IntermediateField.finrank_eq_fixingSubgroup_index, Commute.cfcₙHom, Hyperreal.archimedeanClassMk_pos_of_tendsto, NumberField.place_apply, Submodule.norm_subtypeL, RatFunc.num_inv_dvd, ContinuousLinearMapWOT.hasBasis_seminorms, Submodule.mem_orthogonal', ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, MvPolynomial.finrank_R, hasFDerivAt_finCons', LinearMap.toMatrixOrthonormal_symm_apply, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, contDiffPointwiseHolderAt_iff, ContinuousLinearMap.IsStarNormal.orthogonal_range, segment_eq_Icc, ContinuousLinearMap.aestronglyMeasurable_comp₂, Subspace.dualRestrict_leftInverse, FiniteField.algebraMap_norm_eq_prod_pow, Matrix.posDef_gram_iff_linearIndependent, instPolynormableSpaceForall, WeierstrassCurve.Jacobian.Point.toAffineLift_of_Z_ne_zero, SchwartzMap.smulLeftCLM_const, hasStrictFDerivAt_piLp, NumberField.house_pow_le, Finset.dens_eq_one, MDifferentiableAt.smul_section, Subfield.bot_eq_of_zMod_algebra, Lagrange.eval_basisDivisor_right, trace_eq_trace_adjoin, IntermediateField.coe_isIntegral_iff, LinearMap.toMatrix_innerₛₗ_apply, strictConvexSpace_iff, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub, PointwiseConvergenceCLM.equivWeakDual_symm_apply, hasDerivAt_of_tendstoUniformlyOn, TensorProduct.toLinearEquiv_commIsometry, PadicInt.Coe.ringHom_apply, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, WeierstrassCurve.Jacobian.addY_of_Z_ne_zero, EuclideanGeometry.oangle_midpoint_left, PowerSeries.X_inv, fderiv_fun_sum, AffineMap.hasDerivAt, hasDerivWithinAt_congr_set, Submodule.norm_sq_eq_add_norm_sq_projection, smul_sphere, LinearMap.extendTo𝕜'_apply_re, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, tangentCoordChange_comp, HasFDerivWithinAt.fun_neg, LinearIsometry.norm_iteratedFDeriv_comp_left, NNRat.num_mul_num_eq_num_mul_gcd, LinearMap.range_toContinuousLinearMap, Submodule.orthogonal_gc, NumberField.Embeddings.card, fderiv_const_smul_of_invertible, ContinuousLinearEquiv.dimH_image, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, hasFDerivWithinAt_pow', ContDiffMapSupportedIn.structureMapLM_apply_withOrder, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_right, IsGaloisGroup.fixingSubgroup_fixedPoints, HasFTaylorSeriesUpToOn.continuousLinearMap_comp, IsGaloisGroup.mulEquivAlgEquiv_apply_apply, IsFractionRing.stabilizerHom_surjective, hasStrictDerivAt_finCons', InfiniteGalois.proj_adjoin_singleton_val, normalClosure_def, Finset.dens_sdiff_add_dens, Polynomial.Splits.def, hasDerivWithinAt_taylorWithinEval_at_Icc, LinearMap.BilinForm.toDual_def, dist_iteratedFDerivWithin_zero, curveIntegral_restrictScalars, ContinuousLinearMap.hasFDerivAtFilter, IntermediateField.lift_inf, HasFPowerSeriesOnBall.hasSum, ContinuousLinearMap.isBoundedLinearMap_comp_right, Algebra.QuasiFinite.finite_fiber, quadraticChar_exists_neg_one', Matrix.PosSemidef.toLinearMap₂'_zero_iff, Submodule.starProjection_isSymmetric, HasFDerivAt.iterate, Polynomial.rootSet_C_mul_X_pow, Submodule.starProjection_apply, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, Algebra.QuasiFinite.instFiniteResidueField, NumberField.Embeddings.instNonemptyRingHomOfIsAlgebraicRatOfIsAlgClosed, HasFPowerSeriesWithinAt.pi, Matrix.eRank_diagonal, NormedSpace.isVonNBounded_iff', IsLocalRing.ResidueField.mapEquiv_apply, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv', RCLike.inv_im, WeakDual.isSeqCompact_closedBall, LinearMap.BilinForm.dualBasis_repr_apply, hasStrictDerivAt_finCons, IsFractional.div_of_nonzero, FractionalIdeal.isNoetherian_spanSingleton_inv_to_map_mul, PiTensorProduct.liftEquiv_apply, HasFDerivAt.cexp, DoubleCentralizer.add_snd, Lagrange.degree_basisDivisor_of_ne, has_antideriv_at_fourier_neg, NumberField.InfinitePlace.isRamified_iff, hasFTaylorSeriesUpTo_top_iff', NumberField.InfinitePlace.card_isUnramified, hasStrictDerivAt_zpow, NormedSpace.expSeries_apply_eq, Field.rank_mul_insepDegree_of_isPurelyInseparable, MvPowerSeries.C_inv, fderivWithin_iteratedFDerivWithin, IntermediateField.linearDisjoint_comm', rescale_to_shell, ContinuousLinearMap.rayleighQuotient_add, ContinuousMultilinearMap.contDiff, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, LinearIsometry.toSpanSingleton_apply, hasFDerivAt_iff_tendsto, IsFractionRing.fieldEquivOfAlgEquiv_algebraMap, PolynormableSpace.induced, Polynomial.natSepDegree_eq_natDegree_iff, LinearMap.isSelfAdjoint_iff', Subspace.dual_finrank_eq, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, NumberField.IsCMField.complexEmbedding_complexConj, ContinuousLinearMap.deriv_of_bilinear, sum_embeddings_eq_finrank_mul, Orientation.areaForm'_apply, Padic.padicNormE.is_norm, mem_perfectClosure_iff, VectorBundleCore.coe_coordChange, IntermediateField.smul_mem, tendsto_nat_floor_div_atTop, hasFDerivAtFilter_iff_hasDerivAtFilter, NumberField.InfinitePlace.isComplex_smul_iff, AlgHom.map_fieldRange, innerSLFlip_apply_apply, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable, tendsto_inv_atTop_nhdsGT_zero, ContinuousLinearEquiv.mdifferentiableOn, ContinuousLinearMap.nnnorm_holder_apply_apply_le, IsFractionRing.closure_range_algebraMap, Polynomial.annIdealGenerator_mem, NNRat.natCast_lt_cast, NNRat.tendsto_inv_atTop_nhds_zero_nat, Affine.Triangle.dist_orthocenter_reflection_circumcenter, OrthogonalFamily.hasSum_linearIsometry, Polynomial.hasFDerivAt, ZMod.pow_card_sub_one_eq_one, Asymptotics.isTheta_const_smul_left, FiniteField.instFiniteExtension_1, strictConvex_iff_convex, IntermediateField.extendScalars_self, Polynomial.splits_iff, upperBounds_smul_of_neg, Distribution.mapCLM_apply, WeierstrassCurve.Affine.derivative_addPolynomial_slope, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, Subalgebra.isField_of_algebraic, finrank_euclideanSpace, Polynomial.IsSplittingField.splits, FormalMultilinearSeries.norm_compContinuousLinearMap_le, PowerBasis.equivAdjoinSimple_gen, RatFunc.ofFractionRing_comp_algebraMap, LieModule.exists_nontrivial_weightSpace_of_isNilpotent, Real.hasStrictDerivAt_const_rpow_of_neg, hasDerivAt_inv, WeierstrassCurve.Jacobian.X_eq_iff, Ideal.ResidueField.map_algebraMap, algebraMap_mk, LinearMap.IsPositive.isSelfAdjoint, Field.Emb.Cardinal.equivSucc_coherence, ContinuousLinearMap.bilinear_hasTemperateGrowth, FiniteField.frobeniusAlgEquivOfAlgebraic_symm_apply, Polynomial.IsSplittingField.splits', IntermediateField.finrank_top, LinearMap.mem_span_iff_continuous_of_finite, NNRat.cast_le_one, IsContinuousRiemannianBundle.exists_continuous, Bornology.isVonNBounded_iff_smul_tendsto_zero, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, RatFunc.algebraMap_X, Module.AEval.isTorsion_of_finiteDimensional, NumberField.InfinitePlace.IsRamified.isReal, DoubleCentralizer.norm_snd, NumberField.CMExtension.equivMaximalRealSubfield_apply, Submodule.top_orthogonal_eq_bot, Lagrange.basisDivisor_eq_zero_iff, ConvexOn.sSup_of_nat_affine_eq, ContinuousLinearMap.postcomp_apply, FunctionField.ringOfIntegers.instIsIntegrallyClosedSubtypeMemSubalgebraPolynomial, convexJoin_assoc, Ideal.ResidueField.exists_smul_eq_tmul_one, Submodule.fst_orthogonalDecomposition_apply, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, minpoly.ker_aeval_eq_span_minpoly, ContinuousLinearMap.uncurryLeft_apply, HilbertBasis.dense_span, LinearEquiv.coe_toContinuousLinearEquiv', hasFDerivWithinAt_one, Matrix.rank_eq_finrank_span_row, IsDedekindDomain.FiniteAdeleRing.instIsScalarTower, map_equiv_traceDual, NNRat.cast_sum, IntermediateField.restrictScalars_adjoin_eq_sup, Submodule.orthogonal_orthogonal_eq_closure, RatFunc.intDegree_C, ContinuousLinearEquiv.nhds, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, Submodule.smul_starProjection_singleton, NumberField.Units.mem_torsion, FiniteGaloisIntermediateField.isGalois, LinearMap.BilinForm.dualBasis_injective, ContinuousLinearMap.opNorm_comp_le, contMDiff_smul, MeasureTheory.dist_convolution_le, DoubleCentralizer.nnnorm_fst, ContinuousLinearMap.isUnit_iff_isUnit_toLinearMap, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, with_gaugeSeminormFamily, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, Filter.tendsto_mul_const_atTop_iff_pos, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, PowerSeries.constantCoeff_inv, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, LieAlgebra.IsKilling.apply_coroot_eq_cast, slope_pos_iff, IntermediateField.mem_adjoin_iff_div, contMDiffOn_continuousLinearMapCoordChange, LinearEquiv.isPositive_symm_iff, NumberField.to_finiteDimensional, ContinuousLinearMap.instCompleteSpace, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, Module.Basis.exists_opNNNorm_le, aestronglyMeasurable_smul_const_iff, WeierstrassCurve.Projective.eval_polynomialX_of_Z_ne_zero, absConvexHull_add_subset, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, NNRat.instContinuousSMulOfIsScalarTowerOfRat, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, Convex.exists_forall_hasDerivWithinAt, PiTensorProduct.mapL_mul, cfcHom_real_eq_restrict, Finset.centerMass_mem_convexHull, hasDerivWithinAt_taylor_coeff_within, IntermediateField.Lifts.lt_iff, ContinuousLinearMap.toLinearMap_innerSL_apply, Polynomial.Gal.restrictComp_surjective, NumberField.ComplexEmbedding.IsConj.isReal_comp, HasFPowerSeriesAt.hasStrictDerivAt, Submodule.orthogonalFamily_self, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, IsAlgClosure.equivOfEquiv_comp_algebraMap, IntermediateField.top_toSubalgebra, hasFDerivAt_ofNat, Subfield.roots_X_pow_char_sub_X_bot, IntermediateField.extendScalars_le_iff, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Module.Basis.equivFunL_apply, Representation.isSimpleModule_iff_irreducible_ofModule, Polynomial.natSepDegree_X_pow_char_pow_sub_C, hasFDerivAt_list_prod_finRange', LinearMap.IsSymmetric.adjoint_eq, Trivialization.continuousLinearEquivAt_apply', LinearMap.isPositive_sum, ContinuousMultilinearMap.flipLinear_apply_apply, Submodule.starProjection_norm_le, HasStrictFDerivAt.neg, mfderiv_add, ContinuousAlternatingMap.norm_toContinuousMultilinearMap, HasGradientAt.hasFDerivAt, Lagrange.natDegree_basisDivisor_self, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, PowerSeries.mul_inv_cancel, Finset.addConst_le_card, LinearMap.hasDerivWithinAt, PiLp.volume_preserving_ofLp, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, Finset.dens_mul_card, rescale_to_shell_semi_normed, Localization.subalgebra.isLocalization_ofField, FormalMultilinearSeries.comp_id, IsSepClosed.splits_domain, ContinuousMultilinearMap.hasStrictFDerivAt, Submodule.inner_orthogonalProjection_eq_of_mem_right, Subfield.relfinrank_top_right, Submodule.reflection_reflection, fderivWithin_comp_smul_eq_fderivWithin_smul, ContinuousLinearMap.isLeast_opNNNorm, RatFunc.num_denom_mul, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_one, ContinuousMap.adjoin_id_eq_span_one_union, IsGaloisGroup.fixedPoints_bot, Submodule.isOrtho_iff_le, MeasureTheory.condExp_smul, Polynomial.hilbertPoly_add_left, Finset.expect_boole_mul', hasFTaylorSeriesUpTo_succ_nat_iff_right, PowerBasis.equivAdjoinSimple_symm_gen, FiniteField.isSplittingField_of_nat_card_eq, iteratedFDeriv_add, hasFDerivWithinAt_zero, ContinuousMultilinearMap.isUniformEmbedding_toUniformOnFun, HasFDerivWithinAt.norm_sq, hasFDerivWithinAt_piLp, IntermediateField.coe_val, NNRat.mul_den, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, ContinuousLinearMapWOT.isEmbedding_inducingFn, IsPrimitiveRoot.minpoly_dvd_mod_p, differentiableOn_piLp, Polynomial.SplittingField.splits, ClosedSubmodule.iInf_orthogonal, WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne, Asymptotics.isLittleOTVS_iff_smallSets, hasDerivAt_fourier_neg, nhds_hasBasis_absConvex, Finset.one_le_divConst, Module.End.IsSemisimple.aeval, EuclideanGeometry.reflection_apply_of_mem, norm_fderiv_norm_rpow_le, AlgHom.fieldRange_toSubfield, HasFPowerSeriesOnBall.neg, VectorFourier.fderiv_fourierIntegral, Polynomial.splits_id_iff_splits, ContinuousLinearMap.uncurryBilinear_apply, LinearMap.IsSymmetric.isSymmetric_smul_iff, Matrix.isStrictlyPositive_iff_posDef, groupCohomology.norm_ofAlgebraAutOnUnits_eq, VectorBundle.continuousOn_coordChange', CategoryTheory.finrank_hom_simple_simple_eq_zero_iff, LinearMap.isPositive_linearIsometryEquiv_conj_iff, ZSpan.coe_floor_self, NNRat.preimage_cast_uIcc, HasFDerivWithinAt.smul_const, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, IntermediateField.fixingSubgroup_le, ContinuousLinearMap.mfderiv_eq, Seminorm.sSup_empty, ModP.preVal_mk, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, hasFDerivWithinAt_singleton, LinearEquiv.coe_toContinuousLinearEquiv_symm', OrthonormalBasis.equiv_self_rfl, ContinuousAlternatingMap.isLeast_opNorm, midpoint_le_left, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, RatFunc.valuation_eq_LaurentSeries_valuation, InnerProductSpace.coe_gramSchmidtBasis, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, NormedSpace.isVonNBounded_of_isBounded, HasStrictFDerivAt.add, IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero, iteratedFDeriv_eq_equiv_comp, Submodule.reflection_inv, sum_Ioo_inv_sq_le, NumberField.Units.coe_neg_one, Real.smul_iInf_of_nonpos, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, Unitization.norm_eq_sup, WeierstrassCurve.Projective.addZ_eq, NNRat.preimage_cast_Icc, Real.hasDerivAt_cos, mfderivWithin_comp_of_preimage_mem_nhdsWithin, Matrix.ofLp_toEuclideanCLM, Quaternion.expSeries_even_of_imaginary, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Nat.cast_le_pow_sub_div_sub, summable_pow_div_add, hasDerivAtFilter_iff_isLittleO, Polynomial.IsSplittingField.instIsTorsionFreeSplittingField, AlgebraicClosure.instIsAlgClosure, PrimeSpectrum.residueField_comap, HasStrictFDerivAt.restrictScalars, NumberField.InfinitePlace.card_isUnramified_compl, FiniteField.two_pow_card, AffineIsometry.map_vsub, RatFunc.map_apply_div, PiTensorProduct.mapL_comp, PadicInt.coe_adicCompletionIntegersEquiv_apply, IntermediateField.finrank_eq_finrank_subalgebra, Submodule.norm_starProjection, isCompactOperator_iff_image_closedBall_subset_compact, IntermediateField.finrank_eq_one_iff_eq_top, fderiv_cos, Filter.Tendsto.cfcₙ, Algebra.Transcendental.rank_eq_cardinalMk, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, ordinaryHypergeometric_eq_tsum, FormalMultilinearSeries.isLittleO_one_of_lt_radius, Algebra.instFiniteResidueFieldOfIsUnramifiedAt, hasDerivAt_exp_smul_const, Finset.dens_empty, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', WeierstrassCurve.Affine.map_slope, Meromorphic.fun_smul, Unitary.linearIsometryEquiv_coe_symm_apply, Asymptotics.isBigOTVS_neg_left, NormedSpace.expSeries_apply_eq_div, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, Polynomial.isRoot_gcd_iff_isRoot_left_right, ContDiff.comp_continuousLinearMap, ZMod.sq_add_sq, exists_dual_vector, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, toIsField, NumberField.mixedEmbedding.logMap_eq_logEmbedding, hasFDerivWithinAt_comp_smul_smul_iff, IntermediateField.restrictRestrictAlgEquivMapHom_injective, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_apply, ContinuousLinearMap.rayleighQuotient_le_norm, Mathlib.Meta.NormNum.IsRat.natFloor, IsLocalRing.ResidueField.map_map, IsSepClosed.exists_pow_nat_eq, Nat.choose_lt_pow_div, ZMod.euler_criterion_units, ProbabilityTheory.hasDerivAt_complexMGF, gauge_smul_left_of_nonneg, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff, AffineIsometryEquiv.symm_constVSub, DifferentiableWithinAt.isBigOTVS_sub, ContMDiffWithinAt.smul, LinearMap.isPositive_toContinuousLinearMap_iff, ContinuousLinearMap.norm_def, OrthogonalFamily.summable_of_lp, IsLocalRing.exists_surjective_of_not_isLocalRing, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, LinearIsometryEquiv.analyticWithinAt, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', HasFPowerSeriesAt.apply_eq_zero, Matrix.GeneralLinearGroup.fixpointPolynomial_aeval_eq_zero_iff, NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd', fderivWithin_zero_of_notMem_closure, AddChar.wInner_cWeight_eq_one_iff_eq, ContinuousLinearMap.le_opNorm_of_le, iteratedDeriv_comp_const_smul, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDual, iteratedDerivWithin_one_div, norm_inner_eq_norm_tfae, Cubic.splits_iff_roots_eq_three, ContinuousMultilinearMap.opNorm_pi, curveIntegral_fun_add, ContinuousLinearEquiv.lipschitz, iteratedDeriv_vcomp_three, Submodule.isCompl_orthogonal_of_hasOrthogonalProjection, Algebra.adjoin_eq_top_of_primitive_element, exists_nonneg_right_iff_sameRay, IsCyclotomicExtension.discr_prime_pow_ne_two, Submodule.reflection_mul_reflection, Polynomial.isEquivalent_atTop_div, Real.hasDerivWithinAt_arcsin_Ici, OpenPartialHomeomorph.MDifferentiable.comp_symm_deriv, UniqueDiffWithinAt.smul_iff, HasStrictFDerivAt.arctan, curveIntegral_fun_neg, hasMFDerivAt_inl, HasStrictDerivAt.hasStrictFDerivAt, PowerSeries.mul_inv_rev, FiniteField.coe_frobeniusAlgEquivOfAlgebraic_iterate, NumberField.isFinitePlace_iff, gal_C_isSolvable, deriv.scomp, AnalyticAt.analyticOrderAt_eq_natCast, HasFDerivAtFilter.const_smul, NonUnitalSubalgebra.unitizationAlgEquiv_apply_coe, differentiableAt_finCons, InnerProductSpace.gramSchmidt_triangular, Algebra.normalizedTrace_algebraMap_apply_eq_self, ContinuousMultilinearMap.instContinuousConstSMul, NormedSpace.equicontinuous_TFAE, ContinuousLinearMap.differentiable, hasDerivAt_taylorWithinEval_succ, Submodule.starProjection_map_apply, Bornology.IsBounded.smul₀, LinearMap.dualMap_bijective_iff, NumberField.InfinitePlace.IsUnramified.eq, HasFDerivAt.multiset_prod, LinearMap.star_eq_adjoint, LinearEquiv.toLinearEquiv_toContinuousLinearEquiv, contDiffWithinAt_succ_iff_hasFDerivWithinAt', IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two, IsLocalFrameOn.eventually_eq_sum_coeff_smul, Filter.EventuallyEq.iteratedFDerivWithin', contDiffOn_succ_iff_hasFDerivWithinAt, HasFDerivAt.mul_const, Set.val_unitEquivUnitsInteger_apply_coe, Polynomial.sub_mod, Nat.div_two_lt_floor, differentiableWithinAt_euclidean, ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', IntermediateField.finrank_adjoin_eq_one_iff, ContinuousLinearMap.opNorm_add_le, IsLocalRing.ResidueField.map_residue, ContinuousLinearMap.sSup_sphere_eq_norm, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, DoubleCentralizer.neg_toProd, FormalMultilinearSeries.radius_unshift, IsGaloisGroup.finiteDimensional, HasFPowerSeriesAt.fderiv_eq, CategoryTheory.endomorphism_simple_eq_smul_id, LinearPMap.adjointDomainMkCLM_apply, IntermediateField.normal_iff_forall_map_le', Submodule.restrictScalars_traceDual, LinearMap.BilinForm.dualBasis_eq_iff, spectrum.map_pow_of_nonempty, NumberField.RingOfIntegers.rank, hasStrictFDerivAt_zero, Matrix.isPositive_toEuclideanLin_iff, ContinuousLinearMap.coe_restrictScalarsIsometry, ContinuousLinearMap.memLp_of_bilin, HasFPowerSeriesOnBall.tendstoUniformlyOn, IntermediateField.normal_iff_forall_fieldRange_eq, Polynomial.aeval_conj, ContinuousLinearMap.norm_inr, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, Submodule.starProjection_bot, arithGeom_eq, RootPairing.polarizationEquiv_apply, instIsAbelianGaloisSubtypeMemIntermediateField_1, NumberField.integralBasis_repr_apply, ContinuousLinearMap.differentiableWithinAt, continuousMultilinearCurryFin0_apply, Finset.cast_mulConst_mul_card, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, Polynomial.separable_prod_X_sub_C_iff', EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HasFDerivWithinAt.mapsTo_tangent_cone, Field.finSepDegree_le_finrank, WithAbs.instFiniteDimensional, PiTensorProduct.dualSeminorms_bounded, RootPairing.linearIndepOn_root_baseOf, FormalMultilinearSeries.radius_neg, VectorPrebundle.pretrivialization_linear', Field.nonempty_algHom_of_range_minpoly_subset, FiniteField.splits_X_pow_nat_card_sub_X, HasFDerivWithinAt.mul_const', extDeriv_smul, PointwiseConvergenceCLM.coeLMₛₗ_apply, ContinuousLinearMap.postcompCompactConvergenceCLM_apply, HasStrictFDerivAt.iterate, LaurentSeries.coe_X_compare, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, Submodule.orthogonal_closure, LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, ContinuousMultilinearMap.curryMidEquiv_apply, Finset.dens_biUnion_le, StrictConvexSpace.strictConvex_closedBall, fderiv_const_mul, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq, instArchimedeanNNRat, ApproximatesLinearOn.lipschitz_sub, Matrix.val_planeConformalMatrix, ContinuousMultilinearMap.iteratedFDeriv_eq, FormalMultilinearSeries.le_mul_pow_of_radius_pos, ZSpan.norm_fract_le, differentialIdeal_le_fractionalIdeal_iff, HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal, IntermediateField.finrank_bot, IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zero, ConjRootClass.splits_minpoly, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, ContinuousLinearMap.reApplyInnerSelf_apply, ZSpan.fundamentalDomain_reindex, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, fderiv_exp, Affine.Simplex.direction_mongePlane, DoubleCentralizer.algebraMap_snd, Finset.expect_dite_eq', NormedSpace.expSeries_apply_zero, ConvexCone.smul_mem_iff, IntermediateField.fixingSubgroup_antitone, ContinuousLinearMap.differentiableAt, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, Valuation.Integers.dvdNotUnit_iff_lt, AnalyticAt.analyticOrderNatAt_eq_iff, fderiv_arctan, fderivWithin_const, RatFunc.laurentAux_algebraMap, RCLike.wInner_cWeight_const_left, MeasureTheory.integrable_smul_const, hasFiniteFPowerSeriesOnBall_const, InfiniteGalois.restrict_fixedField, LinearMap.le_def, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, Finset.dens_le_dens_sdiff_add_dens, Mathlib.Tactic.Ring.inv_zero, iteratedFDerivWithin_succ_apply_left, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, HasFDerivAtFilter.fun_const_smul, hasStrictFDerivAt_norm_sq, FractionalIdeal.mem_dual, Matrix.linearIndependent_cols_iff_isUnit, Submodule.starProjection_unit_singleton, SchwartzMap.fourier_evalCLM_eq, RatFunc.algebraMap_eq_C, LinearIsometryEquiv.comp_differentiableWithinAt_iff, tfae_of_isNoetherianRing_of_isLocalRing_of_isDomain, LinearMap.adjoint_toSpanSingleton, DoubleCentralizer.one_snd, Valuation.Integers.valuation_unit, OrthonormalBasis.coe_toBasis, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, Polynomial.natDegree_hilbertPoly_of_ne_zero, Polynomial.div_eq_zero_iff, Polynomial.IsSplittingField.adjoin_rootSet', IsLocalRing.ResidueField.map_id, IntermediateField.sepDegree_bot, convexJoin_convexJoin_convexJoin_comm, ValuationSubring.unitGroup_strictMono, LinearMap.BilinForm.dualSubmodule_dualSubmodule_of_basis, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, contDiffOn_infty_iff_fderiv_of_isOpen, mem_quasispectrum_iff, hasDerivWithinAt_natCast, Algebra.normalizedTrace_self, NumberField.canonicalEmbedding.nnnorm_eq, RatFunc.algebraMap_apply_div, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, galLiftEquiv_symm_apply, convexHull_sum, ContinuousLinearEquiv.analyticOn, RatFunc.div_smul, ContinuousMultilinearMap.opNorm_add_le, fderiv_pow_ring', ContinuousLinearMap.map_sub₂, ContinuousLinearMap.bilinearComp_apply, IntermediateField.algebraMap_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, ContinuousMultilinearMap.instContinuousEval, differentiableAt_piLp, imaginaryPart_eq_neg_I_smul_skewAdjointPart, Submodule.reflection_sub, InfiniteGalois.instCompactSpaceAlgEquivOfIsGalois, IsAlgClosure.equivOfEquiv_symm_algebraMap, TemperedDistribution.instLineDerivSMulReal, iteratedDeriv_comp_neg, fderiv_natCast, IsConjRoot.exists_algEquiv, IntermediateField.finInsepDegree_bot', NumberField.Units.dirichletUnitTheorem.mult_log_place_eq_zero, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_le, SchwartzMap.evalCLM_apply_apply, cfcUnits_pow, Algebra.norm_eq_norm_adjoin, Algebra.IsAlgebraic.algHom_bijective₂, LinearMap.IsSymmetric.natCast, HasFDerivAtFilter.fun_sub, OpenPartialHomeomorph.MDifferentiable.mfderiv_bijective, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, ClosedSubmodule.mem_orthogonal, IsSelfAdjoint.sq_spectrumRestricts, Height.mulHeight_eq, fderiv_const, AddChar.expect_eq_zero_iff_ne_zero, DiffContOnCl.smul_const, NumberField.FinitePlace.coe_apply, Matrix.posDef_iff_eq_conjTranspose_mul_self, MeasureTheory.condExpIndL1_smul', Polynomial.differentiableAt_aeval, Subspace.quotAnnihilatorEquiv_apply, circleEquivGen_symm_apply, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, ContinuousLinearMap.toContinuousLinearEquivOfDetNeZero_apply, WeakDual.CharacterSpace.compContinuousMap_apply, LinearMap.re_inner_adjoint_mul_self_nonneg, PointwiseConvergenceCLM.coeLM_apply, hasDerivAt_id, differentiable_pi, HasFTaylorSeriesUpToOn.fderivWithin, NNRat.cast_pow, Real.hasDerivAt_rpow_const, IntermediateField.restrictScalars_bot_eq_self, ContinuousLinearEquiv.hasFDerivWithinAt, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, ContinuousMultilinearMap.isLeast_opNNNorm, Complex.ofReal_comp_balance, functionField_iff, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, LinearMap.BilinForm.linearIndependent_of_iIsOrtho, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff, RCLike.normSq_mul, LinearMap.isPositive_self_comp_adjoint, PadicInt.toZMod_eq_residueField_comp_residue, RatFunc.eval_C, Polynomial.hilbertPoly_X_pow_succ, Polynomial.isEquivalent_atBot_lead, Lagrange.iterate_derivative_interpolate, FormalMultilinearSeries.id_comp, Finset.mem_convexHull, fderivWithin.log, circleIntegral.integral_smul, ContinuousLinearMap.norm_map_tail_le, deriv_update, Field.finSepDegree_eq_finrank_of_isSeparable, HasFPowerSeriesAt.restrictScalars, AlgebraicClosure.Monics.splits_finsetProd, contMDiffOn_symm_coordChangeL, hasDerivAt_integral_of_dominated_loc_of_deriv_le, tangentBundleCore_coordChange_model_space, Nonneg.coe_nnqsmul, ContinuousLinearMap.instStarModuleId, NumberField.mixedEmbedding.mixedEmbedding_apply_isReal, Polynomial.hasFDerivAt_aeval, Finset.nonneg_addConst_self, IntermediateField.adjoin.range_algebraMap_subset, Seminorm.convex_ball, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, LinearIsometryEquiv.toLinearEquiv_lTensor, DoubleCentralizer.instIsCentralScalar, Matrix.linearIndependent_of_posDef_gram, ContDiffAt.restrictScalars_iteratedFDeriv, exists_dual_vector'', ContinuousLinearMapWOT.instContinuousSMul, Finpartition.coe_energy, PiTensorProduct.injectiveSeminorm_apply, NumberField.Units.dirichletUnitTheorem.log_le_of_logEmbedding_le, ContinuousLinearMap.isBoundedLinearMap_comp_left, LinearIsometryEquiv.toLinearEquiv_smul, MeasureTheory.MemLp.continuousLinearMap_comp, Valuation.HasExtension.instIsScalarTower_valuationSubring', RingHom.SurjectiveOnStalks.residueFieldMap_bijective, NumberField.RingOfIntegers.mk_zero, norm_fderiv_iteratedFDeriv, curveIntegralFun_neg, meromorphicOrderAt_smul, Asymptotics.isLittleOTVS_map, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, conformalFactorAt_inner_eq_mul_inner', InfiniteGalois.limitToAlgEquiv_apply, hasFDerivAtFilter_snd, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, LinearIsometryEquiv.analyticOn, ValuationSubring.algebraMap_apply, LinearIsometryEquiv.analyticAt, IsLocalRing.ResidueField.map_id_apply, Matrix.l2_opNNNorm_def, hasMFDerivAt_const, NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConj, ContinuousLinearEquiv.strictConvex_image, ContinuousMultilinearMap.instIsBoundedSMul, IntermediateField.mem_lift, IntermediateField.isAlgebraic_adjoin_pair, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, instIsDomain, PowerSeries.inv_eq_zero, hasDerivAtFilter_sub_const_iff, CyclotomicRing.instIsScalarTowerCyclotomicField, RatFunc.faithfulSMul, IsRealClosed.exists_eq_pow_of_isSquare, spectrum.hasDerivAt_resolvent, ContinuousLinearMap.integrable_comp, ContinuousLinearMap.adjointAux_adjointAux, HasStrictFDerivAt.const_sub, RatFunc.num_X, Submodule.coe_inner, Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, fderiv_sub, LinearMap.det_map, NumberField.Embeddings.instNonemptyRingHom, hasDerivAt_exp, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, ZSpan.span_top, LinearMap.hasEigenvalue_zero_tfae, hasFDerivAt_single, Ideal.finrank_quotient_map, MvPolynomial.schwartz_zippel_sup_sum, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_orthonormalBasis, MeasureTheory.condExpL2_indicator_of_measurable, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, Complex.hasDerivAt_logTaylor, WithSeminorms.isVonNBounded_iff_finset_seminorm_bounded, iteratedDeriv_vcomp_eq_sum_orderedFinpartition, LinearMap.eq_adjoint_iff, ContinuousLinearMapWOT.instContinuousAdd, WittVector.exists_frobenius_solution_fractionRing, NumberField.mixedEmbedding.norm_smul, Real.hasStrictDerivAt_arsinh, VectorField.mpullbackWithin_smul_apply, Algebra.discr_mul_isIntegral_mem_adjoin, NNReal.coe_nnqsmul, iter_deriv_pow', HasFDerivWithinAt.iterate, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, hasDerivAt_iff_tendsto_slope_zero, HasMFDerivWithinAt.sum, IntermediateField.finrank_sup_le, Orthonormal.inner_right_finsupp, NumberField.InfinitePlace.IsRamified.comap_embedding, ordinaryHypergeometricSeries_apply_eq, LinearMap.norm_extendTo𝕜'_apply_sq, Asymptotics.isLittleOTVS_iff_isLittleO, WithSeminorms.equicontinuous_TFAE, EuclideanSpace.basisFun_repr, ImplicitFunctionData.hasStrictFDerivAt, ContinuousLinearMap.integral_comp_id_comm', Height.AdmissibleAbsValues.mulSupport_finite, UniqueMDiffWithinAt.uniqueDiffWithinAt, NumberField.InfinitePlace.LiesOver.embedding_comp_eq_or_conjugate_embedding_comp_eq, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, ContinuousLinearMap.coprodEquivL_apply_apply, HasFTaylorSeriesUpToOn.hasFDerivAt, Finset.le_card_falling_div_choose, mfderiv_prod_right, LinearIsometry.norm_toContinuousLinearMap_comp, galRestrictHom_symm_algebraMap_apply, hasStrictFDerivAt_inv, RatFunc.algebraMap_C, ContinuousLinearMap.isBigOWith_comp, ContinuousLinearMap.flip_add, exists_pos_left_iff_sameRay, IntermediateField.adjoinRootEquivAdjoin_apply_root, LinearMap.finiteDimensional, hasFiniteFPowerSeriesAt_const, continuous_clm_apply, IntermediateField.fixingSubgroup_isClosed, AffineSubspace.isometryEquivMap.coe_apply, ContinuousAlternatingMap.hasBasis_nhds_zero, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, LinearIsometry.coe_toSpanSingleton, Bornology.isBounded_iff_isVonNBounded, Polynomial.cardPowDegree_apply, spectrum.map_polynomial_aeval_of_nonempty, ContinuousLinearEquiv.isBigO_sub_rev, ContinuousLinearMap.isSelfAdjoint_iff', Submodule.sndL_comp_coe_orthogonalDecomposition, HasFDerivWithinAt.restrictScalars, DoubleCentralizer.pow_toProd, OrthonormalBasis.equiv_apply_euclideanSpace, measurable_fderiv_apply_const, Submodule.le_traceDual, stereographic_neg_apply, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, IsLocalFrameOn.coeff_apply_of_notMem, isSelfAdjoint_starProjection, krullTopology_isTotallySeparated, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, InnerProductSpace.gramSchmidt_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, VectorBundleCore.localTriv_coordChange_eq, Finset.divConst_empty_left, LinearMap.BilinForm.isAdjointPair_iff_eq_of_nondegenerate, ContinuousMultilinearMap.uncurryRight_apply, IntermediateField.rank_bot, eventually_norm_symmL_trivializationAt_self_comp_lt, RCLike.ofReal_pow, ContinuousLinearMap.isVonNBounded_iff, NumberField.FinitePlace.norm_def_int, InnerProductSpace.Core.inner_smul_ofReal_left, mfderivWithin_zero_of_not_mdifferentiableWithinAt, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, fderiv_inv, FiniteField.unit_isSquare_iff, Differentiable.prodMk, Complex.orthonormalBasisOneI_repr_symm_apply, ModelWithCorners.hasMFDerivWithinAt, derivWithin_comp_mul_left, Manifold.riemannianEDist_def, HasFDerivAtFilter.prodMk, hasDerivAt_circleMap, HasFDerivAtFilter.isLittleO, convexHullAddMonoidHom_apply, curveIntegralFun_fun_zero, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, vectorSpan_segment, ContinuousLinearMap.bilinearComp_zero, HasFDerivAt.fun_pow', le_restrictScalars_separableClosure, ZSpan.map, algebraMap.coe_div, IsSimpleModule.finrank_eq_one_of_isMulCommutative, IntermediateField.coe_zero, NumberField.InfinitePlace.isRamified_iff_card_stabilizer_eq_two, X_pow_sub_C_irreducible_of_prime, Submodule.IsLattice.finrank_of_pi, DifferentiableAt.prodMk, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, Finset.convexHull_eq, HasMFDerivWithinAt.mul', ContinuousLinearEquiv.norm_symm_pos, MvPolynomial.aeval_toPolynomialAdjoinImageCompl_eq_zero, Submodule.sInf_orthogonal, ContinuousAlternatingMap.uniformContinuous_coe_fun, ContinuousMultilinearMap.cpolynomialAt, ContinuousLinearMap.NonlinearRightInverse.right_inv, norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, curveIntegralFun_def', PointedContMDiffMap.instIsScalarTowerSomeENatTop, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace, NumberField.RingOfIntegers.instIsTorsionFree, NumberField.discr_eq_basisMatrix_det_sq, IntermediateField.adjoin.algebraMap_mem, Submodule.isOrtho_span, contDiffOn_fderiv_coord_change, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, IsLocalRing.exists_factor_valuationRing, IntermediateField.instIsScalarTowerSubtypeMem_1, RatFunc.num_eq_zero_iff, ZSpan.exist_unique_vadd_mem_fundamentalDomain, ContinuousMultilinearMap.ratio_le_opNorm, arithGeom_same_eq_mul_div, HasFDerivAtFilter.fun_add, ContinuousLinearEquiv.subsingleton_or_nnnorm_symm_pos, ContinuousLinearMap.norm_extendTo𝕜'_bound, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff, slope_def_field, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, HasFDerivWithinAt.hasDerivWithinAt, Matrix.PosSemidef.isUnit_sqrt_iff, cfc_zpow, spectralNorm_smul, hasDerivAt_iff_hasFDerivAt, LieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, Complex.im_balance, Nonneg.coe_inv, Polynomial.eventually_atTop_not_isRoot, HasFiniteFPowerSeriesOnBall.neg, Complex.ofReal_expect, Padic.complete'', Algebra.IsCentral.instContinuousLinearMap, IsSemisimpleRing.exists_algEquiv_pi_matrix_of_isAlgClosed, HasFDerivAtFilter.comp, Polynomial.separable_prod_X_sub_C_iff, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, LinearMap.charpoly_constantCoeff_eq_zero_iff, norm_derivWithin_eq_norm_fderivWithin, Asymptotics.IsEquivalent.pow, lineDifferentiableWithinAt_smul_iff, NumberField.ComplexEmbedding.isConj_apply_apply, Fintype.expect_ite_mem, ArchimedeanClass.mk_ratCast, iteratedFDeriv_zero_apply, IsCyclotomicExtension.Rat.galEquivZMod_restrictNormal_apply, ContinuousLinearMap.le_def, isSolvable_of_isScalarTower, WeakDual.isClosed_closedBall, contDiff_succ_iff_fderiv_apply, WeierstrassCurve.Projective.map_dblU, hasDerivAt_fourier, AlgebraicGeometry.ValuativeCommSq.commSq, coe_lpPiLpₗᵢ, Submodule.complete_of_finiteDimensional, Subfield.bot_eq_of_charZero, VectorBundleCore.localTriv_apply, LinearIsometry.inr_apply, Finset.pluennecke_ruzsa_inequality_pow_div, fderiv_ccos, LinearMap.isPositive_zero, DoubleCentralizer.zero_fst, IntermediateField.finrank_bot_mul_relfinrank, fderiv_update, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, FiniteField.Matrix.charpoly_pow_card, Asymptotics.superpolynomialDecay_mul_param_pow_iff, ContinuousLinearMap.hasFDerivWithinAt, fdifferential_comp, minpoly.dvd_map_of_isScalarTower, LinearIsometry.orthonormal_comp_iff, half_lt_self_iff, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv, WeierstrassCurve.Projective.negDblY_eq, Diffeomorph.uniqueDiffOn_image, ContinuousLinearMap.le_opNorm₂, Algebra.norm_eq_prod_automorphisms, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, slope_fun_def, Seminorm.continuous_iff, HasFDerivAt.smul_const, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, ContinuousLinearMap.norm_uncurryMid, IsLocalFrameOn.linearIndependent, Field.lift_rank_mul_lift_insepDegree_of_isPurelyInseparable, Matrix.sub_scalar_sq_eq_disc, InnerProductSpace.rankOne_def', ContDiff.fderiv_apply, EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, ContinuousLinearMap.opNorm_mul_le, ContinuousLinearMap.uncurryLeft_norm, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_right, hasFDerivAtFilter_fst, Polynomial.exists_approx_polynomial, Submodule.isClosed_orthogonal, Submodule.IsLattice.rank_of_pi, ContinuousLinearMap.opNorm_subsingleton, hasStrictDerivAt_abs_neg, ContinuousLinearMap.holder_smul_right, Filter.EventuallyEq.fderiv, HasFDerivWithinAt.multilinear_comp, HasFPowerSeriesOnBall.tendstoUniformlyOn', HasFPowerSeriesWithinOnBall.const_smul, natDegree_radical_le, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, FiniteField.trace_pow_card, fderiv_apply_one_eq_deriv, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, HasFTaylorSeriesUpToOn.compContinuousLinearMap, hasFDerivAt_zero_of_eventually_const, OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_top, IsUltrametricDist.algNormOfAlgEquiv_apply, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_le_one, IntermediateField.bot_eq_top_iff_finrank_eq_one, ContinuousAlternatingMap.continuous_restrictScalars, HasFPowerSeriesOnBall.sub, IntermediateField.finiteDimensional_adjoin, contDiffAt_succ_iff_hasFDerivAt, ContinuousLinearMap.IsPositive.inner_nonneg_left, IntermediateField.isTranscendenceBasis_adjoin_iff, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, hasFDerivAt_const, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_left, HasFDerivAt.inner, LinearMap.adjoint_lTensor, EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, LinearEquiv.smulOfNeZero_apply, LinearMap.slope_comp, IntermediateField.lift_injective, MeasureTheory.Integrable.convolution_integrand, HasFDerivAtFilter.star, RatFunc.intDegree_add, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, OrthonormalBasis.map_apply, LinearMap.toMatrixOrthonormal_apply, DivisibleHull.qsmul_def, MeasureTheory.condExpL1CLM_lpMeas, HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod, WeierstrassCurve.Projective.eval_polynomialY_of_Z_ne_zero, fderivWithin_exp, FiniteGaloisIntermediateField.adjoin_map, NumberField.InfinitePlace.embedding_of_isReal_apply, Submodule.isSymmetricProjection_starProjection, deriv_inv'', ContinuousLinearMap.mdifferentiableWithinAt, SeparatingDual.completeSpace_continuousLinearMap_iff, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt, OrthogonalFamily.inner_sum, LinearMap.IsPositive.smul_of_nonneg, NormedSpace.vonNBornology_eq, HasStrictFDerivAt.fun_sub, ClosedSubmodule.mem_orthogonal_toSubmodule_iff, HasFDerivAt.lim, hasDerivWithinAt_const, FormalMultilinearSeries.compAlongComposition_norm, Polynomial.tendsto_nhds_iff, ContinuousLinearMap.isometry_mul, Subspace.finrank_add_finrank_dualCoannihilator_eq, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', ContinuousLinearMap.isOpen_injective, isCoveringMapOn_npow, NonUnitalCommCStarAlgebra.toStarModule, Submodule.le_traceDual_comm, ContDiff.continuous_iteratedFDeriv', IsFractionRing.mk'_mk_eq_div, IntermediateField.coe_extendScalars, NumberField.mixedEmbedding.normAtAllPlaces_mixedEmbedding, Polynomial.X_pow_sub_one_separable_iff, NumberField.RingOfIntegers.coe_injective, OrthonormalBasis.sum_repr_symm, HasFDerivAt.const_mul, Meromorphic.pow, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, LieAlgebra.IsKilling.disjoint_ker_weight_corootSpace, Finset.sum_card_slice_div_choose_le_one, StrongDual.toLpₗ_apply, IntermediateField.AdjoinSimple.trace_gen_eq_zero, Orthonormal.inner_left_sum, DoubleCentralizer.sub_toProd, formalMultilinearSeries_geometric_apply_norm, IntermediateField.lift_sepDegree_bot', ContinuousLinearMap.continuous_uncurry_of_multilinear, Polynomial.differentiableOn, Pi.orthonormalBasis.toBasis, LinearIsometry.map_starProjection, tendsto_pow_neg_atTop, IsLocalFrameOn.coeff_apply_zero_at, CyclotomicRing.adjoin_algebra_injective, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, egauge_ball_one_le_of_one_lt_norm, HasFTaylorSeriesUpToOn.add, MeasureTheory.dist_convolution_le', instLiesOverResidueFieldBotIdeal, instIsTopologicalGroupAlgEquiv, isQuotientCoveringMap_zpow, NNRat.addSubmonoid_closure_range_pow, Polynomial.natSepDegree_C_mul, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, HasFDerivAt.mul, tendsto_add_mul_div_add_mul_atTop_nhds, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, IsLocalRing.split_injective_iff_lTensor_residueField_injective, VectorField.lieBracket_const_smul_right, WeierstrassCurve.Projective.addX_eq, Asymptotics.IsBigO.hasFDerivWithinAt, LinearMap.continuous_of_nonzero_on_open, Submodule.inf_orthogonal, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, RatFunc.denom_X, InnerProductSpace.innerSL_norm, hasFDerivAt_exp_zero, NNRat.cast_multisetSum, LinearIsometryEquiv.strictConvex_image, Filter.tendsto_const_mul_pow_atBot_iff, fderiv_add, ContinuousMultilinearMap.isEmbedding_toUniformOnFun, SchwartzMap.le_seminorm, Ioo_subset_openSegment, IsLocalDiffeomorph.mfderivToContinuousLinearEquiv_coe, DoubleCentralizer.nnnorm_fst_eq_snd, isPurelyInseparable_iff_minpoly_eq_X_sub_C_pow, toWeakSpace_closedConvexHull_eq, Unitization.norm_def, IntermediateField.relrank_dvd_rank_top_of_le, convexHull_pi, Finset.addConst_mul_card, Submodule.IsOrtho.le, Submodule.reflection_map, ContinuousAlternatingMap.instT3Space, LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpace, WittVector.RecursionBase.solution_spec, Polynomial.gcd_map, InnerProductSpace.span_gramSchmidt_Iic, MDifferentiableAt.smul, Submodule.det_reflection, ClassGroup.mk_mk0, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, ContinuousLinearMap.measurable_apply, NNRat.preimage_cast_Ici, IsSepClosed.algebraMap_surjective, hasFDerivAtFilter_iff_isLittleOTVS, IntermediateField.finSepDegree_adjoin_simple_le_finrank, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, Matrix.ker_diagonal_toLin', ContinuousMultilinearMap.norm_ofSubsingleton_id_le, ContinuousAlternatingMap.curryLeft_same, ContinuousMultilinearMap.curryRight_apply, NormedSpace.expSeries_apply_eq', ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, Submodule.inner_orthogonalProjection_eq_of_mem_left, ContMDiffWithinAt.mfderivWithin, gal_X_sub_C_isSolvable, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, Polynomial.hilbertPoly_mul_one_sub_succ, differentiableWithinAt_pi, star_nnqsmul, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, toIocDiv_eq_neg_floor, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Hyperreal.instIsStrictOrderedRing, Int.log_natCast, ContinuousLinearMap.extendTo𝕜_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, eventually_norm_symmL_trivializationAt_comp_self_lt, ContinuousLinearMap.IsPositive.add, EuclideanSpace.volume_ball_fin_three, Field.Emb.Cardinal.filtration_apply, FiniteField.isSplittingField_of_card_eq, Mathlib.Tactic.Ring.inv_single, Polynomial.natSepDegree_mul_eq_iff, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff', InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis, CurveIntegrable.fun_neg, MeromorphicAt.pow, AffineSubspace.subtypeₐᵢ_linear, AlgebraicClosure.toSplittingField_coeff, LieModule.traceForm_eq_sum_finrank_nsmul, NNRat.ceil_coe, NumberField.RingOfIntegers.isIntegral_coe, Int.lt_zpow_succ_log_self, mfderivWithin_const, IntermediateField.relrank_dvd_rank_bot, hasStrictFDerivAt_pow', Ideal.finite_mulSupport_coe, Polynomial.hasStrictDerivAt_aeval, AnalyticOn.iteratedFDeriv_comp_perm, ContinuousLinearMap.norm_single, LinearMap.flip_injective_iff₂, VectorPrebundle.exists_coordChange, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, DoubleCentralizer.one_fst, ContinuousLinearMap.norm_extendTo𝕜', ValuationSubring.unitGroup_le_unitGroup, Lagrange.degree_basis, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, IsDedekindDomain.HeightOneSpectrum.coe_mem_adicCompletionIntegers, StrongDual.polar_univ, IsLocalRing.ResidueField.algebraMap_eq, AlgHom.liftNormal_commutes, fderivWithin_eventually_congr_set, Lagrange.eval_basis_of_ne, NumberField.Units.complexEmbedding_apply, IsStronglyTranscendental.iff_of_isFractionRing, LinearIsometry.coe_toAffineIsometry, NumberField.count_multisetInfinitePlace_eq_mult, FractionalIdeal.map_div, Polynomial.isUnit_or_eq_zero_of_isUnit_integerNormalization_primPart, linearIndependent_of_ne_zero_of_inner_eq_zero, WeierstrassCurve.Projective.isUnit_dblZ_of_Y_ne', ContDiffMapSupportedIn.postcompCLM_apply, ValuationSubring.principal_units_le_units, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ContinuousAlternatingMap.curryLeft_zero, IsContDiffImplicitAt.bijective, Polynomial.natSepDegree_smul_nonzero, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, OnePoint.smul_infty_eq_ite, ContinuousAlternatingMap.restrictScalarsLI_apply, fderivWithin_fun_const, PerfectField.splits_of_natSepDegree_eq_one, ContinuousMultilinearMap.opNNNorm_prod, IntermediateField.AdjoinPair.algebraMap_gen₁, ContinuousLinearEquiv.comp_right_differentiableOn_iff, Padic.isAbsoluteValue, OpenPartialHomeomorph.MDifferentiable.mfderiv_surjective, NumberField.fractionalIdeal_rank, ContinuousLinearMap.opENorm_comp_le, hasGradientAt_iff_hasFDerivAt, Asymptotics.IsTheta.isThetaTVS, Asymptotics.isEquivalent_nat_floor, RatFunc.denom_div, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, IsLocalRing.finrank_cotangentSpace_le_one_iff, curveIntegrable_neg_iff, PowerSeries.invOfUnit_eq, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, HasFPowerSeriesOnBall.tendsto_partialSum, maximal_orthonormal_iff_orthogonalComplement_eq_bot, ValuationRing.of_integers, hasMFDerivWithinAt_const, FractionalIdeal.map_inv, iteratedFDeriv_one_apply, ContinuousLinearEquiv.iteratedFDeriv_comp_left, Filter.Tendsto.zero_smul_isBoundedUnder_le, NumberField.InfinitePlace.not_isUnramified_iff, Submodule.reflection_orthogonal, quasispectrum.algebraMap_mem_iff, hasFDerivAt_exp_smul_const_of_mem_ball, fderiv_fun_mul', NumberField.InfinitePlace.isUnramified_iff, IsDiscreteValuationRing.exists_lift_of_le_one, Finset.centerMass_segment', ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, HasFPowerSeriesOnBall.factorial_smul, HasFDerivAt.const_smul, HasFDerivAt.hasLineDerivAt, WeierstrassCurve.Affine.Point.map_map, doublyStochastic_eq_convexHull_permMatrix, derivWithin_pi, ContinuousAlternatingMap.norm_image_sub_le', NormedSpace.expSeries_sum_eq_rat, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, HasFPowerSeriesWithinAt.prod, Valuation.HasExtension.algebraMap_mem_valuationSubring, Module.End.finite_spectrum, IsGalois.intermediateFieldEquivSubgroup_symm_apply, ContMDiffMap.coe_smul, iteratedFDeriv_succ_apply_right, NumberField.InfinitePlace.denseRange_algebraMap_pi, Submodule.isOrtho_top_right, FormalMultilinearSeries.leftInv_coeff_one, LinearMap.IsSymmetric.smul, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, ContinuousLinearMap.hasMFDerivAt, IsAlgClosed.exists_eval₂_eq_zero, TensorProduct.assocIsometry_apply, NumberField.finite_of_discr_bdd, Matrix.toLin_conjTranspose, mdifferentiableOn_continuousLinearMapCoordChange, hasDerivAtFilter_intCast, FixedPoints.toAlgAut_surjective, NumberField.mixedEmbedding.fundamentalCone.mixedEmbedding_preimageOfMemIntegerSet, Orthonormal.inner_finsupp_eq_sum_left, cfcHom_nnreal_eq_restrict, QuasispectrumRestricts.algebraMap_image, fderiv_deriv, Padic.exi_rat_seq_conv, Matrix.IsHermitian.spectral_theorem, PrimeSpectrum.isHomeomorph_comap_of_isPurelyInseparable, IsPurelyInseparable.minpoly_natDegree_eq, integrableOn_cfcₙ, hasFPowerSeriesAt_pi_iff, IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_apply, NumberField.RingOfIntegers.mapRingHom_apply, LieAlgebra.IsKilling.span_weight_isNonZero_eq_top, IntermediateField.LinearDisjoint.of_inf_eq_bot, RatFunc.intDegree_polynomial, norm_cfcₙ_le, toPrincipalIdeal_eq_iff, NumberField.InfinitePlace.isReal_smul_iff, AlgHom.coe_fieldRange, hasDerivWithinAt_univ, Asymptotics.isLittleOTVS_neg_right, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, LinearIsometryEquiv.hasFDerivAt, IntermediateField.adjoin_simple_toSubalgebra_of_isAlgebraic, ContinuousAlternatingMap.uniformContinuous_toContinuousMultilinearMap, Seminorm.ball_zero_absorbs_ball_zero, RatFunc.v_def, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm, minpoly.add_algebraMap, Subfield.relrank_dvd_rank_top_of_le, HasFDerivAtFilter.add, Valuation.Integers.eq_algebraMap_or_inv_eq_algebraMap, ContinuousLinearEquiv.contDiffWithinAt_comp_iff, PointwiseConvergenceCLM.precomp_apply, divRadical_dvd_wronskian_right, NormedSpace.exp_def, Matrix.PosSemidef.sq_sqrt, uniqueMDiffWithinAt_iff, ArchimedeanClass.FiniteResidueField.mk_ne_zero, ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff, LinearIsometryEquiv.rTensor_apply, Polynomial.div_eq_quo_add_rem_div, LinearIsometryEquiv.inner_map_map, LieAlgebra.IsKilling.chainTopCoeff_add_chainBotCoeff, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, NumberField.Units.coe_pow, CategoryTheory.finrank_hom_simple_simple, IsPurelyInseparable.algebraMap_elemReduct_eq', Subspace.dualLift_of_mem, InnerProductSpace.isStarProjection_rankOne_self, coord_norm', StrictConvex.smul, Trivialization.apply_eq_prod_continuousLinearEquivAt, NNRat.cast_min, HasFDerivWithinAt.comp, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, ContinuousLinearMapWOT.ext_dual_iff, LinearIsometry.integral_comp_comm, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, LaurentSeries.LaurentSeries_coe, contDiff_clm_apply_iff, HasFPowerSeriesAt.hasFDerivAt, OrthonormalBasis.measurePreserving_repr_symm, Polynomial.SplittingFieldAux.instIsSplittingFieldNatDegree, Finset.centroid_mem_convexHull, hasStrictFDerivAt_finCons', spec_cfcₙAux, norm_fderiv_norm, ConvexOn.hasDerivWithinAt_sSup_slope_of_mem_interior, root_X_pow_sub_C_pow, ClosedSubmodule.orthogonal_eq_top_iff, fderiv_comp, eventually_enorm_mfderiv_extChartAt_lt, AlgebraicIndependent.liftAlgHom_comp_reprField, Finset.expect_boole_mul, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, EuclideanSpace.piLpCongrLeft_single, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, NumberField.RingOfIntegers.mk_one, hasFDerivAt_exp_smul_const, LinearIsometryEquiv.norm_iteratedFDeriv_comp_right, HasFPowerSeriesOnBall.eventually_hasSum, Field.Algebra.IsSeparable.finSepDegree_eq, ContinuousLinearMap.hasStrictFDerivAt, DivisibleHull.qsmul_of_nonneg, IntermediateField.finrank_top', NumberField.conj_basisMatrix, WeierstrassCurve.Projective.baseChange_add, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, oneTangentSpaceIcc_def, smul_unitBall, LaurentSeries.powerSeries_ext_subring, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, Set.unit_valuation_eq_one, Submodule.mem_projectivization_iff_submodule_le, Lagrange.eval_basisDivisor_left_of_ne, PowerSeries.isNoetherianRing, IsSymmSndFDerivAt.iteratedFDeriv_cons, IntermediateField.inclusion_self, NumberField.Units.abs_det_eq_abs_det, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, Complex.im_comp_balance, IntermediateField.lift_bot, IsPurelyInseparable.algebraMap_iterateFrobenius, Lagrange.natDegree_basisDivisor_of_ne, RCLike.normSq_eq_def', Polynomial.C_mul_dvd, ContinuousLinearMap.comp_analyticOn, Polynomial.isBoundedUnder_abs_atBot_iff, analyticOrderAt_pow, hasStrictDerivAt_const, ContinuousLinearMap.continuousConstSMul, fderiv_finset_prod, ModelWithCorners.hasMFDerivWithinAt_symm, PosSMulStrictMono.nnrat_of_rat, IsGalois.fixedField_top, Bundle.Trivial.trivialization.isLinear, ContinuousLinearMap.coeFn_compLpL, hasStrictFDerivAt_list_prod_attach', stdSimplex.barycenter_apply, IsPrimitiveRoot.norm_pow_sub_one_two, deriv_single, IntermediateField.normalClosure_of_normal, StrongDual.norm_toLpₗ_le, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, hasFDerivWithinAt_euclidean, FractionalIdeal.exists_ne_zero_mem_isInteger, ClosedSubmodule.mem_orthogonal_iff, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, HasFPowerSeriesWithinAt.restrictScalars, DoubleCentralizer.sub_fst, tangentConeAt_real_subset_isRCLikeNormedField, range_deriv_subset_closure_span_image, AbsoluteValue.hasBasis_uniformity, Matrix.PosDef.isStrictlyPositive, Module.Basis.parallelepiped_eq_map, ArchimedeanClass.mk_le_mk_iff_ratCast, Algebra.discr_powerBasis_eq_prod, ContDiffMapSupportedIn.norm_apply_le_seminorm, Polynomial.mem_iff_annIdealGenerator_dvd, NNRat.one_lt_cast, contDiffOn_clm_apply, ContinuousLinearMap.le_opNNNorm, spectrum.subset_polynomial_aeval, FDRep.char_one, ContinuousLinearEquiv.det_coe_symm, NumberField.InfinitePlace.isometry_embedding_of_isReal, IsFractionRing.restrictScalars_fieldEquivOfAlgEquiv, LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range, FormalMultilinearSeries.id_apply_zero, SchwartzMap.hasDerivAt, stabilizer_isOpen_of_isIntegral, FunctionField.ringOfIntegers.instIsDedekindDomainSubtypeMemSubalgebraPolynomialOfIsSeparableRatFunc, Algebra.IsAlgebraic.isNormalClosure_iff, Submodule.starProjection_orthogonal, Seminorm.inf_apply, ClassGroup.mk_eq_mk, PiTensorProduct.mapLMultilinear_apply_apply, ContinuousLinearMap.instNonnegSpectrumClassRealId, iteratedDeriv_comp_two, NumberField.ComplexEmbedding.IsReal.coe_embedding_apply, ContinuousLinearMap.uncurryMid_apply, ContinuousMap.setOfIdeal_eq_compl_singleton, hasFDerivAt_update, Polynomial.div_C, IntermediateField.sup_toSubalgebra_of_left, spectralNorm_extends, isBoundedBilinearMap_apply, HasFPowerSeriesWithinOnBall.coeff_zero, InfiniteGalois.isOpen_iff_finite, RootPairing.restrictScalars_coe_root, FormalMultilinearSeries.analyticOnNhd, galLift_id, InfiniteGalois.mem_range_algebraMap_iff_fixed, hasDerivAtFilter_iff_tendsto, FractionalIdeal.count_zpow_self, Matrix.IsHermitian.eigenvectorUnitary_coe, Polynomial.natSepDegree_pow_of_ne_zero, Polynomial.natSepDegree_one, hasStrictFDerivAt_ringInverse, NumberField.InfinitePlace.even_finrank_of_not_isUnramified, ContDiffOn.continuousOn_fderiv_of_isOpen, Polynomial.leadingCoeff_preHilbertPoly, ContinuousLinearMap.mul_apply', Finset.cast_subConst, LinearMap.finrank_maxGenEigenspace, Field.Emb.Cardinal.deg_lt_aleph0, WeierstrassCurve.Δ_integral_of_isIntegral, ContDiffOn.continuousLinearMap_comp, LinearMap.BilinForm.dualBasis_involutive, HasFDerivAt.fun_sum, stereographic_target, fderiv_zero_of_not_differentiableAt, Unitary.norm_map, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, tendsto_const_mul_pow_nhds_iff, NNRat.instTrivialStar, LinearMap.instStarModuleId, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, Submodule.starProjection_apply_mem, NumberField.inverse_basisMatrix_mulVec_eq_repr, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, RatFunc.denom_div_dvd, InnerProductSpace.rankOne_comp_rankOne, ContinuousLinearMap.opNorm_zero, Polynomial.separable_gcd_right, MeasureTheory.convolution_lsmul_swap, IntermediateField.relfinrank_bot_left, NNReal.coe_expect, Real.hasStrictDerivAt_arctan, HasFTaylorSeriesUpToOn.prodMk, FixedPoints.smul_polynomial, Polynomial.separable_gcd_left, isPurelyInseparable_iff_minpoly_eq_X_pow_sub_C, ContinuousMultilinearMap.norm_iteratedFDeriv_le, ContDiffAt.domDomCongr_iteratedFDeriv, Module.Basis.traceDual_involutive, SpectrumRestricts.starAlgHom_apply, PrimeSpectrum.coe_primesOverOrderIsoFiber_apply_asIdeal, RatFunc.laurent_C, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, LinearMap.BilinForm.orthogonal_span_singleton_eq_toLin_ker, ZLattice.volume_image_eq_volume_div_covolume, hasDerivAtFilter_finCons', NumberField.InfinitePlace.card_real_embeddings, mfderivWithin_prodMap, Polynomial.Gal.splits_in_splittingField_of_comp, LinearIsometry.toLinearMap_rTensor, PiLp.hasStrictFDerivAt_apply, hasStrictFDerivAt_fst, DifferentiableAt.comp_semilinear₁, Matrix.toEuclideanLin_eq_toLin, IsAlgClosed.exists_root, NumberField.Units.coe_injective, Finset.nnratCast_dens, UniqueMDiffOn.uniqueDiffOn_inter_preimage, DoubleCentralizer.pow_fst, RatFunc.rank_ratFunc_ratFunc, IntermediateField.toSubalgebra_injective, StrongDual.toLpₗ_of_not_memLp, isConformalMap_complex_linear_conj, MeromorphicAt.meromorphicTrailingCoeffAt_smul, fderiv_smul_const, PiTensorProduct.mapL_apply, hasDerivWithinAt_finCons', Matrix.isHermitian_iff_isSymmetric, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, mfderiv_sumInr, ContinuousMultilinearMap.norm_iteratedFDeriv_le', support_iteratedFDeriv_subset, hasStrictFDerivAt_finset_prod, convex_RCLike_iff_convex_real, NumberField.Units.coe_one, spectralAlgNorm_extends, Submodule.le_orthogonal_iff_le_orthogonal, fderiv_fun_neg, Lagrange.degree_interpolate_le, curveIntegral_zero, IntermediateField.le_extendScalars_iff, Finset.subConst_le_card, Complex.isOpenQuotientMap_zpow_compl_zero, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, NNRat.cast_max, Submodule.IsOrtho.comap_iff, InnerProductSpace.rankOne_comp, LaurentSeries.powerSeriesRingEquiv_coe_apply, Polynomial.C_div, Submodule.mem_orthogonal, StrongDual.mem_polarSubmodule, exists_dual_vector', derivWithin_inv', Asymptotics.isLittleOTVS_fun_comm, FormalMultilinearSeries.apply_eq_prod_smul_coeff, Asymptotics.IsTheta.const_smul_left, Asymptotics.isLittleOTVS_comm, RatFunc.instIsScalarTowerOfPolynomial, ContinuousLinearMap.hasBasis_nhds_zero_of_basis, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable', minpoly.ofSubring, hasFPowerSeriesWithinAt_pi_iff, isCompactOperator_iff_isCompact_closure_image_closedBall, NumberField.InfinitePlace.Completion.bijective_extensionEmbeddingOfIsReal, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, gal_one_isSolvable, IsLocalRing.instIsScalarTowerResidueFieldCotangentSpace, LinearMap.continuous_of_finiteDimensional, hasDerivAt_iff_isLittleO_nhds_zero, HasFDerivAt.le_of_lip', inner_smul_right, Filter.Tendsto.atTop_smul_const_tendsto_asymptoticNhds, Polynomial.normalize_eq_self_iff_monic, SchwartzMap.tsupport_smulLeftCLM_subset, HasMFDerivAt.sub, IntermediateField.extendScalars.orderIso_symm_apply_coe, InnerProductSpace.toMatrix_rankOne, PowerSeries.Unit_of_divided_by_X_pow_order_nonzero, IsFractionRing.injective_comp_algebraMap, eventually_norm_symmL_trivializationAt_lt, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, cfcₙHom_real_eq_restrict, normal_iff, LinearMap.polar_AbsConvex, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, differentiableAt_euclidean, subsingleton_nnrat_module, AlgHom.card, FormalMultilinearSeries.changeOriginSeries_summable_aux₁, hasFDerivAtFilter_finCons, PiTensorProduct.liftIsometry_comp_mapL, MvPowerSeries.inv_eq_zero, iteratedFDeriv_smul_const_apply, IsAlgClosure.equivOfEquiv_symm_comp_algebraMap, Seminorm.continuous_from_bounded, OrthonormalBasis.reindex_toBasis, ContinuousLinearMap.opNorm_le_iff, slope_pos_iff_gt, RCLike.geometric_hahn_banach_open, Submodule.map_smul', InnerProductSpace.isSymmetric_rankOne_self, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, FractionalIdeal.smul_mem_dual_one, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, Padic.valuation_pow, Finset.dens_filter_add_dens_filter_not_eq_dens, Real.hasDerivAt_cosh, fderiv_const_sub, continuousMultilinearCurryLeftEquiv_apply, tsupport_fderiv_subset, HasFPowerSeriesAt.deriv, NumberField.InfinitePlace.isReal_comap_iff, fderiv_id', ArchimedeanClass.FiniteResidueField.mk_le_mk, LinearIsometryEquiv.symm_rTensor, LinearMap.isSymmetricProjection_iff, uniqueMDiffWithinAt_iff_inter_range, mfderiv_snd, HasMFDerivWithinAt.add, LaurentSeries.powerSeriesEquivSubring_apply, IntermediateField.sepDegree_bot', Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, RootPairing.polarizationEquiv_toLinearMap, HasCompactSupport.iteratedFDeriv, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, TensorProduct.commIsometry_symm, isStarProjection_starProjection, precomp_compactConvergenceCLM_apply, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff, unitary.norm_map, Asymptotics.IsBigOTVS.rfl, Set.EqOn.iteratedFDerivWithin, NumberField.mixedEmbedding.unitSMul_smul, ContinuousLinearEquiv.fderiv, IntermediateField.inclusion_injective, Differential.instDifferentialAlgebraSubtypeMemIntermediateField, Seminorm.bddBelow_range_add, ContinuousAlternatingMap.restrictScalarsCLM_apply, ContMDiffWithinAt.mfderivWithin_apply, Asymptotics.IsLittleOTVS.bot, SchwartzMap.tsupport_fderivCLM_subset, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_left, ContinuousLinearMap.isBigOTVS_comp, Finpartition.IsEquipartition.sum_nonUniforms_lt, WeierstrassCurve.Jacobian.add_of_X_ne, ContinuousLinearEquiv.mdifferentiableWithinAt, one_half_pos, FDRep.simple_iff_end_is_rank_one, hfdifferential_apply, Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sq, IntermediateField.LinearDisjoint.bot_right, ContinuousLinearMap.NonlinearRightInverse.right_inv', ContinuousLinearEquiv.mdifferentiable, AffineSubspace.midpoint_mem_perpBisector, AnalyticAt.exists_eq_sum_add_pow_mul, Ideal.ResidueField.algHom_ext_iff, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, FractionalIdeal.count_neg_zpow, ContinuousLinearMap.integral_comp_L1_comm, curveIntegralFun_add, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, ContinuousLinearMap.opNorm_zero_iff, IsPrimitiveRoot.squarefree_minpoly_mod, LinearEquiv.isSymmetric_symm_iff, Polynomial.isSplittingField_C, InnerProductSpace.gramSchmidt_def'', Real.hasDerivAt_fourierChar, OrthonormalBasis.equiv_symm, AnalyticOnNhd.fderiv, LinearMap.range_smul', AlgebraicClosure.Monics.map_eq_prod, Field.primitive_element_iff_minpoly_degree_eq, WeierstrassCurve.Jacobian.Y_eq_iff', hasDerivAt_intCast, LinearOrderedSemifield.toPosSMulStrictMono_rat, nndist_midpoint_midpoint_le, HasFDerivWithinAt.sub, Seminorm.absorbent_ball_zero, minpoly.dvd_map_of_isScalarTower', HasFDerivAtFilter.fun_neg, LinearEquiv.coe_toContinuousLinearEquiv, PiTensorProduct.liftIsometry_symm_apply, nnnorm_cfcₙHom, SchwartzMap.smulLeftCLM_neg, IntermediateField.map_fixingSubgroup_index, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, AlgHom.fieldRange_eq_top, ContinuousLinearEquiv.comp_differentiableAt_iff, IntermediateField.normal_iff_forall_map_le, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, mfderiv_zero_of_not_mdifferentiableAt, Algebra.IsAlgebraic.bijective_of_isScalarTower', Asymptotics.IsTheta.pow, ValuationSubring.ofPrime_scalar_tower, Trivialization.continuousLinearEquivAt_prod, HasFPowerSeriesAt.const_smul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, iteratedFDeriv_succ_eq_comp_right, ContinuousOn.cfcₙ, SchwartzMap.iteratedPDeriv_eq_iteratedFDeriv, ContinuousMultilinearMap.changeOriginSeries_support, ContinuousLinearEquiv.comp_hasFDerivAt_iff', separableClosure.isAlgebraic, IntermediateField.adjoin_toSubalgebra, IsAlgClosure.ofAlgebraic, tendsto_nat_ceil_div_atTop, curveIntegralFun_sub, Asymptotics.isBigOTVS_fun_comm, FunctionField.ringOfIntegers.algebraMap_injective, ContDiffMapSupportedIn.seminorm_apply, Field.sepDegree_mul_insepDegree, FormalMultilinearSeries.isLittleO_of_lt_radius, tsupport_iteratedFDeriv_subset, OrthogonalFamily.eq_ite, AffineSubspace.sSameSide_smul_vsub_vadd_right, FiniteField.X_pow_card_sub_X_natDegree_eq, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, ContinuousMultilinearMap.hasFDerivAt, ODE.hasDerivWithinAt_picard_Icc, MeasureTheory.lpNorm_const_smul, VectorField.lieBracket_smul_left, Real.iteratedFDeriv_fourier, RatFunc.denom_inv_dvd, Seminorm.smul_closedBall_subset, LieModule.exists_nontrivial_weightSpace_of_isSolvable, instIsScalarTowerCyclotomicField, DoubleCentralizer.algebraMap_fst, NumberField.ComplexEmbedding.isConj_symm, differentiableOn_euclidean, hasDerivWithinAt_diff_singleton, ValuationSubring.surjective_unitGroupToResidueFieldUnits, fderiv_continuousLinearEquiv_comp, FiniteField.pow_dichotomy, nnnorm_fderiv_norm_rpow_le, hasFDerivWithinAt_natCast, NumberField.mixedEmbedding.indexEquiv_apply_isReal, NumberField.ComplexEmbedding.Extension.comp_eq, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, hasStrictFDerivAt_exp_zero_of_radius_pos, div_add_div, ContinuousLinearMap.toBilinForm_injective, quasispectrumRestricts_iff_spectrumRestricts_inr, Ideal.ramificationIdx_mul_inertiaDeg_of_isLocalRing, rootOfSplitsXPowSubC_pow, AlgHom.card_le, InnerProductSpace.mem_span_gramSchmidt, ContinuousLinearMap.mfderivWithin_eq, ContinuousMultilinearMap.nnnorm_ofSubsingleton, inner_smul_real_left, Ideal.ResidueField.lift_algebraMap, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, tsum_prod_pow_eq_tsum_sigma, FiniteField.splits_X_pow_card_sub_X, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, IntermediateField.rank_eq_one_iff, ContDiff.continuous_iteratedFDeriv, TangentBundle.symmL_model_space, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, IsGaloisGroup.intermediateField, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, MeasureTheory.integrable_condExpL2_indicator, Real.hasDerivAt_Gamma_one_half, ImplicitFunctionData.range_rightDeriv, tangentCoordChange_self, toSpanSingleton_derivWithin, HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub, LinearMap.finrank_range_dualMap_eq_finrank_range, EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, fderiv_norm_smul, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, ContinuousAlternatingMap.isLeast_opNNNorm, ContinuousLinearMap.isEmbedding_restrictScalars, lowerBounds_smul_of_neg, Polynomial.natDegree_preHilbertPoly, Finset.cast_mulConst, NNRat.cast_pos, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, HasFiniteFPowerSeriesOnBall.eq_partialSum', Int.clog_zpow, VectorField.mlieBracket_const_smul_left, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, ValuationSubring.principalUnitGroupEquiv_apply, Module.End.eigenspace_div, LinearIsometry.enorm_toContinuousLinearMap, coe_lpBCFₗᵢ_symm, range_mfderiv_coe_sphere, uniqueMDiffOn_iff_uniqueDiffOn, coe_lpPiLpₗᵢ_symm, AlgEquiv.restrictNormalHom_id, Bornology.isVonNBounded_sub, differentiable_piLp, ClosedSubmodule.inf_orthogonal_eq_bot, HasFPowerSeriesOnBall.pi, Affine.Triangle.eulerPoint_eq_midpoint, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, Submodule.reflection_eq_self_iff, galRestrict_apply, Polynomial.span_minpoly_eq_annihilator, stereographic_source, ContinuousMultilinearMap.piₗᵢ_symm_apply, Finset.subConst_mul_card, AlgHom.coe_toContinuousLinearMap, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, ContDiff.iteratedFDeriv_right', Subfield.relrank_top_right, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, NumberField.ComplexEmbedding.IsReal.comp, ContinuousLinearMap.norm_id_le, HasFDerivAt.le_of_lipschitz, AnalyticAt.analyticOrderAt_ne_top, HasFDerivWithinAt.pow', SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, LinearEquiv.canLiftContinuousLinearEquiv, Ring.instFiniteDimensionalFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, IsDedekindDomain.selmerGroup.fromUnit_ker, Matrix.ofLp_toEuclideanLin_apply, IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin, spectralNorm.eq_of_normalClosure', ContinuousOn.cfcₙ_of_mem_nhdsSet, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm', Filter.Tendsto.isVonNBounded_range, NumberField.exists_ideal_in_class_of_norm_le, AffineIndependent.convexHull_inter', Real.hasFDerivAt_fourierIntegral, NumberField.InfinitePlace.Completion.bijective_extensionEmbedding_of_isComplex, intervalIntegral.integral_hasDerivAt_of_tendsto_ae_left, NumberField.mixedEmbedding.normAtPlace_apply, SchwartzMap.integralCLM_apply, Finset.dens_inter_add_dens_union, Polynomial.irreducible_factor, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, NumberField.ComplexEmbedding.lift_comp_algebraMap, PolynormableSpace.withSeminorms', Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, hasDerivAt_one, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, SameRay.exists_nonneg_left, HasStrictFDerivAt.hasStrictDerivAt, LinearMap.BilinForm.finrank_orthogonal, IsAlgClosure.equivOfEquiv_algebraMap, FormalMultilinearSeries.radius_shift, EuclideanSpace.volume_ball_fin_two, Ideal.instLiesOverBotOfIsPrime, ContinuousLinearEquiv.comp_right_differentiableAt_iff, fderivWithin_sqrt, isClosedEmbedding_cfcₙHom_of_cfcHom, fderivWithin_natCast, Finset.card_mul_cast_mulConst, ContinuousMap.spectrum_eq_range, NormedSpace.polar_ball, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, IsZLattice.span_top, IsSepClosed.splits_codomain, innerSLFlip_apply, ContinuousLinearEquiv.differentiableOn, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, ContinuousLinearEquiv.hasStrictFDerivAt, Nat.one_div_cast_nonneg, AlgHom.mem_fieldRange, IsStrictOrderedRing.toHasContinuousInv₀, ContinuousMultilinearMap.hasBasis_nhds_zero_of_basis, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, fderivWithin_derivWithin, Submodule.ker_starProjection, WeakDual.ker_isMaximal, IntermediateField.finrank_fixedField_eq_card, ContinuousLinearEquiv.mfderiv_eq, hasDerivAt_const_mul, Trivialization.coe_continuousLinearEquivAt_eq, hasLineDerivAt_iff_tendsto_slope_zero, Algebra.normalizedTrace_minpoly, InnerProductSpace.toContinuousLinearMap_toDualMap, HasFDerivAt.list_prod', separableClosure.isSepClosure, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, IntermediateField.finrank_comap, Polynomial.coeff_inv_units, FiniteField.pow_finrank_eq_card, InfiniteGalois.toAlgEquivAux_eq_liftNormal, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', separatingDual_iff_injective, minpoly.eq_X_sub_C', RCLike.normSq_pos, EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center, Polynomial.root_gcd_iff_root_left_right, ContinuousLinearEquiv.comp_contDiffWithinAt_iff, isNilpotent_tensor_residueField_iff, Differential.logDeriv_pow, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparable', IsSelfAdjoint.commute_cfcₙHom, Field.primitive_element_iff_minpoly_natDegree_eq, ContinuousLinearMap.measurable_coe, HasFDerivAt.fun_neg, ContinuousLinearMap.analyticOn, fderiv_sinh, ContinuousLinearMap.nndist_le_opNNNorm, Polynomial.IsSeparableContraction.natSepDegree_eq, strictConvex_iff_ordConnected, norm_iteratedFDeriv_prod_le, IntermediateField.normalClosure_def'', inner_eq_ofReal_norm_sq_left_iff, contDiff_nat_iff_continuous_differentiable, QuasispectrumRestricts.nonUnitalStarAlgHom_apply, hasFDerivAt_pow', ContinuousAlternatingMap.hasBasis_nhds_zero_of_basis, NNRat.ofNat_le_cast, absorbent_ball, extremePoints_doublyStochastic, SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv, Valuation.Integers.valuation_pos_iff_ne_zero, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, OrderedFinpartition.compAlongOrderFinpartition_apply, Trivialization.continuousLinearEquivAt_symm_apply, Submodule.topologicalClosure_eq_top_iff, hasDerivAt_abs, mdifferentiableOn_coordChangeL, HasFiniteFPowerSeriesOnBall.add, RatFunc.num_mul_dvd, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, WeierstrassCurve.Projective.addU_smul, iteratedDeriv_comp_const_sub, ContDiffAt.iteratedFDeriv_comp_perm, Polynomial.hasDerivAt, HasFDerivAt.fun_add, Subfield.relrank_eq_rank_of_le, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, Subspace.dualEquivDual_def, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_lt', VectorPrebundle.mk_coordChange, ContinuousLinearMap.opNorm_lsmul_le, PrimeSpectrum.coe_preimageOrderIsoFiber_apply_asIdeal, Field.Emb.Cardinal.strictMono_filtration, convexHull_eq_union_convexHull_finite_subsets, EuclideanSpace.volume_ball, LinearMap.IsSymmetric.zero, IntermediateField.relfinrank_eq_finrank_of_le, OrthonormalBasis.repr_symm_single, FiniteField.nonempty_algHom_extension, NumberField.canonicalEmbedding.norm_le_iff, ContinuousMultilinearMap.instUniformContinuousConstSMul, RootPairing.polarizationEquiv_symm_apply_coroot, WeakDual.CharacterSpace.norm_le_norm_one, IntermediateField.isScalarTower_over_bot, IntermediateField.isSeparable_tower_bot, Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius, FiniteField.isSquare_iff, Matrix.linfty_opNorm_toMatrix, IntermediateField.minpoly_eq, hasDerivAt_natCast, AdjoinRoot.powerBasis_dim, Seminorm.rescale_to_shell, Mathlib.Meta.NormNum.IsRat.natCeil, Submodule.reflection_bot, RootPairing.linearIndepOn_coroot_iff, ContinuousMultilinearMap.opNNNorm_pi, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, Polynomial.natSepDegree_C, NNRat.cast_mul, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.fourier_bilin_convolution_eq_integral, closedBall_normSeminorm, Real.hasStrictDerivAt_cos, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left, ContinuousLinearMap.isPositive_def', ContinuousLinearMap.coe_restrictScalarsL, NNRat.ceil_cast, LinearMap.adjoint_inner_left, Nat.cast_div_le, IntermediateField.mem_toSubalgebra, legendreSym.eq_pow, IntermediateField.isSplittingField_iff, iter_deriv_inv, HasMFDerivAt.comp_hasMFDerivWithinAt, PowerSeries.coeff_inv, AlgEquiv.restrictNormal_commutes, NumberField.InfinitePlace.comap_mk_lift, Matrix.star_dotProduct_gram_mulVec, exists_integral_multiples, hasStrictFDerivAt_exp_zero, ValuationSubring.coe_comap, ContinuousLinearMap.norm_compL_le, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, NumberField.mixedEmbedding_injective, Matrix.vecMul_injective_iff_isUnit, ContMDiffVectorBundle.contMDiffOn_coordChangeL, IntermediateField.bot_toSubfield, EulerSine.antideriv_cos_comp_const_mul, ZMod.orderOf_dvd_card_sub_one, Finset.dens_singleton, curveIntegral_eq_intervalIntegral_deriv, Filter.EventuallyEq.fderivWithin', ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, Field.sepDegree_eq_of_isPurelyInseparable_of_isSeparable, ContinuousLinearMap.inCoordinates_eq, meromorphicOrderAt_smul_of_ne_zero, NumberField.RingOfIntegers.coe_eq_algebraMap, mfderiv_prodMk, NumberField.InfinitePlace.comap_smul, Bornology.isVonNBounded_add, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, Subspace.dualLift_rightInverse, NumberField.InfinitePlace.not_isUnramified_iff_card_stabilizer_eq_two, IntermediateField.topEquiv_symm_apply_coe, HasFPowerSeriesAt.sub, RatFunc.liftOn'_div, hasMFDerivWithinAt_snd, ContDiffAt.continuousLinearMap_comp, ContinuousMultilinearMap.norm_domDomCongr, FiniteGaloisIntermediateField.adjoin_val, FractionalIdeal.spanFinset_coe, HasStrictFDerivAt.fun_neg, hasDerivWithinAt_zpow, LieAlgebra.rank_le_finrank_engel, Finset.centerMass_segment, HasFDerivWithinAt.arctan, ZSpan.quotientEquiv.symm_apply, OrthogonalFamily.range_linearIsometry, HasStrictFDerivAt.sum, NNRat.cast_smul_eq_nnqsmul, ValuationSubring.mem_principalUnitGroup_iff, VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, HasCompactSupport.fderiv_apply, Submodule.ker_orthogonalProjection, EuclideanGeometry.oangle_midpoint_rev_right, NumberField.mem_span_integralBasis, quadraticCharFun_eq_pow_of_char_ne_two, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, innerSL_real_flip, Lagrange.interpolate_eq_add_interpolate_erase, Submodule.reflection_map_apply, Ideal.coe_smul_primesOver_eq_map_galRestrict, HasDerivAt.real_of_complex, Module.mem_support_iff_nontrivial_residueField_tensorProduct, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt', SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, IntermediateField.adjoin_eq_range_algebraMap_adjoin, AffineIsometry.map_vadd, Polynomial.mul_mod, ContinuousMultilinearMap.curry0_norm, ContinuousLinearMap.opNNNorm_mul_flip_apply, ContinuousLinearMap.compLeftContinuousBounded_apply, Submodule.sup_orthogonal_of_hasOrthogonalProjection, Nat.one_div_pos_of_nat, MeasureTheory.lpTrimToLpMeas_ae_eq, ContinuousLinearMap.norm_fst, IsFractionRing.fieldEquivOfAlgEquivHom_injective, ContinuousAlternatingMap.nnnorm_toContinuousMultilinearMap, Algebra.discr_isUnit_of_basis, OrderedFinpartition.applyOrderedFinpartition_apply, HasFPowerSeriesOnBall.hasFDerivAt, MeasureTheory.charFun_eq_charFunDual_toDualMap, IntermediateField.rank_top', IntermediateField.isAlgebraic_adjoin_simple, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, NormedAlgebra.Real.nonempty_algEquiv_or, ContinuousLinearMap.opNNNorm_comp_le, RatFunc.denom_C, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_iSup_right, TensorProduct.toLinearEquiv_assocIsometry, ContinuousMultilinearMap.analyticOn, FormalMultilinearSeries.changeOriginSeries_summable_aux₂, HasMFDerivAt.prod, MeromorphicNFAt.smul_analytic, fderivWithin_csin, ContinuousLinearEquiv.conjContinuousAlgEquiv_ext_iff, RatFunc.num_div_dvd', Module.Projective.exists_dual_eq_one, WeierstrassCurve.Projective.negAddY_eq, Submodule.IsOrtho.disjoint, ContinuousMultilinearMap.curryMid_apply, iteratedDeriv_eq_iteratedFDeriv, OnePoint.smul_infty_def, ZLattice.volume_image_eq_volume_div_covolume', inv_smul_lt_iff_of_neg, IntermediateField.AdjoinSimple.normal_algebraicClosure, PiTensorProduct.mapL_opNorm, ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interior, FiniteGaloisIntermediateField.adjoin_simple_map_algEquiv, SchwartzMap.compCLM_apply, MonoidAlgebra.Submodule.instIsSemisimpleRingAddMonoidAlgebra, iter_deriv_inv', toMatrix_innerSL_apply, OrthonormalBasis.equiv_apply_basis, ClosedSubmodule.sInf_orthogonal, NumberField.RingOfIntegers.HeightOneSpectrum.isNonarchimedean_adicAbv, intervalIntegral.fderivWithin_integral_of_tendsto_ae, NNReal.orderIsoRpow_symm_eq, hasStrictFDerivAt_one, Function.HasTemperateGrowth.smul, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, LaurentSeries.powerSeriesEquivSubring_coe_apply, IntermediateField.normal_iff_forall_map_eq', HasStrictFDerivAt.isBigOTVS_sub, Finset.nonneg_subConst_self, DoubleCentralizer.mul_fst, rescale_to_shell_zpow, Polynomial.isBoundedUnder_abs_atTop_iff, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, WeierstrassCurve.Jacobian.addX_eq, balanced_closedBall_zero, iteratedFDeriv_zero_fun, Submodule.HasOrthogonalProjection.exists_orthogonal, IntermediateField.intermediateFieldMap_apply_coe, HasFDerivAt.prodMk, IntermediateField.topEquiv_apply, ContinuousLinearEquiv.comp_contDiffOn_iff, NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, MDifferentiableAt.coordChangeL, Algebra.discr_eq_det_embeddingsMatrixReindex_pow_two, perfectField_iff_splits_of_natSepDegree_eq_one, Manifold.IsImmersionAt.target_subset_preimage_target, RootPairing.eq_baseOf_iff, Submodule.starProjection_top, LieAlgebra.IsKilling.cartanEquivDual_symm_apply_mem_corootSpace, EulerSine.antideriv_sin_comp_const_mul, hasFDerivAt_sub_const, FixedPoints.toAlgHom_bijective, Lagrange.interpolate_apply, affineCombination_mem_convexHull, IsPurelyInseparable.minpoly_eq_X_pow_sub_C, Submodule.iInf_orthogonal, ContinuousLinearMap.norm_restrictScalars, ContinuousLinearMapWOT.instT3Space, coe_normSeminorm, Algebra.normalizedTrace_algebraMap_apply, IsLocalRing.ResidueField.finite_of_module_finite, ContinuousLinearEquiv.arrowCongrSL_apply, Algebra.normalizedTrace_def, Lagrange.interpolate_eq_iff_values_eq_on, crossProduct_ne_zero_iff_linearIndependent, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, NumberField.Units.dirichletUnitTheorem.logEmbedding_component, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_algebraMap, Ideal.FinrankQuotientMap.span_eq_top, Pretrivialization.continuousLinearMap_apply, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, NumberField.Units.coe_zpow, NumberField.mem_span_basisOfFractionalIdeal, RatFunc.natDegree_num_mul_right_sub_natDegree_denom_mul_left_eq_intDegree, ContDiffBump.convolution_eq_right, Polynomial.IsSplittingField.instFiniteDimensionalSplittingField, hasFDerivWithinAt_fst, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, FiniteField.minpoly_frobeniusAlgHom, ValuationSubring.coe_pointwise_smul, NNRat.preimage_cast_Ico, ModelWithCorners.transContinuousLinearEquiv_range, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, hasFDerivAt_natCast, FormalMultilinearSeries.analyticAt_changeOrigin, mem_convexHull_iff_exists_fintype, ContinuousLinearMap.opNorm_mul_apply_le, hasFDerivAt_intCast, PiTensorProduct.tprodL_apply, CStarMatrix.normedSpaceCore, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt, IntermediateField.AdjoinSimple.isIntegral_gen, HasFPowerSeriesAt.tendsto_partialSum, Differential.logDeriv_algebraMap, Polynomial.aeval_ofReal, Diffeomorph.uniqueDiffOn_preimage, deriv_pow_field, ZSpan.repr_fract_apply, ContinuousLinearMap.orthogonal_range, IsGaloisGroup.fixedPoints, contDiff_one_iff_hasFDerivAt, HasFiniteFPowerSeriesAt.add, Submodule.lipschitzWith_starProjection, HasFPowerSeriesAt.hasDerivAt, hasDerivWithinAt_congr_set', Module.End.IsSemisimple_smul, HasFDerivWithinAt.comp_hasFDerivAt_of_eq, LieAlgebra.IsKilling.rootSystem_pairing_apply, ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk_apply, LieAlgebra.IsKilling.chainTopCoeff_zero_right, map_mem_algebraicClosure_iff, NormedSpace.norm_smul_le, HasFPowerSeriesAt.eventually_hasSum_sub, Polynomial.mem_roots_map, meromorphicOrderAt_pow, ordinaryHypergeometricSeries_eq_zero_iff, Polynomial.hasDerivAt_aeval, ContinuousLinearMap.comp_cpolynomialOn, HasFDerivAt.linear_multilinear_comp, Localization.subalgebra.isFractionRing_ofField, ContinuousLinearMap.opNorm_smul_le, Algebra.IsQuadraticExtension.isCyclic, InnerProductSpace.span_gramSchmidt, Asymptotics.isLittleOTVS_congr, FunctionField.ringOfIntegers.instIsFractionRingSubtypeMemSubalgebraPolynomial, hasDerivAt_gronwallBound, fderiv_zero, hasDerivWithinAt_const_add_iff, convexHull_toCone_isLeast, PerfectField.separable_iff_squarefree, NumberField.mixedEmbedding.logMap_apply, IsDedekindDomain.selmerGroup.fromUnitLift_injective, NNRat.cast_nonpos, EuclideanGeometry.hasFDerivAt_inversion, fderiv_comp', MeasureTheory.convolutionExistsAt_iff_integrable_swap, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, PiLp.hasFDerivAt_ofLp, deriv_div, torusIntegral_smul, ZLattice.comap_comp, Polynomial.Gal.restrict_surjective, WeierstrassCurve.Projective.baseChange_dblU, LinearEquiv.smulOfNeZero_symm_apply, WeierstrassCurve.Projective.eval_polynomial_of_Z_ne_zero, norm_iteratedFDeriv_one, RatFunc.C_injective, Continuous.cfcₙ', VectorField.mpullback_smul, hasDerivAt_ofReal_cpow_const, LinearIsometryEquiv.comp_differentiable_iff, NumberField.InfinitePlace.even_nat_card_aut_of_not_isUnramified, convex_iff_div, hasDerivAt_norm_rpow, hasFDerivAtFilter_id, HasStrictFDerivAt.fun_const_smul, OrthonormalBasis.span_apply, isConformalMap_id, iteratedFDerivWithin_eventually_congr_set', ContinuousMultilinearMap.analyticOnNhd, Module.End.generalized_eigenvec_disjoint_range_ker, instFiniteResidueField, IntermediateField.isPurelyInseparable_bot, NumberField.mixedEmbedding.latticeBasis_apply, ClosedSubmodule.orthogonal_toSubmodule_eq, HasFDerivAt.hasDerivAt, Polynomial.mem_normalizedFactors_iff, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, IsLocalRing.isLocalHom_residue, FiniteField.sum_pow_units, ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal, convexIndependent_iff_finset, pow_div_pow_eventuallyEq_atTop, differentiableAt_finCons', ContinuousLinearMap.isPositive_iff, LaurentSeries.valuation_coe_ratFunc, TensorProduct.mapIsometry_apply, Finset.natCast_card_mul_nnratCast_dens, gal_mul_isSolvable, ContinuousMultilinearMap.compContinuousLinearMapL_apply, Hyperreal.archimedeanClassMk_omega_neg, VectorBundleCore.inCoordinates_eq, Seminorm.smul_closedBall_preimage, HasFDerivWithinAt.unique_on, ValuationSubring.coe_unitGroupMulEquiv_symm_apply, HasStrictFDerivAt.prodMap, MeromorphicOn.extract_zeros_poles, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, VectorField.pullbackWithin_eq, Matrix.IsHermitian.cfcAux_id, cfcₙAux_mem_range_inr, ContinuousLinearMap.norm_bilinearRestrictScalars, NumberField.InfinitePlace.isUnramified_iff_stabilizer_eq_bot, ContinuousLinearMap.nhds_zero_eq, WeierstrassCurve.Jacobian.negAddY_of_Z_ne_zero, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ContinuousMap.adjoin_id_eq_span_one_add, Hyperreal.archimedeanClassMk_coe_nonneg, ContinuousLinearMap.norm_inl, Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparable, AlgebraicIndependent.aevalEquivField_apply_coe, LinearMap.IsSymmetric.sub, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, ProbabilityTheory.covarianceBilin_map, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, LieAlgebra.IsKilling.orthogonal_span_coroot_eq_ker, ContinuousLinearEquiv.comp_differentiable_iff, cfcₙ_norm_sq_nonneg, MvPolynomial.irreducible_toPolynomialAdjoinImageCompl, SchwartzMap.instFourierSMul, HasFPowerSeriesOnBall.prod, IsGaloisGroup.to_isFractionRing, Unitization.nnnorm_eq_sup, SchwartzMap.fourierTransformCLM_apply, AffineSubspace.signedInfDist_singleton, HasFPowerSeriesWithinOnBall.neg, norm_deriv_eq_norm_fderiv, IntermediateField.LinearDisjoint.exists_field_of_isDomain, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Trivialization.symm_continuousLinearEquivAt_eq, IsDiscreteValuationRing.TFAE, Finset.expect_univ, EuclideanGeometry.angle_midpoint_eq_pi, DoubleCentralizer.zero_toProd, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_right, Ideal.factors_span_eq, minpoly_algEquiv_toLinearMap, MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_aux, Finset.one_le_divConst_self, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, ContinuousLinearMap.bilinearComp_zero_left, ContinuousLinearMap.nnnorm_smulRight_apply, Subfield.relfinrank_dvd_finrank_top_of_le, hasFPowerSeriesWithinOnBall_pi_iff, hasDerivAt_zero, LinearIsometryEquiv.smul_trans, Ideal.injective_algebraMap_quotient_residueField, SchwartzMap.fderivCLM_fourier_eq, ContinuousMultilinearMap.instContinuousSMul, spectralNorm.eq_of_tower, withSeminorms_pi, IsAlgClosed.card_roots_map_eq_natDegree_of_leadingCoeff_ne_zero, ContinuousLinearEquiv.contDiffOn_comp_iff, mellin_const_smul, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, FiniteField.instIsCyclicAlgEquivOfFinite, arithGeom_zero_eq_mul_div, NumberField.norm_embedding_le_house, ContMDiffOn.const_smul_section, Finset.cast_addConst_mul_card, FormalMultilinearSeries.ofScalars_smul, SchwartzMap.derivCLM_apply, ContDiffAt.fderiv, Matrix.toLin_finTwoProd_toContinuousLinearMap, HasFPowerSeriesOnBall.eventually_hasSum_sub, Polynomial.mod_X_sub_C_eq_C_eval, TensorProduct.toLinearMap_mapIsometry, ContinuousMultilinearMap.opNNNorm_le_iff, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, NumberField.FinitePlace.norm_eq_one_iff_notMem, NumberField.canonicalEmbedding_injective, Module.End.IsSemisimple_smul_iff, IntermediateField.restrictScalars_toSubalgebra, Valuation.exists_pow_Uniformizer, PowerSeries.eq_inv_iff_mul_eq_one, VectorBundleCore.continuousOn_coordChange, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, hasDerivWithinAt_inter', Submodule.mem_traceDual, ContinuousAlternatingMap.instCompleteSpace, IntermediateField.finiteDimensional_left, mfderiv_comp_apply, NumberField.InfinitePlace.LiesOver.mk_embedding_comp, AffineSubspace.subtypeₐᵢ_linearIsometry, Unitary.inner_map_map, legendreSym.card_sqrts, ContDiffBump.dist_normed_convolution_le, HasFDerivWithinAt.fun_sum, Algebra.normalizedTrace_trans_apply, fderiv_fun_const_smul, hasDerivAt_exp_smul_const_of_mem_ball', Real.hasDerivAt_arctan', TensorProduct.enorm_map, ZMod.gauss_lemma_aux, uniformEquicontinuous_birkhoffAverage, deriv_comp_mul_left, hasDerivAt_neg, LinearMap.IsSymmetric.id, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, isCompactOperator_iff_image_ball_subset_compact, intervalIntegral.integral_hasDerivAt_right, tsupport_fderiv_apply_subset, hasFTaylorSeriesUpToOn_succ_iff_left, LaurentSeries.valuation_compare, mem_segment_iff_div, WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded, Padic.isUniformInducing_cast_withVal, HasCompactSupport.hasDerivAt_convolution_left, Polynomial.hasStrictDerivAt, ArchimedeanClass.mk_ratCast_nonneg, isConjRoot_iff_orbitRel, RingHomClass.toLinearMapClassNNRat, AlgebraicClosure.instIsScalarTower, Hyperreal.tendsto_atBot_iff, IsConformalMap.comp, le_perfectClosure_iff, perfectClosure.isAlgebraic, Polynomial.isUnit_or_eq_zero_of_separable_expand, ContinuousLinearEquiv.isBigO_comp_rev, smul_inv_le_iff_of_neg, Real.hasStrictDerivAt_arcsin, MvPowerSeries.X_inv, AlgHom.bijective, NumberField.IsCMField.complexConj_eq_self_iff, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, HasFPowerSeriesWithinOnBall.add, LinearMap.span_singleton_inf_orthogonal_eq_bot, Commute.cfcₙ, WeierstrassCurve.Jacobian.isUnit_Y_of_Z_eq_zero, ContinuousLinearMap.add_compLp, IntermediateField.isSeparable_sup, curveIntegralFun_restrictScalars, Finset.centerMass_pair, NumberField.mixedEmbedding.commMap_apply_of_isReal, IsFractionRing.num_mul_den_eq_num_iff_eq, FiniteGaloisIntermediateField.finiteDimensional, PowerSeries.ker_coeff_eq_max_ideal, AffineMap.hasStrictDerivAt, InnerProductSpace.toLinearMap_rankOne, div_eq_quo_add_rem_div_add_rem_div, instSecondCountableTopologyContinuousLinearMapIdOfFiniteDimensional, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, meromorphicNFAt_smul_iff_right_of_analyticAt, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, Polynomial.natSepDegree_X_sub_C, ContinuousLinearMap.adjointAux_inner_right, hasFDerivWithinAt_ofNat, HasDerivWithinAt.Ioi_iff_Ioo, RatFunc.algebraMap_apply, MeromorphicOn.smul, MaximalSpectrum.iInf_localization_eq_bot, Finset.subConst_empty_right, HasMFDerivWithinAt.mul, OpenPartialHomeomorph.MDifferentiable.symm_comp_deriv, ContinuousLinearEquiv.isOpen, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, HilbertBasis.repr_self, TensorProduct.commIsometry_apply, ContinuousLinearEquiv.coe_toDiffeomorph, IntermediateField.coe_smul, IsGaloisGroup.fixingSubgroup_bot, Ring.instFaithfulSMulSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, Algebra.IsAlgebraic.algEquivEquivAlgHom_apply, continuousMultilinearCurryRightEquiv_symm_apply', MeasureTheory.condExpInd_smul', NormedSpace.expSeries_sum_eq_div, ContinuousLinearMap.isBigO_sub, IsSepClosure.isAlgClosure_of_perfectField_top, ContinuousAt.cfcₙ, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, DoubleCentralizer.norm_fst, MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eq, measurable_smul_const, IntermediateField.relfinrank_dvd_finrank_top_of_le, IntermediateField.set_range_subset, SchwartzMap.smul_apply, ContDiffMapSupportedIn.continuousSMul, ContinuousLinearMap.prodL_apply, Real.hasStrictDerivAt_sin, StrongDual.zero_mem_polar, RCLike.mul_self_norm, TensorProduct.congrIsometry_symm, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, ContinuousAlternatingMap.norm_ofSubsingleton_id, LinearIsometry.contDiff, Trivialization.continuousLinearMapAt_symmL, Field.finSepDegree_dvd_finrank, LinearMap.isStarProjection_toContinuousLinearMap_iff, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, MeromorphicOn.divisor_smul, Manifold.pathELength_eq_lintegral_mfderiv_Icc, HasFDerivAtFilter.isLittleOTVS, LinearMap.IsSymmetric.orthogonal_range, exists_linearIndependent_algEquiv_apply, iteratedDerivWithin_eq_equiv_comp, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, Polynomial.roots_C_mul_X_sub_C, HasFDerivAt.const_sub, Polynomial.differentiableAt, LinearPMap.adjointDomainMkCLMExtend_apply, nnnorm_cfcₙ_le_iff, InfiniteGalois.restrictNormalHom_continuous, exists_pow_btwn, dimH_orthogonalProjection_le, Algebra.IsSeparable.sepDegree_eq, slope_sub_smul, fderiv_ccosh, LaurentSeries.tendsto_valuation, Submodule.traceDual_bot, galRestrictHom_symm_apply, AlgHom.restrictNormal_comp, instDiscreteTopologySubtypeMemSubmoduleIntComap, Pretrivialization.continuousOn_continuousLinearMapCoordChange, IsLocalRing.ResidueField.instIsScalarTower, ContDiffMapSupportedIn.seminorm_postcompLM_le, IsGaloisGroup.subgroup, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, ContinuousMultilinearMap.bound, DoubleCentralizer.coe_fst, WeierstrassCurve.Jacobian.eval_polynomial_of_Z_ne_zero, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_left, instIsScalarTowerQuotientIdealResidueField, left_le_midpoint, HasStrictFDerivAt.fun_smul, hasStrictFDerivAt_ofNat, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, NumberField.abs_discr_ge_of_isTotallyComplex, FiniteField.bijective_frobeniusAlgHom_pow, Module.End.genEigenspace_div, smul_inv_lt_iff_of_neg, ContDiffPointwiseHolderAt.fderiv, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, Int.log_zpow, fderiv_fun_mul, IsGalois.of_separable_splitting_field_aux, curveIntegral_fun_sub, HasFiniteFPowerSeriesOnBall.finite, IntermediateField.coe_equivMap_apply, Submodule.re_inner_starProjection_nonneg, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, Algebra.instIsEpiOfIsDomainOfIsFractionRing, NumberField.mixedEmbedding.latticeBasis_repr_apply, IsGalois.finiteDimensional_of_finite, LocallyConvexSpace.convex_open_basis_zero, Submodule.adjoint_orthogonalProjection, NumberField.FinitePlace.instMonoidWithZeroHomClassReal, Filter.HasBasis.isBigOTVS_iff, IntermediateField.mem_adjoin_simple_iff, Real.sInf_smul_of_nonpos, wbtw_smul_vadd_smul_vadd_of_nonneg_of_le, HasFDerivAt.pow', NumberField.canonicalEmbedding.apply_at, HasStrictFDerivAt.pow', RatFunc.mk_one, LieAlgebra.IsKilling.finrank_rootSpace_eq_one, Complex.IsConservativeOn.hasDerivAt_wedgeIntegral, hasFDerivWithinAt_iff_hasGradientWithinAt, IntermediateField.finrank_le_of_le_left, Real.fourierIntegral_continuousLinearMap_apply', CurveIntegrable.smul, Finset.mulConst_empty_right, AffineIsometryEquiv.ofEq_rfl, IntermediateField.finInsepDegree_bot, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, Polynomial.isUnit_iff_degree_eq_zero, ContinuousLinearMap.hasFDerivAt_of_bilinear, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, Submodule.isOrtho_bot_right, mfderivWithin_prodMk, LinearMap.adjoint_comp, FormalMultilinearSeries.min_radius_le_radius_add, ContinuousAlternatingMap.opNorm_le_iff, krullTopology_mem_nhds_one_iff, RatFunc.algebraMap_injective, hasStrictDerivAt_one, FormalMultilinearSeries.ofScalars_comp_neg_id, FiniteField.unitsMap_norm_surjective, Nat.choose_le_pow_div, quadraticChar_sq_one', Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, MonoidAlgebra.Submodule.instIsSemisimpleModule, Field.nonempty_algEquiv_of_range_minpoly_eq, AlgEquiv.fieldRange_eq_top, IsPurelyInseparable.minpoly_eq_X_sub_C_pow, HasStrictFDerivAt.multiset_prod, MvPowerSeries.mul_inv_cancel, Finset.dens_biUnion, OpenPartialHomeomorph.MDifferentiable.mfderiv_injective, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, LinearMap.IsPositive.inner_nonneg_right, strictConvex_iff_div, Matrix.toEuclideanLin_apply_piLp_toLp, Finset.centerMass_eq_of_sum_1, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, pow_div_pow_eventuallyEq_atBot, Lagrange.interpolate_empty, LaurentSeries.coe_range_dense, X_pow_sub_C_irreducible_of_prime_pow, InnerProductSpace.span_gramSchmidt_Iio, Field.Emb.Cardinal.iSup_adjoin_eq_top, ContinuousAlternatingMap.curryLeft_add, NumberField.AdeleRing.algebraMap_fst_apply, WeierstrassCurve.Affine.Point.map_some, HasFPowerSeriesAt.pi, LinearMap.dualMap_surjective_iff, smul_ball, ZMod.expand_card, LinearIsometryEquiv.lTensor_def, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', Seminorm.smul_ball_preimage, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', ContDiff.hasStrictDerivAt, LinearIsometry.strictConvexSpace_range_iff, RatFunc.finrank_ratFunc_ratFunc, HasFDerivWithinAt.smul, skewAdjointPart_eq_I_smul_imaginaryPart, NormedSpace.expSeries_eq_expSeries_rat, WeierstrassCurve.Jacobian.nonsingular_of_Z_ne_zero, ContinuousAlternatingMap.prodLIE_apply, Submodule.mem_orthogonal_singleton_iff_inner_left, NumberField.InfinitePlace.Completion.surjective_extensionEmbedding_of_isReal, mfderivWithin_eventually_congr_set, ValueDistribution.logCounting_pow_zero, Padic.rat_dense', LieAlgebra.IsKilling.chainBotCoeff_of_eq_zsmul_add, IntermediateField.toSubalgebra_iSup_of_directed, Manifold.IsImmersionAtOfComplement.writtenInCharts, PowerSeries.intValuation_X, Finset.addConst_empty_left, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, LinearIsometry.inl_apply, hasDerivAt_pow, SchwartzMap.decay, span_flip_eq_top_iff_linearIndependent, NumberField.ComplexEmbedding.IsUnmixed.isReal_iff_isReal, ModelWithCorners.uniqueDiffWithinAt_image, LinearIsometryEquiv.comp_hasFDerivAt_iff', Submodule.mem_adjoint_iff, ZMod.pow_card_pow, FormalMultilinearSeries.summable_nnnorm_mul_pow, RCLike.normSq_div, norm_fderiv_le_of_lipschitzOn, RCLike.im_sq_le_normSq, ContinuousLinearMap.isBoundedLinearMap, LinearMap.isSymmetric_iff_isSelfAdjoint, ContinuousLinearMap.opNorm_le_iff_lipschitz, sub_smul_slope, CPolynomialOn.fderiv, Finset.dens_eq_zero, IsCyclotomicExtension.Rat.finrank, Submodule.reflection_involutive, SchwartzMap.convolution_flip, toIcoMod_zero_one, ContinuousLinearMap.opNorm_flip, Module.Basis.parallelepiped_map, Hyperreal.stdPart_of_tendsto, IsLocalMaxOn.fderivWithin_eq_zero, LinearMap.BilinForm.dualSubmodule_flip_dualSubmodule_of_basis, Int.clog_natCast, Polynomial.cardPowDegree_nonzero, OrderRingHom.subsingleton, continuousOn_integral_bilinear_of_locally_integrable_of_compact_support, ContinuousLinearMap.precompCompactConvergenceCLM_apply, VectorPrebundle.continuousOn_coordChange, IsAlgClosed.eval_surjective, VectorField.mpullbackWithin_apply, LinearMap.isSymmetric_iff_sesqForm, FormalMultilinearSeries.radius_compContinuousLinearMap_le, hasDerivWithinAt_derivWithin_iff, hasDerivAt_sub_const_iff, Subspace.dualLift_injective, hasStrictDerivAt_exp, HasStrictFDerivAt.mul_const', ContinuousLinearMap.IsPositive.adjoint_conj, measurable_fderiv_with_param, Finset.dens_sdiff_add_dens_eq_dens, strictConcaveOn_iff_div, LinearIsometryEquiv.reflections_generate_dim, krullTopology_mem_nhds_one_iff_of_normal, geom₂_sum_of_lt, mfderiv_const, IsConformalMap.smul, iteratedFDeriv_prodMk, isCoveringMap_npow, IsAlgClosed.splits, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection, IntermediateField.finrank_bot', Finset.cast_divConst_mul_card, WeierstrassCurve.Projective.map_addU, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, Algebra.IsAlgebraic.algEquivEquivAlgHom_symm_apply, SchwartzMap.lineDerivOp_apply_eq_fderiv, Real.hasStrictDerivAt_sqrt, Complex.hasDerivAt_Gamma_one, ContinuousLinearMap.exist_extension_of_finiteDimensional_range, ArchimedeanClass.FiniteResidueField.mk_lt_mk, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range, hasFDerivWithinAt_pi, intervalIntegral.integral_smul_const, galLiftEquiv_algebraMap_apply, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, stdSimplex.barycenter_eq_centerMass, Polynomial.deriv, InnerProductSpace.laplacianWithin_smul_nhds, ContinuousLinearMap.differentiableOn, ContinuousMultilinearMap.uncurry0_apply, LinearMap.BilinForm.apply_toDual_symm_apply, differentiableWithinAt_apply, ContinuousLinearMap.isPositive_iff', ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, LinearIsometryEquiv.comp_hasFDerivAt_iff, IsGalois.map_fixingSubgroup, Real.hasDerivAt_tan_of_mem_Ioo, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, Submodule.finrank_add_finrank_orthogonal, NumberField.mixedEmbedding.finrank, ContinuousLinearMap.star_eq_adjoint, IsUnramifiedAtInfinitePlaces.card_infinitePlace, CyclotomicRing.instIsTorsionFreeCyclotomicField, Submodule.orthogonal_eq_top_iff, FractionalIdeal.eq_zero_or_one, ContinuousMultilinearMap.curryLeft_apply, ContinuousAlternatingMap.hasFDerivWithinAt, ValuationSubring.mem_smul_pointwise_iff_exists, Finset.centerMass_smul, WeierstrassCurve.Jacobian.Point.toAffineLift_zero, AlgHom.toContinuousLinearMap_norm, instCharPLinearMapSubtypeMemSubringCenterId, Finset.dens_disjUnion, RatFunc.denom_algebraMap, iteratedDeriv_comp_three, IntermediateField.fixingSubgroup_isOpen, AffineSpace.asymptoticNhds_eq_smul, PiLp.hasFDerivAt_apply, Submodule.lipschitzWith_orthogonalProjection, AffineSubspace.direction_smul, ContMDiffWithinAt.coordChangeL, Polynomial.hasFDerivWithinAt_aeval, HasFPowerSeriesWithinAt.neg, Int.clog_one_right, continuousOn_cfcₙ_setProd, Real.hasDerivAt_exp, fderiv_sqrt, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, toIcoDiv_eq_floor, volume_euclideanSpace_eq_dirac, FGModuleCat.FGModuleCatDual_coe, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, Asymptotics.isThetaTVS_comm, Subfield.lift_rank_comap, hasStrictDerivAt_inv, Polynomial.contDiff_aeval, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, ProperCone.hyperplane_separation_of_notMem, OrderedFinpartition.applyOrderedFinpartition_update_left, FractionalIdeal.exists_eq_spanSingleton_mul, LinearMap.continuous_of_isClosed_ker, Module.ker_algebraMap_end, orthogonalFamily_iff_pairwise, FractionalIdeal.count_zpow, ZSpan.map_fundamentalDomain, tendsto_nat_ceil_mul_div_atTop, RCLike.re_ofReal_pow, FiniteGaloisIntermediateField.adjoin_simple_map_algHom, ContinuousMultilinearMap.norm_compContinuous_linearIsometryEquiv, separableClosure.isSeparable, FormalMultilinearSeries.radius_le_radius_derivSeries, minpoly.natDegree_le, ContinuousAlternatingMap.curryLeftLI_apply, LieAlgebra.IsKilling.chainBotCoeff_le_chainLength, ContinuousLinearMap.norm_single_le_one, Real.nonempty_algEquiv_or, ContMDiffWithinAt.const_smul_section, Padic.coe_withValRingEquiv_symm, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, LinearMap.IsSymmetric.im_inner_apply_self, Submodule.inf_orthogonal_eq_bot, FunctionField.ringOfIntegers.instIsNoetherianPolynomialSubtypeMemSubalgebraOfIsSeparableRatFunc, HasFDerivWithinAt.fun_mul', WeierstrassCurve.Affine.baseChange_slope, uniqueDiffOn_convex_of_isRCLikeNormedField, ContinuousLinearMap.norm_compSL_le, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_left, ContinuousLinearEquiv.uniqueDiffOn_preimage_iff, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, AdjoinRoot.minpoly_powerBasis_gen, RCLike.nnnorm_nnqsmul, ContDiffMapSupportedIn.withSeminorms, differentiableWithinAt_snd, PrimeSpectrum.isHomeomorph_comap_tensorProductMap_of_isPurelyInseparable, Submodule.isOrtho_sSup_left, Bundle.Trivial.trivialization.coordChangeL, MeasureTheory.withDensityᵥ_smul, wbtw_or_wbtw_smul_vadd_of_nonneg, ContDiffAt.exists_eventually_eq_hasDerivAt, DivisibleHull.qsmul_of_nonpos, ContinuousMultilinearMap.analyticWithinAt, Bornology.isVonNBounded_vadd, innerₛₗ_apply, hasFDerivAtFilter_iff_tendsto, InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis, HasFDerivWithinAt.isBigOTVS_sub, Lagrange.sum_basis, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, trace_eq_sum_embeddings, ContinuousLinearEquiv.hasFDerivAt, hasStrictFDerivAt_list_prod, IntermediateField.adjoin.finiteDimensional, IntermediateField.botEquiv_def, InnerProductSpace.isIdempotentElem_rankOne_self_iff, le_algebraicClosure_iff, IsCauSeq.geo_series_const, Filter.EventuallyEq.iteratedFDeriv, ContinuousMultilinearMap.toUniformOnFun_toFun, ContinuousLinearMap.opNorm_nonneg, NNRat.preimage_cast_Ioo, IntermediateField.adjoin_adjoin_comm, IntermediateField.adjoin_eq_top_iff, Pretrivialization.continuousLinearMap_symm_apply, Polynomial.abs_isBoundedUnder_iff, div_le_egauge_ball, hasDerivAtFilter_pi, stereographic_apply, MeasureTheory.inner_condExpL2_eq_inner_fun, StrongDual.toLp_apply, inverse_mfderiv_mul_left, OrthogonalFamily.norm_sum, ContinuousLinearMap.map_smul₂, ContinuousLinearMap.coe_flipₗᵢ, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace, HasFDerivAtFilter.iterate, Submodule.inner_starProjection_left_eq_right, IntermediateField.toSubalgebra_lt_toSubalgebra, Finset.addConst_empty_right, ContinuousLinearMap.normOneClass, MeasureTheory.mem_lpMeas_self, ContinuousLinearMap.opNNNorm_subsingleton, IntermediateField.finSepDegree_bot', ContMDiffAt.mfderiv, ContinuousLinearMap.IsPositive.spectrumRestricts, Module.End.IsSemisimple.minpoly_squarefree, IntermediateField.val_mk, OrthonormalBasis.sum_repr, hasDerivAtFilter_const_add_iff, LinearMap.continuous_iff_isClosed_ker, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, NumberField.InfinitePlace.embedding_injective, Real.iteratedFDeriv_fourierIntegral, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, differentiableAt_snd, ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, IsCoercive.ker_eq_bot, NumberField.InfinitePlace.Completion.surjective_extensionEmbeddingOfIsReal, RatFunc.eq_C_iff, Bornology.isVonNBounded_insert, hasDerivWithinAt_abs_neg, ContinuousLinearEquiv.analyticOnNhd, NumberField.InfinitePlace.mem_stabilizer_mk_iff, RatFunc.num_mul_eq_mul_denom_iff, StieltjesFunction.ae_hasDerivAt, IsConformalMap.injective, mem_galBasis_iff, InnerProductSpaceable.innerProp, fderivWithin_const_apply, IntermediateField.rank_sup_le, IntermediateField.LinearDisjoint.self_right, LinearIsometry.strictConvexSpace_range, ContinuousLinearMap.opNorm_neg, WittVector.RecursionBase.solution_pow, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, FormalMultilinearSeries.ofScalars_series_eq_zero, IsLocalRing.CotangentSpace.span_image_eq_top_iff, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, Field.finSepDegree_eq_finrank_iff, FormalMultilinearSeries.changeOrigin_eval, krullTopology_discreteTopology_of_finiteDimensional, LinearMap.toSeminorm_ball_zero, Lagrange.eval_interpolate_at_node, Valuation.Integers.valuation_irreducible_pos, LinearIsometryEquiv.hasFDerivWithinAt, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, RootPairing.restrictScalars_toLinearMap_apply_apply, LinearMap.finrank_maxGenEigenspace_zero_eq, AlgHom.normal_bijective, NumberField.InfinitePlace.Completion.isometry_extensionEmbedding_of_isReal, Submodule.fstL_comp_coe_orthogonalDecomposition, quadraticChar_apply, inner_smul_left_eq_smul, NumberField.toNNReal_valued_eq_adicAbv, Finset.expect_dite_eq, iter_deriv_inv_linear_sub, MeromorphicOn.pow, RCLike.re_sq_le_normSq, FiniteDimensional.exists_is_basis_integral, Module.Basis.ofZLatticeBasis_comap, isStarProjection_iff_eq_starProjection_range, Int.log_zero_right, ContinuousLinearMap.reApplyInnerSelf_smul, ContinuousLinearMap.add_compLpL, Polynomial.isIntegrallyClosed_iff', NonUnitalCStarAlgebra.toIsScalarTower, convexJoin_left_comm, IntermediateField.coe_pow, LinearIsometryEquiv.symm_units_smul, IsGaloisGroup.mulEquivAlgEquiv_symm_apply, IsHilbertSum.linearIsometryEquiv_symm_apply_single, WittVector.exists_frobenius_solution_fractionRing_aux, AffineIsometryEquiv.map_vadd, closedAbsConvexHull_eq_closure_absConvexHull, exists_embedding_euclidean_of_compact, Complex.norm_fderiv_le_one_of_mapsTo_ball, UnitAddTorus.mFourierBasis_repr, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, VectorFourier.fourierIntegral_continuousMultilinearMap_apply, HasFPowerSeriesAt.prod, Nonneg.coe_div, LinearMap.toSeminorm_apply, AlgEquiv.restrictNormalHom_apply, InfiniteGalois.mk_toAlgEquivAux, hasDerivAt_ofReal_cpow_const', Normal.out, hasStrictDerivAt_natCast, LinearIsometryEquiv.toLinearIsometry_rTensor, Complex.hasDerivAt_Gamma_one_half, VectorPrebundle.contMDiffOn_contMDiffCoordChange, Representation.irreducible_iff_isSimpleModule_asModule, Real.smul_iSup_of_nonneg, Submodule.starProjection_minimal, EuclideanGeometry.orthogonalProjection_linear, instIsAbelianGaloisSubtypeMemIntermediateField, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, ContinuousLinearMap.contMDiffWithinAt, lineDeriv_smul, ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk, PiTensorProduct.mapL_pow, Finset.cast_divConst, LinearMap.continuous_of_isClosed_graph, IntermediateField.adjoin_simple_comm, algebraicClosure.isAlgClosure, DoubleCentralizer.natCast_toProd, OrthonormalBasis.sum_rankOne_eq_id, NumberField.InfinitePlace.mkComplex_coe, ContinuousLinearMap.dslope_comp, mdifferentiableAt_coordChangeL, hasDerivAt_finCons', MeasureTheory.Lp.toTemperedDistribution_toLp_eq, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, AlgEquiv.liftNormal_commutes, ModP.v_p_lt_val, AlgebraicGeometry.geometrically_iff_of_commRing_of_isClosedUnderIsomorphisms, ContinuousLinearMap.unit_le_opNorm, HasFPowerSeriesWithinAt.add, IntermediateField.inclusion_inclusion, Submodule.starProjection_mem_subspace_eq_self, NNRat.cast_lt_one, Field.Emb.Cardinal.adjoin_image_leastExt, ContinuousLinearMap.adjoint_inner_right, exists_extension_norm_eq, HasMFDerivAt.prodMk, FiniteField.X_pow_card_pow_sub_X_natDegree_eq, ContinuousLinearMap.norm_id, FormalMultilinearSeries.id_apply_of_one_lt, hasFDerivAt_integral_of_dominated_of_fderiv_le'', gal_zero_isSolvable, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, HasFDerivWithinAt.fun_pow', FiniteField.bijective_frobeniusAlgEquivOfAlgebraic_pow, sum_Ioc_inv_sq_le_sub, differentiable_pi'', HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, ContDiff.contDiff_fderiv_apply, hasStrictDerivAt_exp_zero_of_radius_pos, LinearMap.isPositive_iff, PowerSeries.C_inv, ContinuousLinearMap.measurable_apply', IntermediateField.le_iff_le, IntermediateField.extendScalars_restrictScalars, FractionalIdeal.map_canonicalEquiv_mk0, NormedSpace.closedBall_inv_subset_polar_closedBall, FiniteField.nonempty_algHom_iff_finrank_dvd, ContDiffMapSupportedIn.postcompLM_apply, NNRat.floor_def, NumberField.IsCMField.RingOfIntegers.complexConj_eq_self_iff, analyticOrderAt_smul, ContinuousLinearMap.norm_smulRightL_le, Real.smul_iSup_of_nonpos, DoubleCentralizer.one_toProd, MeasureTheory.withDensityᵥ_smul', spectralNorm_extends_of_finiteDimensional, Algebra.discr_powerBasis_eq_prod'', convexHull_prod, InfiniteGalois.fixedField_bot, differentiableAt_iff_restrictScalars, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, hasDerivAtFilter_const, smul_mem_asymptoticCone_iff, LinearIsometryEquiv.symm_smul_apply, SchwartzMap.tsupport_derivCLM_subset, RCLike.normSq_zero, hasDerivAt_single, Nat.pow_le_choose, OrthonormalBasis.coe_toBasis_repr_apply, Algebra.adjoin_eq_top_of_intermediateField, FunctionField.inftyValuation.C, Valued.instFaithfulSMulCompletionOfUniformContinuousConstSMul, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, IntermediateField.adjoin_subset_adjoin_iff, inner_smul_right_eq_smul, IsAlgClosed.roots_eq_zero_iff, differentiableOn_apply, NNRat.preimage_cast_Ioc, Algebra.map_intTraceAux, LinearIsometryEquiv.star_eq_symm, ContinuousLinearEquiv.dimH_preimage, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, IntermediateField.mem_extendScalars, minpoly.instIsScalarTowerSubtypeMemSubringSubalgebraIntegralClosure, SchwartzMap.integral_smul_laplacian_right_eq_left, differentiableAt_pi, HasFDerivWithinAt.fun_add, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, hasStrictDerivAt_exp_of_mem_ball, FormalMultilinearSeries.radius_prod_eq_min, ContinuousLinearMapWOT.add_apply, OrthonormalBasis.coe_equiv_euclideanSpace, NumberField.mixedEmbedding.norm_real, RCLike.conjAe_coe, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, hasFDerivAt_zero, ZMod.isCyclic_units_two, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, Valuation.Integers.isUnit_iff_valuation_eq_one, derivWithin_div, NonUnitalCommCStarAlgebra.toSMulCommClass, isAlgClosure_iff, HasFDerivAt.mul_const', IsSepClosed.factors_of_separable, Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, ContinuousAlternatingMap.nnnorm_ofSubsingleton, LieAlgebra.IsKilling.traceForm_coroot, PrimeSpectrum.coe_preimageHomeomorphFiber_symm_apply_coe_asIdeal, WeierstrassCurve.Jacobian.addU_smul, InfiniteGalois.proj_of_le, HasFiniteFPowerSeriesOnBall.fderiv', Finset.expect_apply, WittVector.RecursionBase.solution_spec', Submodule.orthogonalProjectionFn_eq, Module.End.mulSemiringActionToAlgEquiv_conjAct_surjective, ContinuousMultilinearMap.currySum_apply, Submodule.IsOrtho.ge, OpenPartialHomeomorph.MDifferentiable.ker_mfderiv_eq_bot, RootPairing.finrank_rootSpanIn, FiniteField.expand_card, Module.Basis.traceDual_repr_apply, Ideal.finprod_heightOneSpectrum_factorization_coe, FormalMultilinearSeries.ofScalars_comp_neg, SeminormedSpace.Core.norm_smul, Polynomial.differentiableWithinAt_aeval, Submodule.bot_orthogonal_eq_top, signedDist_apply, Unitization.norm_splitMul_snd_sq, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, NNRat.cast_lt, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, ContinuousLinearMap.IsPositive.conj_starProjection, FGModuleCat.FGModuleCatEvaluation_apply', LieModule.traceForm_eq_sum_finrank_nsmul_mul, WeakDual.CharacterSpace.equivAlgHom_coe, HasStrictFDerivAt.fun_pow', convexHull_eq_union, measurable_fderiv, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux, le_egauge_ball_one, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, toPrincipalIdeal_def, Orthonormal.comp_linearIsometryEquiv, quadraticChar_eq_pow_of_char_ne_two, Submodule.map_orthogonal, Complex.re_expect, HasStrictFDerivAt.comp, DoubleCentralizer.natCast_snd, ContDiffMapSupportedIn.bounded_iteratedFDeriv, IntermediateField.coe_type_toSubalgebra, IntermediateField.relrank_eq_rank_of_le, CompactConvergenceCLM.continuousSMul, WeierstrassCurve.Projective.map_add, convexHull_eq, HasFiniteFPowerSeriesOnBall.hasFDerivAt, IntermediateField.lift_adjoin, NNRat.cast_zero, convexJoin_assoc_aux, hasStrictDerivAt_zero, NumberField.basisOfFractionalIdeal_apply, VectorBundleCore.coordChange_linear_comp, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, ContinuousAlternatingMap.alternatizeUncurryFin_add, ContinuousLinearMap.isBigOTVS_fun_comp, Module.Basis.ofZLatticeComap_repr_apply, RCLike.normSq_eq_zero, Mathlib.Meta.Positivity.zpow_zero_pos, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, FormalMultilinearSeries.coeff_iterate_fslope, LinearMap.IsSymmetric.conj_inner_sym, HasFPowerSeriesAt.eq_zero, ContinuousLinearMap.coeFn_compLp, ContinuousLinearMap.flip_zero, FiniteField.Extension.exists_frob_pow_eq, FormalMultilinearSeries.leftInv_removeZero, LieAlgebra.IsKilling.chainBotCoeff_zero_right, IsGaloisGroup.fixedPoints_le_of_le, tendsto_pow_div_pow_atTop_atTop, ContinuousLinearMapWOT.ext_iff, hasStrictDerivAt_exp_smul_const_of_mem_ball', ContinuousAlternatingMap.instT2Space, ContinuousLinearMap.extendTo𝕜'_apply, NumberField.mem_multisetInfinitePlace, ClosedSubmodule.orthogonal_disjoint, fderivWithin_cosh, IsLocalFrameOn.coeff_eq_of_eq, MvPowerSeries.eq_mul_inv_iff_mul_eq, iteratedFDerivWithin_const_of_ne, ContinuousMultilinearMap.norm_ofSubsingleton, ContinuousLinearMap.isAdjointPair_inner, IntermediateField.extendScalars_top, TensorProduct.norm_map, dist_birkhoffAverage_birkhoffAverage_le, analyticOrderNatAt_pow, ContinuousLinearMap.coe_le_coe_iff, AddChar.linearIndependent, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, hasFDerivAtFilter_finCons', ContinuousLinearEquiv.analyticWithinAt, slope_fun_def_field, LinearMap.BilinForm.comp_symmCompOfNondegenerate_apply, IntermediateField.algebraicIndependent_adjoin_iff, IsLocalRing.ResidueField.residue_smul, LinearIsometryEquiv.differentiableAt, Complex.re_nnqsmul, Real.fourier_continuousMultilinearMap_apply, NumberField.InfinitePlace.card_add_two_mul_card_eq_rank, LinearIsometryEquiv.differentiable, NumberField.InfinitePlace.mem_orbit_iff, RatFunc.isScalarTower_liftAlgebra, Unitization.splitMul_injective, NumberField.mixedEmbedding.indexEquiv_apply_isComplex_snd, isInvertible_mfderiv_extChartAt, WeierstrassCurve.Jacobian.map_addU, MDifferentiableAt.smul_const_section, NumberField.InfinitePlace.isUnramifiedIn_comap, IntermediateField.rank_eq_rank_subalgebra, Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial, FormalMultilinearSeries.ofScalars_series_injective, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Nonneg.Icc_subset_segment, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousMultilinearMap.norm_map_insertNth_le, quadraticChar_eq_pow_of_char_ne_two', Asymptotics.IsTheta.const_smul_right, HasFPowerSeriesAt.coeff_zero, Submodule.orthogonal_le_orthogonal_iff, DoubleCentralizer.sub_snd, Algebra.normalizedTrace_trans, RingOfIntegers.algebraMap_norm_algebraMap, ModelWithCorners.coe_transContinuousLinearEquiv, IsSimpleRing.exists_algEquiv_matrix_of_isAlgClosed, SeparatingDual.completeSpace_continuousMultilinearMap_iff, Submodule.orthogonal_le_iff_orthogonal_le, ContMDiffOn.smul_section_of_tsupport, WeierstrassCurve.Jacobian.Y_eq_iff, ContDiffOn.comp_continuousLinearMap, Field.lift_rank_mul_lift_sepDegree_of_isSeparable, LinearMap.BilinForm.orthogonal_eq_top_iff, ContMDiffWithinAt.smul_section, Polynomial.differentiable, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap, Polynomial.rootSet_monomial, ContinuousLinearEquiv.coord_norm', Set.integer_valuation_le_one, NumberField.InfinitePlace.eq_iff_eq, IntermediateField.fixedField_bot, HasFPowerSeriesOnBall.hasSum_sub, ContinuousLinearMap.nnnorm_id, OrderIso.smulRightDual_symm_apply, smul_mem_asymptoticCone, LieAlgebra.IsKilling.chainTopCoeff_of_eq_zsmul_add, Polynomial.isCoprime_map, absConvexHull_eq_convexHull_balancedHull, FractionRing.isScalarTower_liftAlgebra, Bundle.Trivial.symmₗ_trivialization, ProbabilityTheory.hasDerivAt_mgf, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, HasFPowerSeriesAt.eq_zero_of_eventually, hasMFDerivAt_snd, IntermediateField.toSubalgebra_strictMono, Polynomial.IsSeparableContraction.degree_eq, ContinuousLinearMap.isPositive_zero, div_le_egauge_closedBall, hasStrictFDerivAt_inv', IntermediateField.lift_sup, LinearMap.mem_span_iff_bound, Set.Finite.convexHull_eq_image, PowerSeries.inv_eq_inv_aux, Algebra.discr_powerBasis_eq_prod', PadicAlgCl.coe_eq, Polynomial.X_sub_C_mul_removeFactor, uniqueMDiffWithinAt_iff_uniqueDiffWithinAt, Algebra.algebraMap_intTrace, hasFDerivAt_exp_smul_const_of_mem_ball', convexJoin_right_comm, hasDerivAt_mul_const, SameRay.exists_pos_left, LieAlgebra.IsKilling.chainBotCoeff_add_chainTopCoeff, SchwartzMap.smulLeftCLM_sub, Submodule.snd_orthogonalDecomposition_apply, NumberField.FinitePlace.isFinitePlace, hasFDerivAtFilter_natCast, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', cfcₙ_apply_mem_elemental, LinearEquiv.det_coe_symm, asymptoticCone_submodule, Module.Basis.ofZLatticeBasis_repr_apply, wbtw_or_wbtw_smul_vadd_of_nonpos, HasMFDerivAt.sum, normalClosure.normal, EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, intervalIntegral.integral_hasStrictDerivAt_right, MvPolynomial.schwartz_zippel_sum_degreeOf, quasispectrum_eq_spectrum_union_zero, Ideal.inertiaDeg_le_finrank, iteratedDeriv_fun_pow_zero, FixedPoints.toAlgAut_bijective, SchwartzMap.fourier_fderivCLM_eq, SpectrumRestricts.nnreal_iff_spectralRadius_le, right_le_midpoint, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, PadicInt.ker_toZMod, ContinuousLinearMap.integral_comp_id_comm, FiniteField.isSplittingField_sub, hasStrictFDerivAt_exp_smul_const, IsGalois.fixingSubgroup_normal_of_isGalois, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, MDifferentiableOn.smul_section, PrimeSpectrum.coe_primesOverOrderIsoFiber_symm_apply_coe, AbsoluteValue.isEquiv_iff_exists_rpow_eq, SchwartzMap.fourier_convolution_apply, Seminorm.smul_ball_zero, Filter.Tendsto.inv_tendsto_atTop, separableClosure.map_eq_of_separableClosure_eq_bot, mem_openSegment_iff_div, Polynomial.degree_div_le, Asymptotics.isBigOTVS_map, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, MvPowerSeries.invOfUnit_eq, LinearIsometry.norm_toContinuousLinearMap_le, Real.hasStrictDerivAt_tan, AffineSubspace.isometryEquivMap.apply_symm_apply, Submodule.starProjection_le_starProjection_iff, iteratedFDerivWithin_zero_fun, IntermediateField.adjoin_adjoin_left, RCLike.wInner_cWeight_const_right, Finset.expect_div, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, HasStrictFDerivAt.mul, intervalIntegral.integral_hasStrictDerivAt_left, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, ContinuousLinearMap.analyticOnNhd, fderiv_fst, iter_deriv_inv_linear, InfiniteGalois.algEquivToLimit_continuous, divRadical_dvd_wronskian_left, NNRat.cast_le_natCast, IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C', LieAlgebra.isRegular_iff_finrank_engel_eq_rank, IntermediateField.normalClosure_mono, ContinuousAlternatingMap.differentiable, WeakDual.toStrongDual_apply, ContinuousLinearEquiv.uniqueDiffOn_image_iff, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, LinearMap.eq_adjoint_iff_basis_right, IsLocalRing.subsingleton_tensorProduct, CategoryTheory.finrank_endomorphism_simple_eq_one, ContinuousLinearMap.hasMFDerivWithinAt, ContinuousLinearEquiv.nnnorm_symm_pos, InnerProductSpace.laplacian_smul_nhds, convexHull_rangle_single_eq_stdSimplex, IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base, MeasureTheory.lpNorm_expect_le, Submodule.instOrthogonalCompleteSpace, FormalMultilinearSeries.enorm_compContinuousLinearMap_le, IsSepClosed.splits_of_separable, IsUltrametricDist.isPowMul_algNormOfAlgEquiv, LaurentSeries.ratfuncAdicComplRingEquiv_apply, IsSepClosed.exists_root, VectorPrebundle.IsContMDiff.exists_contMDiffCoordChange, trace_eq_sum_automorphisms, IsSelfAdjoint.commute_cfcₙ, Fintype.expect_ite_eq', FormalMultilinearSeries.le_radius_pi, Real.hasDerivAt_arctan, AffineSpace.asymptoticNhds_eq_smul_vadd, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, continuousMultilinearCurryLeftEquiv_symm_apply, Polynomial.Monic.dvd_iff_fraction_map_dvd_fraction_map, Finset.pluennecke_ruzsa_inequality_pow_mul, convexHull_union, WithLp.unitization_mul, FixedPoints.smul, hasDerivAt_exp_smul_const', DoubleCentralizer.instStarModule, quasispectrum.preimage_algebraMap, convexHull_sub, NNRat.addSubmonoid_closure_range_mul_self, IsScalarTower.AlgEquiv.restrictNormalHom_comp_apply, VectorBundleCore.localTriv.isLinear, instOrderIsoClassContinuousLinearMapIdOfNonUnitalAlgEquivClassOfStarHomClassOfContinuousMapClass, hasDerivWithinAt_id, solvableByRad.isIntegral, ContinuousMultilinearMap.smulRightL_apply, ContinuousLinearMap.contDiff, Submodule.le_traceDual_mul_iff, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, ContinuousLinearMap.instBorelSpace, LinearMap.isStarProjection_iff_isSymmetricProjection, LinearIsometryEquiv.toLinearEquiv_rTensor, norm_apply_le_norm_cfcₙ, fderiv_mul_const, innerₛₗ_apply_coe, ContinuousLinearMap.isUniformEmbedding_toUniformOnFun, minpoly.natSepDegree_eq_one_iff_eq_expand_X_sub_C, fderiv_csinh, exists_pos_left_iff_sameRay_and_ne_zero, ClassGroup.equiv_mk0, NumberField.RingOfIntegers.map_mk, HasStrictFDerivAt.fun_add, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, IsLocalMinOn.fderivWithin_nonneg, instExpCharLinearMapSubtypeMemSubringCenterId, ContinuousLinearMap.norm_snd_le, IntermediateField.sup_toSubalgebra_of_right, Submodule.orthogonalDecomposition_apply, iteratedFDeriv_succ_eq_comp_left, IntermediateField.algebraAdjoinAdjoin.instFaithfulSMulSubtypeMemSubalgebraAdjoinAdjoin, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff, Submodule.isOrtho_self, LinearIsometryEquiv.toLinearIsometry_lTensor, WeierstrassCurve.Jacobian.neg_of_Z_ne_zero, fderiv_of_notMem_tsupport, ContinuousLinearMap.smul_compLpL, AddChar.wInner_cWeight_eq_boole, DifferentiableOn.prodMk, Representation.is_simple_module_iff_irreducible_ofModule, IntermediateField.insepDegree_bot, hasStrictFDerivAt_const, FormalMultilinearSeries.summable_norm_mul_pow, ContinuousLinearMap.contMDiffOn, Polynomial.Gal.restrictProd_injective, IsFractionRing.algEquiv_commutes, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv, contMDiffOn_coordChangeL, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, IntermediateField.equivOfEq_apply, SpectrumRestricts.rightInvOn, ContinuousLinearEquiv.arrowCongrSL_symm_apply, NormedSpace.ext_iff, Nat.inv_pos_of_nat, IntermediateField.rank_bot', OpenPartialHomeomorph.MDifferentiable.range_mfderiv_eq_univ, krullTopology_t2, ContinuousLinearMap.nnbound, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, convexHull_list_sum, ContinuousLinearMap.opNorm_mulLeftRight_le, DoubleCentralizer.intCast_fst, NNRat.mul_num, gauge_smul_left, PointwiseConvergenceCLM.evalCLM_apply, Algebra.norm_algebraMap, IsPurelyInseparable.algebraMap_elemReduct_eq, ClosedSubmodule.orthogonal_closure, NumberField.mixedEmbedding.fundamentalCone.mem_idealSet, ContDiffPointwiseHolderAt.iteratedFDeriv, IntermediateField.le_sup_toSubalgebra, ContinuousLinearMap.norm_compLpL_le, ZSpan.vadd_mem_fundamentalDomain, LinearMap.toSeminormFamily_apply, perfectClosure.map_eq_of_algEquiv, Polynomial.rootSet_X_pow, algebraicClosure.map_eq_of_algEquiv, AddChar.map_neg_eq_conj, RatFunc.denom_add_dvd, Module.End.mem_spectrum_iff_isRoot_charpoly, Field.nonempty_algHom_of_minpoly_eq, mfderiv_fst, ContDiffMapSupportedIn.structureMapCLM_zero_injective, ContinuousAlternatingMap.neg_one_pow_smul_map_insertNth, Finset.pluennecke_ruzsa_inequality_nsmul_sub, RCLike.iInter_halfSpaces_eq, mfderivWithin_fst, NumberField.IsCMField.infinitePlace_complexConj, NumberField.prod_archAbsVal_eq, Polynomial.rootSet_prod, Hyperreal.stdPart_omega, IntermediateField.isAlgebraic_adjoin_iff_bot, ContinuousMultilinearMap.piₗᵢ_apply, meromorphicAt_smul_iff_of_ne_zero, Module.Basis.traceDual_powerBasis_eq, NumberField.ComplexEmbedding.isReal_comp_iff, RCLike.normSq_to_complex, Derivation.leibniz_div_const, Matrix.PosSemidef.sqrt_mul_self, ContDiffAt.continuousAt_iteratedFDeriv, Polynomial.not_irreducible_C, ZSpan.fract_apply, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, Real.deriv_arcsin_aux, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, IsLocalMin.fderiv_eq_zero, Finset.dens_eq_sum_dens_fiberwise, IntermediateField.fieldRange_val, IntermediateField.liftAlgEquiv_apply, ContinuousLinearMap.cpolynomialOn, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, LinearMap.coe_toContinuousLinearMap_symm, Matrix.range_diagonal, NumberField.ComplexEmbedding.IsConj.comp, IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable, HasFDerivWithinAt.finset_prod, ContinuousAlternatingMap.nnnorm_constOfIsEmpty, hasStrictFDerivAt_list_prod', RatFunc.num_div_denom, ContinuousLinearMap.le_opENorm, continuousMultilinearCurryFin1_symm_apply, IntermediateField.insepDegree_top, ValuationSubring.subtype_apply, Quaternion.hasSum_expSeries_of_imaginary, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, Trivialization.symmL_apply, ContinuousMultilinearMap.opNorm_le_iff, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, StrongDual.mem_polar_iff, separableClosure_le_separableClosure_iff, FormalMultilinearSeries.radius_pi_le, MeasureTheory.lpMeasToLpTrim_ae_eq, Submodule.orthogonal_eq_inter, ContinuousLinearMap.mdifferentiableOn, RCLike.normSq_add, AffineSubspace.sOppSide_smul_vsub_vadd_left, MeasureTheory.eLpNorm_condExpL2_le, RCLike.div_re, ContinuousLinearMap.lsmul_flip_apply, IsGaloisGroup.card_eq_finrank, ContinuousAlternatingMap.alternatizeUncurryFin_curryLeft, hasDerivAt_iff_tendsto, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, HasStrictFDerivAt.smul_const, FixedPoints.coe_algebraMap, ContinuousLinearEquiv.coord_self, sub_smul_dslope, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, cardinalMk_algHom, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, ContinuousAlternatingMap.unit_le_opNorm, RCLike.geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, IsGalois.tfae, norm_iteratedFDeriv_smul_le, ContDiffAt.differentiableAt_iteratedFDeriv, NNRat.floor_natCast_div_natCast, WeierstrassCurve.Projective.dblX_eq, LinearMap.IsPositive.adjoint_eq, SMulCommClass.nnrat, Trivialization.prod_apply', fderivWithin_zero_of_not_differentiableWithinAt, IntermediateField.transcendental_adjoin_iff, ContinuousLinearMap.sSup_unitClosedBall_eq_norm, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, NumberField.InfinitePlace.isUnramified_iff_mult_le, iteratedDeriv_vcomp_two, ContinuousLinearEquiv.coord_norm, ContinuousAlternatingMap.opNNNorm_le_iff, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic, ContinuousOn.continuousOn_iteratedFDeriv, intervalIntegral.integral_hasDerivAt_left, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1, MeasureTheory.lpMeasToLpTrim_smul, Real.hasStrictDerivAt_const_rpow, Submodule.starProjection_orthogonal_val, VectorField.lieBracketWithin_eq, Polynomial.natSepDegree_mul, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, MDifferentiableOn.smul_section_of_tsupport, isStarProjection_iff_eq_starProjection, LinearEquiv.conjAlgEquiv_surjective, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, RCLike.geometric_hahn_banach_point_closed, LinearMap.IsSymmetricProjection.le_iff_range_le_range, ContinuousLinearMap.map_add₂, hasDerivWithinAt_intCast, Module.End.hasEigenvalue_iff_mem_spectrum, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, Polynomial.natDegree_mod_lt, IntermediateField.rank_comap, VectorPrebundle.coordChange_apply, LieAlgebra.IsKilling.chainTopCoeff_le_chainLength, ContinuousMultilinearMap.norm_map_cons_le, LinearMap.not_hasEigenvalue_zero_tfae, NumberField.InfinitePlace.even_card_aut_of_not_isUnramifiedIn, ContinuousMultilinearMap.norm_smulRight, EuclideanGeometry.orthogonalProjection_apply, Module.Basis.extendOfIsLattice_apply, hasFDerivAt_exp_zero_of_radius_pos, LSeries_hasDerivAt, separableClosure.separableClosure_eq_bot, Polynomial.div_C_mul, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_right, Algebra.IsAlgebraic.range_eval_eq_rootSet_minpoly, IntermediateField.rank_bot_mul_relrank, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, Real.hasDerivAt_fourierIntegral, IsLocalRing.instFiniteResidueField, ContinuousLinearEquiv.strictConvex_preimage, ordinaryHypergeometricSeries_eq_zero_of_neg_nat, NumberField.mixedEmbedding.mixedEmbedding_apply_isComplex, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, ContinuousAlternatingMap.bound, Nat.cast_le_pow_div_sub, IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_C, ContinuousLinearMap.hasDerivWithinAt, differentiableWithinAt_piLp, LinearIsometry.rTensor_apply, hasStrictFDerivAt_pow, ArchimedeanClass.mk_div, FormalMultilinearSeries.derivSeries_apply_diag, NormedSpace.polar_closedBall, Submodule.norm_orthogonalProjection, SameRay.exists_nonneg_right, AnalyticAt.fderiv, Bundle.Prod.contMDiffVectorBundle, ContinuousLinearEquiv.differentiableWithinAt, IntermediateField.sup_toSubalgebra_of_isAlgebraic_right, NumberField.canonicalEmbedding_eq_basisMatrix_mulVec, fderiv_comp_smul, Submodule.instHasOrthogonalProjectionTop, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, LinearMap.BilinForm.eq_top_of_restrict_nondegenerate_of_orthogonal_eq_bot, ContinuousLinearMap.opNorm_lsmul, LinearIsometry.toLinearMap_lTensor, Submodule.comap_smul', IntermediateField.toSubalgebra_le_toSubalgebra, convexOn_iff_div, ValuationSubring.ker_unitGroupToResidueFieldUnits, HasFPowerSeriesWithinOnBall.hasSum, Valuation.HasExtension.instIsScalarTower_valuationSubring, coe_innerₛₗ_apply, FormalMultilinearSeries.norm_changeOriginSeriesTerm, NumberField.mixedEmbedding.fundamentalCone.mem_integerSet, PiLp.hasStrictFDerivAt_ofLp, fderivWithin_arctan, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, Nonneg.coe_zpow, Module.Basis.continuous_coe_repr, ContinuousLinearMap.norm_id_of_nontrivial_seminorm, NumberField.InfinitePlace.comap_id, curveIntegral_add, IsAlgClosed.isAlgClosure_of_transcendence_basis, HasGradientAt.hasDerivAt, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv, hasDerivAt_exp_zero, GenContFract.sub_convs_eq, HasFTaylorSeriesUpTo.zero_eq', InfiniteGalois.limitToAlgEquiv_symm_apply, AffineSubspace.setOf_sOppSide_eq_image2, NumberField.coe_discr, galRestrict'_comp, ContinuousLinearEquiv.analyticAt, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, LinearMap.finrank_maxGenEigenspace_eq, ProbabilityTheory.gaussianPDFReal_mul, InnerProductSpace.continuousLinearMapOfBilin_apply, Circle.toUnits_apply, ContinuousMultilinearMap.norm_def, Polynomial.degree_mod_lt, NormedSpace.double_dual_bound, instFieldContMDiffRing, NNRat.instIsTopologicalSemiring, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, IntermediateField.adjoin_toSubfield, spectralAlgNorm_isPowMul, inv_smul_le_iff_of_neg, MeasureTheory.convolution_eq_swap, ContinuousLinearMap.map_zero₂, isInvertible_mfderivWithin_extChartAt_symm, ModelWithCorners.coe_transContinuousLinearEquiv_symm, fderivWithin_def, UniformCauchySeqOnFilter.one_smulRight, mulInvariantVectorField_smul, differentiable_finCons, ContDiff.fderiv_right, hasDerivAt_const_add_iff, HasFDerivAt.prodMap, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, Polynomial.hilbertPoly_mul_one_sub_pow_add, VectorField.mlieBracketWithin_apply, HasFPowerSeriesWithinOnBall.tendsto_partialSum, homothety_inv_two, IsTranscendenceBasis.lift_rank_eq_max_lift, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', ContinuousAlternatingMap.opNorm_pi, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, ValuationSubring.smul_mem_pointwise_smul, IntermediateField.finiteDimensional_map, FormalMultilinearSeries.id_apply_one, strictConvexOn_iff_div, ContinuousLinearEquiv.comp_contDiff_iff, minpoly.degree_dvd, fderiv_csin, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, ContinuousLinearMap.norm_snd, ZSpan.repr_floor_apply, IsPurelyInseparable.isPRadical, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv, MvRatFunc.rank_eq_max_lift, separableClosure.map_eq_of_algEquiv, NumberField.Units.finrank_mul_regulator_eq_det, IsPrimitiveRoot.lcm_totient_le_finrank, IsPurelyInseparable.instNonemptyAlgHomOfPerfectField, MeasureTheory.condExpIndSMul_ae_eq_smul, ContinuousAlternatingMap.uniformContinuous_restrictScalars, HasFTaylorSeriesUpTo.fderiv, ContinuousLinearMap.iteratedFDeriv_comp_right, linearIndependent_pow, norm_fderiv_le_of_lip', RatFunc.aeval_X_left_eq_algebraMap, IsSepClosure.isAlgClosure_of_perfectField, LieAlgebra.IsKilling.span_weight_eq_top, ContinuousMultilinearMap.apply_zero_uncurry0, ContinuousMap.idealOf_compl_singleton_isMaximal, Polynomial.residueFieldMapCAlgEquiv_symm_X, IntermediateField.finSepDegree_top, fderiv_cosh, Polynomial.IsSplittingField.adjoin_rootSet_eq_range, IntermediateField.lift_rank_comap, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, ValuationRing.coe_equivInteger_apply, support_fderiv_subset, HasStrictFDerivAt.fun_mul, IsLocalFrameOn.generating, ContDiff.continuousLinearMap_comp, ContinuousLinearMap.precomp_apply, ContinuousLinearMap.norm_holderL_le, hasFDerivWithinAt_pow, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, Real.compact_inner_le_weight_mul_Lp_of_nonneg, PolynormableSpace.withSeminorms, contDiff_infty_iff_fderiv, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, hasDerivWithinAt_inv, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Asymptotics.isBigOTVS_prodMk_left, MeasureTheory.lpMeas.ae_fin_strongly_measurable', gaugeSeminormFamily_ball, spectralNorm_eq_of_equiv, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, hasStrictDerivAt_id, Polynomial.splits_iff_splits, curveIntegral_sub, Polynomial.Monic.irreducible_iff_irreducible_map_fraction_map, AlgHom.restrictNormal_commutes, quadraticCharFun_zero, RCLike.sqrt_normSq_eq_norm, WeierstrassCurve.Jacobian.isUnit_X_of_Z_eq_zero, mdifferentiable_smul_section, NNRat.cast_lt_natCast, Matrix.IsHermitian.charpoly_eq, RatFunc.associated_num_inv, HasFDerivWithinAt.mul', IntermediateField.normalClosure_le_iff_of_normal, FiniteField.orderOf_frobeniusAlgHom, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, HasGradientAt.fderiv_apply, SchwartzMap.instFourierInvSMul, ContinuousAlternatingMap.instContinuousEval, differentiableWithinAt_complex_iff_differentiableWithinAt_real, tsub_div, ContinuousLinearMap.comp_analyticOnNhd, TemperedDistribution.derivCLM_apply_apply, ValuationSubring.comap_comap, NNRat.cast_natCast, AffineSubspace.setOf_wSameSide_eq_image2, LinearIsometryEquiv.integrable_comp_iff, AlgHom.fieldRange_of_normal, range_derivWithin_subset_closure_span_image, NumberField.instIsLocalizedModuleIntSubtypeMemSubmoduleRingOfIntegersCoeToSubmoduleValFractionalIdealNonZeroDivisorsRestrictScalarsSubtype, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, IntermediateField.Lifts.eq_iff, Module.End.genEigenspace_le_genEigenspace_finrank, norm_iteratedFDeriv_zero, algebraMap.coe_expect, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, FiniteField.even_card_iff_char_two, NumberField.FinitePlace.norm_le_one, geom_sum₂_Ico, hasDerivWithinAt_Ici_of_tendsto_deriv, NumberField.Units.sum_mult_mul_log, Polynomial.hasFDerivWithinAt, LinearMap.BilinForm.finrank_add_finrank_orthogonal, MeasureTheory.condExpIndSMul_smul', LinearMap.hasDerivAt, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, norm_iteratedFDeriv_eq_norm_iteratedDeriv, MDifferentiableWithinAt.smul, HasMFDerivWithinAt.comp, Complex.isometryOfOrthonormal_symm_apply, Real.hasStrictDerivAt_rpow_const, Field.Emb.Cardinal.adjoin_basis_eq_top, ContinuousLinearMap.postcompUniformConvergenceCLM_apply, VectorField.lieBracket_smul_right, NumberField.ComplexEmbedding.IsReal.isConjGal_one, HasFDerivAtFilter.restrictScalars, RCLike.normSq_apply, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, NumberField.ComplexEmbedding.conjugate_coe_eq, NumberField.Embeddings.range_eval_eq_rootSet_minpoly, Finset.subConst_empty_left, Ideal.algebraMap_residueField_eq_zero, LinearMap.flip_surjective_iff₂, IntermediateField.adjoin_eq_adjoin_pow_expChar_of_isSeparable', CurveIntegrable.sub, HasFiniteFPowerSeriesOnBall.fderiv_eq, smul_closedBall, ContMDiffOn.smul, NumberField.ComplexEmbedding.lift_algebraMap_apply, IntermediateField.iInf_toSubalgebra, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, NumberField.InfiniteAdeleRing.ringEquiv_mixedSpace_apply, IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton, IsGaloisGroup.card_fixingSubgroup_eq_finrank, IntermediateField.normalClosure_map_eq, Complex.hasDerivAt_log_sub_logTaylor, hasStrictDerivAt_iff_hasStrictFDerivAt, UniformConvergenceCLM.instContinuousSemilinearMapClass, ContinuousLinearEquiv.comp_contDiffAt_iff, WeierstrassCurve.j_of_isShortNF, WithSeminorms.isVonNBounded_iff_seminorm_bounded, ContinuousAlternatingMap.hasFDerivAt, WithAbs.instIsSeparable, FormalMultilinearSeries.summable, HasFPowerSeriesAt.locally_zero_iff, hasDerivAt_iff_tendsto_slope, intervalIntegral.fderiv_integral, PiTensorProduct.mapL_add, Lagrange.eval_basis_self, fderiv_fun_const, ContinuousLinearMap.analyticAt_bilinear, inner_gradient_left, eventually_norm_trivializationAt_lt, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_left, TensorProduct.congrIsometry_apply, IntermediateField.relrank_bot_left, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff', Complex.ofReal_nnqsmul, ConvexOn.exists_affine_le_of_lt, HasFPowerSeriesAt.hasStrictFDerivAt, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, ModelWithCorners.uniqueDiffOn_preimage_source, MvPowerSeries.mul_inv_rev, MeasureTheory.integral_prod_smul, ContinuousLinearMap.toPointwiseConvergenceCLM_apply, LaurentSeries.mem_integers_of_powerSeries, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, Ideal.bijective_algebraMap_quotient_residueField, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, Polynomial.IsPrimitive.isUnit_iff_isUnit_map, algebraMap_galRestrict'_apply, isBoundedLinearMap_continuousMultilinearMap_comp_linear, Numbering.dens_prefixed, RingOfIntegers.coe_algebraMap_norm, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, innerSL_apply_coe, differentiableOn_finCons, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, hasDerivAt_exp_of_mem_ball, AffineSubspace.sSameSide_smul_vsub_vadd_left, ContinuousLinearMap.bound, hasStrictDerivAt_exp_smul_const_of_mem_ball, MeasureTheory.eLpNorm_le_eLpNorm_fderiv, NumberField.mixedEmbedding.convexBodySum_volume, Polynomial.IsSplittingField.IsScalarTower.splits, ContMDiff.const_smul_section, tendsto_algebraMap_inv_atTop_nhds_zero_nat, ContinuousLinearMap.isPositive_one, Finset.dens_union_le, Polynomial.monic_annIdealGenerator, IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletion, LieModule.Weight.toLinear_neg, ContinuousLinearMap.isPositive_sum, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, RatFunc.algebraMap_monomial, Real.hasDerivAt_Gamma_nat, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, Polynomial.hilbertPoly_zero_right, HasStrictFDerivAt.inner, WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero, Height.AdmissibleAbsValues.product_formula, galRestrictHom_apply, RatFunc.denom_dvd, Algebra.Etale.iff_exists_algEquiv_prod, ZSpan.fract_eq_fract, HasMFDerivAt.comp, hasDerivAt_pi, ContinuousLinearMap.toUniformConvergenceCLM_symm_apply, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, derivWithin_fun_inv', Lagrange.natDegree_basis, Meromorphic.fun_pow, hasFDerivAt_inv', LinearMap.toMatrix_adjoint, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Algebra.IsAlgebraic.bijective_of_isScalarTower, hasDerivWithinAt_finCons, Finset.expect_eq_sum_div_card, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, IntermediateField.le_normalClosure, CFC.abs_smul, Subspace.map_dualCoannihilator, FormalMultilinearSeries.rightInv_coeff, Meromorphic.smul, OpenPartialHomeomorph.unitBallBall_symm_apply, hasDerivAt_zpow, ContinuousLinearMapWOT.instContinuousLinearMapClass, MeasureTheory.AEStronglyMeasurable.convolution_integrand', FormalMultilinearSeries.summable_norm_apply, FDRep.scalar_product_char_eq_finrank_equivariant, ContinuousMultilinearMap.norm_constOfIsEmpty, uniqueDiffOn_extChartAt_target, cfcₙHom_of_cfcHom_map_quasispectrum, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, IntermediateField.equivOfEq_trans, mfderiv_neg, VectorBundle.pullback, convexOn_zpow, hasFDerivWithinAt_of_subsingleton, WeierstrassCurve.Jacobian.equation_of_Z_ne_zero, Polynomial.annIdealGenerator_eq_zero_iff, isClosedMap_smul_left, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, ContinuousLinearMap.integral_comp_comm, hasFDerivWithinAt_iff_tendsto, FormalMultilinearSeries.compAlongOrderedFinpartition_apply, IntermediateField.normalClosure_def', LinearMap.im_inner_adjoint_mul_self_eq_zero, Valuation.HasExtension.coe_algebraMap_valuationSubring_eq, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, ValuationSubring.algebraMap_injective, fderiv_pi, ContinuousLinearMapWOT.sub_apply, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', autAdjoinRootXPowSubC_root, ContinuousLinearMap.map_neg₂, Matrix.l2_opNorm_def, IsAlgClosed.surjective_restrictDomain_of_isAlgebraic, EuclideanGeometry.Sphere.secondInter_map, PowerSeries.Inv_divided_by_X_pow_order_rightInv, OrthogonalFamily.linearIsometry_apply, ContinuousMultilinearMap.le_opNNNorm, HasFiniteFPowerSeriesOnBall.sub, Ideal.ResidueField.liftₐ_algebraMap, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Bornology.isVonNBounded_singleton, Matrix.toEuclideanLin_toLp, ModuleCat.isScalarTower_of_algebra_moduleCat, IsDedekindDomain.HeightOneSpectrum.adicCompletion.mul_nonZeroDivisor_mem_adicCompletionIntegers, IntermediateField.mem_bot, nnnorm_cfcₙ_le, ZMod.euler_criterion, NumberField.hermiteTheorem.rank_le_rankOfDiscrBdd, ContinuousLinearMapWOT.continuous_dual_apply, continuous_stereoInvFun, ContinuousLinearMap.iteratedFDeriv_comp_left, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center, Submodule.orthogonalProjection_eq_zero_iff, ContinuousLinearMap.holderL_apply_apply, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, StrongDual.mem_polar_singleton, FormalMultilinearSeries.comp_rightInv_aux2, ZSpan.coe_fract_self, AddChar.expect_apply_eq_ite, IntermediateField.adjoin_algebraic_toSubalgebra, Field.sepDegree_le_rank, ContinuousMultilinearMap.opNorm_prod, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, Asymptotics.isLittleOTVS_insert, Real.hasDerivAt_sinh, FractionalIdeal.finprod_heightOneSpectrum_factorization_principal_fraction, isClosedEmbedding_smul_left, MeasureTheory.condExpL1CLM_smul, isConformalMap_const_smul, add_div_two_lt_right, wbtw_midpoint, hasDerivWithinAt_iff_tendsto_slope', MeasureTheory.AEStronglyMeasurable.convolution_integrand, Complex.norm_fderiv_le_div_of_mapsTo_ball, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1, norm_innerSL_le, MeromorphicAt.smul, Algebra.QuasiFinite.instIsArtinianRingFiber, AffineSubspace.subtypeₐᵢ_toAffineMap, IsFractionRing.num_mul_den_eq_num_iff_eq', IntermediateField.mem_restrict, HasStrictFDerivAt.sub, OrthonormalBasis.measurePreserving_measurableEquiv, IsDedekindDomain.integer_univ, ContinuousLinearMap.isLeast_opNorm, fderiv_const_smul_of_field, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, ContinuousLinearMap.IsPositive.isSelfAdjoint, spectrum.map_pow_of_pos, HasLineDerivAt.smul, MvPolynomial.isAlgebraic_of_mem_vars_of_forall_totalDegree_le, OrthonormalBasis.sum_repr', Finset.expect_ite_eq, continuousMultilinearCurryRightEquiv_apply, Valuation.leSubmodule_comap_algebraMap_eq_leIdeal, Seminorm.convex_closedBall, hasStrictFDerivAt_intCast, Submodule.coe_orthogonalProjection_apply, ContinuousLinearMap.integrable_of_bilin_of_bdd_right, NumberField.Units.dirichletUnitTheorem.exists_unit, Submodule.starProjection_coe_eq_isCompl_projection, IsLocalDiffeomorphAt.mfderivToContinuousLinearEquiv_coe, HasFDerivAt.neg, ContDiffMapSupportedIn.structureMapLM_zero_apply, ContinuousMap.idealOfSet_ofIdeal_isClosed, RCLike.ofRealAm_coe, Matrix.linearIndependent_cols_of_invertible, RCLike.normSq_one, LinearMap.BilinForm.isAdjointPairLeftAdjointOfNondegenerate, LinearMap.injective_iff_antilipschitz, AffineIndependent.convexHull_inter, ContinuousAlternatingMap.prodLIE_symm_apply, analyticOrderAt_smul_eq_top_of_right, fderiv_comp_deriv_of_eq, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_apply, Polynomial.monic_normalize, Polynomial.map_dvd_map', DifferentiableOn.hasDerivAt, ContinuousLinearMapWOT.instContinuousNeg, Bornology.sUnion_isVonNBounded_eq_univ, ArchimedeanClass.FiniteElement.mk_natCast, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ContinuousLinearMap.apply_apply', HasFPowerSeriesWithinAt.hasFDerivWithinAt, NumberField.ComplexEmbedding.isConj_one_iff, PowerSeries.smul_inv, Finset.divConst_empty_right, LinearIsometryEquiv.norm_iteratedFDeriv_comp_left, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, IntermediateField.LinearDisjoint.isDomain, PosSMulMono.toPosSMulReflectLE, tendsto_pow_atTop_nhds_zero_iff, ContDiff.fderiv, Submodule.starProjection_apply_eq_zero_iff, ContMDiffAt.smul_section, fderiv_list_prod', SchwartzMap.fourier_convolution, HasMFDerivWithinAt.prod, AnalyticOnNhd.eval_continuousLinearMap', IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int, ConvexOn.hasDerivWithinAt_leftDeriv_of_mem_interior, Module.Basis.norm_repr_le_norm, PadicInt.coe_dpow_eq, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, IntermediateField.finrank_dvd_of_le_right, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, Orthonormal.inner_right_fintype, HasMFDerivAt.mul', ContinuousLinearMap.flipₗᵢ_symm, ImplicitFunctionData.rightDeriv_fderiv_implicitFunction, Asymptotics.IsBigOTVS.refl, two_mul_le_add_mul_sq, NumberField.InfinitePlace.comap_surjective, WeierstrassCurve.Jacobian.add_of_Z_eq_zero, Asymptotics.isTheta_const_smul_right, HasFDerivAt.star_star, ContinuousLinearMap.postcomp_uniformConvergenceCLM_apply, ZMod.orderOf_units_dvd_card_sub_one, IsGalois.splits, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, hasDerivAt_of_tendsto_locally_uniformly_on', Polynomial.resultant_eq_zero_iff, NumberField.InfinitePlace.card_complex_embeddings, HasGradientWithinAt.hasFDerivWithinAt, ContinuousLinearMap.dist_le_opNorm, FormalMultilinearSeries.rightInv_coeff_one, IntermediateField.fixingSubgroup_bot, hasFDerivAt_exp, ContinuousAlternatingMap.opNNNorm_prod, IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expChar, IsAlgClosed.splits_domain, mfderivWithin_id, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Pi.orthonormalBasis_repr, CyclotomicRing.eq_adjoin_primitive_root, Polynomial.hasDerivWithinAt, ZSpan.mem_fundamentalDomain, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, uniqueDiffWithinAt_extChartAt_target, IntermediateField.finrank_le_of_le_right, ApproximatesLinearOn.lipschitzOnWith, Polynomial.mod_def, norm_fderiv_norm_id_rpow, ContinuousLinearMap.isBigOTVS_id, LinearMap.isAdjointPair_inner, MeasureTheory.condExpIndL1Fin_smul', LinearMap.IsPositive.adjoint_conj, ContinuousLinearMap.norm_holder_apply_apply_le, Polynomial.Gal.card_of_separable, LinearMap.isPositive_one, Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iff, Finset.Nonempty.dens_pos, mfderivWithin_sumSwap, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Affine.Simplex.affineSpan_pair_eq_altitude_iff, LinearMap.orthogonal_span_singleton_eq_to_lin_ker, Polynomial.pairwise_coprime_X_sub_C, Matrix.sub_scalar_sq_eq_discr, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, absorbent_ball_zero, SMulCommClass.nnrat', ContinuousAlternatingMap.continuous_toContinuousMultilinearMap, Submodule.norm_subtypeL_le, RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_u, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, IsUltrametricDist.isPowMul_invariantExtension, isGalois_bot, hasDerivWithinAt_iff_tendsto_slope, fderiv_const_smul, hasFDerivAtFilter_pi', measurable_fderiv_apply_const_with_param, constFormalMultilinearSeries_apply_succ, IntermediateField.mem_fixingSubgroup_iff, FormalMultilinearSeries.continuousOn, Polynomial.natSepDegree_X_pow, hasFDerivAt_inv, IntermediateField.intermediateFieldMap_symm_apply_coe, mfderiv_prod_left, IntermediateField.finrank_dvd_of_le_left, Affine.Simplex.direction_altitude, LinearIsometryEquiv.symm_lTensor, ContinuousLinearMap.coe_ofIsClosedGraph, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, DoubleCentralizer.toProdHom_apply, ContinuousAlternatingMap.enorm_toContinuousMultilinearMap, NNRat.cast_le_ofNat, Submodule.isOrtho_bot_left, ContinuousMultilinearMap.isUniformInducing_toUniformOnFun, LieAlgebra.IsKilling.mem_sl2SubalgebraOfRoot_iff, NumberField.mixedEmbedding.norm_unit, algebraMap_galRestrictHom_apply, Algebra.prod_embeddings_eq_finrank_pow, DoubleCentralizer.mul_snd, HasFDerivWithinAt.comp_hasFDerivAt, hasMFDerivWithinAt_inl, ContinuousLinearMap.fpowerSeries_apply_one, IntermediateField.map_id, fderiv_continuousLinearEquiv_comp', Finset.nnratCast_dens_mul_natCast_card, ContinuousLinearMap.smulRightL_apply_apply, continuousOn_clm_apply, logDeriv_pow, Set.Finite.convexHull_eq, Real.hasDerivAt_sqrt, ContinuousLinearMapWOT.ContinuousLinearMap.continuous_toWOT, LinearMap.range_smul, SchwartzMap.one_add_le_sup_seminorm_apply, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, HasFDerivAt.fun_mul', Seminorm.continuous_iff_continuous_comp, Hyperreal.stdPart_epsilon, minpoly.eq_X_sub_C, constFormalMultilinearSeries_zero, Polynomial.SplittingField.adjoin_rootSet, OpenPartialHomeomorph.unitBallBall_apply, isSplittingField_iff_intermediateField, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, ContinuousMultilinearMap.instIsTopologicalAddGroup, half_le_self_iff, Asymptotics.IsBigO.isBigOTVS, IsScalarTower.nnrat, LinearPMap.adjointAux_inner, HasStrictFDerivAt.mul_const, Asymptotics.isLittleOTVS_neg_left, Real.hasDerivWithinAt_arccos_Iic, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, ContDiffBump.convolution_tendsto_right_of_continuous, LinearIsometryEquiv.toContinuousLinearEquiv_smul, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, FractionalIdeal.den_mem_inv, NumberField.ComplexEmbedding.IsConj.isUnramified_mk_iff, ContinuousMultilinearMap.norm_compContinuousLinearMap_le, Lagrange.nodal_erase_eq_nodal_div, ContinuousLinearMap.opNNNorm_mul_apply, AbsoluteValue.isEquiv_iff_isHomeomorph, isGalois_iff_isGalois_bot, eventually_norm_mfderiv_extChartAt_lt, ContinuousMultilinearMap.curryFinFinset_apply, InfiniteGalois.fixingSubgroup_isClosed, IsSepClosed.surjective_restrictDomain_of_isSeparable, EuclideanGeometry.orthogonalProjection_eq_iff_mem, NormedField.nhdsWithin_isUnit_neBot, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, Submodule.le_traceDual_iff_map_le_one, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, OrderedFinpartition.applyOrderedFinpartition_update_right, ConjRootClass.irreducible_minpoly, FiniteField.algebraMap_norm_eq_pow_sum, eq_midpoint_of_dist_eq_half, Field.insepDegree_le_of_left_le, IntermediateField.finiteDimensional_adjoin_pair, IsLocalRing.instIsScalarTowerResidueField, IsLocalRing.ResidueField.lift_residue_apply, MvPowerSeries.smul_inv, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, Ideal.finite_mulSupport_inv, VectorBundleCore.coordChange_comp, SchwartzMap.denseRange_toLpCLM, IntermediateField.normal_sup, IsAlgClosed.associated_iff_roots_eq_roots, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_eq_one_iff, hasFDerivAt_fst, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, Asymptotics.isLittleOTVS_sup, wbtw_smul_vadd_smul_vadd_of_nonpos_of_le, IntermediateField.coe_algebraMap_apply, mfderiv_comp_mfderivWithin_of_eq, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, LinearMap.IsSymmetric.coe_re_inner_apply_self, SchwartzMap.integrable_pow_mul_iteratedFDeriv, FormalMultilinearSeries.radius_eq_liminf, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, NumberField.IsCMField.complexConj_torsion, Polynomial.residueFieldMapCAlgEquiv_algebraMap, HasFTaylorSeriesUpToOn.restrictScalars, starConvex_iff_div, ContinuousLinearMap.apply_apply, ContinuousLinearEquiv.comp_differentiableWithinAt_iff, Submodule.traceDual_top, Asymptotics.isThetaTVS_iff_isTheta, hasFDerivAt_pi', ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnits_comp_quotientGroup_mk, RatFunc.toFractionRingAlgEquiv_apply, OrthogonalFamily.summable_iff_norm_sq_summable, ContinuousLinearMap.norm_map_removeNth_le, Module.End.exists_isNilpotent_isSemisimple, Polynomial.isCoprime_iff_aeval_ne_zero, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, LieModule.range_traceForm_le_span_weight, iteratedFDeriv_neg, separableClosure.isGalois, Real.fourierIntegral_continuousMultilinearMap_apply', ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, IsSymmSndFDerivWithinAt.eq, ContinuousLinearMap.map_smulₛₗ₂, CurveIntegrable.add, Asymptotics.superpolynomialDecay_param_pow_mul_iff, geom₂_sum_of_gt, PiTensorProduct.mapLMultilinear_opNorm, hasDerivWithinAt_inter, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, ContinuousMultilinearMap.norm_image_sub_le', hasFPowerSeriesAt_iff', NumberField.InfinitePlace.apply, LinearMap.canLiftContinuousLinearMap, LinearIsometryEquiv.differentiableOn, RCLike.geometric_hahn_banach_closed_compact, WeierstrassCurve.Jacobian.isUnit_addZ_of_X_ne, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, inner_gradient_right, hasDerivAt_exp_smul_const_of_mem_ball, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, IntermediateField.restrictScalars_adjoin, hasStrictDerivAt_exp_zero, Transcendental.linearIndependent_sub_inv, NonUnitalCStarAlgebra.toSMulCommClass, Submodule.orthogonalProjection_norm_le, HasFDerivAt.mul', NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_add_le_max, DoubleCentralizer.intCast_toProd, Matrix.PosDef.posDef_sqrt, IntermediateField.finrank_adjoin_simple_eq_one_iff, Function.HasTemperateGrowth.isBigO_uniform, differentiableOn_snd, norm_cfcₙ_le_iff, iteratedFDerivWithin_zero_apply, EuclideanSpace.volume_closedBall, FiniteField.natCard_algEquiv_extension, FractionalIdeal.coe_mk0, ClassGroup.mk_def, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, fderiv_single, IsSepClosed.exists_aeval_eq_zero, ContinuousMap.idealOfSet_ofIdeal_eq_closure, finrank_euclideanSpace_fin, ValuationSubring.coe_unitGroupToResidueFieldUnits_apply, Submodule.orthogonalProjection_orthogonal, Set.Finite.isVonNBounded, slope_def_module, Real.hasStrictDerivAt_exp, openSegment_subset_union, Nat.cast_inv_le_one, LinearMap.finrank_eigenspace_le, ContinuousLinearEquiv.arrowCongrSL_toLinearEquiv_symm_apply, Algebra.finite_of_essFiniteType_of_isAlgebraic, algebraMap.coe_zpow, inv_eq_of_aeval_divX_ne_zero, Height.logHeight_pow, le_egauge_closedBall_one, hasFDerivAt_list_prod_attach', Polynomial.isRoot_of_isRoot_iff_dvd_derivative_mul, instSubsingletonAlgHomOfIsPurelyInseparable, Polynomial.IsSplittingField.map, MonoidWithZeroHomClass.ext_nnrat_iff, MeasureTheory.AEStronglyMeasurable.convolution_integrand_swap_snd, LinearIsometryEquiv.rTensor_def, MeasureTheory.norm_condExpL2_le_one, ContinuousLinearEquiv.mdifferentiableAt, HasCompactSupport.convolution_integrand_bound_right, ValuationSubring.coe_subtype, MeromorphicAt.meromorphicTrailingCoeffAt_pow, bddAbove_smul_iff_of_neg, LinearMap.mem_span_iff_continuous, HasFPowerSeriesWithinOnBall.hasFDerivWithinAt, fderivWithin_mem_iff, Padic.isDenseInducing_cast_withVal, Ideal.Fiber.exists_smul_eq_one_tmul, UniqueMDiffOn.uniqueDiffWithinAt_range_inter, AddChar.inv_apply_eq_conj, Valuation.HasExtension.algebraMap_residue_eq_residue_algebraMap, Asymptotics.isBigOTVS_comm, DifferentiableAt.lineDeriv_eq_fderiv, OrthonormalBasis.repr_reindex, Ideal.ResidueField.mapₐ_apply, normalClosure.is_finiteDimensional, ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply, NNRat.cast_lt_ofNat, Nat.one_div_lt_one_div, MeasureTheory.condExpL2_comp_continuousLinearMap, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, FormalMultilinearSeries.ofScalars_norm_eq_mul, isBoundedBilinearMap_smulRight, inCoordinates_tangent_bundle_core_model_space, isOpen_setOf_linearIndependent, NormedSpace.expSeries_hasSum_exp_of_mem_ball, LinearIsometryEquiv.differentiableWithinAt, Polynomial.separable_map, IntermediateField.finiteDimensional_sup, IntermediateField.Lifts.le_iff, VectorBundle.prod, Algebra.normalizedTrace_self_apply, AnalyticOnNhd.eval_continuousLinearMap, Finset.card_mul_cast_divConst, hasStrictFDerivAt_pi, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_sup_left, Polynomial.normalizedFactors_cyclotomic_card, ContinuousLinearMap.adjoint_innerSL_apply, NumberField.InfinitePlace.comap_embedding_of_isReal, ZLattice.coe_comap, LSeries.hasDerivAt_term, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, Valuation.Integers.bijective_algebraMap_of_subsingleton_units_mrange, Submodule.IsOrtho.comap, hasFDerivAt_iff_isLittleO_nhds_zero, Finset.expect_ite_eq', LinearMap.BilinForm.isCompl_orthogonal_of_restrict_nondegenerate, OrthogonalFamily.inner_right_fintype, Finset.dens_univ, geom_sum_Ico_le_of_lt_one, Finset.cast_addConst, Asymptotics.isLittleO_pow_pow_atTop_of_lt, Valuation.coeff_zero_minpoly, ContDiffMapSupportedIn.structureMapLM_apply, RatFunc.map_apply_div_ne_zero, Finset.mulConst_le_divConst_sq, RCLike.normSq_sub, trace_adjoinSimpleGen, IntermediateField.fixingSubgroup_sup, ContinuousLinearMap.coprodEquivL_symm_apply, VectorPrebundle.contMDiffCoordChange_apply, isBoundedLinearMap_prod_multilinear, AlgEquiv.eq_linearEquivConjAlgEquiv, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Orthonormal.inner_sum, differentiableWithinAt_fst, IntermediateField.normal_iff_normalClosure_eq, EuclideanGeometry.reflection_apply, continuousOn_coordChange, HasCompactSupport.convolution_integrand_bound_right_of_subset, LinearIsometryEquiv.comp_fderiv', IntermediateField.rank_adjoin_simple_eq_one_iff, Polynomial.coeff_preHilbertPoly_self, LinearPMap.adjoint_apply_of_dense, PadicInt.val_toZMod_eq_zmodRepr, HasStrictDerivAt_ofNat, Real.fourier_smul_convolution_eq, IsSepClosed.exists_eval₂_eq_zero, NNRat.preimage_cast_Iio, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, DoubleCentralizer.smul_snd, RCLike.wInner_cWeight_eq_smul_wInner_one, inverse_mfderiv_add_left, postcomp_compactConvergenceCLM_apply, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, HasFiniteFPowerSeriesAt.comp, NumberField.ComplexEmbedding.orderOf_isConj_two_of_ne_one, ContinuousMap.idealOfSet_isMaximal_iff, IntermediateField.AdjoinPair.algebraMap_gen₂, ContinuousLinearMap.integral_id_map, hasDerivWithinAt_iff_tendsto, NNRat.ofNat_lt_cast, PrimeSpectrum.nontrivial_iff_mem_rangeComap, MeasureTheory.condExpL2_const_inner, NumberField.house.basis_repr_norm_le_const_mul_house, balancedHull_convexHull_subseteq_absConvexHull, curveIntegrable_restrictScalars_iff, LinearMap.IsSymmetric.intCast, SpectrumRestricts.nnreal_iff_nnnorm, cyclotomicCharacter.continuous, IsCoercive.isClosed_range, Submodule.mem_traceDual_iff_isIntegral, LieAlgebra.IsKilling.rootSystem_root_apply, NumberField.IsCMField.Units.complexConj_eq_self_iff, ContinuousLinearMap.toWOT_apply, Polynomial.IsPrimitive.dvd_iff_fraction_map_dvd_fraction_map, IntermediateField.isIntegral_iff, Subfield.toIsStrictOrderedRing, mem_contMDiffFiberwiseLinear_iff, RatFunc.denom_zero, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, curveIntegralFun_def, ArchimedeanClass.FiniteResidueField.instIsOrderedRing, Submodule.coe_prodEquivOfClosedCompl, left_lt_add_div_two, IsDedekindDomain.HeightOneSpectrum.adicAbv_coe_lt_one_iff, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, ContinuousLinearMap.intervalIntegral_comp_comm, hasDerivAt_finCons, Asymptotics.IsThetaTVS.rfl, inner_eq_ofReal_norm_sq_right_iff, HasFDerivAt.smul, Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, homothety_one_half, RatFunc.associated_denom_inv, ContinuousLinearMap.contMDiffAt, IsLocalRing.residue_surjective, isOpen_setOf_nat_le_rank, FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin, SchwartzMap.smulLeftCLM_smul, CurveIntegrable.neg, PadicInt.toZMod_spec, isClosed_setOf_isCompactOperator, DoubleCentralizer.coe_snd, ContinuousMultilinearMap.fin0_apply_norm, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, Algebra.botEquiv_symm_apply, WeierstrassCurve.Projective.isUnit_addZ_of_X_ne, tendsto_nhdsGT_zero_of_comp_inv_tendsto_atTop, MeasureTheory.integral_convolution, ValuationSubring.principalUnitGroup_injective, contractLeft_assoc_coevaluation', Int.clog_zero_right, ContinuousLinearMap.le_opNorm_enorm, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum, fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, DivisibleHull.nnqsmul_mk, separableClosure.normalClosure_eq_self, fderiv_sin, ArchimedeanClass.mk_inv, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, hasStrictDerivAt_pow, Projectivization.Subspace.mem_submodule_iff, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, IsAlgClosed.dvd_iff_roots_le_roots, OrthonormalBasis.tensorProduct_repr_tmul_apply, Derivation.evalAt_apply, IntermediateField.coe_map, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, TrivSqZeroExt.snd_expSeries_of_smul_comm, ContinuousMultilinearMap.norm_curryMid, ConvexOn.univ_sSup_of_nat_affine_eq, AddChar.expect_eq_ite, NNRat.cast_mul_of_ne_zero, ContinuousLinearEquiv.comp_right_differentiable_iff, convexHull_range_eq_exists_affineCombination, LinearMap.trace_map, ContinuousAlternatingMap.ratio_le_opNorm, WeierstrassCurve.j_of_isCharThreeJNeZeroNF_of_char_three, IntermediateField.adjoin.powerBasis_dim, TensorProduct.assocIsometry_symm_apply, hasFDerivAt_exp_of_mem_ball, LaurentSeries.valuation_X_pow, InnerProductSpace.gramSchmidt_mem_span, SimpContFract.determinant_aux, ModelWithCorners.uniqueDiffOn, norm_iteratedFDeriv_fderiv, NormedSpace.dual_def, LinearMap.IsSymmetric.add, HasFDerivAtFilter.hasDerivAtFilter, NumberField.house_eq_sup', TensorProduct.inner_map_map, IsGalois.of_fixedField_normal_subgroup, RCLike.geometric_hahn_banach_open_open, IntermediateField.Lifts.nonempty_algHom_of_exist_lifts_finset, Polynomial.residueFieldMapCAlgEquiv_symm_C, const_smul_mfderiv, fderiv_norm_sq, Filter.EventuallyEq.hasDerivAtFilter_iff, instProperSpaceSubtypeMemSubmoduleOfCompleteSpaceOfLocallyCompactSpace, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, IntermediateField.essFiniteType_iff, Field.Emb.cardinal_separableClosure, HasMFDerivAt.const_smul, IntermediateField.AdjoinSimple.algebraMap_gen, Valuation.Integers.dvd_iff_le, Subspace.finrank_add_finrank_dualAnnihilator_eq, Lagrange.interpolate_singleton, Complex.ofReal_choose, IntermediateField.isPurelyInseparable_sup, Polynomial.isCoprime_iff_aeval_ne_zero_of_isAlgClosed, TensorProduct.toLinearMap_mapInclIsometry, NonUnitalCommCStarAlgebra.toIsScalarTower, mfderivWithin_snd, Function.HasTemperateGrowth.isBigO, Polynomial.eventually_no_roots, NumberField.FinitePlace.norm_def, FormalMultilinearSeries.hasFPowerSeriesOnBall, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_adj, ContinuousLinearMap.coe_mulₗᵢ, OrthogonalFamily.inner_right_dfinsupp, ContinuousLinearMap.isUnit_iff_bijective, NumberField.mixedEmbedding.convexBodySum_mem, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', ClassGroup.equiv_mk, PowerSeries.X_eq_normalizeX, Real.smul_iInf_of_nonneg, UniqueDiffWithinAt.of_real, orthonormal_span, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, ContinuousLinearMap.innerSL_apply_comp, conformalAt_iff', TensorProduct.lidIsometry_symm_apply, ContinuousLinearMap.instStarOrderedRingRCLike, surjective_stereographic, Representation.isSemisimpleModule_iff_isSemisimpleRepresentation_ofModule, ContinuousLinearMap.mdifferentiableAt, NonnegSpectrumClass.iff_spectrum_nonneg, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, MeasureTheory.AEStronglyMeasurable.convolution_integrand_snd, Matrix.mulVec_injective_iff_isUnit, hasDerivAt_abs_pos, ContinuousAlternatingMap.instContinuousEvalConst, PiTensorProduct.injectiveSeminorm_def, ContinuousLinearMap.coeFn_holder, NNRat.castOrderEmbedding_apply, ContDiffMapSupportedIn.structureMapLM_eq, hasStrictFDerivAt_id, HilbertBasis.hasSum_repr_symm, PosSMulStrictMono.toPosSMulReflectLT, ContinuousAlternatingMap.norm_image_sub_le, IsGalois.mem_bot_iff_fixed, hasStrictFDerivAt_sub_const, ContinuousLinearMap.coe_deriv₂, IsDedekindDomain.selmerGroup.valuation_ker_eq, IsMIntegralCurveAt.eventually_hasDerivAt, ContinuousLinearEquiv.symm_conjContinuousAlgEquiv_apply_apply, IsAlgClosed.exists_aeval_eq_zero, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, hasFDerivAt_stereoInvFunAux_comp_coe, LinearIsometryEquiv.comp_hasStrictFDerivAt_iff, LinearMap.adjoint_id, inner_smul_left, contDiff_succ_iff_hasFDerivAt, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, mfderiv_prod_eq_add_apply, LieAlgebra.IsKilling.coe_corootSpace_eq_span_singleton, FiniteField.finrank_extension, Matrix.linearIndependent_rows_iff_isUnit, ValuationSubring.principalUnitGroup_symm_apply, MeasureTheory.condExpL2_indicator_nonneg, ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, PadicInt.coe_pow, Submodule.coe_prodEquivOfClosedCompl_symm, DoubleCentralizer.add_toProd, PowerSeries.inv_mul_cancel, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, IntermediateField.algebra_adjoin_le_adjoin, HasFDerivWithinAt.sum, TemperedDistribution.smulLeftCLM_apply_apply, X_pow_sub_C_irreducible_iff_of_prime, FractionalIdeal.finprod_heightOneSpectrum_factorization', IsPurelyInseparable.algebraMap_iterateFrobeniusₛₗ, selfAdjoint.val_nnqsmul, Subspace.dualPairing_eq, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, hasFDerivAt_pi, NumberField.InfinitePlace.IsUnramified.comap, wbtw_smul_vadd_smul_vadd_of_nonneg_of_nonpos, mfderivWithin_comp, Polynomial.map_normalize, fderiv_inner_apply, RatFunc.algebraMap_comp_C, differentiableOn_fst, AffineIsometryEquiv.pointReflection_midpoint_right, hasFDerivWithinAt_snd, Icc_subset_segment, IsBoundedLinearMap.isLinearMap_and_continuous_iff_isBoundedLinearMap, ContMDiff.coordChangeL, RatFunc.ofFractionRing_algebraMap, RatFunc.eval_algebraMap, Module.Basis.traceDual_injective, Submodule.map_smul, differentiableWithinAt_finCons, fderiv_const_apply, Real.hasStrictDerivAt_log_of_pos, FormalMultilinearSeries.ofScalars_norm, ContinuousMultilinearMap.norm_ofSubsingleton_id, IsPurelyInseparable.elemExponent_def, HasFDerivWithinAt.fun_mul, hasFTaylorSeriesUpToOn_pi, RCLike.normSq_conj, IsCyclotomicExtension.discr_prime_pow, NNRat.preimage_cast_uIoc, NNRat.subsingleton_ringHom, HasStrictFDerivAt.smul, ContinuousLinearMap.orthogonal_ker, AnalyticAt.hasStrictDerivAt, LinearMap.ker_smul, Nonneg.segment_eq_Icc, iter_deriv_pow, Asymptotics.IsThetaTVS.refl, ContinuousLinearMap.continuousAt_uncurry_of_multilinear, inv_add_inv, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, HasStrictFDerivAt.finset_prod, ContMDiff.smul_section, contDiffWithinAt_succ_iff_hasFDerivWithinAt, Filter.EventuallyEq.hasDerivWithinAt_iff, Asymptotics.IsBigO.hasFDerivAt, WeierstrassCurve.Jacobian.isUnit_addU_of_Y_ne, hasFDerivWithinAt_apply, SeminormFamily.basisSets_smul_left, ArchimedeanClass.stdPart_eq_sSup, InnerProductSpace.norm_rankOne, FixedPoints.minpoly.of_eval₂, Urysohns.CU.lim_eq_midpoint, HasFDerivAt.fun_sub, Complex.hasDerivAt_Gamma_nat, Subspace.dualEquivDual_apply, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two, ContMDiffMap.coeFnLinearMap_apply, Submodule.isHilbertSumOrthogonal, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, RCLike.inv_re, DoubleCentralizer.neg_fst, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, LinearMap.BilinForm.apply_dualBasis_right, PiTensorProduct.mapLMultilinear_toFun_apply, FunctionField.ringOfIntegers.not_isField, IsAlgClosed.ringHom_bijective_of_isIntegral, HasFiniteFPowerSeriesOnBall.fderiv, ContinuousLinearEquiv.norm_pos, HasFDerivAt.comp, real_inner_I_smul_self, LinearIsometry.lTensor_def, Hyperreal.archimedeanClassMk_epsilon_pos, Finset.dens_pos, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, Orthonormal.inner_right_sum, circleEquivGen_apply, cfcUnits_zpow, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff, IntermediateField.finite_of_fg_of_isAlgebraic, minpoly.isIntegrallyClosed_eq_field_fractions', ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, Algebra.traceMatrix_eq_embeddingsMatrixReindex_mul_trans, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Finset.nonneg_subConst, fderiv_eq_smul_deriv, unitary.inner_map_map, NNRat.cast_lt_zero, LinearMap.IsPositive.conj_adjoint, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Polynomial.IsSplittingField.finiteDimensional, LinearMap.ker_toContinuousLinearMap, IntermediateField.isScalarTower_mid, IntermediateField.finSepDegree_bot, ZLattice.comap_refl, hasStrictFDerivAt_exp_smul_const_of_mem_ball, exists_pos_right_iff_sameRay_and_ne_zero, Hyperreal.tendsto_atTop_iff, RCLike.norm_nnqsmul, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le, LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, LinearMap.IsSymmetric.pow, hasFDerivAt_prodMk_right, DoubleCentralizer.toProdMulOppositeHom_apply, IsGalois.ofDual_intermediateFieldEquivSubgroup_apply, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', ContinuousLinearMap.coeFn_compLp', gal_X_isSolvable, LinearMap.withSeminorms_induced, RatFunc.num_denom_neg, IsCyclotomicExtension.discr_prime_pow_ne_two', ContinuousLinearEquiv.mfderivWithin_eq, Finpartition.IsEquipartition.card_interedges_sparsePairs_le', MDifferentiableWithinAt.smul_section, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, degree_radical_le, ContMDiffOn.smul_section, curveIntegralFun_zero, perfectClosure.isPurelyInseparable, AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn, iteratedFDeriv_add_apply', hasFDerivAtFilter_intCast, iteratedFDeriv_succ_apply_left, Polynomial.valuation_X_eq_neg_one, IsSymmSndFDerivAt.eq, hasFDerivAtFilter_one, Submodule.orthogonalProjectionFn_mem, LinearMap.IsPositive.re_inner_nonneg_left, iteratedFDeriv_const_of_ne, IntermediateField.isSeparable_adjoin_iff_isSeparable, hasDerivWithinAt_sub_const_iff, AbsoluteValue.eq_trivial_of_isEquiv_trivial, Lagrange.eval_basis_not_at_node, ContinuousLinearMapWOT.zero_apply, LinearMap.range_lt_top_of_det_eq_zero, FDRep.finrank_hom_simple_simple, AffineSubspace.sOppSide_smul_vsub_vadd_right, HasFDerivWithinAt.list_prod', NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, prod_galRestrict_eq_norm, IsDedekindDomain.HeightOneSpectrum.adicAbv_of_mk', fderiv_inv', LinearMap.BilinForm.isCompl_span_singleton_orthogonal, IntermediateField.sepDegree_top, Module.Basis.traceDual_eq_iff, ContinuousLinearEquiv.contDiff, ContinuousLinearMapWOT.ext_inner_iff, ContinuousLinearMap.coeFn_ofIsClosedGraph, RatFunc.monic_denom, NormedSpace.exp_eq_expSeries_sum, ZMod.pow_div_two_eq_neg_one_or_one, Trivialization.localFrame_apply_of_mem_baseSet, Continuous.fderiv_one, GaloisField.splits_zmod_X_pow_sub_X, VectorField.mlieBracket_const_smul_right, norm_inner_div_norm_mul_norm_eq_one_iff, MeasureTheory.lpMeas.aestronglyMeasurable, IsLocalMinOn.fderivWithin_eq_zero, tendsto_zero_geometric_tsum_pnat, RCLike.geometric_hahn_banach_open_point, WeierstrassCurve.Affine.Point.map_id, FormalMultilinearSeries.comp_assoc, PiTensorProduct.tprodL_coe, ModelWithCorners.extChartAt_transContinuousLinearEquiv_target, HasFPowerSeriesWithinAt.comp, NNRat.cast_listSum, Submodule.mem_iff_norm_starProjection, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, Real.hasDerivAt_negMulLog, Localization.subalgebra.instIsFractionRingSubtypeMemSubalgebra, LinearMap.BilinForm.span_singleton_sup_orthogonal_eq_top, continuousMultilinearCurryFin1_apply, IsCoercive.antilipschitz, PiLp.hasStrictFDerivAt_toLp, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, LineDifferentiableAt.smul, hasFDerivWithinAt_id, Orthonormal.comp_linearIsometry, hasStrictFDerivAt_euclidean, LinearMap.dualAnnihilator_ker_eq_range_flip, hasFDerivAt_finset_prod, Hyperreal.coeRingHom_toFun, unitary.linearIsometryEquiv_coe_apply, HilbertBasis.finite_spans_dense, nnnorm_cfcₙ_lt, Trivialization.coordChangeL_prod, mfderiv_id, IntermediateField.extendScalars_le_extendScalars_iff, Fintype.expect_eq_sum_div_card, IntermediateField.coe_one, Finset.centerMass_mem_convexHull_of_nonpos, mfderivWithin_comp_of_eq
toInv 📖	CompOp	4 math math: zpow_neg', mul_inv_cancel, div_eq_mul_inv, inv_zero
toNNRatCast 📖	CompOp	2 math math: nnratCast_def, nnqsmul_def
zpow 📖	CompOp	3 math math: zpow_zero', zpow_neg', zpow_succ'

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
div_eq_mul_inv 📖	mathematical	—	toDiv NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring CommSemiring.toSemiring toCommSemiring toInv	—	—
inv_zero 📖	mathematical	—	toInv AddMonoid.toZero AddCommMonoid.toAddMonoid NonUnitalNonAssocSemiring.toAddCommMonoid NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring CommSemiring.toSemiring toCommSemiring	—	—
mul_inv_cancel 📖	mathematical	—	NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring CommSemiring.toSemiring toCommSemiring toInv Semiring.toOne	—	—
nnqsmul_def 📖	mathematical	—	nnqsmul NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring CommSemiring.toSemiring toCommSemiring NNRat.cast toNNRatCast	—	—
nnratCast_def 📖	mathematical	—	NNRat.cast toNNRatCast toDiv Semiring.toNatCast CommSemiring.toSemiring toCommSemiring NNRat.num NNRat.den	—	—
toNontrivial 📖	mathematical	—	Nontrivial	—	—
zpow_neg' 📖	mathematical	—	zpow toInv	—	—
zpow_succ' 📖	mathematical	—	zpow NonUnitalNonAssocSemiring.toMul NonUnitalSemiring.toNonUnitalNonAssocSemiring Semiring.toNonUnitalSemiring CommSemiring.toSemiring toCommSemiring	—	—
zpow_zero' 📖	mathematical	—	zpow Semiring.toOne CommSemiring.toSemiring toCommSemiring	—	—

(root)

Definitions

Name	Category	Theorems
DivisionSemiring 📖	CompData	—

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