toAddGroup 📖 | CompOp | 1713 mathmath: IsPrimitiveRoot.subOneIntegralPowerBasis_gen_prime, AffineSubspace.wOppSide_lineMap_right, QuaternionAlgebra.coe_sub, Num.cast_to_int, Int.ceil_lt_iff, sub_pow_eq_mul_pow_sub_pow_div_char_of_commute, minpoly_sub_algebraMap_splits, continuousOn_ceil, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two', AffineMap.lineMap_apply_module, Subgroup.isRegularAtInfty_iff, Lagrange.eval_iterate_derivative_eq_sum, Units.divp_sub, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_injective, RingHom.ker_evalRingHom, AddValuation.map_sub_swap, AffineMap.hasStrictDerivAt_lineMap, PadicInt.coe_sub, even_sub_one, Finset.affineCombination_vsub, AffineMap.lineMap_vsub_left, Matrix.invOf_fromBlocks₂₂_eq, abs_lt_of_sq_lt_sq, Polynomial.ascPochhammer_smeval_neg_eq_descPochhammer, PowerSeries.coeff_mul_one_sub_of_lt_order, Matrix.det_apply, strictConvexOn_iff_slope_strict_mono_adjacent, derivationToSquareZeroOfLift_apply, CauSeq.lt_irrefl, IsStarNormal.one_sub, selfAdjoint.val_div, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_apply, Int.cast_neg, MonomialOrder.monic_X_sub_C, sub_pow_expChar_pow_of_commute, Int.smul_one_eq_cast, ContinuousAffineMap.lineMap_apply', Valuation.isEquiv_iff_val_sub_one_lt_one, smooth_barycentric_coord, SimpleGraph.deleteFar_iff, SimpleGraph.lapMatrix_toLinearMap₂', exists_isIntegral_sub_of_isIntegralElem_of_mul_mem_range, sign_mul_self, CompleteOrthogonalIdempotents.pair_iff, GradedRing.GradeZero.isNoetherianRing, toIcoDiv_mul_sub_self, Matrix.add_mul_mul_invOf_mul_eq_one, IsPrimitiveRoot.zeta_sub_one_prime_of_two_pow, emultiplicity_sub_of_gt, Matrix.abs_det_reindex, ofBoolRing_sub, IsIdempotentElem.coe_compl, AffineMap.lineMap_linear, Lagrange.eval_interpolate_not_at_node', Ideal.toCotangent_eq, Nat.cast_descFactorial_two, Filter.Tendsto.lineMap, ConvexOn.monotoneOn_slope_lt, abs_sub_round, WeierstrassCurve.Projective.eval_polynomial, Finset.affineCombination_apply_eq_lineMap_sum, CentroidHom.toEnd_sub, IdealFilter.ringFilterBasis_sets, Finset.prod_one_sub_ordered, WeierstrassCurve.c_relation, curveIntegrable_segment, IsIdempotentElem.add_sub_mul, CauSeq.sup_inf_distrib_right, one_add_le_one_add_mul_one_sub, concaveOn_iff_slope_anti_adjacent, arithGeom_eq', SimpleGraph.DeleteFar.le_card_sub_card, right_lt_lineMap_iff_one_lt, Subfield.zsmul_mem, IsLprojection.Lnorm, AddCommGroup.intIsScalarTower, WeierstrassCurve.Affine.cyclic_sum_Y_mul_X_sub_X, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv, RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraCartanSubalgebra, CauSeq.inv_aux, zsmul_eq_mul, one_le_pow_mul_abs_eval_div, CategoryTheory.CatCenter.app_sub, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous_ne_zero, Polynomial.toFinsupp_zsmul, Quaternion.imI_sub, AffineMap.pi_lineMap_apply, FermatLastTheoremForThreeGen.Solution.lambda_sq_not_dvd_a_add_eta_sq_mul_b, pow_four_add_four_mul_pow_four', TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure, WeierstrassCurve.Projective.negY_eq, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_fromSpec, dist_sq_lineMap_lineMap_of_inner_eq_zero, Int.cast_abs, sub_pow_expChar_of_commute, QuaternionGroup.a_mul_xa, ArithmeticFunction.coe_moebius_mul_coe_zeta, RingHom.IsIntegralElem.sub, abs_dvd, Convex.lineMap_mem, QuaternionAlgebra.star_eq_two_re_sub, stdSimplexHomeomorphUnitInterval_symm_apply_coe, Matrix.abs_det_submatrix_equiv_equiv, abs_eq_iff_mul_self_eq, FermatLastTheoremForThreeGen.Solution.lambda_dvd_a_add_eta_sq_mul_b, Algebra.Generators.toAlgHom_ofComp_localizationAway, IsIdempotentElem.one_sub, Matrix.IsHermitian.fromBlocks₂₂, PowerSeries.invOneSubPow_inv_eq_one_sub_pow, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_preimage_basicOpen, WeierstrassCurve.ofJNe0Or1728_Δ, AlgebraicGeometry.Proj.pow_apply, Lagrange.leadingCoeff_basis, abs_smul, IsNilpotent.isUnit_sub_one, Int.ceil_div_ceil_inv_sub_one, IsCyclic.val_mulAutMulEquiv_apply, ArithmeticFunction.intCoe_one, WeakSpace.instIsTopologicalAddGroup, toIocMod_sub_self_eq_mul, geom₂_sum, IsAlgebraic.sub, AntivaryOn.sub_smul_sub_nonpos, abs_le_of_sq_le_sq, sbtw_iff_mem_image_Ioo_and_ne, toIcoDiv_sub_natCast_mul', StrictConcaveOn.slope_anti_adjacent, SetTheory.Game.birthday_sub_le, Algebra.Presentation.localizationAway_relation, Wbtw.right_mem_image_Ici_of_left_ne, WeierstrassCurve.Projective.addY_of_X_eq', Finset.affineCombinationLineMapWeights_apply_left, cross_cross, IsCoprime.abs_right_iff, IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two_pow, AffineMap.lineMap_rev_mem_affineSpan_pair, Order.pred_iterate, Matrix.transpose_eq_intCast, Matrix.det_vandermonde, Polynomial.Splits.eval_derivative, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_hom_apply_asIdeal, IsNilpotent.isNilpotent_exp_sub_one, same_sub_div, div_sub_same, AlgebraicGeometry.Proj.mul_apply, WeierstrassCurve.Jacobian.negAddY_eq, IsLocalRing.isUnit_or_isUnit_one_sub_self, ZNum.of_natCast, Int.floor_sub_one, HomogeneousLocalization.mk_zero, Subring.mk_eq_zero, lintegral_fderiv_lineMap_eq_edist, MvPolynomial.vars_sub_of_disjoint, Cubic.disc_eq_prod_three_roots, round_sub_intCast, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective, round_sub_one, toIcoDiv_sub_intCast_mul', AbsoluteValue.abs_abv_sub_le_abv_sub, CauSeq.sup_idem, Quaternion.imI_mul, CliffordAlgebra.contractRight_mul_ι, Valued.toUniformSpace_eq, Lagrange.eval_interpolate_not_at_node, AffineBasis.linear_eq_sumCoords, MonomialOrder.degree_sub_le, CauSeq.cauchy₂, SetTheory.PGame.quot_right_distrib_sub, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, sub_sq, self_sub_toIocMod_eq_mul, cfc_sub, Polynomial.abc, AffineSubspace.sOppSide_lineMap_left, euler_four_squares, Polynomial.map_sub_roots_sprod_eq_prod_map_eval, IsPrimitiveRoot.zeta_sub_one_prime_of_ne_two, lineMap_inv_two, LieModule.genWeightSpaceChain_def', CongruenceSubgroup.strictPeriods_Gamma0, Polynomial.Splits.eval_root_derivative, IsPrimitiveRoot.subOneIntegralPowerBasis_gen, HenselianLocalRing.is_henselian, Height.logHeight₁_sub_le, sub_inv_antitoneOn_Ioi, Subring.toAddSubgroup_mono, cfcₙ_sub, WeierstrassCurve.Jacobian.negY_eq, IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one', WeierstrassCurve.ofJNe0Or1728_c₄, abs_dvd_abs, ContinuousAffineMap.coe_lineMap_eq, toIocMod_sub_natCast_mul', dvd_sub_self_left, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.structurePresheafInCommRing_obj_carrier, MvPowerSeries.coeff_mul_right_one_sub_of_lt_weightedOrder, div_two_sub_self, AffineBasis.coord_apply_ne, FermatLastTheoremForThreeGen.lambda_pow_four_dvd_c_cube, IsPrimitiveRoot.prod_one_sub_pow_eq_order, Quaternion.mul_imK, Matrix.det_projVandermonde, Convex.mapsTo_lineMap, Matrix.fromBlocks_eq_of_invertible₁₁, IsPrimitiveRoot.pow_sub_one_eq_geom_sum_mul_geom_sum_inv_mul_pow_sub_one, Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence, jacobiSum_trivial_trivial, UInt8.toBitVec_zsmul, sum_eight_sq_mul_sum_eight_sq, Function.Antiperiodic.sub_int_mul_eq, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, pow_sub_one_mul_geom_sum_eq_pow_sub_one_mul_geom_sum, curveIntegralFun_segment, CauSeq.const_lt, coeff_minpolyDiv_sub_pow_mem_span, Ring.inverse_sub_inverse, Commute.geom_sum₂_mul, selfAdjoint.val_one, Set.Ioo.one_minus_pos, AddSubgroup.intCast_mem_zmultiples_one, Int.range_castAddHom, Nat.abs_cast, EuclideanDomain.mul_sub_div_left, Mathlib.Tactic.Linarith.sub_nonpos_of_le, IsIdempotentElem.one_sub_mul_self, ContinuousAffineMap.lineMap_toAffineMap, wbtw_lineMap_iff, IsAlgebraic.zsmul, nndist_right_lineMap, UInt64.toBitVec_zsmul, Quaternion.sub_imJ, CliffordAlgebra.changeFormAux_changeFormAux, CliffordAlgebra.ι_mul_ι_comm, SimpleGraph.farFromTriangleFree_iff, sbtw_iff_left_ne_and_right_mem_image_Ioi, Matrix.PosDef.fromBlocks₁₁, RingSubgroupsBasis.rightMul, AffineEquiv.apply_lineMap, Finset.prod_sub, WeierstrassCurve.b₈_of_isCharNeTwoNF, Even.zpow_abs, Polynomial.update_eq_add_sub_coeff, CauSeq.inf_comm, Cubic.discr_eq_prod_three_roots, AlgebraicGeometry.Proj.one_apply, WeierstrassCurve.Projective.dblU_eq, FermatLastTheoremForThreeGen.Solution.hab, LinearMap.BilinForm.sub_left, Nat.cast_sub, Valuation.ltAddSubgroup_monotone, Polynomial.bernoulli_generating_function, FermatLastTheoremForThreeGen.Solution.a_add_eta_mul_b, Lagrange.coeff_eq_sum, IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two, nndist_left_lineMap, Set.Icc.one_sub_mem, sub_pow_eq_mul_pow_sub_pow_div_expChar, CHSH_inequality_of_comm, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, WithLp.idemSnd_compl, AffineBasis.coord_apply, WeierstrassCurve.Affine.equation_iff', NonarchimedeanRing.left_mul_subset, gaussSum_mul, LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, OrthogonalIdempotents.prod_one_sub, toIcoMod_sub_self_eq_mul, Int.cast_sub, affineHomeomorph_symm_apply, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two, monotoneOn_descPochhammer_eval, bernoulliPowerSeries_mul_exp_sub_one, PowerSeries.IsWeierstrassDivisorAt.coeff_seq_succ_sub_seq_mem, Int.ceil_sub_intCast, HomogeneousLocalization.awayMap_mk, Int.cast_zero, AddConstMapClass.map_sub_nat', IsAbsoluteValue.abv_sub, Hyperreal.infinite_abs_iff, List.SortedLE.wbtw, toIocMod_sub_natCast_mul, affineSpan_eq_affineSpan_lineMap_units, CauSeq.cauchy, multiplicity_sub_of_gt, GenContFract.abs_sub_convergents_le', lineMap_mono_endpoints, Matrix.add_mul_mul_inv_eq_sub', Polynomial.valuation_of_mk, MvPowerSeries.substAlgHom_eq_aeval, arithGeom_zero_eq_mul_div', IsPrimitiveRoot.powerBasis_gen_mem_adjoin_zeta_sub_one, IsLprojection.Lcomplement, instIsPushoutFractionRingPolynomial_1, Matrix.add_mul_mul_inv_eq_sub, minpoly_algebraMap_sub_splits, Polynomial.disc_of_degree_eq_two, DirichletCharacter.eval_modulus_sub, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_pow_ne_two, AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalk, AbsoluteValue.map_sub_eq_zero_iff, HenselianRing.is_henselian, CauSeq.not_limZero_of_pos, mul_sub_mul_div_mul_nonpos_iff, sub_half_lt_round, MvPowerSeries.coeff_mul_prod_one_sub_of_lt_order, AlgebraicGeometry.Proj.sub_apply, AffineMap.lineMap_injective, Polynomial.ofFinsupp_sub, USize.toBitVec_zsmul, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, Subalgebra.coe_sub, MulRingSeminorm.map_mul', Lagrange.interpolate_eq_sum, ConcaveOn.antitoneOn_slope_gt, Commute.inv_sub_inv, WeierstrassCurve.Jacobian.negAddY_of_X_eq', GradedTensorProduct.tmul_coe_mul_coe_tmul, LieModule.coe_chainTop, CauSeq.coe_sup, IsAbsoluteValue.abs_isAbsoluteValue, one_sub_mul, ZMod.cast_sub', Ideal.span_singleton_abs, ZNum.of_intCast, cross_cross_eq_smul_sub_smul, affineCombination_mem_affineSpan_pair, ConvexOn.secant_mono_aux3, SignType.map_cast, mul_neg_geom_sum, Mathlib.Meta.NormNum.isNNRat_abs_neg, abs_inv, minpoly.sub_algebraMap, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_ne_two, PowerSeries.intValuation_eq_of_coe, Matrix.IsParabolic.sub_eigenvalue_sq_eq_zero, PrimeSpectrum.basicOpen_eq_zeroLocus_of_isIdempotentElem, IsLprojection.coe_compl, NonarchimedeanRing.to_nonarchimedeanAddGroup, AlgebraicGeometry.stalkToFiberRingHom_homogeneousLocalizationToStalk, Matrix.charpoly_sub_scalar, IsValuativeTopology.isTopologicalAddGroup, ZNum.cast_succ, CliffordAlgebra.map_mul_map_of_isOrtho_of_mem_evenOdd, selfAdjoint.instNontrivialSubtypeMemAddSubgroup, Polynomial.eval_derivative_of_splits, Polygon.edgeSet_eq_image_edgePath, CauSeq.mul_pos, self_sub_toIocDiv_mul, Subring.toAddSubgroup_lt_toAddSubgroup, divRadical_dvd_derivative, Polynomial.leadingCoeff_mul_prod_normalizedFactors, Ring.choose_neg, sq_add_mul_sq_mul_sq_add_mul_sq, complEDS₂_three, Subfield.coe_zero, WeierstrassCurve.Jacobian.eval_polynomialX, toIocMod_sub_intCast_mul', Hyperreal.isSt_iff_abs_sub_lt_delta, WeierstrassCurve.c₆_of_isCharThreeJNeZeroNF, PrimeSpectrum.zeroLocus_eq_basicOpen_of_isIdempotentElem, IsLocalization.mk'_sub, AffineMap.apply_lineMap, SetTheory.PGame.quot_left_distrib_sub, Matrix.adjugate_fin_three, WeierstrassCurve.Projective.eval_polynomialX, self_sub_toIcoMod_eq_mul, Subring.neg_mem', Subring.coe_toAddSubgroup, Subring.pointwise_smul_toAddSubgroup, selfAdjoint.val_zpow, AffineMap.hasDerivAt_lineMap, HomogeneousLocalization.val_zsmul, PowerSeries.mk_add_choose_mul_one_sub_pow_eq_one, Finset.cast_card_union, sq_le_sq, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen_prime, Nat.cast_pred, Polynomial.coeff_X_sub_C_mul, Matrix.inv_sub_inv, dvd_pow_pow_sub_self_of_dvd, abs_pow_eq_one, Int.ceil_eq_iff, AlgebraicGeometry.Proj.SpecMap_awayMap_awayι_assoc, AffineMap.left_vsub_lineMap, abs_neg_one_pow, Mathlib.Tactic.Zify.Nat.cast_sub_of_add_le, WeierstrassCurve.Projective.negAddY_eq', AffineMap.hasDerivWithinAt_lineMap, WeierstrassCurve.Projective.Y_sub_Y_mul_Y_sub_negY, WeierstrassCurve.Affine.slope_of_Y_ne, IsCyclotomicExtension.Rat.p_mem_span_zeta_sub_one, Int.ceil_sub_natCast, CliffordAlgebra.changeForm_ι_mul, RingSubgroupsBasis.hasBasis_nhds_zero, xInTermsOfW_eq, StarAlgHom.realContinuousMapOfNNReal_apply, Set.Icc.one_sub_le_one, curveIntegral_segment, sub_pow_char_pow_of_commute, RootPairing.GeckConstruction.lie_h_e, IsIdempotentElem.ker_toSpanSingleton_eq_span, CauSeq.add_pos, AffineBasis.toMatrix_apply, Quaternion.star_eq_two_re_sub, StrictConvexOn.secant_strict_mono_aux3, sub_mem_pNilradical_iff_pow_expChar_pow_eq, AffineMap.lineMap_vsub_right, ZMod.instIsSimpleAddGroup, Finset.prod_sub_ordered, sign_mul_abs, SimpleGraph.farFromTriangleFree.le_card_sub_card, PowerSeries.coe_sub, WeierstrassCurve.Δ_of_char_three, AffineMap.lineMap_continuous, PrimeSpectrum.isIdempotentElemEquivClopens_one_sub, Algebra.mul_sub_algebraMap_commutes, Quaternion.sub_re_self, Int.fract_sub_one, SimpContFract.determinant, abs_mul, Subring.sub_mem, abs_one_div, sub_sq_comm, Function.support_intCast, CommRingCat.coproductCocone_inl, spectrum.resolvent_eq, sub_smul, Valuation.map_sub_eq_of_lt_right, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff', dist_lineMap_left, FormalMultilinearSeries.ofScalars_sub, IsPrimitiveRoot.sub_one_norm_isPrimePow, abs_div, MonovaryOn.sub_mul_sub_nonneg, abs_sub_round_div_natCast_eq, AlgebraicGeometry.Proj.valuativeCriterion_existence, IsDedekindDomain.exists_forall_sub_mem_ideal, lineMap_lt_right_iff_lt_one, Algebra.SubmersivePresentation.jacobianRelations_spec, lineMap_le_lineMap_iff_of_lt', RingSubgroupsBasis.leftMul, monovaryOn_iff_forall_smul_nonneg, ConvexOn.secant_mono_aux2, lineMap_strict_mono_endpoints, WeierstrassCurve.Projective.polynomialZ_eq, Polynomial.coeff_mul_X_sub_C, MulSemiringActionHom.map_sub, Polynomial.disc_of_degree_eq_three, Polynomial.eval_monomial_one_add_sub, ContinuousOn.lineMap, StrictConcaveOn.secant_strict_mono, LieModule.exists_forall_mem_corootSpace_smul_add_eq_zero, bddAbove_slope_gt_of_mem_interior, IsIdempotentElem.mul_one_sub_self, CauSeq.sub_apply, Sbtw.right_mem_image_Ioi, bernoulli'PowerSeries_mul_exp_sub_one, right_lt_lineMap_iff_lt, HahnSeries.cardSuppLTSubfield_carrier, MvPolynomial.IsHomogeneous.sub, dvd_mul_sub_mul_mul_gcd_of_dvd, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff, lineMap_mem_openSegment, sub_inv_antitoneOn_Icc_left, Matrix.det_eq_detp_sub_detp, ModularFormClass.one_mem_strictPeriods_SL2Z, Even.sub_odd, sub_smul_slope_vadd, geom_sum_inv, Commute.sub_sq, AbsoluteValue.abs_apply, MulAlgebraNorm.toFun_eq_coe, Int.floor_sub_ofNat, Subgroup.two_mul_withInfty_mem_strictPeriods, right_le_lineMap_iff_le, ConvexOn.slope_mono_adjacent, MvPolynomial.vars_sub_subset, List.exists_map_eq_of_sorted_nonempty_iff_sbtw, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_two, invOf_sub_invOf, exists_isIntegral_leadingCoeff_pow_smul_sub_of_isIntegralElem_of_mul_mem_range, Int.fract_eq_fract, AffineMap.lineMap_lineMap_right, ConcaveOn.slope_anti, AlgebraicGeometry.ProjectiveSpectrum.Proj.isLocalization_atPrime, EuclideanDomain.sub_mul_div_right, Quaternion.mul_re, abs_sq, abs_lt_iff_mul_self_lt, AlgebraicIndependent.lift_reprField, ZNum.cast_add, AlgebraicGeometry.Proj.instLocallyOfFiniteTypeToSpecZeroOfFiniteTypeSubtypeMemOfNatNat, Valued.toIsUniformAddGroup, IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two, IsPrimitiveRoot.prod_pow_sub_one_eq_order, PowerSeries.normalized_count_X_eq_of_coe, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, WeierstrassCurve.Affine.addX_eq_addX_negY_sub, WeierstrassCurve.Jacobian.addX_eq', IsCyclic.val_inv_mulAutMulEquiv_apply, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous, Int.sub_one_lt_floor, KaehlerDifferential.D_apply, Nat.cast_card_eq_zero, IsValuativeTopology.mem_nhds_iff', AbsoluteValue.le_sub, QuaternionAlgebra.Basis.j_mul_k, preNormEDS'_odd, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two', AffineMap.lineMap_mem, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, AffineMap.lineMap_mono, AffineMap.right_vsub_lineMap, frobenius_sub, WeierstrassCurve.Affine.slope_of_X_ne, WeierstrassCurve.VariableChange.inv_def, Wbtw.left_mem_image_Ici_of_right_ne, Valuation.map_sub_swap, NumberField.RingOfIntegers.mk_sub_mk, ZMod.val_sub, AlgebraicGeometry.Proj.isSeparated, WittVector.mul_polyOfInterest_aux4, Lagrange.eval_nodal, WeierstrassCurve.Projective.negAddY_of_X_eq', AffineSubspace.wOppSide_lineMap_left, HomogeneousLocalization.mk_pow, Monovary.sub_mul_sub_nonneg, uniform_continuous_npow_on_bounded, KaehlerDifferential.one_smul_sub_smul_one_mem_ideal, Quaternion.sub_self_im, IsIntegral.sub, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι, Valuation.map_sub, sub_pow_char, Mathlib.Tactic.Ring.sub_pf, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, Int.fract_div_mul_self_add_zsmul_eq, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen, EuclideanDomain.mul_sub_div_right, arithGeom_same_eq_mul_div', sbtw_iff_right_ne_and_left_mem_image_Ioi, ArchimedeanClass.mk_sub_stdPart_pos, Subring.mem_closure_iff, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, one_add_mul_sub_le_pow, Int.cast_negSucc, IsLprojection.join, HasProd.abs, lineMap_le_left_iff_nonpos, KummerDedekind.emultiplicity_factors_map_eq_emultiplicity, AffineMap.vadd_lineMap, Subgroup.strictPeriods_eq_zmultiples_one_of_T_mem, mem_affineSpan_pair_iff_exists_lineMap_rev_eq, geom_sum_Ico_mul, toIcoMod_eq_add_fract_mul, toIocMod_eq_sub_fract_mul, Subring.zsmul_mem, segment_eq_image, self_dvd_abs, NonUnitalSubalgebra.coe_sub, LaurentSeries.exists_Polynomial_intValuation_lt, FermatLastTheoremForThreeGen.Solution'.ha, IsPrimitiveRoot.finite_quotient_span_sub_one', HomogeneousLocalization.awayMapₐ_apply, Polynomial.eval₂_sub, IsPrimitiveRoot.minpoly_sub_one_eq_cyclotomic_comp, round_le, geom_sum_Ico_mul_neg, abs_sub_round_eq_min, toIcoMod_sub_natCast_mul', geom_sum_eq, instFaithfulSMulIntOfCharZero, TwoSidedIdeal.mem_jacobson_iff, Function.Antiperiodic.nat_mul_sub_eq, Matrix.schur_complement_eq₂₂, Commute.sq_sub_sq, tendsto_arithGeom_nhds_of_lt_one, ConcaveOn.antitoneOn_slope_lt, ArithmeticFunction.intCoe_mul, GenContFract.of_convergence_epsilon, HomogeneousLocalization.val_sub, Polynomial.Splits.aeval_eq_prod_aroots, IsPrimitiveRoot.associated_sub_one_map_sub_one, AlgebraicGeometry.ProjIsoSpecTopComponent.fromSpec_toSpec, Matrix.adjugate_fin_three_of, Int.fract_sub_natCast, IsPrimitiveRoot.finite_quotient_span_sub_one, CliffordAlgebra.contractLeft_ι_mul, Differential.logDeriv_div, QuadraticAlgebra.mul_star, ArchimedeanClass.FiniteElement.val_sub, mul_one_sub, AddConstMapClass.map_sub_ofNat', monovary_iff_forall_smul_nonneg, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, FermatLastTheoremForThreeGen.a_cube_b_cube_congr_one_or_neg_one, exists_abs_lt, Ideal.mem_jacobson_iff, dvd_pow_sub_one_of_dvd, IsUnit.sub_iff, Submodule.toIntSubmodule_toAddSubgroup, CompleteOrthogonalIdempotents.option, QuaternionAlgebra.re_mul, ArithmeticFunction.coe_zeta_mul_coe_moebius, List.exists_map_eq_of_sorted_nonempty_iff_wbtw, Valuation.map_sub_le, AffineMap.vsub_lineMap, lineMap_le_right_iff_le, StrictConvexOn.secant_strict_mono_aux1, dist_lineMap_right, abs_mul_sign, WeakDual.instIsTopologicalAddGroup, toIcoMod_sub_intCast_mul, IsPrimitiveRoot.associated_map_sub_one_map_sub_one, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, IsCoprime.abs_right, complEDS'_odd, toIocDiv_sub_natCast_mul, Complex.selfAdjointEquiv_apply, MonomialOrder.degree_X_sub_C, WithLp.idemFst_compl, openSegment_eq_image, MeasureTheory.hausdorffMeasure_lineMap_image, Int.abs_fract, Function.Periodic.sub_int_mul_eq, HomogeneousLocalization.mk_one, Subfield.sub_mem, sub_div, wbtw_zero_one_iff, xInTermsOfW_aux, PowerSeries.sub_const_eq_X_mul_shift, MvPowerSeries.coeff_mul_right_one_sub_of_lt_order, IsIdempotentElem.ker_toSpanSingleton_one_sub_eq_span, AffineMap.lineMap_apply_module', Subalgebra.sub_mem, ContinuousAffineMap.apply_lineMap', HomogeneousLocalization.awayMap_fromZeroRingHom, Subgroup.commensurable_strictPeriods_periods, smul_add_one_sub_smul, QuaternionAlgebra.imK_mul, EuclideanDomain.mod_eq_sub_mul_div, AffineSubspace.wSameSide_lineMap_left, ContinuousWithinAt.lineMap, MvPolynomial.degreeOf_sub_le, slope_pos_iff, LieModule.exists₂_genWeightSpace_smul_add_eq_bot, signedDist_lineMap_lineMap, WeierstrassCurve.variableChange_def, HomogeneousLocalization.instIsScalarTowerSubtypeMemOfNatLocalization, Int.ceil_sub_one, Polynomial.map_sub_sprod_roots_eq_prod_map_eval, Hyperreal.infinitesimal_sub_st, AffineBasis.sum_coord_apply_eq_one, HomogeneousLocalization.zero_eq, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Function.Periodic.nat_mul_sub_eq, LieModule.genWeightSpace_chainBotCoeff_sub_one_zsmul_sub, Polynomial.evalEval_sub, CharTwo.two_zsmul, MvPolynomial.combinatorial_nullstellensatz_exists_linearCombination, RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra', Lagrange.leadingCoeff_eq_sum, Hyperreal.infinitePos_abs_iff_infinite_abs, wittStructureRat_rec, geom_sum_mul, Polynomial.Splits.eval_eq_prod_roots_of_monic, HomogeneousLocalization.mk_mul, abs_mul_self, IsCauSeq.cauchy₃, PowerSeries.invUnitsSub_mul_sub, AffineBasis.coord_apply_combination_of_notMem, Int.le_ceil_iff, CliffordAlgebra.EquivEven.Q'_apply, Matrix.det_one_sub_mul_comm, WeierstrassCurve.Affine.addPolynomial_eq, iccHomeoI_apply_coe, one_le_sq_iff_one_le_abs, Matrix.add_mul_mul_invOf_mul_eq_one', RatFunc.valuation_eq_LaurentSeries_valuation, GaussianInt.toComplex_sub, WeierstrassCurve.variableChange_a₂, Num.cast_sub', IsCyclotomicExtension.Rat.Three.eta_sq, odd_sq_dvd_geom_sum₂_sub, IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero, LieAlgebra.SpecialLinear.sl_bracket, one_add_le_one_sub_mul_one_add, WeierstrassCurve.Projective.addZ_eq, dvd_mul_sub_mul_mul_left_of_dvd, Nat.cast_le_pow_sub_div_sub, Quaternion.sub_self_re, AffineMap.lineMap_vsub, RingSubgroupsBasis.mem_addGroupFilterBasis, MvPowerSeries.comp_subst_apply, IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one, Order.IsPredPrelimit.lt_sub_natCast, MonomialOrder.sPolynomial_def, RingHom.map_sub, exists_jacobiSum_eq_neg_one_add, CliffordAlgebra.changeForm_ι_mul_ι, toIcoMod_sub_ofNat_mul', Valuation.mem_leAddSubgroup_iff, AffineMap.lineMap_eq_lineMap_iff, Nat.abs_sub_ceil_le, complEDS₂_four, Matrix.det_fromBlocks₁₁, AddChar.val_mem_rootsOfUnity, StrictConvexOn.slope_strict_mono_adjacent, IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two, lineMap_lt_left_iff_lt, List.exists_map_eq_of_sorted_iff_sbtw, Algebra.Norm.Transitivity.det_det_aux, Sbtw.of_lt_of_lt, Finset.sum_Ico_by_parts, mul_sub_mul_div_mul_neg, Height.mulHeight₁_sub_le, EuclideanDomain.div_sub_div_of_dvd, Matrix.add_mul_mul_mul_invOf_eq_one, RingSubgroupsBasis.hasBasis_nhds, arithGeom_eq, PowerSeries.one_sub_pow_add_mul_invOneSubPow_val_eq_one_sub_pow, toIocDiv_sub_ofNat_mul, sub_pow, Quaternion.imK_mul, Matrix.det_fromBlocks_one₁₁, AffineMap.image_uIcc, AffineMap.lineMap_vadd_apply, Matrix.discr_of_card_eq_two, ZMod.intCast_cast_sub, LieRing.of_associative_ring_bracket, IsPrimitiveRoot.finite_quotient_toInteger_sub_one, sub_one_lt, associated_abs_left_iff, MvPolynomial.degrees_sub_le, PowerSeries.sub_const_eq_shift_mul_X, IsLocalization.Away.quotient_of_isIdempotentElem, complEDS_odd, wittStructureRat_rec_aux, one_sub_invOf_two, WeierstrassCurve.Projective.eval_polynomialZ, Polynomial.eval_eq_prod_roots_sub_of_splits_id, PowerSeries.WithPiTopology.one_sub_mul_tsum_pow_of_constantCoeff_eq_zero, Units.divp_sub_divp_same, MvPowerSeries.WithPiTopology.one_sub_mul_tsum_pow_of_constantCoeff_eq_zero, Algebra.Generators.ker_localizationAway, spectrum.mem_resolventSet_iff, LinearMap.BilinForm.sub_apply, strictConcaveOn_iff_slope_strict_anti_adjacent, Commute.div_sub_div, one_div_mul_sub_mul_one_div_eq_one_div_add_one_div, AlgebraicGeometry.Proj.awayι_toSpecZero, Subring.coe_eq_zero_iff, Commute.geom_sum₂_Ico, IsPrimitiveRoot.norm_toInteger_sub_one_eq_one, rat_mul_continuous_lemma, PowerSeries.one_sub_pow_mul_invOneSubPow_val_add_eq_invOneSubPow_val, Lagrange.iterate_derivative_interpolate, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two', nndist_lineMap_right, Ring.choose_neg', PrimeSpectrum.isIdempotentElemEquivClopens_symm_sup, Polynomial.C_sub, mul_sub_one, sectionOfRetractionKerToTensorAux_prop, AbsoluteValue.map_units_int_smul, Commute.geom_sum₂, RingSubgroupsBasis.inter, OrthogonalIdempotents.surjective_pi, Multipliable.abs, ConvexOn.secant_mono, IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver', Polynomial.aeval_eq_prod_aroots_sub_of_monic_of_splits, Polynomial.isNilpotent_iterate_newtonMap_sub_of_isNilpotent, WeierstrassCurve.Jacobian.Y_sub_Y_add_Y_sub_negY, IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one', alternating_series_error_bound, round_sub_ofNat, Asymptotics.superpolynomialDecay_iff_abs_isBoundedUnder, Valued.cauchy_iff, Algebra.FormallyUnramified.one_tmul_sub_tmul_one_mul_elem, signedDist_lineMap_left, Algebra.Generators.comp_localizationAway_ker, AffineMap.lineMap_apply_zero, pow_two_sub_pow_two, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, Finset.affineCombination_affineCombinationLineMapWeights, self_sub_toIcoDiv_mul, Wbtw.of_le_of_le, ConvexOn.secant_mono_aux1, WeierstrassCurve.Affine.addY_sub_negY_addY, Summable.one_sub_mul_tsum_pow, MvPolynomial.universalFactorizationMapPresentation_relation, AffineMap.fst_lineMap, ConvexOn.slope_mono, ArchimedeanClass.FiniteResidueField.mk_eq_mk, cross_apply, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff_of_mem, Commute.sub_dvd_pow_sub_pow, Valuation.map_one_sub_of_lt, Matrix.isUnit_fromBlocks_iff_of_invertible₂₂, Ideal.exists_forall_sub_mem_ideal, self_mul_sign, BooleanRing.sub_eq_add, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq, WeierstrassCurve.Projective.polynomialX_eq, inv_sub_inv, CauSeq.le_sup_left, MvPolynomial.eval₂_sub, toIocMod_sub_ofNat_mul, WeierstrassCurve.c₆_of_isCharTwoJNeZeroNF, IsCyclotomicExtension.Rat.isPrime_span_zeta_sub_one', AlgebraicGeometry.Proj.awayι_toSpecZero_assoc, Nat.abs_sub_floor_le, arithGeom_same_eq_mul_div, slope_def_field, eq_lineMap_of_dist_eq_mul_of_dist_eq_mul, IsCyclotomicExtension.Rat.liesOver_span_zeta_sub_one, Algebra.mul_sub_algebraMap_pow_commutes, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, Int.fract_sub_self, LieModule.genWeightSpace_chainTopCoeff_add_one_zsmul_add, tsirelson_inequality, Set.Icc.mem_iff_one_sub_mem, tendsto_floor_left', SimpleGraph.lapMatrix_mulVec_apply, LieModule.genWeightSpace_le_genWeightSpaceChain, ArchimedeanClass.stdPart_sub_eq_right, Hyperreal.IsSt.sub, AffineMap.lineMap_apply, Matrix.fromBlocks_eq_of_invertible₂₂, AffineBasis.coord_apply_eq, Polynomial.Splits.eval_eq_prod_roots, Subgroup.instDiscreteTopStrictPeriods, AffineBasis.coord_apply_centroid, IsCyclotomicExtension.norm_zeta_sub_one_of_prime_ne_two, WeierstrassCurve.Projective.negDblY_eq, AlgebraicGeometry.Proj.zero_apply, left_le_lineMap_iff_le, slope_fun_def, Prime.abs, sbtw_mul_sub_add_iff, Int.fract_add, quadratic_eq_zero_iff, Matrix.sub_scalar_sq_eq_disc, sq_lt_one_iff_abs_lt_one, conjneg_sub, IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic, Commute.mul_geom_sum₂, natDegree_radical_le, Matrix.disc_fin_two, Quaternion.sub_im, isStarProjection_one_sub_iff, Polynomial.sub_dvd_eval_sub, CauSeq.const_sub, toIcoMod_sub_intCast_mul', PreTilt.pow_dvd_untiltAux_sub_untiltAux, ZMod.cast_sub, Int.fract_neg, sub_pow_char_pow, StrictConvexOn.secant_strict_mono_aux2, Ideal.Quotient.eq, selfAdjoint.val_inv, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.one_mem', IsValuativeTopology.hasBasis_nhds, WeierstrassCurve.Projective.addZ_eq', Matrix.schur_complement_eq₁₁, diffToIdealOfQuotientCompEq_apply, mem_affineSpan_pair_iff_exists_lineMap_eq, AbsoluteValue.IsAdmissible.exists_approx, openSegment_eq_image_lineMap, Subgroup.relIndex_strictPeriods, ZMod.cast_neg_one, Matrix.invOf_add_mul_mul, Set.Ioo.mem_iff_one_sub_mem, List.Sorted.sbtw, Subring.toAddSubgroup_strictMono, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.homogeneous, wbtw_iff_right_eq_or_left_mem_image_Ici, CauSeq.const_le, WittVector.frobeniusPolyAux_eq, PreTilt.pow_dvd_one_untiltAux_sub_one, Int.ceil_eq_add_one_sub_fract, DihedralGroup.sr_mul_sr, SignType.intCast_cast, WeierstrassCurve.Projective.addX_eq, abs_unit_intCast, Matrix.det_fromBlocks_one₂₂, wbtw_iff_left_eq_or_right_mem_image_Ici, CauSeq.lim_sub, ContMDiffRing.toLieAddGroup, IsCyclotomicExtension.norm_zeta_sub_one_of_isPrimePow, ZMod.cast_zero, AddConstMapClass.map_sub_int', AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_isIso, lineMap_lt_map_iff_slope_lt_slope, mul_geom_sum, left_lt_lineMap_iff_lt, Algebra.Generators.cMulXSubOneCotangent_eq, Int.self_sub_floor, toIocDiv_eq_neg_floor, UInt16.toBitVec_zsmul, PowerSeries.IsWeierstrassDivisorAt.coeff_seq_mem, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two, toIcoMod_sub_natCast_mul, ArithmeticFunction.log_mul_moebius_eq_vonMangoldt, sq_lt_sq, QuotientAddGroup.mk_nat_mul, CHSH_id, Matrix.submatrix_succAbove_det_eq_negOnePow_submatrix_succAbove_det', IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver, MonoidHom.map_sub_swap, AffineMap.lineMap_anti, IsPrimitiveRoot.subOnePowerBasis_dim, Matrix.isUnit_fromBlocks_iff_of_invertible₁₁, IsPrimitiveRoot.subOnePowerBasis_gen, MulRingNormClass.eq_zero_of_map_eq_zero, AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_apply, spectrum.singleton_sub_eq, MulRingNormClass.toAddGroupNormClass, Odd.sub_even, Quaternion.sub_imI, HomogeneousLocalization.one_eq, Valuation.mem_ltAddSubgroup_iff, isIdempotentElem_iff_one_sub_mul_self, WeierstrassCurve.variableChange_a₄, AbsoluteValue.le_add, AffineSubspace.sSameSide_lineMap_right, IntermediateField.sub_mem, CauSeq.sup_comm, Matrix.PosDef.fromBlocks₂₂, WeierstrassCurve.c₆_of_isCharNeTwoNF, MvPowerSeries.WithPiTopology.tsum_pow_mul_one_sub_of_constantCoeff_eq_zero, RatFunc.ofFractionRing_sub, Ring.DirectLimit.quotientMk_of, Commute.pow_dvd_sub_pow_of_pow_eq_zero_left, Subgroup.strictPeriods_le_periods, RatFunc.v_def, IsPrimitiveRoot.associated_pow_add_sub_sub_one, divRadical_dvd_wronskian_right, continuous_barycentric_coord, pow_four_add_four_mul_pow_four, Nat.one_sub_one_div_cast_nonneg, add_sub_div_two_lt, AffineMap.lineMap_same_apply, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, Mathlib.Tactic.Linarith.sub_neg_of_lt, KaehlerDifferential.submodule_span_range_eq_ideal, IsCyclotomicExtension.Rat.Three.lambda_dvd_or_dvd_sub_one_or_dvd_add_one, Int.cast_list_sum, selfAdjoint.val_pow, AlgebraicIndependent.liftAlgHom_comp_reprField, sectionOfRetractionKerToTensor_algebraMap, HomogeneousLocalization.algebraMap_eq, bddBelow_slope_lt_of_mem_interior, RatFunc.ofFractionRing_neg, AbsoluteValue.IsAdmissible.exists_partition, Algebra.SubmersivePresentation.sum_jacobianRelationsOfHasCoeffs_mul_relationOfHasCoeffs, wbtw_one_zero_iff, LaurentSeries.powerSeries_ext_subring, AffineMap.lineMap_apply_ring, AffineSubspace.sOppSide_lineMap_right, NonarchimedeanRing.is_nonarchimedean, WeierstrassCurve.Jacobian.polynomialZ_eq, MulRingNorm.toFun_eq_coe, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two, CongruenceSubgroup.strictPeriods_Gamma1, WeierstrassCurve.Jacobian.dblU_eq, IsPrimitiveRoot.norm_pow_sub_one_two, Int.cast_mul_eq_zsmul_cast, preNormEDS'_even, Algebra.Extension.Cotangent.mk_eq_mk_iff_sub_mem, AbsoluteValue.hasBasis_uniformity, Subfield.mem_toAddSubgroup, ArchimedeanClass.mk_le_mk_iff_ratCast, Algebra.discr_powerBasis_eq_prod, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, even_sub_two, QuaternionGroup.xa_mul_xa, Int.self_sub_fract, FermatLastTheoremForThreeGen.Solution'.hcdvd, Matrix.transpose_intCast, AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj, Matrix.add_mul_mul_mul_invOf_eq_one', Subring.sInf_toAddSubgroup, MulAlgebraNormClass.toSeminormClass, Mathlib.Tactic.RingNF.add_neg, Sbtw.left_mem_image_Ioi, Mathlib.Meta.NormNum.isNNRat_abs_nonneg, one_sub_le_one_add_mul_one_sub, IsPrimitiveRoot.toInteger_sub_one_dvd_prime, Ring.multichoose_eq, Rat.cast_abs, LieModule.genWeightSpaceChain_def, CauSeq.coe_sub, Polynomial.eval_eq_prod_roots_sub_of_monic_of_splits_id, CauSeq.inf_le_right, Valuation.map_sub_eq_of_lt_left, WeierstrassCurve.Δ_of_isCharNeTwoNF, AffineMap.coe_lineMap, MvPowerSeries.coeff_mul_left_one_sub_of_lt_weightedOrder, CauSeq.Completion.ofRat_sub, Set.Ioo.one_sub_mem, sq_eq_sq_iff_abs_eq_abs, LaurentSeries.powerSeriesRingEquiv_coe_apply, lineMap_le_map_iff_slope_le_slope, AbsoluteValue.IsAdmissible.exists_partition', Finset.sum_range_by_parts, AffineMap.lineMap_eq_right_iff, Valuation.ltAddSubgroup_le_leAddSubgroup, Int.sub_floor_div_mul_nonneg, abs_pow_sub_pow_le, ContinuousAffineMap.apply_lineMap, Quaternion.imJ_mul, AlgebraicGeometry.Proj.instUniversallyClosedToSpecZeroOfFiniteTypeSubtypeMemOfNatNat, AlgebraicGeometry.Proj.add_apply, mul_geom_sum₂_Ico, Int.image_fract, WeierstrassCurve.Jacobian.equation_iff, slope_pos_iff_gt, IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two, Polynomial.aeval_derivative_of_splits, IsCoprime.abs_left_iff, one_lt_sq_iff_one_lt_abs, AffineBasis.coords_apply, selfAdjoint.val_qsmul, Finset.prod_range_natCast_sub, AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrier, NonarchimedeanRing.mul_subset, Quaternion.coe_sub, AlgebraicGeometry.ProjectiveSpectrum.Proj.isIso_toSpec, IsCoprime.abs_left, Module.Basis.abs_det_adjustToOrientation, WeierstrassCurve.Projective.negDblY_eq', odd_sub_two, Rat.cast_sub_of_ne_zero, AffineMap.lineMap_apply_one, CauSeq.exists_lt, AffineMap.lineMap_apply', Odd.sub_odd, Ideal.exists_mul_add_sub_mem_of_mem_jacobson, AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div, ArithmeticFunction.moebius_mul_log_eq_vonMangoldt, Subgroup.strictWidthInfty_mem_strictPeriods, ZNum.cast_bit0, ZNum.cast_bitm1, IsPrimitiveRoot.toInteger_sub_one_dvd_prime', spectrum.mem_iff, right_le_lineMap_iff_one_le, lineMap_le_lineMap_iff_of_lt, Polynomial.existsUnique_nilpotent_sub_and_aeval_eq_zero, half_sub, Polynomial.coeff_sub, IsPrimitiveRoot.ntRootsFinset_pairwise_associated_sub_one_sub_of_prime, List.exists_map_eq_of_sorted_iff_wbtw, FermatLastTheoremForThreeGen.Solution'.hb, abs_neg_one_zpow, ArchimedeanClass.mk_le_mk_iff_denselyOrdered, Int.fract_sub_intCast, mul_sub_mul_div_mul_nonpos, Zsqrtd.mul_star, AddValuation.map_sub, MvPolynomial.eval_sub, CharTwo.sub_eq_add, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, Field.isSeparable_sub, Commute.mul_neg_geom_sum₂, Complex.coe_selfAdjointEquiv, MvPolynomial.totalDegree_sub, Valuation.IsEquiv.val_sub_one_lt_one_iff, RingPreordering.mem_supportAddSubgroup, IsPrimitiveRoot.card_quotient_toInteger_sub_one, WeierstrassCurve.b_relation_of_char_three, IsValuativeTopology.hasBasis_nhds', isVisible_iff_lineMap, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle, Matrix.eval_charpoly, RingPreordering.one_notMem_supportAddSubgroup, Matrix.det_fromBlocks₂₂, AddSubgroup.intCast_mul_mem_zmultiples, lineMap_le_right_iff_le_one, Polynomial.leadingCoeff_sub_of_degree_eq, List.Sorted.wbtw, IsMprojection.Mnorm, Summable.tsum_pow_mul_one_sub, Nat.one_sub_one_div_cast_le_one, UInt32.toBitVec_zsmul, LinearMap.BilinForm.IsSymm.polarization, LieModule.coe_chainBot, Nat.abs_floor_sub_le, Polynomial.Splits.aeval_eq_prod_aroots_of_monic, Mathlib.Tactic.ComputeDegree.coeff_sub_of_eq, sq_add_sq_mul_sq_add_sq, inv_sub_inv', associated_abs_right_iff, Subring.coe_zero, IsLprojection.coe_sdiff, AffineBasis.surjective_coord, ContinuousMap.Homotopy.affine_apply, WeierstrassCurve.b_relation, complEDS₂_mul_b, Polynomial.coe_sub, CauSeq.le_total, ValuationSubring.mem_principalUnitGroup_iff, monovary_iff_forall_mul_nonneg, WeierstrassCurve.Jacobian.Y_sub_Y_mul_Y_sub_negY, AffineMap.lineMap_eq_left_iff, Valued.mem_nhds, PowerSeries.WithPiTopology.tsum_pow_mul_one_sub_of_constantCoeff_eq_zero, Polynomial.resultant_eq_prod_roots_sub, AddMonoidAlgebra.supDegree_sub_lt_of_leadingCoeff_eq, Algebra.Presentation.relation_comp_localizationAway_inl, IsCyclotomicExtension.Rat.isPrime_span_zeta_sub_one, WeierstrassCurve.Projective.negAddY_eq, SubringClass.addSubgroupClass, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, abs_sub_sq, dvd_mul_sub_mul_mul_right_of_dvd, Polynomial.aeval_eq_prod_aroots_sub_of_splits, Hyperreal.infinite_iff_abs_lt_abs, Polynomial.newtonMap_apply_of_isUnit, WeierstrassCurve.Jacobian.addX_eq, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, Quaternion.sub_im_self, MvPolynomial.coeff_sub, Multipliable.abs_tprod, dist_left_lineMap, selfAdjoint.val_ratCast, iccHomeoI_symm_apply_coe, CongruenceSubgroup.strictPeriods_Gamma, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_two, AntivaryOn.sub_mul_sub_nonpos, sub_mul_sub_pos_iff, QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff, AlgebraicGeometry.Proj.pullbackAwayιIso_hom_awayι_assoc, sub_pow_two, RingQuot.sub_quot, lineMap_lt_right_iff_lt, Algebra.SubmersivePresentation.exists_sum_eq_σ_jacobian_mul_σ_jacobian_inv_sub_one, AddValuation.map_sub_eq_of_lt_left, WeierstrassCurve.b₈_of_char_three, map_le_lineMap_iff_slope_le_slope, AffineMap.coe_homothetyAffine, geom_sum₂_mul, AffineMap.snd_lineMap, LucasLehmer.X.one_add_α_pow_q, Polynomial.aeval_root_derivative_of_splits, Complex.ofReal_zsmul, IsLprojection.Lcomplement_iff, IsAbsoluteValue.sub_abv_le_abv_sub, lineMap_one_half, Polynomial.taylor_eval_sub, one_sub_le_one_sub_mul_one_add, Polynomial.mem_normalizedFactors_iff, List.SortedLT.sbtw, toIocDiv_sub_natCast_mul', GradedTensorProduct.comm_coe_tmul_coe, Complex.selfAdjointEquiv_symm_apply, AlgebraicIndependent.aevalEquivField_apply_coe, AlgebraicGeometry.Proj.SpecMap_awayMap_awayι, IsCauSeq.cauchy₂, Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_top, IsStarProjection.two_mul_sub_one_mem_unitary, CauSeq.le_sup_right, CompleteOrthogonalIdempotents.of_isIdempotentElem, Ideal.factors_span_eq, HomogeneousLocalization.val_neg, Set.cast_ncard_sdiff, WeierstrassCurve.Jacobian.eval_polynomial, one_sub_dvd_one_sub_pow, arithGeom_zero_eq_mul_div, dvd_sub_self_right, WeierstrassCurve.Projective.addX_eq', Ideal.Quotient.mk_eq_mk_iff_sub_mem, Int.ceil_sub_self_eq, Algebra.Extension.Hom.sub_aux, IsNilpotent.isUnit_one_sub, instIsPushoutFractionRingPolynomial, PowerBasis.exists_gen_dvd_sub, Matrix.submatrix_succAbove_det_eq_negOnePow_submatrix_succAbove_det, AffineSubspace.sSameSide_lineMap_left, lineMap_le_left_iff_le, AffineMap.lineMap_lineMap_left, WeierstrassCurve.c₄_of_isCharNeTwoNF, WittVector.polyOfInterest_vars_eq, Ideal.sub_mem, descPochhammer_eval_eq_ascPochhammer, descPochhammer_eval_eq_prod_range, toIcoDiv_sub_ofNat_mul, Matrix.det_vandermonde_sub, ArchimedeanClass.stdPart_sub, Finset.cast_card_erase_of_mem, ZNum.cast_bit1, QuadraticAlgebra.norm_def, IsCyclic.mulAutMulEquiv_symm_apply_symm_apply, pow_abs, Int.abs_one_sub_fract, RootPairing.GeckConstruction.lie_h_f, slope_sub_smul, LaurentSeries.tendsto_valuation, preNormEDS_even, Subgroup.strictPeriods_SL2Z, FreeCommRing.isSupported_sub, derivationOfSectionOfKerSqZero_apply_coe, Complex.ofReal_comp_zsmul, pow_one_sub_dvd_pow_mul_sub_one, AffineMap.lineMap_same, ArchimedeanClass.stdPart_sub_eq_left, SkewMonoidAlgebra.intCast_def, cross_dot_cross, sectionOfRetractionKerToTensorAux_algebraMap, PowerSeries.invOneSubPow_eq_inv_one_sub_pow, Continuous.lineMap, AbsoluteValue.map_sub, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two, dvd_abs, signedDist_right_lineMap, AddValuation.map_le_sub, ArchimedeanClass.mk_sub_pos_iff, RingPreordering.coe_supportAddSubgroup, Units.sub_divp, Mathlib.Tactic.Module.NF.sub_eq_eval₂, toIocDiv_sub_intCast_mul', AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div, WeierstrassCurve.Jacobian.addY_of_X_eq', Matrix.IsHermitian.fromBlocks₁₁, RatFunc.neg_def, Valuation.map_sub_of_right_eq_zero, WeierstrassCurve.Jacobian.polynomialX_eq, abs_mul_abs_self, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, uzpow_sub, segment_eq_image_lineMap, TensorProduct.tmul_of_gradedMul_of_tmul, sub_smul_slope, Matrix.invOf_add_mul_mul', AffineMap.lineMap_continuous_uncurry, Polynomial.discr_of_degree_eq_two, Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul, Subring.toAddSubgroup_le_toAddSubgroup, Nat.cast_choose_two, Subgroup.mem_strictPeriods_iff, MvPolynomial.psum_eq_mul_esymm_sub_sum, AbsoluteValue.sub_le, RootPairing.GeckConstruction.lie_e_lie_f_apply, nndist_lineMap_lineMap, geom_sum_Ico', Int.cast_subNatNat, ZMod.instIsAddCyclic, CancelDenoms.sub_subst, Polynomial.toFinsupp_sub, selfAdjoint.val_nnratCast, Valuation.leAddSubgroup_zero, QuaternionAlgebra.Basis.j_mul_i, sub_mul_sub_nonpos_iff, AlgebraicGeometry.ProjectiveSpectrum.Proj.stalkMap_toSpec, jacobiSum_eq_sum_sdiff, toIcoDiv_eq_floor, Finset.cast_card_sdiff, QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff, AbsoluteValue.IsAdmissible.exists_approx_aux, Subring.mem_toAddSubgroup, Subring.instNoZeroDivisorsSubtypeMem, sub_sq', div_sub_div_same, StrictConvexOn.secant_strict_mono, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.relevant, antivaryOn_iff_forall_mul_nonpos, FreeRing.coe_sub, Set.Icc.one_sub_nonneg, MvPolynomial.support_sub, WeierstrassCurve.Affine.evalEval_polynomial, Int.cast_eq_zero, AffineMap.comp_lineMap, Int.abs_sub_lt_one_of_floor_eq_floor, IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen, Polynomial.eval₂_derivative_of_splits, IsAbsoluteValue.abs_abv_sub_le_abv_sub, sub_one_div_inv_le_two, CompleteOrthogonalIdempotents.prod_one_sub, QuaternionAlgebra.mk_mul_mk, sq_le_one_iff_abs_le_one, AffineBasis.coord_vadd, KaehlerDifferential.span_range_eq_ideal, ContinuousAt.lineMap, cfc_tsub, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_abs, MulRingSeminorm.toFun_eq_coe, Hyperreal.coe_abs, QuaternionAlgebra.imJ_mul, norm_sub_le_mul_volume_of_norm_fderiv_le, sbtw_lineMap_iff, AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap, Nat.sub_one_lt_floor, AlgebraicGeometry.mem_basicOpen_den, Valued.hasBasis_uniformity, Int.ceil_sub_ofNat, Int.fract_eq_zero_or_add_one_sub_ceil, IsStarProjection.one_sub, AffineSubspace.wSameSide_lineMap_right, Complex.re_zsmul, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, Localization.neg_mk, Polynomial.homogenize_sub, Ideal.Quotient.mk_eq_one_iff_sub_mem, abs_dvd_self, Quaternion.im_sub, Matrix.det_fin_two_of, IsPrimitiveRoot.self_sub_one_pow_dvd_order, sum_Ioc_inv_sq_le_sub, toIcoDiv_sub_natCast_mul, WithIdealFilter.instIsTopologicalAddGroup, Matrix.det_neg_eq_smul, signedDist_lineMap_right, ConvexOn.monotoneOn_slope_gt, AffineMap.lineMap_symm, Algebra.discr_powerBasis_eq_prod'', Matrix.disc_of_card_eq_two, MvPolynomial.degreeOf_sub_lt, sub_half, sub_inv_antitoneOn_Icc_right, preNormEDS_odd, Commute.mul_geom_sum₂_Ico, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, Polynomial.ofFinsupp_zsmul, round_eq_iff, round_sub_natCast, AddValuation.map_sub_eq_of_lt_right, IsCyclic.mulAutMulEquiv_symm_apply_apply, descPochhammer_succ_eval, isOpenMap_barycentric_coord, algebraMap.coe_sub, IsCoprime.abs_abs_iff, AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.zero_mem', Subring.toAddSubgroup_eq_top, MvPolynomial.totalDegree_sub_C_le, div_sub_one, MvPowerSeries.comp_subst, WeierstrassCurve.Affine.evalEval_polynomialX, Mathlib.Tactic.Zify.Nat.cast_sub_of_lt, Int.preimage_ceil_singleton, Nat.abs_ofNat, RingQuot.Rel.sub_right, antivary_iff_forall_mul_nonpos, IsCyclotomicExtension.Rat.associated_norm_zeta_sub_one, Derivation.commutator_apply, geom_sum_mul_neg, CliffordAlgebra.ofEven_ι, ZNum.cast_to_int, Function.Periodic.sub_nat_mul_eq, IsCyclotomicExtension.norm_zeta_pow_sub_one_two, Int.floor_sub_natCast, MonomialOrder.leadingCoeff_sub_of_lt, IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_one, Quaternion.sub_re, Subalgebra.zsmul_mem, IsIdempotentElem.one_sub_iff, WeierstrassCurve.Δ_of_isCharThreeJNeZeroNF, slope_fun_def_field, Finset.sum_Ioc_by_parts, ZMod.eq_one_or_isUnit_sub_one, div_sub', LucasLehmer.ω_pow_formula, RingQuot.Rel.sub_left, QuotientAddGroup.mk_int_mul, PowerSeries.substAlgHom_eq_aeval, sq_abs, Subfield.coe_toAddSubgroup, Valuation.coe_ltAddSubgroup, toIocDiv_sub_intCast_mul, AffineMap.lineMap_apply_ring', FermatLastTheoremForThreeGen.Solution.associated_of_dvd_a_add_eta_mul_b_of_dvd_a_add_eta_sq_mul_b, Polynomial.newtonMap_apply, Algebra.IsAlgebraic.rank_fractionRing_mvPolynomial, PosNum.cast_sub', toIocMod_sub_ofNat_mul', Algebra.discr_powerBasis_eq_prod', sq_dvd_add_pow_sub_sub, IsStarProjection.one_sub_mul_self, fwdDiff_addChar_eq, SpectrumRestricts.nnreal_iff_spectralRadius_le, ZMod.cast_sub_one, zsmul_one, CauSeq.lt_total, sub_pow_char_of_commute, Hyperreal.abs_omega, WeierstrassCurve.Jacobian.negAddY_eq', divRadical_dvd_wronskian_left, normEDS_odd, antivaryOn_iff_forall_smul_nonpos, tendsto_floor_left, RatFunc.sub_def, WithIdealFilter.mem_nhds_iff, WeierstrassCurve.Jacobian.addX_of_X_eq', odd_sub_one, dist_right_lineMap, AffineBasis.affineCombination_coord_eq_self, Associated.abs_right, WittVector.mul_polyOfInterest_aux5, Subgroup.HasDetPlusMinusOne.abs_det, Matrix.intCast_apply, DividedPowers.isSubDPIdeal_inf_iff, ClassGroup.mem_finsetApprox, Quaternion.re_sub, stdSimplexEquivIcc_symm_apply_coe, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen, AffineBasis.coe_coord_of_subsingleton_eq_one, antivary_iff_forall_smul_nonpos, map_lt_lineMap_iff_slope_lt_slope, Commute.pow_dvd_sub_pow_of_pow_eq_zero_right, EuclideanDomain.xgcdAux_rec, gauge_smul_left, IsPrimitiveRoot.zeta_sub_one_prime, DihedralGroup.r_mul_sr, toIcoDiv_sub_intCast_mul, sub_pow_eq_mul_pow_sub_pow_div_char, ConcaveOn.slope_anti_adjacent, MvPowerSeries.coeff_mul_left_one_sub_of_lt_order, abs_one, Matrix.det_fin_two, Quaternion.mul_imI, PreTilt.pow_dvd_mul_untiltAux_sub_untiltAux_mul, Nat.Prime.dvd_add_pow_sub_pow_of_dvd, RingHom.sub_mem_ker_iff, RingSubgroupsBasis.mem_addGroupFilterBasis_iff, WeierstrassCurve.Projective.dblX_eq, MonomialOrder.degree_sub_leadingTerm_lt_degree, CauSeq.exists_gt, ZNum.cast_sub, KaehlerDifferential.DLinearMap_apply, Units.divp_sub_divp, Valuation.map_sub_lt, Hyperreal.abs_lt_real_iff_infinitesimal, Int.preimage_fract, AffineBasis.coord_smul, AffineBasis.coord_apply_combination_of_mem, WittVector.peval_polyOfInterest', PowerSeries.invUnitsSub_mul_X, Nat.cast_le_pow_div_sub, Antivary.sub_smul_sub_nonpos, abs_le_one_iff_mul_self_le_one, odd_abs, div_sub_div, MvPolynomial.C_sub, GenContFract.sub_convs_eq, IsPrimitiveRoot.associated_sub_one_pow_sub_one_of_coprime, LieAlgebra.SpecialLinear.val_singleSubSingle, sbtw_zero_one_iff, AffineIndependent.affineCombination_eq_lineMap_iff_weight_lineMap, CauSeq.trichotomy, Polynomial.shiftedLegendre_eval_symm, lineMap_lt_lineMap_iff_of_lt', cross_cross_eq_smul_sub_smul', Mathlib.Tactic.Ring.smul_eq_intCast, QuaternionAlgebra.imI_mul, WeierstrassCurve.Projective.equation_iff, Path.segment_apply, lipschitzWith_lineMap, IsCyclotomicExtension.Rat.Three.cube_sub_one_eq_mul, sub_pow_eq_mul_pow_sub_pow_div_expChar_of_commute, geom_sum_Ico, AffineMap.lineMap_apply_one_sub, AffineBasis.linear_combination_coord_eq_self, Matrix.det_fin_three, Affine.Simplex.interior_eq_image_Ioo, Order.IsPredLimit.lt_sub_natCast, one_sub_div, FermatLastTheoremForThreeGen.Solution.associated_of_dvd_a_add_b_of_dvd_a_add_eta_sq_mul_b, CauSeq.equiv_def₃, geom_sum₂_Ico, mul_sub_mul_div_mul_neg_iff, Ideal.IsLocal.mem_jacobson_or_exists_inv, Quaternion.sub_imK, toIocDiv_sub_ofNat_mul', FermatLastTheoremForThreeGen.lambda_sq_dvd_c, ContinuousAlgHom.map_sub, lineMap_mono_left, RingPreordering.supportAddSubgroup_eq_bot, sum_four_sq_mul_sum_four_sq, WeierstrassCurve.Projective.dblX_eq', AddConstMapClass.map_sub_int, LaurentSeries.mem_integers_of_powerSeries, IsConjRoot.sub_algebraMap, Polynomial.descPochhammer_smeval_eq_ascPochhammer, AlgebraicGeometry.Proj.res_apply, sub_dvd_pow_sub_pow, Complex.im_zsmul, AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen, Polynomial.roots_countP_pos_le_signVariations, instFiniteDimensionalQuotientPolynomialIdealSpanSingletonSetSmithCoeffs, IsLprojection.coe_sup, Polynomial.eval_sub, AffineIndependent.units_lineMap, isIdempotentElem_iff_mul_one_sub_self, Valuation.leAddSubgroup_monotone, lineMap_slope_lineMap_slope_lineMap, sbtw_one_zero_iff, Polynomial.monomial_sub, FermatLastTheoremForThreeGen.Solution.lambda_sq_not_dvd_a_add_eta_mul_b, PowerSeries.trunc_sub, EuclideanGeometry.Sphere.secondInter_eq_lineMap, Subring.toAddSubgroup_injective, lineMap_strict_mono_left, weightedVSub_mem_vectorSpan_pair, IsPrimitiveRoot.associated_pow_sub_one_pow_of_coprime, Int.cast_negOfNat, Hyperreal.infinitePos_abs_iff_infinite, PowerSeries.WithPiTopology.multipliable_one_sub_X_pow, AbsoluteValue.sub_le_add, GaussianInt.mod_def, sub_one_dvd_pow_sub_one, ArithmeticFunction.intCoe_apply, Subgroup.widthInfty_mem_periods, sub_div', sub_self_div_two, PEquiv.toMatrix_swap, Subfield.coe_sub, MvPowerSeries.comp_substAlgHom, PowerSeries.rescale_neg_one_invOneSubPow, antilipschitzWith_lineMap, Function.Antiperiodic.int_mul_sub_eq, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec.image_basicOpen_eq_basicOpen, CauSeq.sup_inf_distrib_left, abs_zpow, lineMap_slope_slope_sub_div_sub, AlgebraicGeometry.Proj.instIsProperToSpecZeroOfFiniteTypeSubtypeMemOfNatNat, tendsto_pow_atTop_nhds_zero_iff, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, zsmul_eq_mul', HomogeneousLocalization.Away.finiteType, CauSeq.inf_idem, sub_mul_sub_nonneg_iff, Commute.isNilpotent_sub, AlgebraicGeometry.Proj.instQuasiCompactToSpecZeroOfFiniteTypeSubtypeMemOfNatNat, PowerSeries.coeff_mul_prod_one_sub_of_lt_order, C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum, Quaternion.re_mul, EuclideanDomain.sub_mul_div_left, MvPolynomial.IsSymmetric.sub, EuclideanGeometry.inversion_eq_lineMap, AffineMap.lineMap_mem_affineSpan_pair, PowerSeries.mk_one_mul_one_sub_eq_one, Nonneg.orderedSub, Matrix.sub_scalar_sq_eq_discr, dist_sq_lineMap_of_inner_eq_zero, AlgebraicGeometry.Proj.stalkIso'_symm_mk, signedDist_left_lineMap, WittVector.wittSub_zero, IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two', WeierstrassCurve.variableChange_a₆, ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_sub_of_squarefree, Nat.abs_ceil_sub_le, sub_pow_expChar_pow, wbtw_iff_of_le, Commute.geom_sum₂_Ico_mul, Sbtw.mem_image_Ioo, Int.fract_mul_natCast, IsAbsoluteValue.abv_sub_le, Quaternion.imK_sub, pow_two_pow_sub_pow_two_pow, Matrix.invOf_fromBlocks₁₁_eq, Algebra.FormallyUnramified.iff_exists_tensorProduct, AlgebraNormClass.toSeminormClass, FermatLastTheoremForThreeGen.Solution'.multiplicity_lambda_c_finite, Derivation.map_sub, AffineMap.lineMap_vadd, CharP.intCast_eq_zero_iff, Subgroup.instDiscreteTopPeriods, IsPrimitiveRoot.norm_sub_one_two, SetTheory.PGame.quot_sub, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, IsIntegral.zsmul, Surreal.dyadicMap_apply_pow, RingSubgroupsBasis.mul, MonomialOrder.degree_sub_of_lt, IsStarProjection.mul_one_sub_self, MulRingSeminormClass.toAddGroupSeminormClass, IsPrimitiveRoot.pow_sub_pow_eq_prod_sub_mul, sub_inv_antitoneOn_Iio, MulRingSeminorm.map_one', Polynomial.aeval_sub, Transcendental.linearIndependent_sub_inv, WithIdeal.instIsUniformAddGroup, PrimeSpectrum.isIdempotentElemEquivClopens_symm_compl, IntermediateField.zsmul_mem, Mathlib.Meta.NormNum.isNat_abs_neg, Algebra.IsAlgebraic.rank_fractionRing_polynomial, Even.pow_abs, rat_inv_continuous_lemma, Polynomial.discr_of_degree_eq_three, AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijective, Function.Periodic.int_mul_sub_eq, slope_def_module, Antivary.sub_mul_sub_nonpos, Int.fract_sub_ofNat, FermatLastTheoremForThreeGen.ex_cube_add_cube_eq_and_isCoprime_and_not_dvd_and_dvd, Valuation.map_sub_of_left_eq_zero, inv_eq_of_aeval_divX_ne_zero, left_lt_lineMap_iff_pos, toIcoDiv_sub_ofNat_mul', Subring.toAddSubgroup_top, abs_le_iff_mul_self_le, Localization.sub_mk, Finset.abs_prod, WeierstrassCurve.Jacobian.eval_polynomialZ, spectrum.sub_singleton_eq, geom_sum_Ico_le_of_lt_one, LieAlgebra.SpecialLinear.singleSubSingle_sub_singleSubSingle', jacobiSum_one_one, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, Set.Ioo.one_minus_lt_one, instIsAddKleinFourProdZModOfNatNat, exists_rat_near, lineMap_strict_mono_right, wbtw_mul_sub_add_iff, CauSeq.const_pos, FermatLastTheoremForThreeGen.Solution.lambda_dvd_a_add_eta_mul_b, IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one, AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjective, PowerSeries.IsWeierstrassDivisorAt.coeff_div_sub_seq_mem, MonomialOrder.degree_sub_leadingTerm_lt_iff, Hyperreal.coe_sub, IsLocalRing.isUnit_one_sub_self_of_mem_nonunits, Monovary.sub_smul_sub_nonneg, MonomialOrder.degree_sub_leadingTerm_le, AffineMap.homothety_eq_lineMap, IsCoprime.abs_abs, sq_sub_sq, Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero, sub_div_sub_smul_slope_add_sub_div_sub_smul_slope, normEDS_even, AffineMap.lineMap_vadd_lineMap, Field.mod_eq, Int.sub_floor_div_mul_lt, SimpContFract.determinant_aux, MulAlgebraNorm.smul', abs_pow, sub_pow_expChar, CauSeq.coe_inf, Rat.cast_sub, lineMap_lt_lineMap_iff_of_lt, LinearMap.BilinForm.apply_smul_sub_smul_sub_eq, Quaternion.imJ_sub, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_two, sub_mul_sub_neg_iff, GenContFract.abs_sub_convs_le, RootPairing.GeckConstruction.e_lie_u, lineMap_mono_right, Function.Antiperiodic.sub_nat_mul_eq, dist_lineMap_lineMap, AffineMap.lineMap_vsub_lineMap, Path.eqOn_extend_segment, MvPowerSeries.coeff_mul_prod_one_sub_of_lt_weightedOrder, Subgroup.hasDetPlusMinusOne_iff_abs_det, Ring.choose_smul_choose, MonovaryOn.sub_smul_sub_nonneg, selfAdjoint.val_nnqsmul, CauSeq.inf_le_left, CompleteOrthogonalIdempotents.bijective_pi, WittVector.nth_mul_coeff', IdealFilter.isUniform_iff_exists_ringFilterBasis, ClassGroup.exists_mem_finset_approx', nndist_lineMap_left, retractionOfSectionOfKerSqZero_tmul_D, instIsPushoutFractionRingMvPolynomial_1, rat_add_continuous_lemma, toIocDiv_mul_sub_self, sub_one_mul, Int.floor_sub_intCast, CauSeq.cauchy₃, LinearMap.BilinForm.sub_right, Associated.abs_left, WittVector.peval_polyOfInterest, ClassGroup.exists_mem_finsetApprox, spectrum.notMem_iff, left_le_lineMap_iff_nonneg, Polynomial.eval_multiset_prod_X_sub_C_derivative, lineMap_lt_left_iff_neg, HomogeneousLocalization.mk_add, mul_self_sub_one, Finset.cast_card_inter, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two, toIcoMod_sub_ofNat_mul, FermatLastTheoremForThreeGen.Solution.associated_of_dvd_a_add_b_of_dvd_a_add_eta_mul_b, Quaternion.mul_imJ, circleEquivGen_apply, Algebra.Generators.C_mul_X_sub_one_mem_ker, IsPrimitiveRoot.zeta_sub_one_prime', Hyperreal.IsSt.infinitesimal_sub, Mathlib.Meta.NormNum.isNat_abs_nonneg, ArchimedeanClass.FiniteElement.mk_sub_mk, degree_radical_le, Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_sup, Polynomial.valuation_X_eq_neg_one, IsPrimitiveRoot.pow_sub_one_mul_geom_sum_eq_pow_sub_one_mul_geom_sum, Lagrange.eval_basis_not_at_node, LieAlgebra.SpecialLinear.sl_non_abelian, WeierstrassCurve.Projective.Y_sub_Y_add_Y_sub_negY, IsLprojection.compl_mul, IsPrimitiveRoot.toInteger_sub_one_not_dvd_two, IsCyclotomicExtension.Rat.Three.lambda_dvd_mul_sub_one_mul_sub_eta_add_one, FermatLastTheoremForThreeGen.lambda_sq_dvd_or_dvd_or_dvd, AlgebraicGeometry.homogeneousLocalizationToStalk_stalkToFiberRingHom, instIsPushoutFractionRingMvPolynomial, Matrix.discr_fin_two, Int.fract_eq_iff, abs_two, convexOn_iff_slope_mono_adjacent, IsStarProjection.one_sub_nonneg, toIocMod_sub_intCast_mul, PowerSeries.IsWeierstrassDivisionAt.coeff_f_sub_r_mem, monovaryOn_iff_forall_mul_nonneg
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toAddMonoidWithOne 📖 | CompOp | 4208 mathmath: List.norm_prod_le, ArithmeticFunction.vonMangoldt.residueClass_eq, ValuativeRel.ValueGroupWithZero.mk_one_one, IsCyclotomicExtension.Rat.Three.eta_sq_add_eta_add_one, MvPolynomial.eval_indicator_apply_eq_one, hasFDerivAt_iff_hasDerivAt, ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_one, Quaternion.normSq_eq_zero, HomotopyCategory.spectralObjectMappingCone_δ'_app, one_le_div_iff, Num.cast_to_int, GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_one, ZMod.addOrderOf_coe, CategoryTheory.InjectiveResolution.Hom.hom'_f, Int.ceil_lt_iff, DerivedCategory.instIsLocalizationCochainComplexIntQQuasiIsoUp, KaehlerDifferential.kerCotangentToTensor_toCotangent, Matrix.isTotallyUnimodular_iff, CategoryTheory.ShortComplex.ShortExact.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoX₃CochainComplexMapSingleFunctorOfNatX₁, Quaternion.star_mul_self, WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero, ComplexShape.embeddingUpIntDownInt_f, MvPolynomial.dvd_monomial_one_iff_exists, Quaternion.coe_normSq_add, continuousOn_ceil, vsub_midpoint, Lagrange.interpolate_one, CauSeq.const_one, RootPairing.pairing_two_two_iff, CochainComplex.triangleOfDegreewiseSplit_obj₁, ZMod.isUnit_iff_coprime, charP_of_card_eq_prime, Algebra.FormallyUnramified.one_tmul_mul_elem, WeierstrassCurve.coeff_Ψ₂Sq, CochainComplex.mappingConeCompTriangleh_comm₁_assoc, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two', IsCyclotomicExtension.neZero_of_mem, AffineMap.lineMap_apply_module, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_symm_apply, Quaternion.star_imJ, Algebra.charP_iff, Lagrange.eval_iterate_derivative_eq_sum, Algebra.Generators.baseChange_val, TrivSqZeroExt.exp_inr, Matrix.list_prod_inv_reverse, LucasLehmer.X.fst_natCast, RingHom.ker_evalRingHom, RCLike.one_re, AddCircle.exists_gcd_eq_one_of_isOfFinAddOrder, even_sub_one, ofBoolRing_one, Quaternion.re_star, ordinaryHypergeometric_sum_eq, DihedralGroup.r_one_zpow, Matrix.invOf_fromBlocks₂₂_eq, RingHom.compLeftContinuousBounded_apply_apply, hasSum_geometric_of_norm_lt_one, CochainComplex.HomComplex.Cochain.fromSingleMk_neg, QuaternionAlgebra.natCast_re, List.nnnorm_prod, Quaternion.add_imJ, CategoryTheory.DifferentialObject.shiftFunctor_obj_d, IntermediateField.aeval_gen_minpoly, CochainComplex.mappingCone.δ_inl, CochainComplex.mappingCone.inl_v_descCochain_v_assoc, RootPairing.pairing_smul_root_eq_of_not_linearIndependent, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_neg, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, Quaternion.instSMulCommClass, Module.Relations.Solution.ofπ'_var, QuaternionAlgebra.self_add_star, Quaternion.add_imK, LinearMap.IsSymmetric.inner_map_polarization, Algebra.Presentation.differentials.comm₁₂_single, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_apply, uniq_inv_of_isField, IsStarNormal.one_sub, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add, AddChar.mulShift_one, DerivedCategory.right_fac, RootPairing.linearIndepOn_root_baseOf', Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, ZMod.pow_card_sub_one, PadicInt.lift_sub_val_mem_span, Algebra.TensorProduct.intCast_def', QuaternionGroup.a_one_pow_n, Int.smul_one_eq_cast, NormedRing.inverse_one_sub_norm, Quaternion.im_add, sq_eq_one_iff, Valuation.isEquiv_iff_val_sub_one_lt_one, SimpleGraph.deleteFar_iff, SimpleGraph.lapMatrix_toLinearMap₂', Quaternion.snd_imJ_dualNumberEquiv_symm, dist_midpoint_right, NormedSpace.expSeries_eq_ofScalars, Real.fourierCoeff_tsum_comp_add, sign_mul_self, Polynomial.dickson_one_one_mul, CompleteOrthogonalIdempotents.pair_iff, Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col, RootPairing.coroot_eq_polarizationEquiv_apply_root, Subring.center.smulCommClass_right, Quaternion.imI_zero, hasStrictFDerivAt_list_prod_finRange', Matrix.add_mul_mul_invOf_mul_eq_one, CFC.sqrt_eq_one_iff', CFC.posPart_one, InnerProductSpace.rankOne_one_left_eq_innerSL, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_symm_apply, CochainComplex.mappingCone.inr_f_d_assoc, CliffordAlgebraQuaternion.j_quaternionBasis, IsPrimitiveRoot.zeta_sub_one_prime_of_two_pow, Fin.isAddFreimanIso_Iio, bernsteinPolynomial.eval_at_1, Quaternion.imJ_im, Quaternion.coe_natCast, Quaternion.instNoZeroDivisors, PowerSeries.heval_C, modularCyclotomicCharacter.id, Quaternion.neg_re, IsIdempotentElem.coe_compl, PadicInt.valuation_p, tendsto_ceil_right', quadraticChar_card_card, CliffordAlgebra.foldl_prod_map_ι, EuclideanSpace.orthonormal_single, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, CochainComplex.HomComplex.Cochain.δ_single, Polynomial.resultant_X_add_C_right, Nat.cast_descFactorial_two, UnitAddCircle.lintegral_preimage, meromorphicOrderAt_const_ofNat, Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty, abs_sub_round, Metric.unitSphere.coe_one, round_neg_two_inv, Valuation.map_one_add_of_lt, AffineMap.hasDerivAtFilter, Int.floor_one, CochainComplex.mappingConeCompTriangle_obj₂, Int.cast_natCast, Finset.prod_one_sub_ordered, CFC.le_one, Odd.intCast_zmod_two, QuaternionGroup.orderOf_a_one, Quaternion.star_smul, Matrix.one_div_pow, WeierstrassCurve.c_relation, Matrix.det_add_replicateCol_mul_replicateRow, Algebra.normalizedTrace_eq_of_finiteDimensional, ZMod.LFunction_stdAddChar_eq_expZeta, Subgroup.HasDetPlusMinusOne.isParabolic_iff_of_upperTriangular, Polynomial.Chebyshev.U_eval_one, MvPolynomial.universalFactorizationMap_comp_map, BoundedContinuousFunction.algebraMap_apply, Rep.diagonalSuccIsoFree_inv_hom_single, spectrum.subset_closedBall_norm_mul, derivWithin_id', WeierstrassCurve.toCharNeTwoNF_t, one_add_le_one_add_mul_one_sub, Zsqrtd.nonneg_smul, ZMod.val_eq_one, AlgebraicGeometry.StructureSheaf.const_mul_rev, CFC.posPart_natCast, DirichletCharacter.LSeries_eulerProduct_tprod, CochainComplex.HomComplex.Cocycle.equivHom_symm_apply, WeierstrassCurve.Jacobian.add_of_Y_ne', round_add_natCast, arithGeom_eq', CliffordAlgebra.foldr'_ι, CochainComplex.isStrictlyGE_shift, SimpleGraph.DeleteFar.le_card_sub_card, right_lt_lineMap_iff_one_lt, Nat.Ioc_filter_modEq_cast, CochainComplex.mappingCone.id, CFC.one_le, WeierstrassCurve.coeff_preΨ', MeasureTheory.lpNorm_fun_div_natCast, UnitAddCircle.intervalIntegral_preimage, IsLprojection.Lnorm, Polynomial.smul_mem_rootSet, PreTilt.valAux_eq, hasSum_choose_mul_geometric_of_norm_lt_one, WittVector.verschiebung_zmod, CochainComplex.shiftFunctorZero_eq, TwoSidedIdeal.one_mem_iff, Int.cast_one_le_of_pos, RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraCartanSubalgebra, tsum_coe_mul_geometric_of_norm_lt_one', norm_natCast_eq_mul_norm_one, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, HasStrictDerivAt.pow, spinGroup.coe_star_mul_self, one_le_pow_mul_abs_eval_div, CategoryTheory.InjectiveResolution.ι'_f_zero, AddChar.exists_divisor_of_not_isPrimitive, Algebra.Generators.cotangentSpaceBasis_apply, CliffordAlgebra.involute_prod_map_ι, Quaternion.imI_sub, NormedSpace.invOf_exp_of_mem_ball, Subring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallNeg, Quaternion.one_imI, Asymptotics.isLittleOTVS_one, TwoSidedIdeal.one_mem, Quaternion.rank_eq_four, CochainComplex.mappingCone.liftCochain_v_snd_v_assoc, not_isUnit_prime_of_dvd_card, ZMod.orderOf_one_add_mul_prime, ContinuousLinearMap.hasDerivAtFilter, FermatLastTheoremForThreeGen.Solution.lambda_sq_not_dvd_a_add_eta_sq_mul_b, pow_four_add_four_mul_pow_four', RootPairing.root_coroot_two, ModuleCat.extendScalarsId_hom_app_one_tmul, Quaternion.star_eq_neg, CochainComplex.mappingCone.inr_f_fst_v, IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRoots, CochainComplex.isStrictlyLE_iff, ordinaryHypergeometric_radius_top_of_neg_nat₃, aeval_wittPolynomial, WittVector.ghostComponent_verschiebungFun, Int.fract_add_one, Quaternion.finrank_eq_four, inner_self_eq_one_of_norm_eq_one, NumberField.RingOfIntegers.instSMulDistribClass, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, pinGroup.coe_star_mul_self, FiniteField.isSquare_neg_one_iff, ArithmeticFunction.coe_moebius_mul_coe_zeta, CochainComplex.HomComplex.Cochain.leftShift_smul, WeierstrassCurve.Projective.nonsingularLift_some, Polynomial.resultant_add_left_deg, IncidenceAlgebra.eulerChar_prod, KaehlerDifferential.mvPolynomialBasis_repr_D_X, Quaternion.intCast_imK, QuaternionAlgebra.star_eq_two_re_sub, stdSimplexHomeomorphUnitInterval_symm_apply_coe, AlgebraicGeometry.StructureSheaf.const_self, PadicInt.appr_spec, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, Algebra.PowerBasis.norm_gen_eq_coeff_zero_minpoly, CochainComplex.HomComplex.Cochain.fromSingleEquiv_fromSingleMk, ZMod.invDFT_apply, CancelDenoms.cancel_factors_le, FermatLastTheoremForThreeGen.Solution.lambda_dvd_a_add_eta_sq_mul_b, Algebra.Generators.toAlgHom_ofComp_localizationAway, IsIdempotentElem.one_sub, RCLike.sub_conj, continuousOn_floor, Matrix.Pivot.listTransvecCol_mul_last_col, WeierstrassCurve.ofJNe0Or1728_Δ, QuaternionAlgebra.Basis.i_mul_i, FirstOrder.Field.realize_genericMonicPolyHasRoot, Quaternion.star_imI, AddChar.wInner_cWeight_self, IsNilpotent.isUnit_sub_one, CochainComplex.mappingCone.triangle_mor₁, AbsoluteValue.map_units_intCast, DirichletCharacter.LSeries_modOne_eq, cfc_const_one, Quaternion.coe_inv, WittVector.eq_iterate_verschiebung, IsCyclic.val_mulAutMulEquiv_apply, seminormFromConst_seq_one, FiniteField.isSquare_two_iff, ArithmeticFunction.intCoe_one, HomologicalComplex₂.shiftFunctor₂XXIso_refl, hasDerivAt_neg', sum_hom_units, Algebra.IsPushout.cancelBaseChange_tmul, Quaternion.normSq_natCast, CochainComplex.mappingCone.liftCochain_v_snd_v, IsCyclotomicExtension.discr_odd_prime, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, dist_left_midpoint, fwdDiff_iter_pow_eq_zero_of_lt, ComplexShape.instIsTruncLENatIntEmbeddingUpIntLE, WeierstrassCurve.Projective.equiv_some_of_Z_ne_zero, descPochhammer_succ_comp_X_sub_one, Module.exists_dual_forall_apply_eq_one, HahnSeries.SummableFamily.powers_zero, IsPrimitiveRoot.mem_nthRootsFinset, Quaternion.im_intCast, Quaternion.imJ_smul, Int.floor_add_one, Quaternion.imK_natCast, Polynomial.leadingCoeff_det_X_one_add_C, eventually_homothety_image_subset_of_finite_subset_interior, ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_three, sbtw_iff_mem_image_Ioo_and_ne, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, toIcoDiv_sub_natCast_mul', CochainComplex.instIsStrictlyLEObjHomologicalComplexIntUpSingle, ModularGroup.bottom_row_coprime, Algebra.FormallyUnramified.lmul_elem, QuotSMulTop.equivTensorQuot_naturality, List.nnnorm_prod_le', Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, round_two_inv, CliffordAlgebraDualNumber.equiv_symm_eps, LinearMap.IsReflective.apply_self_mul_coroot_apply, DirichletCharacter.LSeriesSummable_of_one_lt_re, WeierstrassCurve.variableChange_a₁, Algebra.Presentation.localizationAway_relation, Wbtw.right_mem_image_Ici_of_left_ne, Polynomial.aeval_iterate_derivative_of_ge, Finset.box_succ_disjUnion, Fin.sum_neg_one_pow, selfAdjoint.norm_sq_expUnitary_sub_one, SpecialLinearGroup.mem_center_iff_spec, Finset.affineCombinationLineMapWeights_apply_left, DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso, Rep.diagonalHomEquiv_symm_apply, SetTheory.PGame.quot_one, FormalMultilinearSeries.derivSeries_coeff_one, AddChar.sum_mulShift, MulAlgebraNorm.extends_norm', PadicInt.sub_zmodRepr_mem, Int.fract_add_fract_le, IsUltrametricDist.norm_add_one_le_max_norm_one, tsum_choose_mul_geometric_of_norm_lt_one', IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two_pow, ZMod.cast_one, Submodule.top_eq_ofList_cons_smul_iff, WeierstrassCurve.leadingCoeff_preΨ', Int.cast_div_ofNat_charZero, Int.cast_le_neg_one_of_neg, Hyperreal.epsilon_mul_omega, Order.pred_iterate, cfc_apply_one, Polynomial.dickson_two_one_eq_chebyshev_S, CategoryTheory.DifferentialObject.d_squared_apply, iteratedDeriv_pow, hasSum_coe_mul_geometric_of_norm_lt_one', Subring.closure_singleton_one, UpperHalfPlane.specialLinearGroup_apply, AffineMap.hasDerivWithinAt, RCLike.conj_nat_cast, IncidenceAlgebra.moebius_inversion_top, Quaternion.add_re, isUltrametricDist_iff_forall_norm_natCast_le_one, EuclideanSpace.basisFun_apply, Rat.cast_mk', IsNilpotent.isNilpotent_exp_sub_one, same_sub_div, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_postcomp, div_sub_same, tsum_coe_mul_geometric_of_norm_lt_one, ComplexShape.instIsRelIffNatIntEmbeddingUpIntLE, IsLocalRing.isUnit_or_isUnit_one_sub_self, WeierstrassCurve.Projective.polynomial_relation, hasDerivAt_exp_zero_of_radius_pos, FractionalIdeal.one_mem_one, ZNum.of_natCast, Int.floor_sub_one, ZMod.exists_sq_eq_neg_one_iff, ValuativeRel.inv_srel_one, Finpartition.IsEquipartition.card_biUnion_offDiag_le', ZMod.natCast_natAbs_valMinAbs, WittVector.factorPowSucc_comp_fontaineThetaModPPow, Subring.mk_eq_zero, PadicInt.norm_p_pow, Polynomial.Chebyshev.S_eq_U_comp_half_mul_X, SetTheory.Game.birthday_natCast, LaurentSeries.valuation_single_zpow, ZMod.wilsons_lemma, CStarAlgebra.mem_Icc_iff_norm_le_one, DihedralGroup.r_pow, Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_center, CochainComplex.instLinearIntFunctorSingleFunctors, FirstOrder.Field.charP_of_model_fieldOfChar, tendsto_fract_left', round_sub_one, RatFunc.mk_smul, PreTilt.coeff_pow_p, Quaternion.imI_mul, WeierstrassCurve.ofJ_1728_of_two_ne_zero, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, SpecialLinearGroup.mem_center_iff, WittVector.verschiebung_coeff_succ, Hyperreal.coe_ofNat, WeierstrassCurve.Δ_of_isCharTwoJEqZeroNF, Algebra.FormallyUnramified.finite_of_free_aux, WeierstrassCurve.isCharTwoJNeZeroNF_iff, NormedSpace.exp_series_hasSum_exp', IsNilpotent.exp_mul_exp_neg_self, Function.Antiperiodic.int_even_mul_periodic, ExpChar.pow_prime_pow_mul_eq_one_iff, Quaternion.snd_re_dualNumberEquiv_symm, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_C, Quaternion.coe_ratCast, Quaternion.imJ_one, summable_norm_mul_geometric_of_norm_lt_one, ContFract.convs_eq_convs', minpoly_algHom_toLinearMap, Polynomial.chebyshev_U_eq_dickson_two_one, sub_sq, CochainComplex.mappingCone.d_snd_v, Matrix.det_succ_row, DirichletCharacter.LSeries_twist_vonMangoldt_eq, CochainComplex.HomComplex.Cochain.rightUnshift_neg, WittVector.mul_polyOfInterest_aux2, Algebra.PreSubmersivePresentation.baseChange_jacobian, autEquivZmod_symm_apply_natCast, CochainComplex.HomComplex.Cochain.δ_fromSingleMk, nndist_midpoint_right, UnitAddTorus.mFourierSubalgebra_closure_eq_top, WeierstrassCurve.Jacobian.eval_polynomialY, FractionalIdeal.one_le, WeierstrassCurve.Affine.CoordinateRing.coe_basis, Polynomial.map_sub_roots_sprod_eq_prod_map_eval, ContinuousMultilinearMap.mkPiRing_apply_one_eq_self, GenContFract.of_partNum_eq_one_and_exists_int_partDen_eq, RootPairing.coxeterWeightIn_eq_four_iff_not_linearIndependent, iter_deriv_zpow', IsAlgebraic.invOf, IsPrimitiveRoot.zeta_sub_one_prime_of_ne_two, Matrix.adjugate_fin_succ_eq_det_submatrix, IsSl2Triple.lie_lie_smul_f, QuaternionAlgebra.natCast_im, lineMap_inv_two, CochainComplex.HomComplex.Cochain.map_v, ModularGroup.bottom_row_surj, Quaternion.coe_pow, PresheafOfModules.Derivation.d_map, Quaternion.ratCast_re, KaehlerDifferential.kerToTensor_apply, Quaternion.imJ_fst_dualNumberEquiv, quadraticChar_two, CategoryTheory.DifferentialObject.shiftFunctor_obj_obj, CStarAlgebra.norm_le_natCast_iff_of_nonneg, IsFractionRing.mk'_eq_one_iff_eq, round_eq_div, DirichletCharacter.LFunction_eq_LSeries, Algebra.SubmersivePresentation.ofSubsingleton_algebra_algebraMap, ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, Algebra.Presentation.differentials.hom₁_single, Matrix.det_le, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_hom_app, IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one', CochainComplex.ConnectData.map_comp_map, RingOfIntegers.exponent_eq_sInf, WeierstrassCurve.ofJNe0Or1728_c₄, RingHom.SurjectiveOnStalks.exists_mul_eq_tmul, Quaternion.im_re, Matrix.PosSemidef.natCast, Module.Basis.det_isEmpty, TrivSqZeroExt.instNormOneClass, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe, CochainComplex.HomComplex.leftHomologyData_K_coe, CochainComplex.mappingConeCompTriangle_mor₃, CochainComplex.HomComplex.Cochain.shift_add, ExpChar.expChar_center_iff, OrthonormalBasis.repr_self, IntermediateField.natCast_mem, Polynomial.aeval_sumIDeriv, toIocMod_sub_natCast_mul', WeierstrassCurve.Jacobian.addXYZ_of_X_eq, CancelDenoms.cancel_factors_lt, PadicComplex.coe_natCast, LieModule.trace_toEnd_genWeightSpace, NumberField.Embeddings.pow_eq_one_of_norm_le_one, ZMod.val_natCast_of_lt, DirichletCharacter.norm_LSeries_product_ge_one, CochainComplex.HomComplex.Cochain.comp_id, Ring.choose_eq_smul, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, norm_sub_mul_le', GenContFract.succ_nth_fib_le_of_nth_den, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_add, div_two_sub_self, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_sub, Polynomial.resultant_comm, ZMod.stdAddChar_coe, CategoryTheory.ProjectiveResolution.cochainComplex_d, Function.Antiperiodic.int_odd_mul_antiperiodic, CochainComplex.HomComplex.Cochain.toSingleMk_neg, PadicInt.irreducible_p, FermatLastTheoremForThreeGen.lambda_pow_four_dvd_c_cube, WeierstrassCurve.leadingCoeff_preΨ₄, CochainComplex.HomComplex.Cochain.ofHom_v_comp_d, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂_assoc, WeierstrassCurve.Projective.add_of_Z_eq_zero, IsPrimitiveRoot.prod_one_sub_pow_eq_order, Polynomial.dickson_one_one_eq_chebyshev_C, WittVector.factorPowSucc_fontaineThetaModPPow_eq, Polynomial.aeval_iterate_derivative_self, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, IntermediateField.isScalarTower, KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, WeierstrassCurve.b₂_of_isCharThreeJNeZeroNF, QuotSMulTop.equivTensorQuot_naturality_mk, Matrix.rank_one, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CochainComplex.HomComplex.Cochain.map_zero, Subring.mem_pointwise_smul_iff_inv_smul_mem, Quaternion.mul_imK, CochainComplex.cm5b.fac, Convex.mapsTo_lineMap, AbsoluteValue.eq_on_nat_iff_eq_on_int, Matrix.fromBlocks_eq_of_invertible₁₁, IsPrimitiveRoot.pow_sub_one_eq_geom_sum_mul_geom_sum_inv_mul_pow_sub_one, RatFunc.eval_one, Quaternion.star_re, DerivedCategory.singleFunctorsPostcompQIso_inv_hom, CochainComplex.instIsCompatibleWithShiftHomologicalComplexIntUpQuasiIso, Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence, WeierstrassCurve.Projective.Point.zero_point, continuousOn_fract, jacobiSum_trivial_trivial, QuaternionAlgebra.Basis.j_mul_j, Int.ceil_one_add, Quaternion.coe_commutes, CochainComplex.HomComplex.Cochain.toSingleMk_v, CliffordAlgebra.toProd_ι_tmul_one, Matrix.isTotallyUnimodular_iff_fintype, ModularGroup.coe_apply_complex, CochainComplex.HomComplex.leftHomologyData'_i, tsum_geometric_of_norm_lt_one, Nonneg.canonicallyOrderedAdd, List.norm_prod_le', Rep.finsuppToCoinvariantsTensorFree_single, ZMod.natCast_eq_one_iff_odd, Module.Relations.Solution.IsPresentation.linearEquiv_symm_var, CochainComplex.IsKInjective.rightOrthogonal, toIcoMod_add_natCast_mul, CStarAlgebra.mem_Icc_iff_nnnorm_le_one, Matrix.charpoly_natCast, pow_sub_one_mul_geom_sum_eq_pow_sub_one_mul_geom_sum, FirstOrder.Field.realize_eqZero, ZMod.completedLFunction_def_even, CochainComplex.ConnectData.cochainComplex_X, dvd_geom_sum₂_iff_of_dvd_sub, selfAdjoint.val_one, AddChar.IsPrimitive.zmod_char_eq_one_iff, CochainComplex.IsKInjective.Qh_map_bijective, Ordinal.toGame_one, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, Set.Ioo.one_minus_pos, ComplexShape.Embedding.embeddingUpInt_areComplementary, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_apply, AddSubgroup.intCast_mem_zmultiples_one, CochainComplex.HomComplex.Cochain.shift_neg, ZMod.natCast_self, CategoryTheory.DifferentialObject.shiftZero_hom_app_f, HomotopyCategory.instIsHomologicalIntUpHomologyFunctor, UniformSpace.Completion.coe_eq_one_iff, Finset.prod_indicator_biUnion_finset_sub_indicator, Int.range_castAddHom, Nat.abs_cast, Height.logHeight₁_one, ExteriorAlgebra.algebraMap_eq_one_iff, formalMultilinearSeries_geometric_apply_norm_le, Quaternion.imJ_zero, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, ZNum.gcd_to_nat, IsIdempotentElem.one_sub_mul_self, IsCoprime.mulVecSL, DirichletCharacter.LFunction_changeLevel, WittVector.iterate_verschiebung_mul, charP_of_ne_zero, wbtw_lineMap_iff, SeparatingDual.exists_eq_one, Quaternion.instFree, DerivedCategory.subsingleton_hom_of_isStrictlyLE_of_isStrictlyGE, nndist_right_lineMap, Quaternion.sub_imJ, neg_one_smul, Subring.mem_pointwise_smul_iff_inv_smul_mem₀, Polynomial.resultant_X_sub_C_right, MvPolynomial.sum_antidiagonal_card_esymm_psum_eq_zero, NormedSpace.expSeries_apply_eq_div', SimpleGraph.farFromTriangleFree_iff, sbtw_iff_left_ne_and_right_mem_image_Ioi, QuotSMulTop.map_comp_mkQ, NormedRing.inverse_one_sub_nth_order, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, ArchimedeanClass.mk_natCast, Quaternion.im_smul, ZMod.not_isUnit_of_mem_primeFactors, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, WittVector.verschiebung_nonzero, Int.floor_eq_zero_iff, TensorProduct.flip_mk_surjective, ZMod.cast_eq_val, complEDS_one, Finset.prod_sub, WeierstrassCurve.b₈_of_isCharNeTwoNF, CochainComplex.homotopyUnop_hom_eq, Quaternion.imI_fst_dualNumberEquiv, LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, CochainComplex.HomComplex.Cochain.toSingleMk_add, iteratedDerivWithin_eq_iteratedFDerivWithin, Quaternion.im_zero, AlgebraicGeometry.Proj.one_apply, WeierstrassCurve.Projective.dblU_eq, FermatLastTheoremForThreeGen.Solution.hab, mul_neg_one_pow_eq_zero_iff, Quaternion.algebraMap_def, Nat.cast_sub, CochainComplex.mappingCone.inr_f_d, Nat.eq_sq_add_sq_iff_eq_sq_mul, CauSeq.one_apply, SetTheory.PGame.quot_natCast, Matrix.vandermonde_succ, le_one_div_of_neg, Algebra.trace_algebraMap, Quaternion.imJ_coe, FermatLastTheoremForThreeGen.Solution.a_add_eta_mul_b, ZMod.natCast_zmod_surjective, Matrix.TransvectionStruct.det, PadicInt.maximalIdeal_eq_span_p, ZMod.minOrder_of_prime, mem_rootsOfUnity_iff_mem_nthRoots, CochainComplex.HomComplex.δ_v, RatFunc.coe_X, IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two, CochainComplex.instIsStrictlyGEObjHomologicalComplexIntUpSingle, Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, CHSH_inequality_of_comm, AdjoinRoot.smul_mk, CochainComplex.HomComplex.Cochain.comp_v, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, PadicInt.norm_lt_one_iff_dvd, AffineBasis.coord_apply, Quaternion.normSq_smul, ArithmeticFunction.coe_coe, Quaternion.coe_re, MeromorphicOn.divisor_natCast, NonarchimedeanRing.left_mul_subset, CochainComplex.HomComplex.Cochain.comp_zero_cochain_v, HomologicalComplex.dgoToHomologicalComplex_obj_d, PadicInt.mul_inv, IntermediateField.charZero, IsAlgebraic.nsmul, RCLike.I_mul_I, gaussSum_mul, ZMod.eq_zero_iff_even, Ideal.absNorm_mem, LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, OrthogonalIdempotents.prod_one_sub, CochainComplex.mappingCone.inr_f_descShortComplex_f_assoc, CochainComplex.HomComplex.Cochain.neg_v, Asymptotics.IsBigO.listProd, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, FiniteField.cast_card_eq_zero, Matrix.updateRow_eq_transvection, CochainComplex.HomComplex.Cochain.sub_v, GaussianInt.natCast_natAbs_norm, PerfectClosure.instCharP, WeierstrassCurve.Affine.polynomial_eq, Matrix.mul_inv_of_invertible, WeierstrassCurve.Jacobian.Point.fromAffine_some, AffineBasis.toMatrix_mul_toMatrix, FormalMultilinearSeries.ofScalars_apply_zero, ZMod.LFunction_eq_LSeries, DualNumber.inv_eps, WeierstrassCurve.Jacobian.add_of_Y_eq, Odd.neg_one_zpow, CochainComplex.mappingCone.liftCochain_v_descCochain_v, SameRay.exists_eq_smul_add, Subring.list_prod_mem, round_natCast, HahnSeries.SummableFamily.powers_of_not_orderTop_pos, fourierCoeff_bernoulli_eq, Polynomial.resultant_X_pow_right, AffineMap.homothety_one, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two, CochainComplex.mappingCone.lift_f_fst_v, monotoneOn_descPochhammer_eval, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop, CliffordAlgebra.foldl_one, Matrix.SpecialLinearGroup.coe_one, spectrum.norm_le_norm_mul_of_mem, CochainComplex.XIsoOfEq_shift, Finset.mem_convexHull', ZMod.LFunction_def_odd, AddConstMapClass.map_sub_nat', HasStrictFDerivAt.list_prod', Quaternion.smul_imK, Polynomial.isPrimitive_iff_content_eq_one, GradedTensorProduct.auxEquiv_one, WeierstrassCurve.ofJ0_Δ, LinearMap.BilinForm.apply_dualBasis_left, toIocMod_sub_natCast_mul, Matrix.det_add_mul, geom_sum_pos_iff, div_le_one_iff, GenContFract.abs_sub_convergents_le', LieAlgebra.Orthogonal.jb_transform, HomogeneousLocalization.val_one, FreeRing.coe_one, NormedSpace.exp_eq_tsum, PowerSeries.binomialSeries_add, Polynomial.dvd_comp_C_mul_X_add_C_iff, DirichletCharacter.mul_delta, Polynomial.algEquivCMulXAddC_symm_eq, Matrix.PosSemidef.one, TensorProduct.toMatrix_assoc, CochainComplex.HomComplex.Cochain.rightUnshift_comp, CochainComplex.HomComplex.Cochain.rightUnshift_units_smul, PresheafOfModules.Derivation.postcomp_d_apply, ComplexShape.eulerCharSignsUpInt_χ, Finset.sum_indicator_mod, HomologicalComplex.dgoEquivHomologicalComplex_unitIso, CochainComplex.mappingCone.inr_triangleδ, exteriorPower.ιMultiDual_apply_diag, Int.floor_natCast, multipliable_one_add_of_summable, CochainComplex.HomComplex.Cochain.ofHoms_comp, LucasLehmer.X.ofNat_fst, Matrix.Pivot.mul_listTransvecRow_last_col, CFC.one_le_iff, PresheafOfModules.Derivation.d_one, Polynomial.X_pow_sub_one_splits, arithGeom_zero_eq_mul_div', IsPrimitiveRoot.powerBasis_gen_mem_adjoin_zeta_sub_one, IsLprojection.Lcomplement, geom_series_succ, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_eq, DoubleCentralizer.norm_def, Quaternion.normSq_le_zero, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_sub, PadicInt.exists_mem_range, ArithmeticFunction.moebius_mul_coe_zeta, Matrix.det_one_add_smul, PreTilt.mk_comp_untilt_eq_coeff_zero, Polynomial.disc_of_degree_eq_two, DirichletCharacter.eval_modulus_sub, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_pow_ne_two, ExteriorAlgebra.ιMulti_zero_apply, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁, CochainComplex.HomComplex.leftHomologyData_π_hom_apply, EulerProduct.eulerProduct_completely_multiplicative, NormMulClass.toNormSMulClass_op, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_sub, even_neg_two, Real.not_summable_indicator_one_div_natCast, Padic.instCharZero, ModularGroup.tendsto_abs_re_smul, tsum_geometric_le_of_norm_lt_one, CochainComplex.instIsStrictlyLEExtendNatIntEmbeddingDownNatOfNat, IsOfFinOrder.eq_neg_one, spinGroup.coe_mul_star_self, Quaternion.inv_def, CongruenceSubgroup.Gamma1_mem', Algebra.Generators.H1Cotangent.δAux_C, NormedSpace.exp_eq_tsum_div, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, UInt16.toBitVec_nsmul, toIocDiv_natCast_mul_add, sub_half_lt_round, Polynomial.Chebyshev.leadingCoeff_U_natCast, WittVector.mk_pow_fontaineTheta, UnitAddTorus.mFourierCoeff_toLp, algebraRat.charZero, FirstOrder.Ring.realize_termOfFreeCommRing, CochainComplex.mappingCone.id_X, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, LieAlgebra.Orthogonal.indefiniteDiagonal_assoc, ZMod.minOrder, seminormFromBounded_one_le, GradedTensorProduct.tmul_coe_mul_one_tmul, GenContFract.convs'_succ, ModuleCat.RestrictionCoextensionAdj.counit'_app, CochainComplex.HomComplex.Cochain.single_zero, CochainComplex.mappingCone.inr_descShortComplex_assoc, PreTilt.coeff_frobeniusEquiv_symm, Rat.isNat_intCeil_ofIsNNRat, hasDerivAt_id', ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, SameRay.exists_eq_smul, Matrix.IsHermitian.eigenvectorUnitary_mulVec, IsSimpleRing.one_mem_of_ne_zero_mem, QuadraticAlgebra.norm_eq_one_iff_mem_unitary, ZMod.exists_sq_eq_two_iff, toIocMod_natCast_mul_add, PresheafOfModules.Derivation.d_mul, ContinuousLinearMap.deriv, WittVector.verschiebung_injective, RootPairing.Base.cartanMatrixIn_apply_same, Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap, IsIdempotentElem.spectrum_subset, Quaternion.zero_imJ, Module.Basis.sumQuot_repr_left, ZNum.cmp_to_int, HasDerivAt.pow, Polynomial.prod_roots_eq_coeff_zero_of_monic_of_splits, ZMod.inv_neg_one, ContinuousMap.HomotopyRel.trans_apply, instSMulDistribClassSubtypeMemSubalgebraIntegralClosure, ZMod.χ₈'_nat_eq_if_mod_eight, PadicInt.inv_mul, Matrix.GeneralLinearGroup.upperRightHom_apply, CochainComplex.mappingConeCompHomotopyEquiv_comm₂_assoc, multipliable_norm_one_add_of_summable_norm, one_sub_mul, Matrix.adjugate_fin_one, spinGroup.mul_star_self_of_mem, WittVector.coeff_p, Int.floor_div_natCast, ZNum.of_intCast, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_sub, Algebra.discr_powerBasis_eq_norm, jacobiSum_one_nontrivial, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id, PowerSeries.binomialSeries_zero, Complex.exp_nsmul, QuadraticForm.polarBilin_tmul, openSegment_eq_image', SignType.map_cast, ContinuousLinearMap.hasDerivAt, CliffordAlgebra.foldr_prod_map_ι, mul_neg_geom_sum, Quaternion.smul_im, archimedean_iff_nat_le, IsPrimitiveRoot.norm_eq_neg_one_pow, CochainComplex.HomComplex.leftHomologyData_i_hom_apply, PadicInt.fwdDiff_tendsto_zero, Subring.closure_singleton_natCast, Quaternion.normSq_nonneg, HomotopyCategory.instAdditiveIntUpShiftFunctor, WeierstrassCurve.b₂_of_isCharTwoJNeZeroNF, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_ne_two, Quaternion.instNontrivial, CochainComplex.HomComplex.Cochain.fromSingleMk_postcomp, Set.pairwise_disjoint_Ioo_add_intCast, WeierstrassCurve.Projective.addXYZ_of_X_eq, CochainComplex.mappingCone.d_snd_v'_assoc, IncidenceAlgebra.moebius_inversion_bot, instIsLocalizationHomologicalComplexIntUpHomotopyCategoryQuotientHomotopyEquivalences, QuotSMulTop.map_surjective, PrimeSpectrum.basicOpen_eq_zeroLocus_of_isIdempotentElem, Matrix.mem_unitaryGroup_iff, Int.fract_one_add, AddChar.sum_eq_card_of_eq_one, IsLprojection.coe_compl, Polynomial.derivative_X_sub_C_sq, FreeLieAlgebra.liftAux_map_smul, DirichletCharacter.sum_characters_eq, Module.Relations.Solution.ofQuotient_var, ModularGroup.denom_apply, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, WeierstrassCurve.b₂_of_isCharNeTwoNF, CochainComplex.HomComplex.Cochain.shift_zero, ZNum.cast_succ, HasDerivAt.fun_pow, ArithmeticFunction.vonMangoldt.residueClass_apply, Complex.lift_apply, Finset.univ_of_card_le_three, CategoryTheory.Functor.instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh, WeierstrassCurve.Jacobian.polynomialY_eq, Quaternion.coe_zpow, Polygon.edgeSet_eq_image_edgePath, ZNum.mod_to_int, logDeriv_fun_pow, WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero, Quaternion.im_one, CochainComplex.shiftFunctorZero_inv_app_f, GradedTensorProduct.tmul_one_mul_one_tmul, ZMod.natCast_self', WeierstrassCurve.Jacobian.equiv_zero_of_Z_eq_zero, FirstOrder.Field.instModelACFOfCharPOfIsAlgClosed, AffineMap.homothety_neg_one_apply, MeasureTheory.lpNorm_mul_natCast, hasDerivWithinAt_neg, Quaternion.imJ_nnratCast, Unitary.norm_sub_one_lt_two_iff, Subfield.list_prod_mem, Ring.choose_neg, IsCoprime.vecMulSL, LinearMap.trace_one, PresheafOfModules.unit_map_one, AddChar.zmod_add, Subfield.coe_zero, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_zero, QuadraticMap.associated_apply, WeierstrassCurve.Jacobian.eval_polynomialX, WeierstrassCurve.a₁_of_isCharTwoJNeZeroNF, Quaternion.re_zero, NormedSpace.expSeries_sum_eq, CochainComplex.HomComplex.Cochain.leftShift_comp, DoubleCentralizer.nnnorm_def, Matrix.one_fromCols_isTotallyUnimodular_iff, CharP.charP_center_iff, WeierstrassCurve.c₆_of_isCharThreeJNeZeroNF, Affine.Triangle.prod_eq_prod_one_sub_of_mem_line_point_lineMap, Polynomial.Chebyshev.U_eval_neg_one, LieAlgebra.LoopAlgebra.toFinsupp_symm_single, PrimeSpectrum.zeroLocus_eq_basicOpen_of_isIdempotentElem, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_symm_apply, Int.cast_two, ZMod.natCast_rightInverse, FloorSemiring.tendsto_pow_div_factorial_atTop, Padic.valuation_p, Matrix.toLinearEquiv'_symm_apply, CliffordAlgebra.evenOdd.gradedMonoid, WeierstrassCurve.Projective.eval_polynomialX, PowerSeries.constantCoeff_invUnitsSub, ValuativeRel.div_vle_one_iff, LinearMap.hasStrictDerivAt, CochainComplex.triangleOfDegreewiseSplit_obj₂, sub_eq_add_neg, Matrix.SpecialLinearGroup.det_coe, Matrix.PosDef.natCast, UInt64.toBitVec_nsmul, PowerSeries.mk_add_choose_mul_one_sub_pow_eq_one, WeierstrassCurve.toCharNeTwoNF_s, Summable.tendsto_alternating_series_tsum, LinearMap.det_eq_one_of_not_module_finite, Matrix.SpecialLinearGroup.map_apply_coe, Subring.coe_pointwise_smul, Finset.cast_card_union, RingHom.isIntegralElem_one, Polynomial.nthRoots_two_one, CliffordAlgebraQuaternion.k_quaternionBasis, Quaternion.re_add_im, IsPrimitiveRoot.coe_autToPow_apply, WeierstrassCurve.variableChange_b₈, Nat.cast_pred, List.nnnorm_prod_le, Polynomial.cauchyBound_smul, CharP.subring', zmod_val_inv_nsmul_nsmul, CochainComplex.HomComplex.Cochain.zero_cochain_comp_v, CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id_assoc, IsInvariantSubring.smul_mem, Polynomial.UniversalFactorizationRing.jacobian_resentation, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, PadicInt.norm_natCast_zmodRepr_eq_one_iff_ne, Ring.choose_zero_right, Rep.coindVEquiv_symm_apply_coe, RingEquiv.map_neg_one, CochainComplex.g_shortComplexTruncLEX₃ToTruncGE, Quaternion.fst_imK_dualNumberEquiv_symm, midpoint_eq_smul_add, Int.cast_neg_natCast, abs_pow_eq_one, Int.ceil_eq_iff, CharP.natCast_gcdA_mul_intCast_eq_gcd, gaussSum_frob, DirichletCharacter.LSeriesSummable_mul, Matrix.mem_specialOrthogonalGroup_iff, CochainComplex.homologyFunctor_shift, abs_neg_one_pow, midpoint_sub_right, Mathlib.Tactic.Zify.Nat.cast_sub_of_add_le, Matrix.vandermonde_eq_projVandermonde, Quaternion.coe_zero, DerivedCategory.instIsTriangulatedHomotopyCategoryIntUpQh, AddCommGroupWithOne.ext_iff, WeierstrassCurve.Affine.slope_of_Y_ne, ValuativeRel.one_rel_inv, PowerBasis.leftMulMatrix, ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_three, Algebra.SubmersivePresentation.ofSubsingleton_relation, RCLike.ofReal_natCast, Seminorm.gaugeSeminorm_ball, IsCyclotomicExtension.Rat.p_mem_span_zeta_sub_one, CochainComplex.HomComplex.Cochain.toSingleMk_v_eq_zero, Int.ceil_sub_natCast, SimpleGraph.isUniform_one, RingHom.charP_iff_charP, mem_affineSpan_iff_eq_affineCombination, Int.cast_negOnePow, xInTermsOfW_eq, Ring.uniformContinuousConstSMul, Set.Icc.one_sub_le_one, WeierstrassCurve.c₄_of_isCharThreeJNeZeroNF, ValuativeRel.zero_srel_one, IsIdempotentElem.ker_toSpanSingleton_eq_span, deriv_id'', IsSl2Triple.HasPrimitiveVectorWith.exists_nat, Function.mulSupport_intCast, OrthonormalBasis.coe_ofRepr, convexHull_basis_eq_stdSimplex, Module.Basis.trace_traceDual_mul, SimpleGraph.lapMatrix_mulVec_const_eq_zero, Polynomial.smeval_neg_nat, coevaluation_apply_one, CliffordAlgebraQuaternion.i_quaternionBasis, CochainComplex.isKInjective_shift_iff, mul_neg_geom_series, Quaternion.star_eq_two_re_sub, div_le_one_of_ge, Polynomial.dickson_one_one_comp_comm, CochainComplex.isStrictlyGE_iff, Function.FactorizedRational.mulSupport, WithAbs.tendsto_one_div_one_add_pow_nhds_one, ModularGroup.c_eq_zero, ZMod.val_one'', Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec, IsLocalRing.map_tensorProduct_mk_eq_top, AffineMap.lineMap_vsub_right, PadicInt.mahlerSeries_apply_nat, WeierstrassCurve.Affine.slope_of_Y_ne', GradedTensorProduct.includeLeft_apply, QuaternionAlgebra.star_smul', ArchimedeanClass.orderHom_zero, WeierstrassCurve.b₆_of_isCharTwoJNeZeroNF, Polynomial.Splits.coeff_zero_eq_prod_roots_of_monic, Polynomial.X_pow_sub_one_eq_prod, Int.floor_le_iff, Matrix.one_fromRows_isTotallyUnimodular_iff, Quaternion.one_im, IsCyclotomicExtension.Rat.inertiaDegIn_of_not_dvd, ext_iff, sign_mul_abs, SimpleGraph.farFromTriangleFree.le_card_sub_card, IsAbsoluteValue.abv_one, WeierstrassCurve.leadingCoeff_Ψ₂Sq, Quaternion.im_natCast, Polynomial.coeff_zero_eq_leadingCoeff_mul_prod_roots_of_splits, ZMod.natCast_pow_eq_zero_of_le, WeierstrassCurve.Δ_of_char_three, PowerSeries.mk_one_pow_eq_mk_choose_add, Quaternion.star_add_self, PrimeSpectrum.isIdempotentElemEquivClopens_one_sub, RootPairing.EmbeddedG2.twoShortAddLongRoot_eq, DirichletCharacter.LSeries_changeLevel, WeierstrassCurve.Jacobian.polynomial_relation, Quaternion.sub_re_self, Matrix.TransvectionStruct.det_toMatrix_prod, KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one, Int.fract_sub_one, Int.cast_natAbs, CochainComplex.HomComplex.Cochain.leftShift_rightShift_eq_negOnePow_rightShift_leftShift, Asymptotics.isEquivalent_nat_ceil, iteratedDeriv_fun_id_zero, abs_one_div, unitary.norm_sub_eq, SetTheory.Game.birthday_one, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_hom_app_f, IsNilpotent.exp_smul, LinearEquiv.det_symm_mul_det, CochainComplex.mappingCone.lift_f_fst_v_assoc, DualNumber.maximalIdeal_eq_span_singleton_eps, round_add_one, ZMod.toAddCircle_inj, Path.Homotopy.hcomp_apply, IsUnit.natCast_factorial_iff_of_charP, ZMod.completedLFunction_def_odd, ModuleCat.exteriorPower.iso₀_hom_apply, DerivedCategory.to_singleFunctor_obj_eq_zero_of_injective, norm_natCast, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, IsPrimitiveRoot.sub_one_norm_isPrimePow, GenContFract.IntFractPair.nth_stream_fr_lt_one, Odd.natCast_zmod_two, prodXSubSMul.smul, DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE, spectrum.spectralRadius_one, abs_sub_round_div_natCast_eq, isSMulRegular_submodule_iff_right_eq_zero_of_smul, norm_commutator_sub_one_le, CharP.exists', ZMod.mul_inv_of_unit, ZMod.inv_one, CochainComplex.HomComplex.Cochain.leftShift_rightShift, Convex.mem_Ioo, ComplexShape.embeddingUpNat_f, Hyperreal.coe_eq_one, CochainComplex.HomComplex.Cochain.ofHom_neg, Fin.isAddFreimanIso_Iic, CochainComplex.isSplitEpi_to_singleFunctor_obj_of_projective, lineMap_lt_right_iff_lt_one, GradedTensorProduct.auxEquiv_symm_one, deriv_pow, Algebra.SubmersivePresentation.jacobianRelations_spec, QuadraticAlgebra.lift_apply_apply, CharP.orderOf_eq_two_iff, Padic.norm_natCast_lt_one_iff, Matrix.PosSemidef.sqrt_eq_one_iff, BoundedContinuousFunction.coe_natCast, IntermediateField.AdjoinSimple.norm_gen_eq_one, Quaternion.imK_coe, Algebra.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, charZero_of_inj_zero, Int.ceil_eq_zero_iff, CochainComplex.HomComplex.Cochain.zero_v, WeierstrassCurve.Projective.polynomialZ_eq, bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt, Polynomial.disc_of_degree_eq_three, Matrix.toLpLin_one, Module.Basis.trace_mul_traceDual, QuadraticAlgebra.norm_eq_one, hasDerivAtFilter_neg, Polynomial.eval_monomial_one_add_sub, DerivedCategory.instLinearCochainComplexIntQ, tsum_pow_div_one_sub_eq_tsum_sigma, ZMod.val_inv_mul, div_neg_self, IsIdempotentElem.mul_one_sub_self, Polynomial.fwdDiff_iter_degree_add_one_eq_zero, iUnion_Icc_intCast, EuclideanDomain.mod_one, Sbtw.right_mem_image_Ioi, GenContFract.zeroth_cont_eq_h_one, Rat.cast_list_prod, Matrix.invOf_eq_nonsing_inv, HomologicalComplex.dgoEquivHomologicalComplex_functor, ComplexShape.instIsTruncGENatIntEmbeddingUpIntGE, Finpartition.IsEquipartition.sum_nonUniforms_lt', meromorphicOrderAt_const_natCast, Matrix.inv_smul, CochainComplex.isZero_of_isStrictlyLE, ZMod.valMinAbs_natCast_of_le_half, toIocMod_add_natCast_mul', hasDerivWithinAt_pow, Padic.norm_p_pow, Quaternion.add_imI, Padic.norm_p_lt_one, PadicInt.norm_ascPochhammer_le, UInt32.toBitVec_nsmul, Ideal.iInf_span_singleton_natCast, Quaternion.smul_coe, natCast_floor_eq_intCast_floor, ZMod.valMinAbs_natCast_of_half_lt, QuaternionAlgebra.im_natCast, NormedSpace.norm_expSeries_summable_of_mem_ball', eq_affineCombination_of_mem_affineSpan_image, Quaternion.instIsDomain, div_lt_one_of_neg, neg_one_pow_char, Matrix.equiv_compl_fromCols_mul_fromRows_eq_one_comm, Matrix.SpecialLinearGroup.isCoprime_col, Matrix.det_sum_le, Int.divisorsAntidiag_natCast, Int.fract_natCast, Subring.closure_insert_natCast, DualNumber.isMaximal_span_singleton_eps, AlgebraicClosure.instCharP, ValuativeRel.one_vle_div_iff, geom_sum_inv, ModularGroup.T_mul_apply_one, CauSeq.Completion.ofRat_one, Commute.sub_sq, iUnion_Ioc_add_intCast, IsPrimitiveRoot.norm_eq_one, CFC.sqrt_eq_one_iff, AddCircle.addOrderOf_div_of_gcd_eq_one, Quaternion.neg_imJ, Matrix.det_eq_sum_column_mul_submatrix_succAbove_succAbove_det, CochainComplex.instAdditiveIntFunctorSingleFunctors, Ideal.Quotient.smul_top, CochainComplex.shiftFunctor_obj_X, nnnorm_natAbs, CochainComplex.mappingConeCompHomotopyEquiv_comm₁, ContinuousLinearMap.derivWithin, WeierstrassCurve.variableChange_b₂, HahnSeries.SummableFamily.embDomain_succ_smul_powers, CharP.ringChar_zero_iff_CharZero, neg_div_self, Matrix.TransvectionStruct.inv_mul, ExpChar.of_injective_algebraMap', Quaternion.coe_smul, dist_right_midpoint, ZMod.val_cast_of_lt, Int.Ioo_eq_finset_map, Int.lt_floor_add_one, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_two, HomotopyCategory.mappingCone_triangleh_distinguished, Polynomial.IsPrimitive.content_eq_one, ordinaryHypergeometricSeries_apply_eq', invOf_sub_invOf, IncidenceAlgebra.mu_ofDual, spectrum.one_eq, CliffordAlgebra.range_ι_le_evenOdd_one, ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf, Quaternion.imI_neg, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂, Field.DirectLimit.exists_inv, UnitAddCircle.measure_univ, UInt8.toBitVec_nsmul, Polynomial.derivative_X_sub_C_pow, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂, meromorphicOrderAt_id, Matrix.TransvectionStruct.toMatrix_reindexEquiv_prod, ringExpChar.eq_iff, mul_gaussSum_inv_eq_gaussSum, Quaternion.mul_re, CFC.le_one_iff, Quaternion.imI_nnratCast, LinearMap.deriv, CochainComplex.HomComplex.Cochain.map_add, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj_assoc, ZNum.cast_add, Algebra.Extension.Hom.sub_one_tmul, ZNum.cast_lt, WeierstrassCurve.Jacobian.dblXYZ_of_Z_ne_zero, CategoryTheory.ProjectiveResolution.extMk_hom, Finset.tendsto_Ioo_neg, SpecialLinearGroup.det_eq_one, Finpartition.isUniform_one, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux, complEDS₂_zero, Matrix.one_zpow, CochainComplex.mappingCone.triangleRotateShortComplex_X₂, CochainComplex.HomComplex.Cochain.fromSingleMk_v, Polynomial.isRoot_of_unity_of_root_cyclotomic, Polynomial.descPochhammer_smeval_eq_descFactorial, EuclideanDomain.xgcdAux_val, Quaternion.imK_fst_dualNumberEquiv, Quaternion.imK_nnratCast, zsmul_succ', FDRep.average_char_eq_finrank_invariants, wittPolynomial_one, WeierstrassCurve.variableChange_b₆, WeierstrassCurve.Δ_of_isShortNF, CochainComplex.HomComplex.Cochain.fromSingleMk_add, IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two, IsPrimitiveRoot.prod_pow_sub_one_eq_order, Height.logHeight_one, Matrix.J_squared, Ideal.Quotient.index_eq_zero, IsNilpotent.isUnit_add_one, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_neg, Subring.mem_inv_pointwise_smul_iff, WeierstrassCurve.Jacobian.negMap_of_Z_eq_zero, Nat.cast_natAbs, Matrix.nonsing_inv_mul, Algebra.Generators.H1Cotangent.δAux_toAlgHom, IsCyclic.val_inv_mulAutMulEquiv_apply, Int.sub_one_lt_floor, CochainComplex.HomComplex.Cochain.shift_smul, nnnorm_algebraMap, KaehlerDifferential.D_apply, Nat.cast_card_eq_zero, Matrix.eRank_one, RootPairing.EmbeddedG2.long_eq_three_mul_short, Polynomial.Chebyshev.T_eval_one, Asymptotics.IsBigOWith.pow', QuaternionAlgebra.Basis.j_mul_k, preNormEDS'_odd, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two', Matrix.GeneralLinearGroup.coe_one, hasDerivAtFilter_id, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_apply, odd_neg_one, iUnion_Ico_add_intCast, round_natCast_add, CochainComplex.HomComplex.Cochain.ofHomotopy_refl, MulSemiringAction.charpoly_eq_prod_smul, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, Int.cast_add, WeierstrassCurve.b₆_of_isShortNF, MulSemiringAction.smul_coeff_charpoly, CategoryTheory.ProjectiveResolution.Hom.hom'_f_assoc, hasDerivAt_update, quadraticCharFun_one, AffineMap.right_vsub_lineMap, HomologicalComplex.dgoToHomologicalComplex_obj_X, Quaternion.re_fst_dualNumberEquiv, IsDivSequence.smul, IsFractionRing.charP_of_isFractionRing, Int.ceil_add_one, iteratedDeriv_fun_id, Quaternion.eq_re_of_eq_coe, OrthonormalBasis.singleton_apply, Matrix.IsTotallyUnimodular.fromCols_one, Complex.liftAux_neg_I, CochainComplex.mappingCone.ext_from_iff, AddChar.mulShift_unit_eq_one_iff, RCLike.sqrt_one, EuclideanDomain.div_self, inner_eq_sum_norm_sq_div_four, Rat.cast_lt_natCast, Quaternion.imK_zero, Wbtw.left_mem_image_Ici_of_right_ne, MvPowerSeries.rescaleAlgHom_one, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, one_le_cfc_iff, IntermediateField.charP', CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, Polynomial.preHilbertPoly_eq_choose_sub_add, selfAdjoint.unitarySelfAddISMul_coe, WittVector.mul_polyOfInterest_aux4, Matrix.det_permutation, neg_one_pow_expChar, NNRat.mk_natCast, tendsto_nat_floor_mul_div_atTop, affineHomeomorph_image_I, DerivedCategory.instIsIsoMapCochainComplexIntQ, Int.ModEq.listProd_map, AddChar.pow_mulShift, ValuativeRel.one_rel_div_iff, Finset.sum_centroidWeights_eq_one_of_card_eq_add_one, DirichletCharacter.LSeries.mul_mu_eq_one, ModularGroup.coe_T_inv, Polynomial.leadingCoeff_X_pow_sub_C, ZNum.le_to_int, ModularGroup.T_inv_mul_apply_one, Set.pairwise_disjoint_Ico_add_intCast, CochainComplex.HomComplex.Cocycle.toSingleMk_zero, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_apply, Matrix.PosDef.one, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, Rat.cast_mkRat_of_ne_zero, KaehlerDifferential.one_smul_sub_smul_one_mem_ideal, Quaternion.norm_coe, Quaternion.sub_self_im, CochainComplex.HomComplex.Cochain.leftUnshift_v, IsSl2Triple.lie_h_e_smul, Matrix.UnitaryGroup.one_apply, IsNilpotent.isUnit_one_add, MulChar.sum_one_eq_card_units, Rat.valuation_le_one_iff_den, PresheafOfModules.Derivation.congr_d, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, DirichletCharacter.sum_char_inv_mul_char_eq, CochainComplex.mappingConeCompHomotopyEquiv_comm₁_assoc, CharZero.charZero_iff_forall_prime_ne_zero, RCLike.add_conj, RootPairing.Base.eq_one_or_neg_one_of_mem_support_of_smul_mem, div_le_one_of_neg, CochainComplex.ConnectData.map_f, GradedTensorProduct.tmul_one_mul_coe_tmul, ArchimedeanClass.mk_natCast_nonneg, CFC.abs_natCast, ZMod.val_one', ZMod.coe_int_inv_mul_eq_one, RCLike.im_eq_conj_sub, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂, hasFDerivAt_list_prod', CliffordAlgebra.invOf_ι_mul_ι_mul_ι, AddChar.to_mulShift_inj_of_isPrimitive, Nimber.instCharPOfNatNat, EuclideanDomain.gcdB_zero_left, arithGeom_same_eq_mul_div', EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, Finset.norm_prod_one_add_sub_one_le, Polynomial.smul_mem_rootSet_iff, sbtw_iff_right_ne_and_left_mem_image_Ioi, MeasureTheory.lpNorm_fun_mul_natCast, CochainComplex.mappingCone.triangleRotateShortComplex_X₃, PerfectClosure.natCast_eq_iff, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, Char.card_pow_card, AddCircle.coe_fract, Int.cast_negSucc, PadicInt.coe_one, iteratedDerivWithin_comp_three, Finset.centerMass_smul_left, LieSubmodule.mem_baseChange_iff, PowerSeries.coeff_invUnitsSub, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow', CochainComplex.HomComplex.Cochain.rightShift_leftShift, iter_deriv_zpow, instSMulDistribClassAlgEquiv, MulSemiringAction.smul_charpoly, Matrix.transvection_zero, RootPairing.pairing_neg_one_neg_four_iff, Summable.hasProdUniformlyOn_nat_one_add, geom_sum_Ico_mul, KaehlerDifferential.ker_map, instQFactorsThroughHomotopyIntUp, WeierstrassCurve.Jacobian.nonsingularLift_some, WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis, Matrix.IsTotallyUnimodular.apply, segment_eq_image, hasFDerivWithinAt_iff_hasDerivWithinAt, Int.fract_add_natCast, nndist_left_midpoint, CStarRing.instNormOneClassOfNontrivial, AffineIsometryEquiv.dist_pointReflection_self, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, FermatLastTheoremForThreeGen.Solution'.ha, IsPrimitiveRoot.finite_quotient_span_sub_one', IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite, ordinaryHypergeometricSeries_apply_zero, IsPrimitiveRoot.minpoly_sub_one_eq_cyclotomic_comp, Quaternion.one_imK, CharP.subring, trace_eq_finrank_mul_minpoly_nextCoeff, NormedSpace.expSeries_summable', MulChar.val_neg_one_eq_one_of_odd_order, geom_sum_Ico_mul_neg, LinearOrderedField.inducedOrderRingHom_toFun, Nat.range_mul_add, abs_sub_round_eq_min, CategoryTheory.DifferentialObject.shiftZero_inv_app_f, CochainComplex.HomComplex.Cochain.ofHom_v, toIcoMod_sub_natCast_mul', MeasureTheory.L2.inner_indicatorConstLp_one, hasStrictFDerivAt_iff_hasStrictDerivAt, CochainComplex.HomComplex.Cochain.ofHom_sub, geom_sum_eq, CochainComplex.instLinearHomologicalComplexIntUpShiftFunctor, binomialSeries_apply, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, DerivedCategory.instAdditiveHomotopyCategoryIntUpQh, Unitary.norm_sub_one_sq_eq, Matrix.IsTotallyUnimodular.one_fromRows, TwoSidedIdeal.mem_jacobson_iff, PosNum.cast_to_int, isCyclotomicExtension_iff_eq_adjoin, isQuasiregular_iff_isUnit, Ring.choose_zero_ite, Function.Antiperiodic.nat_mul_sub_eq, ValuativeRel.zero_vlt_one, AddChar.zmodChar_apply', EulerProduct.eulerProduct_completely_multiplicative_tprod, CochainComplex.HomComplex.Cochain.leftUnshift_smul, Rat.natCast_le_cast, summable_prod_mul_pow, dist_right_pointReflection, PiToModule.fromMatrix_apply_single_one, CochainComplex.mappingCone.inr_f_snd_v, Quaternion.normSq_inv, iteratedDeriv_mul, IntermediateField.adjoin_one, QuadraticMap.associated_toQuadraticMap, QuaternionAlgebra.star_add_self, toIcoDiv_zero_one, CochainComplex.instIsKInjectiveObjIntShiftFunctor, LinearMap.isPositive_natCast, quadratic_eq_zero_iff_discrim_eq_sq, Algebra.normalizedTrace_eq_of_fininteDimensional, CochainComplex.mappingConeCompTriangle_mor₃_naturality, eventually_homothety_mem_of_mem_interior, CategoryTheory.Functor.instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, IsPrimitiveRoot.associated_sub_one_map_sub_one, Quaternion.imI_im, one_div_le_one_div_of_neg, CochainComplex.HomComplex.Cochain.shiftLinearMap_apply, Int.fract_sub_natCast, ZMod.algebraOfModule.proof, eq_pos_convex_span_of_mem_convexHull, IsPrimitiveRoot.finite_quotient_span_sub_one, Matrix.UnitaryGroup.one_val, neg_one_pow_eq_pow_mod_two, FiniteField.isSquare_neg_two_iff, Matrix.TransvectionStruct.prod_mul_reverse_inv_prod, Zsqrtd.le_arch, WeierstrassCurve.Projective.addXYZ_neg, PreTilt.coeff_frobenius, ringExpChar.of_eq, DualNumber.exists_mul_left_or_mul_right, mul_one_sub, FGModuleCat.FGModuleCatCoevaluation_apply_one, legendreSym.at_two, Matrix.SpecialLinearGroup.isCoprime_row, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, Int.fract_one, one_lt_div_of_neg, DerivedCategory.instIsLocalizationHomotopyCategoryIntUpQhQuasiIso, Int.fract_periodic, FermatLastTheoremForThreeGen.a_cube_b_cube_congr_one_or_neg_one, CancelDenoms.cancel_factors_ne, Ideal.mem_jacobson_iff, Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_det, trace_eq_trace_adjoin, dvd_pow_sub_one_of_dvd, NormedSpace.expSeries_div_hasSum_exp_of_mem_ball, Matrix.permMatrix_l2_opNorm_le, NumberField.Ideal.liesOver_primesOverSpanEquivMonicFactorsMod_symm, Summable.alternating, ZMod.isSquare_neg_one_iff, CompleteOrthogonalIdempotents.option, ZMod.val_one_eq_one_mod, Mathlib.Tactic.Ring.natCast_int, AffineMap.hasDerivAt, QuaternionAlgebra.imK_natCast, Int.ceil_add_natCast, MonomialOrder.span_leadingTerm_eq_span_monomial', HomologicalComplex₂.shiftFunctor₁XXIso_refl, ArithmeticFunction.coe_zeta_mul_coe_moebius, iteratedDerivWithin_zpow, Polynomial.det_taylorLinearEquiv_toLinearMap, Int.cast_four, Polynomial.SplittingField.instExpChar, AddConstMapClass.map_add_int, IncidenceAlgebra.sum_Icc_mu_left, ZMod.lift_castAddHom, Quaternion.im_coe, Finset.weightedVSubVSubWeights_apply_right, Quaternion.re_exp, ZMod.mul_val_inv, PadicInt.coe_natCast, Subring.mem_smul_pointwise_iff_exists, dist_lineMap_right, CochainComplex.mappingCone.triangleRotateShortComplex_X₁, MeasureTheory.lpNorm_fun_natCast_mul, Quaternion.algebraMap_injective, Field.DirectLimit.mul_inv_cancel, abs_mul_sign, PowerSeries.exp_pow_sum, CharP.addOrderOf_one, NormedDivisionRing.to_normOneClass, ZMod.cast_natCast', ContinuousMap.HomotopyWith.trans_apply, AdjoinRoot.smul_of, quadratic_eq_zero_iff_of_discrim_eq_zero, RCLike.sqrt_eq_real_add_ite, PreTilt.coeff_iterate_frobeniusEquiv_symm, DerivedCategory.left_fac_of_isStrictlyLE_of_isStrictlyGE, CategoryTheory.Free.embedding_map, CochainComplex.shiftFunctor_map_f', IsPrimitiveRoot.associated_map_sub_one_map_sub_one, WittVector.bind₁_wittMulN_wittPolynomial, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, CochainComplex.mappingCone.ext_to_iff, ArchimedeanClass.stdPart_one, one_div_lt_of_neg, CochainComplex.ConnectData.restrictionLEIso_inv_f, IsLprojection.coe_top, ZMod.cast_one', ArchimedeanClass.exists_nat_ge_of_mk_nonneg, NormedSpace.expSeries_apply_eq, PiLp.basisFun_apply, WeierstrassCurve.coeff_Φ, IsCyclotomicExtension.zeta_pow, Polynomial.fwdDiff_iter_eq_zero_of_degree_lt, PadicInt.denseRange_natCast, UnitAddTorus.mFourier_norm, WeierstrassCurve.b₆_of_isCharThreeJNeZeroNF, Int.natCast_mul_floor_div_cancel, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, toIocDiv_sub_natCast_mul, ExteriorAlgebra.liftAlternating_one, Matrix.eval_charpolyRev, Matrix.GeneralLinearGroup.continuous_upperRightHom, PadicAlgCl.valuation_p, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π', CochainComplex.HomComplex.Cochain.rightShift_zero, sum_embeddings_eq_finrank_mul, tendsto_nat_floor_div_atTop, hasFDerivAtFilter_iff_hasDerivAtFilter, openSegment_eq_image, ZMod.lift_comp_coe, Rep.freeLiftLEquiv_apply, Zsqrtd.natCast_im, PadicComplex.valuation_p, AlgebraicGeometry.StructureSheaf.const_one, Matrix.adjugate_eq_one_of_card_eq_one, ZMod.pow_card_sub_one_eq_one, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃, wbtw_zero_one_iff, IncidenceAlgebra.zeta_prod_apply, one_lt_div_iff, CategoryTheory.ProjectiveResolution.Hom.hom'_f, xInTermsOfW_aux, Quaternion.normSq_eq_norm_mul_self, Ring.descPochhammer_smeval_add, Summable.summable_log_norm_one_add, CochainComplex.singleFunctor_obj_d, Matrix.adjugate_apply, norm_natAbs, ascPochhammer_eval_eq_zero_iff, Matrix.det_transvection_of_ne, Ideal.Quotient.stabilizerHom_apply, IsIdempotentElem.ker_toSpanSingleton_one_sub_eq_span, Ideal.ResidueField.exists_smul_eq_tmul_one, Profinite.NobelingProof.factors_prod_eq_basis_of_ne, ModularGroup.T_pow_mul_apply_one, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, CoxeterSystem.lengthParity_comp_simple, smul_add_one_sub_smul, CochainComplex.quasiIso_shift_iff, RCLike.one_im, nndist_midpoint_left, RCLike.toZeroLEOneClass, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, Finset.centroidWeights_apply, RCLike.natCast_re, CochainComplex.HomComplex.Cochain.rightUnshift_v, HomotopyCategory.composableArrowsFunctor_obj, ModularGroup.exists_row_one_eq_and_min_re, addRothNumber_le_ruzsaSzemerediNumber, WeierstrassCurve.variableChange_def, Int.ceil_sub_one, Int.coe_castAddHom, AffineBasis.sum_coord_apply_eq_one, ZMod.natCast_eq_natCast_iff', CliffordAlgebra.GradedAlgebra.ι_apply, HasFPowerSeriesAt.hasStrictDerivAt, Matrix.charpoly_one, ComplexShape.instIsRelIffNatIntEmbeddingDownNat, Function.Periodic.nat_mul_sub_eq, ZMod.natCast_eq_iff, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, hasFDerivAt_list_prod_finRange', AddChar.mulShift_apply, ZMod.AddAutEquivUnits_apply, ZMod.natCast_val, LinearMap.hasDerivWithinAt, summable_choose_mul_geometric_of_norm_lt_one, Module.Relations.map_single, CochainComplex.shiftFunctorAdd'_inv_app_f', RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra', QuaternionAlgebra.Basis.lift_one, WeierstrassCurve.Jacobian.addMap_of_Z_ne_zero, QuadraticAlgebra.norm_natCast, ContinuousMap.adjoin_id_eq_span_one_union, Matrix.TransvectionStruct.mul_sumInl_toMatrix_prod, CochainComplex.exactAt_of_isLE, WittVector.mul_polyOfInterest_vars, baseChange_ext_iff, jacobiSym.at_neg_two, DerivedCategory.instHasLeftCalculusOfFractionsHomotopyCategoryIntUpQuasiIso, geom_sum_mul, ordinaryHypergeometric_radius_top_of_neg_nat₂, IsUltrametricDist.nnnorm_add_one_le_max_nnnorm_one, QuotSMulTop.equivQuotTensor_naturality, Quaternion.coe_imI, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, ModuleCat.free_ε_one, Int.ModEq.listProd_map_one, eq_affineCombination_of_mem_affineSpan_of_fintype, ZMod.natCast_comp_val, Int.le_ceil_iff, Asymptotics.continuousAt_iff_isLittleO, Rat.isNat_intFract_of_isInt, Matrix.det_one_sub_mul_comm, ZMod.natCast_eq_zero_iff, WeierstrassCurve.Affine.addPolynomial_eq, iccHomeoI_apply_coe, KaehlerDifferential.derivationQuotKerTotal_apply, ModP.preVal_mk, AdicCompletion.transitionMap_comp_reduceModIdeal, QuaternionAlgebra.Basis.k_self, one_le_sq_iff_one_le_abs, Orthonormal.linearIsometryEquiv_symm_apply_single_one, nndist_midpoint_midpoint_le', RingPreordering.one_notMem_support, CommRingCat.Colimits.quot_one, Matrix.add_mul_mul_invOf_mul_eq_one', AddChar.tendsto_eval_one_sub_pow, Valuation.one_srel_iff, CStarAlgebra.inv_le_one, WeierstrassCurve.variableChange_a₂, Num.cast_sub', Subring.smul_closure, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, ModP.v_p_lt_preVal, dist_homothety_self, IsCyclotomicExtension.Rat.Three.eta_sq, Quaternion.imJ_neg, odd_sq_dvd_geom_sum₂_sub, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_zero, IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero, sum_Ioo_inv_sq_le, NumberField.Units.coe_neg_one, Matrix.SpecialLinearGroup.scalar_eq_coe_self_center, WeierstrassCurve.variableChange_a₃, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, one_add_le_one_sub_mul_one_add, CochainComplex.mappingCone.map_inr, cfc_predicate_one, Num.cast_ofZNum, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, TruncatedWittVector.charP_zmod, summable_pow_div_add, CochainComplex.shiftFunctorAdd'_eq, Quaternion.sub_self_re, EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers, NormedSpace.expSeries_div_summable, CochainComplex.shiftFunctorAdd'_inv_app_f, mahler_natCast_eq, DihedralGroup.orderOf_r_one, FiniteField.two_pow_card, ZMod.toAddCircle_natCast, Subfield.coe_one, HomotopyCategory.instLinearIntUpShiftFunctor, summable_descFactorial_mul_geometric_of_norm_lt_one, IsSimpleRing.one_mem_of_ne_bot, CochainComplex.mappingCone.liftCochain_v_fst_v, tsum_choose_mul_geometric_of_norm_lt_one, ordinaryHypergeometric_eq_tsum, quadraticChar_neg_two, IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one, NormedSpace.expSeries_apply_eq_div, Order.IsPredPrelimit.lt_sub_natCast, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, Algebra.Generators.H1Cotangent.δAux_ofComp, exists_jacobiSum_eq_neg_one_add, IsCoprime.exists_SL2_row, Matrix.SpecialLinearGroup.ext_iff, Module.Relations.Quotient.linearMap_ext_iff, Quaternion.intCast_imI, Padic.norm_natCast_eq_one_iff, IsScalarTower.rat, AddChar.wInner_cWeight_eq_one_iff_eq, iteratedDerivWithin_one_div, CochainComplex.HomComplex.Cochain.fromSingleMk_zero, Nat.Partition.powerSeriesMk_card_restricted_eq_powerSeriesMk_card_countRestricted, Nat.abs_sub_ceil_le, ZMod.dft_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, Quaternion.fst_imJ_dualNumberEquiv_symm, CochainComplex.mappingCone.decomp_from, IsCyclotomicExtension.discr_prime_pow_ne_two, CochainComplex.mappingCone.inl_v_triangle_mor₃_f_assoc, PadicInt.mahlerTerm_one, Matrix.fromRows_one_isTotallyUnimodular_iff, Matrix.det_fromBlocks₁₁, QuaternionAlgebra.re_natCast, Nat.cast_choose_eq_descPochhammer_div, AbsoluteValue.exists_one_lt_lt_one_pi_of_not_isEquiv, bijective_rootsOfUnityAddChar, HomotopyCategory.Pretriangulated.distinguished_cocone_triangle, Quaternion.zero_imK, Pell.pellZd_succ_succ, IsCyclotomicExtension.Rat.inertiaDeg_eq, WeierstrassCurve.ofJ1728_j, SimpleGraph.not_isUniform_iff, AddChar.mulShift_mul, CochainComplex.mappingConeCompTriangle_mor₁, CochainComplex.mappingCone.inr_triangleδ_assoc, Matrix.vecMul_permMatrix, dist_self_homothety, CochainComplex.cm5b.instIsStrictlyGEBiprodIntMappingConeIdIOfHAddOfNat, WeierstrassCurve.c₆_of_isCharTwoJEqZeroNF, IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two, ZMod.inv_mul_of_unit, Matrix.toLpLin_symm_id, CochainComplex.HomComplex.Cochain.leftShift_zero, Polynomial.eval_iterate_derivative_rootMultiplicity, GenContFract.convs_succ, CochainComplex.mappingCone.inl_v_snd_v_assoc, IsCyclotomicExtension.neZero_of_mem', Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub, Finset.sum_centroidWeights_eq_one_of_card_ne_zero, iteratedDerivWithin_fun_id, CliffordAlgebra.reverse_prod_map_ι, LinearMap.BilinForm.dualBasis_eq_iff, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_zero, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π'_assoc, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, iUnion_Icc_add_intCast, Polynomial.comp_neg_X_leadingCoeff_eq, WittVector.iterate_verschiebung_coeff_eq_zero, Int.Icc_eq_finset_map, MatrixModCat.mem_toModuleCatObj, Matrix.add_mul_mul_mul_invOf_eq_one, Differential.logDeriv_one, QuaternionAlgebra.star_add_self', arithGeom_eq, NormedRing.inverse_add, RCLike.re_eq_add_conj, CochainComplex.instLinearIntShiftFunctor, sub_pow, Nat.forall_exists_prime_gt_and_eq_mod, MixedCharZero.charP_quotient, AdjoinRoot.root_isInv, Quaternion.imK_mul, CStarAlgebra.nnnorm_le_one_iff_of_nonneg, Matrix.det_fromBlocks_one₁₁, CochainComplex.triangleOfDegreewiseSplit_mor₂, nonunits.subset_compl_ball, Polynomial.Chebyshev.C_eval_two, Summable.multipliableLocallyUniformlyOn_one_add, Matrix.discr_of_card_eq_two, Set.Icc.instIsCancelMulZero, IsPrimitiveRoot.finite_quotient_toInteger_sub_one, odd_add_two, Int.absNorm_under_mem, HomologicalComplex.dgoEquivHomologicalComplex_counitIso, Quaternion.coe_div, sub_one_lt, NormOneClass.induced, PadicInt.zmodRepr_spec, Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, NormedSpace.expSeries_apply_zero, HomotopyCategory.instLinearIntUpSingleFunctor, PresheafOfModules.unitHomEquiv_apply_coe, LieModule.trace_comp_toEnd_genWeightSpace_eq, WittVector.ker_map_le_ker_mk_comp_ghostComponent, CochainComplex.HomComplex.Cochain.ofHoms_v_comp_d, CochainComplex.mappingCone.inr_f_triangle_mor₃_f, NormedSpace.invOf_exp, ModuleCat.FreeMonoidal.εIso_inv_freeMk, FormalMultilinearSeries.ofScalarsSum_zero, Padic.valuation_p_lt_one, Path.Homotopy.trans_apply, IsLocalization.Away.quotient_of_isIdempotentElem, Finset.weightedVSub_const_smul, Height.fun_logHeight_one, DerivedCategory.isLE_Q_obj_iff, GradedTensorProduct.includeRight_apply, SimpleGraph.DeleteFar.le_card_edgeFinset, CochainComplex.cm5b.fac_assoc, ComplexShape.eulerCharSignsDownInt_χ, ZNum.cast_inj, Polynomial.natDegree_hilbertPoly_of_ne_zero, DualNumber.exp_eps, HomotopyCategory.instAdditiveIntUpSingleFunctor, round_eq, IsCyclotomicExtension.Rat.inertiaDegIn_eq_of_not_dvd, Polynomial.Chebyshev.iterate_derivative_U_eval_one_dvd, isIdempotentElem_one_sub_one_sub_pow_pow, PosNum.to_int_eq_succ_pred, Polynomial.eval_one_cyclotomic_prime_pow, WittVector.fontaineThetaModPPow_teichmuller, intCast_negSucc, one_sub_invOf_two, WeierstrassCurve.Projective.eval_polynomialZ, trace_eq_sum_roots, CategoryTheory.DifferentialObject.shiftFunctorAdd_hom_app_f, Polynomial.cyclotomic_coeff_zero, WittVector.verschiebung_coeff_zero, Matrix.invOf_fromBlocks_zero₁₂_eq, EulerProduct.eulerProduct_completely_multiplicative_hasProd, WeierstrassCurve.Jacobian.addXYZ_neg, Algebra.Generators.ker_localizationAway, Polynomial.Chebyshev.iterate_derivative_T_eval_one_dvd, Polynomial.Chebyshev.derivative_U_eval_one, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, RatFunc.div_smul, DirichletCharacter.LSeriesSummable_twist_vonMangoldt, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv, derivWithin_pow_field, GenContFract.of_s_head_aux, LinearMap.trace_id, midpoint_vsub_left, Summable.multipliableLocallyUniformlyOn_nat_one_add, CochainComplex.triangleOfDegreewiseSplit_obj₃, iteratedDeriv_comp_neg, Quaternion.im_imJ, WithVal.instIsScalarTower_1, Polynomial.resultant_X_sub_C_pow_right, logDeriv_id, CochainComplex.shiftFunctorZero'_hom_app_f, unitary.two_mul_one_sub_le_norm_sub_one_sq, one_div_mul_sub_mul_one_div_eq_one_div_add_one_div, NormedRing.inverse_one_sub, LinearMap.IsSymmetric.natCast, Quaternion.intCast_imJ, Subring.coe_eq_zero_iff, PadicInt.norm_natCast_zmodRepr_eq_one_iff, LinearMap.conjugate_apply, circleEquivGen_symm_apply, Polynomial.resultant_succ_left_deg, HomogeneousLocalization.val_natCast, HomotopyCategory.Pretriangulated.contractible_distinguished, IsPrimitiveRoot.norm_toInteger_sub_one_eq_one, Matrix.charmatrix_natCast, Quaternion.mul_star_eq_coe, toIcoDiv_add_natCast_mul, Polynomial.one_mem_nthRootsFinset, hasDerivAt_id, seminormFromBounded_one, KaehlerDifferential.kerTotal_map, DirichletCharacter.modOne_eq_one, DirichletCharacter.convolution_twist_vonMangoldt, Quaternion.fst_imI_dualNumberEquiv_symm, ComplexShape.instIsRelIffNatIntEmbeddingUpIntGE, Finset.mem_convexHull, ZNum.cast_le, deriv_update, Zsqrtd.nsmul_val, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two', Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, orthonormal_subtype_iff_ite, Summable.hasProdLocallyUniformlyOn_one_add, nndist_lineMap_right, Complex.ofReal_nsmul, ContinuousMap.Homotopy.trans_apply, ComplexShape.instIsRelIffIntEmbeddingDownIntUpInt, WeierstrassCurve.Projective.dblXYZ_of_Z_eq_zero, EisensteinSeries.vecMul_SL2_mem_gammaSet, spectrum.isUnit_one_sub_smul_of_lt_inv_radius, mul_sub_one, sectionOfRetractionKerToTensorAux_prop, Summable.multipliableUniformlyOn_one_add, ModuleCat.free_η_freeMk, Finpartition.coe_energy, CochainComplex.mappingCone.triangle_mor₂, ValuativeRel.inv_rel_one, OrthogonalIdempotents.surjective_pi, CliffordAlgebra.ofBaseChangeAux_ι, NumberField.RingOfIntegers.mk_zero, CochainComplex.HomComplex.Cocycle.leftUnshift_coe, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_of_eq, IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver', binomialSeries_radius_eq_top_of_nat, Ideal.natCast_mem_of_charP_quotient, Int.Ioc_eq_finset_map, IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one', Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, groupHomology.inhomogeneousChains.d_single, alternating_series_error_bound, TwoSidedIdeal.listProd_mem, IsDedekindDomain.HeightOneSpectrum.intValuation.map_one', CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id, PeriodPair.order_weierstrassP, LucasLehmer.X.one_fst, ZMod.val_neg_one, Quaternion.normSq_add, Nat.setOf_prime_and_eq_mod_infinite, CochainComplex.mappingCone.d_snd_v_assoc, WeierstrassCurve.Projective.Point.fromAffine_some, Algebra.FormallyUnramified.one_tmul_sub_tmul_one_mul_elem, Algebra.Generators.comp_localizationAway_ker, CochainComplex.instAdditiveIntShiftFunctor, LieAlgebra.Orthogonal.s_as_blocks, Representation.coind'_apply_apply, MvPolynomial.mul_esymm_eq_sum, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, WittVector.exists_frobenius_solution_fractionRing, Quaternion.neg_im, CategoryTheory.HasExt.hasSmallLocalizedShiftedHom_of_isLE_of_isGE, WittVector.ghostComponentModPPow_teichmuller_coeff, ModularForm.slash_action_eq'_iff, CochainComplex.shiftFunctor_map_f, AlgebraicGeometry.Scheme.basicOpen_one, iter_deriv_pow', CochainComplex.quasiIsoAt_shift_iff, WittVector.iterate_verschiebung_iterate_frobenius, CochainComplex.mappingCone.d_snd_v', EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, LinearOrderedField.inducedMap_one, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_apply, CliffordAlgebra.changeForm_one, surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar, ordinaryHypergeometricSeries_apply_eq, Matrix.det_eq_one_of_card_eq_zero, CochainComplex.instIsKProjectiveObjIntShiftFunctor, ZMod.χ₄_nat_one_mod_four, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, pow_zmod_val_inv_pow, IntermediateField.list_prod_mem, prodXSubSMul.coeff, GenContFract.first_contAux_eq_h_one, AddConstMapClass.map_add_int', Summable.one_sub_mul_tsum_pow, WeierstrassCurve.Projective.negMap_of_Z_ne_zero, MvPolynomial.universalFactorizationMapPresentation_relation, Polynomial.Chebyshev.derivative_U_eval_one_dvd, inv_eq_self₀, CategoryTheory.HasExt.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoOfIsGEOfIsLEOfNat, jacobiSym.neg, Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero, QuadraticAlgebra.lift_symm_apply_coe, Int.floor_eq_iff, Algebra.PreSubmersivePresentation.aevalDifferential_single, Num.ofZNum_toNat, CancelDenoms.cancel_factors_eq, deriv_neg'', SimpleGraph.unreduced_edges_subset, IsCyclotomicExtension.iff_singleton, CochainComplex.HomComplex.Cochain.rightShift_smul, RatFunc.instIsScalarTowerPolynomial, NormedSpace.exp_zero, Valuation.map_one_sub_of_lt, RootPairing.pairing_same, CochainComplex.HomComplex.Cochain.map_comp, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow, Quaternion.imI_star, Matrix.isUnit_fromBlocks_iff_of_invertible₂₂, Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq, WittVector.verschiebung_mul_frobenius, Nat.Ico_filter_modEq_cast, CliffordAlgebraQuaternion.ofQuaternion_mk, Matrix.SpecialLinearGroup.SL2_inv_expl, self_mul_sign, Quaternion.imI_smul, WeierstrassCurve.b₄_of_isShortNF, spectralNorm_one, Module.Relations.solutionFinsupp_var, Matrix.BlockTriangular.toBlock_inverse_mul_toBlock_eq_one, WeierstrassCurve.Projective.polynomialX_eq, WeierstrassCurve.c₄_of_isShortNF, Matrix.mem_specialUnitaryGroup_iff, RCLike.ofReal_alg, CochainComplex.homotopyOp_hom_eq, CochainComplex.mappingCone.inr_f_descCochain_v_assoc, CochainComplex.HomComplex.Cochain.map_sub, ofBoolAlg_sdiff, IntermediateField.coe_zero, ProjectiveSpectrum.zeroLocus_singleton_one, IsLocalization.mem_invSubmonoid_iff_exists_mk', AddChar.mulShift_spec', IsPrimitiveRoot.card_nthRootsFinset, Finset.convexHull_eq, CochainComplex.HomComplex.Cocycle.homOf_f, RingPreordering.neg_one_notMem', WeierstrassCurve.Projective.neg_of_Z_ne_zero, CharP.intCast_mul_natCast_gcdA_eq_gcd, Quaternion.imK_star, QuotSMulTop.map_exact, WeierstrassCurve.c₆_of_isCharTwoJNeZeroNF, RootPairing.Base.toCoweightBasis_repr_coroot, IsCyclotomicExtension.Rat.isPrime_span_zeta_sub_one', Nat.abs_sub_floor_le, Algebra.SubmersivePresentation.ofSubsingleton_val, arithGeom_same_eq_mul_div, CochainComplex.IsKProjective.Qh_map_bijective, not_summable_indicator_mod_of_antitone_of_neg, ringExpChar.expChar, CochainComplex.mappingCone.d_fst_v_assoc, geom_sum_eq_zero_iff_neg_one, Quaternion.normSq_exp, HasFDerivWithinAt.hasDerivWithinAt, AddChar.zmodChar_apply, CochainComplex.homOfDegreewiseSplit_f, IsCyclotomicExtension.Rat.liesOver_span_zeta_sub_one, IsCyclotomicExtension.neZero, Matrix.det_succ_column, Matrix.cRank_one, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, CStarAlgebra.one_le_inv_iff_le_one, AddChar.starComp_apply, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, Polynomial.resultant_C_left, CochainComplex.shiftFunctorAdd_inv_app_f, tsirelson_inequality, Algebra.PreSubmersivePresentation.ofBijectiveAlgebraMap_jacobian, ComplexShape.boundaryGE_embeddingUpIntGE_iff, DerivedCategory.isGE_Q_obj_iff, AffineMap.derivWithin, Set.Icc.mem_iff_one_sub_mem, Rep.standardComplex.d_of, Quaternion.star_add_self', tendsto_floor_left', stdSimplexHomeomorphUnitInterval_apply_coe, IsLprojection.coe_one, SimpleGraph.lapMatrix_mulVec_apply, LucasLehmer.X.mul_fst, RootPairing.coxeterWeightIn_le_four, CochainComplex.mappingCone.map_id, Valuation.map_one, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, ZMod.gauss_lemma, Matrix.fromBlocks_eq_of_invertible₂₂, GenContFract.of_s_head, GenContFract.of_partNum_eq_one, AffineBasis.coord_apply_eq, WeierstrassCurve.b₈_of_isCharThreeJNeZeroNF, AffineBasis.coord_apply_centroid, RootPairing.EmbeddedG2.pairing_long_short, WeierstrassCurve.Projective.polynomialY_eq, ZMod.LFunction_def_even, IsStarProjection.le_one, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_inv_app, segment_eq_image', Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, Matrix.SpecialLinearGroup.coe_inv, ZMod.lift_comp_castAddHom, IsCyclotomicExtension.norm_zeta_sub_one_of_prime_ne_two, Finset.sum_affineCombinationLineMapWeights, RCLike.sqrt_neg_one, Subring.smul_mem_pointwise_smul_iff₀, ZMod.exponent, ZMod.orderOf_one_add_four_mul, CliffordAlgebra.foldr_one, WeierstrassCurve.Projective.negDblY_eq, PresheafOfModules.Derivation'.d_app, Set.pairwise_disjoint_Ioc_intCast, sbtw_mul_sub_add_iff, quadratic_eq_zero_iff, Zsqrtd.instCharZero, Matrix.sub_scalar_sq_eq_disc, sq_lt_one_iff_abs_lt_one, isUnit_iff_not_dvd_char, CochainComplex.mappingConeCompTriangle_obj₃, IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic, Subfield.one_mem, Matrix.disc_fin_two, DerivedCategory.instEssSurjHomotopyCategoryIntUpQh, CategoryTheory.ProjectiveResolution.π'_f_zero, fderiv_apply_one_eq_deriv, IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite, IsCoprime.exists_SL2_col, PiToModule.fromEnd_apply_single_one, Quaternion.sub_im, isStarProjection_one_sub_iff, RootPairing.coroot_root_two, Finset.affineCombinationSingleWeights_apply_self, LucasLehmer.X.instCharP, CochainComplex.mappingCone.inl_v_fst_v, AlgebraicGeometry.StructureSheaf.const_algebraMap, meromorphicTrailingCoeffAt_id_sub_const, PreTilt.pow_dvd_untiltAux_sub_untiltAux, DirichletCharacter.LSeriesSummable_iff, Int.fract_neg, Nat.prime_iff_fac_equiv_neg_one, WeierstrassCurve.Jacobian.nonsingularLift_zero, WittVector.ghostComponent_verschiebung, MvPolynomial.universalFactorizationMapPresentation_algebra_algebraMap, Quaternion.im_exp, DivisibleHull.qsmul_def, Quaternion.re_one, CochainComplex.isLE_iff, toIcoMod_add_natCast_mul', CochainComplex.ConnectData.cochainComplex_d, Valuation.one_vlt_iff, Subring.exists_list_of_mem_closure, ZMod.cast_natCast, IsPrimitiveRoot.neZero', openSegment_eq_image_lineMap, Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one, ZMod.cast_neg_one, Matrix.invOf_add_mul_mul, logDeriv_id', ZMod.χ₈_nat_mod_eight, Set.Ioo.mem_iff_one_sub_mem, Matrix.Pivot.mul_listTransvecRow_last_row, QuaternionAlgebra.self_add_star', AlgebraicGeometry.Proj.basicOpen_one, wbtw_iff_right_eq_or_left_mem_image_Ici, HomotopyCategory.instIsTriangulatedIntUpSubcategoryAcyclic, one_mem_inv_coe_ideal, archimedean_iff_nat_lt, PadicInt.fwdDiff_iter_le_of_forall_le, IsStarProjection.mem_Icc, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, hasSum_geom_series_inverse, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, PadicInt.mem_span_pow_iff_le_valuation, Quaternion.zero_re, LinearMap.det_id, NormedSpace.norm_expSeries_summable', HomologicalComplex.homologicalComplexToDGO_map_f, formalMultilinearSeries_geometric_eq_ofScalars, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f, PreTilt.pow_dvd_one_untiltAux_sub_one, toIocMod_natCast_mul_add', eq_affineCombination_of_mem_affineSpan, IsNilpotent.exp_zero, Int.ceil_eq_add_one_sub_fract, one_le_cfc, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, SignType.intCast_cast, NormedSpace.norm_expSeries_div_summable_of_mem_ball, even_add_one, ZMod.natCast_zmod_val, abs_unit_intCast, LieAlgebra.toEnd_pow_apply_mem, Matrix.det_fromBlocks_one₂₂, CochainComplex.exists_iso_single, Matrix.det_nonsing_inv_mul_det, hasSum_coe_mul_geometric_of_norm_lt_one, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, Valuation.one_vle_iff, cfc_one, QuaternionGroup.a_one_pow, IsLocalization.toInvSubmonoid_mul, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_symm_apply, wbtw_iff_left_eq_or_right_mem_image_Ici, Matrix.SpecialLinearGroup.coe_pow, CochainComplex.HomComplex.Cochain.shift_units_smul, IsCyclotomicExtension.norm_zeta_sub_one_of_isPrimePow, GradedTensorProduct.algebraMap_def', HomotopyCategory.instIsTriangulatedIntUp, ValuativeRel.one_vlt_inv, Polynomial.discr_of_degree_eq_one, Function.Antiperiodic.add_nat_mul_eq, WeierstrassCurve.Projective.addMap_of_Y_eq, CFC.eq_one_of_spectrum_subset_one, Polynomial.dickson_one_one_charP, SimpleGraph.FarFromTriangleFree.lt_half, Submodule.det_reflection, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, ZMod.isUnit_prime_iff_not_dvd, round_eq_zero_iff, CochainComplex.ConnectData.restrictionLEIso_hom_f, selfAdjoint.star_coe_unitarySelfAddISMul, deriv_neg', WeakDual.CharacterSpace.eq_set_map_one_map_mul, Quaternion.smul_re, Quaternion.self_add_star', mul_geom_sum, Algebra.Generators.cMulXSubOneCotangent_eq, ArchimedeanClass.stdPart_natCast, RootPairing.RootPositiveForm.two_mul_apply_root_root, NormedSpace.expSeries_apply_eq', Polynomial.content_one, CochainComplex.exactAt_of_isGE, CochainComplex.shiftFunctorAdd_eq, DerivedCategory.instFaithfulFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_symm_apply, neg_npow_assoc, Quaternion.coe_mul_eq_smul, hasSum_choose_mul_geometric_of_norm_lt_one', CochainComplex.mappingCone.inr_f_descCochain_v, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, NumberField.absNorm_differentIdeal, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two, Quaternion.instIsStarNormal, Ring.choose_natCast, CochainComplex.cm5b.instQuasiIsoIntP, toIcoMod_sub_natCast_mul, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃, ascPochhammer_eval_neg_coe_nat_of_lt, SymplecticGroup.inv_left_mul_aux, QuotientAddGroup.mk_nat_mul, natCast_ceil_eq_intCast_ceil, Ring.multichoose_succ_neg_natCast, Polynomial.dickson_one_one_zmod_p, IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver, normEDS_one, CategoryTheory.DifferentialObject.objEqToHom_d, Int.floor_natCast_add, Matrix.adjugate_def, ZMod.coe_int_mul_val_inv, IsPrimitiveRoot.subOnePowerBasis_dim, Matrix.isUnit_fromBlocks_iff_of_invertible₁₁, IsPrimitiveRoot.subOnePowerBasis_gen, LieModule.exists_genWeightSpace_smul_add_eq_bot, ModuleCat.MonoidalCategory.rightUnitor_inv_apply, CharP.charP_to_charZero, Quaternion.summable_coe, EqualCharZero.pnatCast_eq_natCast, summable_norm_pow_mul_geometric_div_one_sub, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂_assoc, CategoryTheory.DifferentialObject.eqToHom_f', DirichletCharacter.absicssaOfAbsConv_eq_one, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁, Quaternion.zero_imI, CochainComplex.mappingCone.isZero_X_iff, QuaternionAlgebra.Basis.k_mul_k, Int.uIcc_eq_finset_map, Asymptotics.isEquivalent_nat_floor, Quaternion.sub_imI, isIdempotentElem_iff_one_sub_mul_self, WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eq, inhomogeneousCochains.d_hom_apply, Algebra.Generators.toKaehler_tmul_D, WeierstrassCurve.variableChange_a₄, Quaternion.imJ_snd_dualNumberEquiv, Quaternion.star_im, preNormEDS_one, ValuativeRel.not_vle_one_zero, Rep.coind'_ext_iff, doublyStochastic_eq_convexHull_permMatrix, neg_one_eq_invOf_mul_add_invOf_mul_iff, LinearPMap.map_smul, NumberField.RingOfIntegers.instCharZero, Quaternion.re_natCast, homothety_invOf_two, IsPrimitiveRoot.norm_eq_one_of_linearly_ordered, Matrix.det_succ_column_zero, HilbertBasis.repr_symm_single, NumberField.finite_of_discr_bdd, WeierstrassCurve.c₆_of_isCharNeTwoNF, WittVector.map_verschiebung, WittVector.verschiebung_frobenius, DerivedCategory.instIsGEObjCochainComplexIntQOfIsGE, fderiv_deriv, Ring.choose_add_smul_choose, Ring.DirectLimit.quotientMk_of, Rat.cast_def, WittVector.one_coeff_zero, IsEllDivSequence.smul, Complex.expMonoidHom_apply, Complex.coe_imAddGroupHom, LinearMap.det_eq_sign_charpoly_coeff, IsNilpotent.exp_neg_mul_exp_self, RatFunc.instCharZero, PadicInt.isUnit_den, AddCommGroup.intCast_modEq_intCast', IsPrimitiveRoot.associated_pow_add_sub_sub_one, CochainComplex.mappingConeCompHomotopyEquiv_comm₂, NormedSpace.exp_def, pow_four_add_four_mul_pow_four, norm_algebraMap, Nat.one_sub_one_div_cast_nonneg, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom_assoc, add_sub_div_two_lt, ExteriorAlgebra.ιMulti_apply, RCLike.norm_natCast, MulSemiringAction.charpoly_eq, PadicInt.norm_le_pow_iff_mem_span_pow, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, Quaternion.snd_imK_dualNumberEquiv_symm, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, Int.floor_add_natCast, KaehlerDifferential.submodule_span_range_eq_ideal, exists_signed_sum', IsCyclotomicExtension.Rat.Three.lambda_dvd_or_dvd_sub_one_or_dvd_add_one, Int.cast_list_sum, iteratedDerivWithin_pow, sectionOfRetractionKerToTensor_algebraMap, NumberField.RingOfIntegers.mk_one, WeierstrassCurve.coeff_preΨ₄, CochainComplex.HomComplex.δ_zero_cochain_v, CochainComplex.HomComplex.Cochain.units_smul_v, ZMod.χ₄_nat_three_mod_four, Algebra.SubmersivePresentation.sum_jacobianRelationsOfHasCoeffs_mul_relationOfHasCoeffs, Finset.weightedVSubVSubWeights_apply_left, AffineBasis.toMatrix_row_sum_one, wbtw_one_zero_iff, CochainComplex.HomComplex.Cochain.δ_toSingleMk, UnitAddCircle.measurePreserving_mk, ModuleCat.MonoidalCategory.leftUnitor_inv_apply, Finset.tendsto_Icc_neg, CauSeq.coe_one, descPochhammer_eval_eq_descFactorial, Quaternion.sq_eq_neg_normSq, AffineMap.lineMap_apply_ring, CochainComplex.cm5b.instMonoFIntI, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, PadicInt.zmodRepr_natCast, Lagrange.eval_basisDivisor_left_of_ne, Polynomial.eval_one_cyclotomic_not_prime_pow, mul_self_eq_one_iff, WeierstrassCurve.Jacobian.polynomialZ_eq, CochainComplex.HomComplex.CohomologyClass.toHom_bijective, Quaternion.imK_neg, EqualCharZero.nonempty_algebraRat_iff, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two, Int.fract_natCast_add, Quaternion.coe_one, QuaternionAlgebra.natCast_imK, hasStrictFDerivAt_list_prod_attach', stdSimplex.barycenter_apply, WeierstrassCurve.Jacobian.dblU_eq, PadicInt.valuation_one, IsPrimitiveRoot.norm_pow_sub_one_two, ZMod.lift_coe, deriv_single, PadicInt.norm_natCast_zmodRepr_eq, Quaternion.imK_ratCast, ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_coprime, HomogeneousLocalization.NumDenSameDeg.num_one, Set.pairwise_disjoint_Ioc_add_intCast, Matrix.vandermonde_cons, geom_sum_neg_iff, FDRep.char_one, CochainComplex.HomComplex.Cochain.fromSingleMk_precomp, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, even_sub_two, SubringClass.coe_natCast, Polynomial.eval_one_cyclotomic_prime, QuaternionGroup.xa_mul_xa, IntermediateField.charP, FermatLastTheoremForThreeGen.Solution'.hcdvd, Matrix.Pivot.listTransvecCol_mul_last_row_drop, hasFPowerSeriesOnBall_inv_one_sub, WeierstrassCurve.b₂_of_isCharTwoJNeZeroNF_of_char_two, Matrix.add_mul_mul_mul_invOf_eq_one', CochainComplex.HomComplex.Cochain.leftUnshift_add, DirichletCharacter.mul_convolution_distrib, CochainComplex.isGE_iff, jacobiSum_nontrivial_inv, exteriorPower.presentation_relation, hasFPowerSeriesOnBall_inverse_one_sub, NormedSpace.expSeries_div_summable_of_mem_ball, ZMod.intCast_eq_one_iff_odd, CochainComplex.HomComplex.Cocycle.fromSingleMk_zero, Mathlib.Tactic.RingNF.rat_rawCast_neg, CategoryTheory.DifferentialObject.shiftFunctor_map_f, Matrix.nonsing_inv_cancel_or_zero, Sbtw.left_mem_image_Ioi, Polynomial.leadingCoeff_preHilbertPoly, PadicInt.ker_toZModPow, spectralAlgNorm_one, ordinaryHypergeometric_zero, Algebra.trace_algebraMap_of_basis, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, iUnion_Ico_intCast, one_sub_le_one_add_mul_one_sub, HomotopyCategory.instIsCompatibleWithShiftHomologicalComplexIntUpHomotopic, IsPrimitiveRoot.toInteger_sub_one_dvd_prime, Rat.instCharZero, Ring.multichoose_eq, one_le_norm_one, FixedPoints.smul_polynomial, AddChar.mulShift_zero, Quaternion.tsum_coe, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom, parallelogram_law, Complex.instIsAddTorsionFree, AnalyticAt.hasFPowerSeriesAt, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, fwdDiff_iter_eq_factorial, Asymptotics.IsTheta.listProd, CFC.negPart_one, CoxeterSystem.lengthParity_simple, midpoint_vsub_right, CochainComplex.mappingCone.inr_f_fst_v_assoc, Module.FaithfullyFlat.one_tmul_eq_zero_iff, WeierstrassCurve.Δ_of_isCharNeTwoNF, CategoryTheory.ProjectiveResolution.instProjectiveXIntCochainComplex, WittVector.mul_polyOfInterest_aux1, Height.mulHeight₁_eq_mulHeight, Cubic.prod_X_sub_C_eq, Quaternion.continuous_im, CategoryTheory.DifferentialObject.objEqToHom_refl, RootPairing.InvariantForm.apply_eq_or_aux, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, Asymptotics.Filter.Tendsto.isBigOTVS_one, Quaternion.sq_eq_normSq, CochainComplex.mappingCone.inl_v_d_assoc, CochainComplex.shiftFunctorZero'_inv_app_f, NumberField.Units.coe_one, CochainComplex.mappingCone.cocycleOfDegreewiseSplit_triangleRotateShortComplexSplitting_v, Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_row, Matrix.det_neg, TannakaDuality.FiniteGroup.sumSMulInv_single_id, Quaternion.re_coe, IsRealClosed.toIsSemireal, inner_eq_neg_one_iff_of_norm_eq_one, CochainComplex.HomComplex.Cochain.rightShift_units_smul, LieModule.chainTopCoeff_add_one, neg_one_pow_char_pow, CochainComplex.isZero_of_isStrictlyGE, CliffordAlgebra.invOf_ι, CategoryTheory.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoObjCochainComplexCompSingleFunctorOfNatOfHasExt, ZMod.natCast_eq_zero_iff_even, AffineMap.lineMap_eq_right_iff, ZMod.charP, HomologicalComplex.dgoToHomologicalComplex_map_f, neg_one_geom_sum, PadicInt.hasSum_mahler, LinearMap.IsReflective.dvd_two_mul, DerivedCategory.exists_iso_Q_obj_of_isGE_of_isLE, LinearMap.equivariantProjection_apply, IncidenceAlgebra.mu_eq_neg_sum_Ioc_of_ne, WittVector.ghostComponent_zero_verschiebung, abs_pow_sub_pow_le, Int.ceil_lt_add_one, Quaternion.imJ_mul, Complex.im_nsmul, HomotopyCategory.instIsTriangulatedIntUpMapHomotopyCategory, geom_series_mul_one_add, dist_pointReflection_right, Int.image_fract, Surreal.nat_toGame, LaurentPolynomial.toLaurent_support, Quaternion.im_nnratCast, IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two, CochainComplex.HomComplex.Cochain.rightUnshift_smul, RootPairing.pairingIn_one_four_iff, LinearEquiv.coord_self, Int.cast_list_prod, HomotopyCategory.composableArrowsFunctor_map, inner_eq_one_iff_of_norm_eq_one, one_lt_sq_iff_one_lt_abs, HasFPowerSeriesAt.deriv, GradedTensorProduct.includeLeftRingHom_apply, ZMod.orderOf_one_add_prime, AddChar.starComp_eq_inv, Finset.prod_range_natCast_sub, LinearMap.IsReflective.coroot_apply_self, WittVector.coeff_p_pow, ArchimedeanClass.FiniteElement.val_one, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, IsSemisimpleModule.exists_end_algEquiv, CochainComplex.instQuasiIsoIntMapHomologicalComplexUpShiftFunctor, DerivedCategory.instEssSurjArrowHomotopyCategoryIntUpMapArrowQh, Finpartition.IsEquipartition.sum_nonUniforms_lt, WeierstrassCurve.Jacobian.add_of_X_ne, Quaternion.coe_sub, LinearMap.det_eq_one_of_finrank_eq_zero, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom'_assoc, WeierstrassCurve.Projective.negDblY_eq', AnalyticAt.exists_eq_sum_add_pow_mul, QuotSMulTop.equivQuotTensor_naturality_mk, ValuativeRel.div_rel_one_iff, odd_sub_two, SimpleGraph.le_card_nonuniformWitness, CategoryTheory.DifferentialObject.shiftFunctorAdd_inv_app_f, IsPrimitiveRoot.nthRoots_one_nodup, preNormEDS_mul_complEDS₂, Rat.instIsScalarTowerRight, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, Module.Basis.det_self, Subfield.charP, LieModule.toEnd_baseChange, iteratedDerivWithin_mul, Quaternion.natCast_im, QuadraticAlgebra.instCharZero, AffineMap.lineMap_apply_one, IncidenceAlgebra.one_prod_one, ZMod.addOrderOf_coe', CategoryTheory.InjectiveResolution.extEquivCohomologyClass_add, RootPairing.pairingIn_neg_one_neg_four_iff, Quaternion.self_mul_star, WeierstrassCurve.leadingCoeff_Φ, Polynomial.eval_sumIDeriv_of_pos, LieAlgebra.IsKilling.root_apply_coroot, ZMod.LSeriesSummable_of_one_lt_re, CharP.sq_add_sq, MvPolynomial.dvd_monomial_mul_iff_exists, DirichletCharacter.LSeries_eulerProduct_hasProd, spectrum.differentiableOn_inverse_one_sub_smul, Ideal.exists_mul_add_sub_mem_of_mem_jacobson, AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div, ValuationSubring.ofPrime_scalar_tower, Quaternion.imJ_ratCast, Polynomial.dickson_one_one_eq_chebyshev_T, localization_unit_isIso, ZNum.cast_bit0, tendsto_nat_ceil_div_atTop, RCLike.ofReal_one, RootPairing.GeckConstruction.ω_mul_ω, RootPairing.GeckConstruction.f_lie_v_ne, logDeriv_inv, Rat.cast_natCast, ZNum.cast_bitm1, IntermediateField.expChar, CochainComplex.HomComplex.Cochain.smul_v, CochainComplex.isSplitMono_from_singleFunctor_obj_of_injective, Algebra.norm_eq_one_of_not_exists_basis, Valuation.srel_one_iff, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_r, HomotopyCategory.quasiIso_eq_subcategoryAcyclic_W, IsPrimitiveRoot.toInteger_sub_one_dvd_prime', FiniteField.pow_dichotomy, ZNum.abs_to_nat, gaussSum_mul_gaussSum_pow_orderOf_sub_one, right_le_lineMap_iff_one_le, Quaternion.im_neg, PadicInt.instNormOneClass, UpperHalfPlane.coe_specialLinearGroup_apply, ZMod.χ₄_eq_neg_one_pow, preNormEDS'_two, CategoryTheory.InjectiveResolution.Hom.hom'_f_assoc, RCLike.natCast_im, tsum_prod_pow_eq_tsum_sigma, half_sub, WittVector.StandardOneDimIsocrystal.frobenius_apply, Quaternion.im_imK, Quaternion.neg_imK, AddConstMapClass.map_int_add, IsPrimitiveRoot.ntRootsFinset_pairwise_associated_sub_one_sub_of_prime, Quaternion.imK_intCast, CochainComplex.HomComplex.Cochain.δ_shift, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, ZMod.cast_descFactorial, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, CochainComplex.HomComplex.Cochain.fromSingleMk_sub, FermatLastTheoremForThreeGen.Solution'.hb, GradedTensorProduct.algebraMap_def, HahnSeries.SummableFamily.one_sub_self_mul_hsum_powers, CochainComplex.mappingCone.inl_v_descShortComplex_f_assoc, Rat.smul_one_eq_cast, CochainComplex.IsKProjective.leftOrthogonal, abs_neg_one_zpow, Mathlib.Meta.NormNum.IsInt.to_isNat, Polynomial.SplittingField.instCharZero, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, Polynomial.Chebyshev.iterate_derivative_U_eval_one, Hyperreal.coe_one, DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective, MatrixModCat.isScalarTower_toModuleCat, Polynomial.chebyshev_T_eq_dickson_one_one, RootPairing.GeckConstruction.e_lie_v_ne, Module.FaithfullyFlat.tensorProduct_mk_injective, ZMod.toAddCircle_intCast, orderOf_neg_one, IsPrimitiveRoot.primitiveRoots_one, IsCyclotomicExtension.union_left, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, LieAlgebra.IsKilling.eq_neg_one_or_eq_zero_or_eq_one_of_eq_smul, DerivedCategory.exists_iso_Q_obj_of_isGE, Quaternion.normSq_def', SimpContFract.of_isContFract, tsum_dirichletSummand, ZMod.Ico_map_valMinAbs_natAbs_eq_Ico_map_id, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_inv_app, Matrix.mem_orthogonalGroup_iff, Quaternion.imI_add, GenContFract.zeroth_contAux_eq_one_zero, CochainComplex.cm5b.instInjectiveXIntI, MeasureTheory.lpNorm_one, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, CochainComplex.cm5b.instMonoIntI, RCLike.norm_two, Matrix.inv_mul_of_invertible, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, toIcoMod_natCast_mul_add, QuaternionAlgebra.Basis.i_self, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_apply, HasStrictFDerivAt.hasStrictDerivAt, descPochhammer_eval_coe_nat_of_lt, Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow, ValuationSubring.one_mem, GenContFract.of_one_le_get?_partDen, Valuation.vle_one_iff, Quaternion.ratCast_im, CongruenceSubgroup.Gamma1_mem, LieAlgebra.LoopAlgebra.residuePairing_apply_apply, IsLocalization.toInvSubmonoid_eq_mk', PolynomialLaw.neg_def, KaehlerDifferential.kerTotal_mkQ_single_smul, Matrix.SpecialLinearGroup.coe_transpose, PresheafOfModules.Derivation.d_app, Valuation.IsEquiv.val_sub_one_lt_one_iff, IsIntegral.nsmul, jacobiSym.at_two, fderivWithin_derivWithin, isIntegral_one, ComplexShape.instIsRelIffNatIntEmbeddingUpNat, FiniteDimensional.exists_mul_eq_one, RCLike.sqrt_neg_I, Rat.isNat_intFloor_ofIsNNRat, Algebra.normalizedTrace_minpoly, ZMod.toAddCircle_apply, HasFDerivAt.list_prod', IsPrimitiveRoot.card_quotient_toInteger_sub_one, Matrix.permMatrix_mulVec, Polynomial.Chebyshev.C_eval_neg_two, ZMod.inv_mul_eq_one_of_isUnit, Differential.logDeriv_pow, RingPreordering.one_notMem_supportAddSubgroup, Matrix.SpecialLinearGroup.coe_GL_coe_matrix, ZMod.natCast_smul_units, extremePoints_doublyStochastic, Matrix.det_fromBlocks₂₂, LieAlgebra.Orthogonal.jd_transform, DirichletCharacter.LSeries_eulerProduct_exp_log, lineMap_le_right_iff_le_one, ZNum.to_of_int, Quaternion.imK_smul, iteratedDeriv_comp_const_sub, Finset.sum_centroidWeights_eq_one_of_nonempty, legendreSym.eq_one_iff', IsCyclotomicExtension.Rat.inertiaDegIn_eq, tendsto_fract_left, OrthonormalBasis.repr_symm_single, FixedBy.intermediateField_mem_iff, Quaternion.star_imK, GenContFract.fib_le_of_contsAux_b, Unitary.two_mul_one_sub_le_norm_sub_one_sq, RootPairing.polarizationEquiv_symm_apply_coroot, CauSeq.one_not_equiv_zero, ofBoolAlg_top, WeakDual.CharacterSpace.norm_le_norm_one, FiniteField.isSquare_iff, Subring.one_mem_toNonUnitalSubring, IsMprojection.Mnorm, exteriorPower.zeroEquiv_ιMulti, RatFunc.instExpChar, Summable.tsum_pow_mul_one_sub, Nat.one_sub_one_div_cast_le_one, Quaternion.im_star, Matrix.SpecialLinearGroup.eq_scalar_center_equiv_rootsOfUnity, LinearMap.BilinForm.IsSymm.polarization, ZMod.val_natCast, odd_add_one, Matrix.fromCols_mul_fromRows_eq_one_comm, CochainComplex.isKProjective_iff_leftOrthogonal, Quaternion.coe_mul, Representation.FiniteCyclicGroup.coinvariantsKer_leftRegular_eq_ker, LieModule.eventually_genWeightSpace_smul_add_eq_bot, Quaternion.ratCast_imI, Matrix.Pivot.mul_listTransvecRow_last_col_take, Nat.abs_floor_sub_le, Matrix.det_eq_sum_row_mul_submatrix_succAbove_succAbove_det, Int.fract_div_natCast_eq_div_natCast_mod, Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero, WittVector.iterate_verschiebung_mul_coeff, ZMod.ker_intCastAddHom, isUnit_iff_not_dvd_char_of_ringChar_ne_zero, Polynomial.content_X, QuaternionAlgebra.natCast_imI, iter_deriv_inv, Complex.lift_symm_apply_coe, Polynomial.discr_C, Int.floor_pos, WittVector.bind₁_verschiebungPoly_wittPolynomial, CategoryTheory.InjectiveResolution.extMk_hom, integralClosure.coe_smul, Subring.coe_zero, IsLprojection.coe_sdiff, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, CategoryTheory.InjectiveResolution.cochainComplex_d_assoc, RCLike.sqrt_I, Path.trans_apply, Matrix.GeneralLinearGroup.coe_map_mul_map_inv, WeierstrassCurve.b_relation, AddChar.IsPrimitive.compMulHom_of_isPrimitive, QuadraticMap.associated_linMulLin, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, Ideal.natAbs_det_equiv, ArchimedeanClass.mk_map_of_archimedean, Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype, Units.val_set_image_rootsOfUnity_two, ValuationSubring.mem_principalUnitGroup_iff, quadraticCharFun_eq_pow_of_char_ne_two, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq, WeierstrassCurve.Projective.add_of_Y_eq, Matrix.of_mem_specialOrthogonalGroup_fin_two_iff, RCLike.nnnorm_two, Matrix.SpecialLinearGroup.toLin'_to_linearMap, Quaternion.normSq_zpow, Quaternion.coe_nnratCast, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, HasDerivWithinAt.fun_pow, Finset.centerMass_ite_eq, PreTilt.exists_smodEq_untiltAux, QuaternionAlgebra.Basis.j_self, IsNilpotent.exp_eq_sum, ZMod.orderOf_one_add_mul_prime_pow, Polynomial.leadingCoeff_X_sub_C, CochainComplex.shortComplexTruncLE_shortExact, Matrix.det_mul_add_one_comm, IsCyclotomicExtension.Rat.isPrime_span_zeta_sub_one, FirstOrder.Field.instModelField, Fin.addRothNumber_le_rothNumberNat, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_zero, WeierstrassCurve.Φ_two, iteratedDeriv_eq_iteratedFDeriv, Height.fun_mulHeight_one, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, Quaternion.coe_starAe, iter_deriv_inv', abs_sub_sq, CochainComplex.cm5b.i_f_comp, CochainComplex.HomComplex.Cochain.δ_rightUnshift, neg_add_cancel, FloorSemiring.eventually_mul_pow_lt_factorial_sub, EqualCharZero.iff_not_mixedCharZero, Finset.box_succ_eq_sdiff, Matrix.linfty_opNormOneClass, PresheafOfModules.Derivation'.app_apply, MeasureTheory.lpNorm_div_natCast, CochainComplex.mappingCone.inr_snd, legendreSym.at_neg_one, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, IsFractionRing.mul_inv_cancel, WeierstrassCurve.twoTorsionPolynomial_of_char_three, Quaternion.sub_im_self, Quaternion.inner_self, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_neg, WeierstrassCurve.Projective.add_of_X_ne, CochainComplex.mappingCone.decomp_to, ModP.preVal_zero, iccHomeoI_symm_apply_coe, Matrix.SpecialLinearGroup.SL2_inv_expl_det, Rep.leftRegularHomEquiv_symm_single, CochainComplex.HomComplex.leftHomologyData_H_coe, ZMod.isUnit_prime_of_not_dvd, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_two, FiniteField.isSquare_odd_prime_iff, Algebra.normalizedTrace_def, CochainComplex.HomComplex.leftHomologyData'_K_coe, ModularGroup.tendsto_lcRow0, Matrix.submatrixEquivInvertibleEquivInvertible_apply, IntermediateField.adjoin_natCast, pow_pow_zmod_val_inv, CochainComplex.HomComplex.Cochain.leftUnshift_units_smul, QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff, Algebra.Extension.tensorCotangentInvFun_smul_mk, CochainComplex.mappingCone.inl_fst, pow_eq_one_iff_of_ne_zero, sub_pow_two, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_apply, Matrix.charmatrix_one, mem_convexHull_iff_exists_fintype, Algebra.SubmersivePresentation.exists_sum_eq_σ_jacobian_mul_σ_jacobian_inv_sub_one, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₃, deriv_pow_field, RatFunc.instCharP, CochainComplex.HomComplex.Cocycle.shift_coe, Matrix.Pivot.listTransvecCol_mul_last_row, HasFPowerSeriesAt.hasDerivAt, pinGroup.star_mul_self_of_mem, Module.Finite.toModuleEnd_moduleEnd_surjective, Quaternion.im_imI, isAlgebraic_nat, quadraticChar_odd_prime, meromorphicOrderAt_pow, ordinaryHypergeometricSeries_eq_zero_iff, ZMod.isSquare_neg_one_iff', round_le_add_half, Matrix.num_one, AbsoluteValue.map_units_int, Quaternion.self_add_star, Quaternion.normSq_def, ComplexShape.embeddingUpIntLE_f, Quaternion.continuous_coe, WeierstrassCurve.Affine.evalEval_polynomialY, Quaternion.imK_one, CochainComplex.mappingCone.liftCochain_v_fst_v_assoc, Quaternion.ratCast_imK, IsLprojection.Lcomplement_iff, PreTilt.untiltAux_smodEq_untiltFun, isCyclotomicExtension_iff, lineMap_one_half, self_eq_inv₀, CliffordAlgebra.contractRight_one, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_hom_app_f, Valuation.rel_one_iff, HomotopyCategory.mem_subcategoryAcyclic_iff, Quaternion.coe_commute, CochainComplex.isStrictlyLE_shift, ModularGroup.abs_c_le_one, Int.fract_eq_self, Quaternion.coe_injective, CliffordAlgebraDualNumber.equiv_ι, QuaternionAlgebra.imI_natCast, Algebra.Presentation.algebraTensorAlgEquiv_symm_relation, WeierstrassCurve.Projective.Point.zero_def, CochainComplex.ConnectData.restrictionGEIso_inv_f, PadicInt.norm_p, cfc_unitary_iff, isLittleO_coe_const_pow_of_one_lt, one_sub_le_one_sub_mul_one_add, Subring.center.smulCommClass_left, CochainComplex.instFullIntSingleFunctor, HasFDerivAt.hasDerivAt, Matrix.diagonalInvertibleEquivInvertible_symm_apply, SimpleGraph.right_nonuniformWitnesses_card, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₁, PadicInt.valuation_p_pow_mul, FiniteField.sum_pow_units, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_span, Int.fract_lt_one, toIocDiv_sub_natCast_mul', Quaternion.ratCast_imJ, ZMod.lift_injective, LinearMap.transvection.det, Polynomial.disc_C, ZMod.mul_inv_eq_gcd, WeierstrassCurve.Projective.add_of_Y_ne', CochainComplex.HomComplex.Cochain.δ_rightShift, DerivedCategory.right_fac_of_isStrictlyLE, ContinuousMap.adjoin_id_eq_span_one_add, Matrix.posDef_natCast_iff, CochainComplex.ConnectData.map_id, Multiset.esymm_neg, WeierstrassCurve.Projective.neg_of_Z_eq_zero, Height.logHeight₁_eq_logHeight, HahnSeries.inv_def, Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_top, IsStarProjection.two_mul_sub_one_mem_unitary, PowerSeries.invOneSubPow_val_eq_mk_sub_one_add_choose_of_pos, SL_reduction_mod_hom_val, CompleteOrthogonalIdempotents.of_isIdempotentElem, QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last, Matrix.Represents.one, CliffordAlgebra.reverse.map_one, PadicInt.fwdDiff_mahlerSeries, CochainComplex.HomComplex.Cochain.leftShift_v, CochainComplex.mappingCone.d_fst_v'_assoc, PowerSeries.exp_pow_eq_rescale_exp, minpoly_algEquiv_toLinearMap, Set.cast_ncard_sdiff, even_add_two, deriv_id, Quaternion.re_neg, CochainComplex.HomComplex.Cochain.rightUnshift_add, Quaternion.re_im, Quaternion.imI_intCast, LinearEquiv.det_mul_det_symm, one_sub_dvd_one_sub_pow, CochainComplex.HomComplex.Cochain.toSingleMk_zero, arithGeom_zero_eq_mul_div, CochainComplex.homologySequenceδ_quotient_mapTriangle_obj, Quaternion.star_mul_eq_coe, Matrix.det_vandermonde_id_eq_superFactorial, FreeLieAlgebra.Rel.smulOfTower, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, ComplexShape.embeddingDownNat_f, IncidenceAlgebra.zeta_mul_mu, HomotopyCategory.homologyFunctor_shiftMap_assoc, CochainComplex.mappingCone.inl_v_d, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, Valuation.vlt_one_iff, PadicInt.zmodRepr_natCast_zmodRepr, IsFractionRing.charP, USize.toBitVec_nsmul, WeierstrassCurve.Jacobian.dblXYZ_of_Z_eq_zero, minpoly.one, Int.ceil_sub_self_eq, PadicInt.pow_p_dvd_int_iff, IsNilpotent.isUnit_one_sub, Finset.weightedVSubOfPoint_const_smul, ZMod.gauss_lemma_aux, Asymptotics.isEquivalent_iff_tendsto_one, hasDerivAt_neg, LinearMap.derivWithin, CochainComplex.isZero_of_isGE, CochainComplex.shiftFunctor_obj_X', RootPairing.EmbeddedG2.pairing_short_long, HomotopyCategory.distinguished_iff_iso_trianglehOfDegreewiseSplit, KaehlerDifferential.derivationTensorProduct_algebraMap, CochainComplex.HomComplex.Cochain.shift_v, ComplexShape.σ_def, AlgebraicClosure.instIsScalarTower, PrimeSpectrum.isIdempotentElemEquivClopens_symm_top, LinearMap.IsProj.trace, CochainComplex.shiftFunctorZero_hom_app_f, Unitary.norm_sub_eq, Polynomial.SplittingField.instCharP, Metric.unitClosedBall.coe_one, preNormEDS'_one, one_div_lt_one_div_of_neg_of_lt, CochainComplex.mappingCone.inr_f_snd_v_assoc, derivWithin_fun_pow, Algebra.norm_one_add_smul, AffineMap.lineMap_lineMap_left, RootPairing.coxeterWeight_eq_four_iff_not_linearIndependent, AffineMap.hasStrictDerivAt, WittVector.verschiebung_shift, WeierstrassCurve.c₄_of_isCharNeTwoNF, Convex.mem_Icc, Quaternion.normSq_neg, summable_indicator_mod_iff_summable, HilbertBasis.repr_self, nnnorm_commutator_sub_one_le, WittVector.polyOfInterest_vars_eq, WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basis, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end, round_eq_half_ceil_two_mul, descPochhammer_eval_eq_ascPochhammer, Polynomial.resultant_deriv, NormedSpace.expSeries_sum_eq_div, Zsqrtd.natCast_val, Asymptotics.IsLittleO.listProd, PreTilt.coeff_iterate_frobenius, Complex.ofReal_comp_nsmul, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, CochainComplex.triangleOfDegreewiseSplit_mor₃, summable_pow_mul_geometric_of_norm_lt_one, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, ZMod.toAddCircle_injective, toIocDiv_add_natCast_mul', descPochhammer_eval_eq_prod_range, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk, lt_one_div_of_neg, StandardEtalePair.aeval_X_g_mul_mk_X, Even.natCast_zmod_two, MvPolynomial.pderiv_inr_universalFactorizationMap_X, CochainComplex.HomComplex.Cochain.shiftAddHom_apply, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, ZNum.of_to_int, Subfield.expChar, RootPairing.pairingIn_two_two_iff, GenContFract.zeroth_den_eq_one, Matrix.mem_unitaryGroup_iff', Finset.cast_card_erase_of_mem, ZNum.cast_bit1, Int.preimage_floor_singleton, Int.abs_one_sub_fract, CategoryTheory.InjectiveResolution.instQuasiIsoIntι', ValuativeRel.one_vle_inv, IsUltrametricDist.norm_natCast_le_one, AddCircle.addOrderOf_eq_pos_iff, PadicInt.p_nonunit, PadicInt.limNthHom_one, Polynomial.disc_of_degree_eq_one, PreTilt.valAux_one, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, IsAdjoinRootMonic.coeff_one, Quaternion.one_imJ, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₂, NormedSpace.expSeries_div_hasSum_exp, CongruenceSubgroup.Gamma1_to_Gamma0_mem, Ideal.Quotient.smulCommClass', CochainComplex.HomComplex.Cochain.δ_leftUnshift, AdicCompletion.one_apply, HomotopyCategory.spectralObjectMappingCone_ω₁, DirichletCharacter.apply_eq_toArithmeticFunction_apply, WeierstrassCurve.Projective.negMap_of_Z_eq_zero, Matrix.diagonalInvertibleEquivInvertible_apply, Nat.norm_cast_le, pow_one_sub_dvd_pow_mul_sub_one, LieModule.traceForm_genWeightSpace_eq, Polynomial.Splits.coeff_zero_eq_leadingCoeff_mul_prod_roots, Surreal.zero_toGame, PresheafOfModules.Sheafify.one_smul, SkewMonoidAlgebra.intCast_def, Units.val_oneSub, GenContFract.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero, CochainComplex.mappingCone.d_fst_v', QuaternionAlgebra.natCast_imJ, sectionOfRetractionKerToTensorAux_algebraMap, Prod.card_box_succ, WeierstrassCurve.Jacobian.nonsingular_some, PowerSeries.invOneSubPow_eq_inv_one_sub_pow, Finset.centroid_pair, IsCyclotomicExtension.iff_adjoin_eq_top, FormalMultilinearSeries.ofScalars_comp_neg_id, Unitization.instNormOneClass, Affine.Simplex.point_vsub_centroid_eq_smul_vsub, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, CochainComplex.shiftFunctorAdd'_hom_app_f', mem_fintypeAffineCoords_iff_sum, gaussSum_pow_eq_prod_jacobiSum, SubringClass.toNormOneClass, IntermediateField.one_mem, Quaternion.coe_imK, KaehlerDifferential.mvPolynomialBasis_repr_D, CochainComplex.mappingCone.inl_v_descCochain_v, CochainComplex.HomComplex.Cochain.leftShift_add, CategoryTheory.DifferentialObject.eqToHom_f'_assoc, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, WeierstrassCurve.Affine.CoordinateRing.basis_zero, IsPrimitiveRoot.neg_one, FirstOrder.Field.model_hasChar_of_charP, FixedDetMatrices.smul_def, WeierstrassCurve.Projective.addMap_of_Z_ne_zero, WeierstrassCurve.Projective.equiv_zero_of_Z_eq_zero, Tactic.NormNum.isNat_realSqrt_neg, CochainComplex.HomComplex.Cochain.leftShift_comp_zero_cochain, AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃_assoc, ZNum.cast_mul, CochainComplex.shiftEval_hom_app, WeierstrassCurve.Jacobian.polynomialX_eq, normEDS_ofNat, SimpleGraph.FarFromTriangleFree.lt_one, QuaternionGroup.xa_sq, HahnSeries.orderTop_self_sub_one_pos_iff, SimpleGraph.left_nonuniformWitnesses_card, RootPairing.Base.toWeightBasis_repr_root, ZNum.div_to_int, Matrix.invertibleEquivDetInvertible_apply, discrim_eq_sq_of_quadratic_eq_zero, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, hasDerivAt_pow, Matrix.adjugate_subsingleton, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, HomologicalComplex.homologicalComplexToDGO_obj_d, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal, LieAlgebra.IsKilling.chainLength_smul, IsEllSequence.smul, PadicInt.norm_sub_zmodRepr_lt_one, segment_eq_image_lineMap, one_div_le_of_neg, Matrix.invOf_add_mul_mul', Algebra.Norm.Transitivity.mul_auxMat_toSquareBlock_eq, Matrix.det_matrixOfPolynomials, CochainComplex.instHasMapBifunctorObjIntShiftFunctor_1, Polynomial.discr_of_degree_eq_two, WeierstrassCurve.b₆_of_isCharNeTwoNF, DirichletCharacter.not_LSeriesSummable_at_one, PadicInt.mahlerEquiv_apply, ZMod.one_eq_zero_iff, CochainComplex.HomComplex.Cocycle.equivHomShift_comp, Submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul, toIcoMod_zero_one, Int.Ico_eq_finset_map, LinearEquiv.toSpanNonzeroSingleton_one, Nat.cast_choose_two, Subgroup.mem_strictPeriods_iff, CochainComplex.cm5b.i_f_comp_assoc, CliffordAlgebra.EquivEven.e0_mul_e0, MvPolynomial.psum_eq_mul_esymm_sub_sum, Matrix.cramer_one, CochainComplex.HomComplex_X, CochainComplex.instIsStrictlyGEExtendNatIntEmbeddingUpNatOfNat, CochainComplex.ConnectData.homologyMap_map_of_eq_succ, UniqueFactorizationDomain.radical_neg_one, CFC.one_rpow, CochainComplex.HomComplex.leftHomologyData'_H_coe, seminormFromBounded_ge, ZMod.val_one, CochainComplex.mappingCone.triangleRotateShortComplex_g, HasDerivWithinAt.pow, Matrix.det_one, CliffordAlgebra.toProd_one_tmul_ι, CochainComplex.shiftFunctor_obj_d', Matrix.GeneralLinearGroup.val_swap, Rat.cast_le_natCast, geom_sum_Ico', stdSimplex.barycenter_eq_centerMass, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, Int.cast_subNatNat, QuadraticAlgebra.norm_one, Matrix.adjugate_one, Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq, Quaternion.coe_imJ, CliffordAlgebra.even.lift.aux_apply, CochainComplex.instHasMapBifunctorObjIntShiftFunctor, EisensteinSeries.vecMulSL_gcd, Algebra.SubmersivePresentation.ofSubsingleton_algebra_smul, PowerSeries.rescale_neg_one_X, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, PowerSeries.constantCoeff_exp, WittVector.bind₁_onePoly_wittPolynomial, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, PolynomialLaw.toFun_neg, Polynomial.fwdDiff_iter_degree_eq_factorial, NumberField.to_charZero, instCharPLinearMapSubtypeMemSubringCenterId, norm_intCast_eq_abs_mul_norm_one, iteratedDeriv_comp_three, ZNum.lt_to_int, CochainComplex.HomComplex.Cocycle.equivHom_apply, RingCat.Colimits.quot_one, Matrix.det_isEmpty, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, jacobiSum_eq_sum_sdiff, QuotSMulTop.map_comp, Finset.cast_card_sdiff, Field.DirectLimit.inv_mul_cancel, Polynomial.content_primPart, QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff, Int.ModEq.listProd_one, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f, fderivWithin_list_prod', FreeLieAlgebra.instIsCentralScalar, Matrix.SpecialLinearGroup.coe_GLPos_coe_GL_coe_matrix, OrthonormalBasis.inner_eq_one, Subring.instNoZeroDivisorsSubtypeMem, sub_sq', cfc_le_one, tendsto_nat_ceil_mul_div_atTop, NumberField.house_nat_mul, CharP.charP_zero_iff_charZero, iteratedDerivWithin_id, Int.cast_three, Set.Icc.one_sub_nonneg, Matrix.mem_specialOrthogonalGroup_fin_two_iff, ZMod.valMinAbs_natCast_eq_self, GaussianInt.prime_of_nat_prime_of_mod_four_eq_three, AddCircle.nsmul_eq_zero_iff, Zsqrtd.norm_natCast, WittVector.wittOne_zero_eq_one, nnnorm_commutator_units_sub_one_le, RootPairing.Base.eq_one_or_neg_one_of_mem_support_of_smul_mem_aux, WeierstrassCurve.Projective.nonsingular_some, charP_of_prime_pow_injective, Polynomial.rootSet.coe_smul, rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val, ZMod.natCast_mod, Int.abs_sub_lt_one_of_floor_eq_floor, CochainComplex.mappingCone.inr_descShortComplex, ModuleCat.extendScalarsComp_hom_app_one_tmul, Module.Relations.Solution.ofπ_var, DerivedCategory.instAdditiveCochainComplexIntQ, ContinuousLinearMap.det_smulRight, Polynomial.dickson_two_one_eq_chebyshev_U, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, hasStrictFDerivAt_list_prod, CFC.sqrt_one, Summable.hasProdLocallyUniformlyOn_nat_one_add, ArchimedeanClass.FiniteElement.mk_one, CochainComplex.cm5b.I_d, Quaternion.re_snd_dualNumberEquiv, CochainComplex.triangleOfDegreewiseSplit_mor₁, ZMod.val_two_eq_two_mod, Matrix.invOf_fromBlocks_zero₂₁_eq, Ideal.univ_eq_iUnion_image_add, CompleteOrthogonalIdempotents.prod_one_sub, Matrix.IsTotallyUnimodular.one_fromCols, WittVector.verschiebung_frobenius_comm, bernsteinPolynomial.eval_at_0, sq_le_one_iff_abs_le_one, QuaternionAlgebra.coe_natCast, Quaternion.re_add, ZMod.toCircle_intCast, KaehlerDifferential.span_range_eq_ideal, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, WeierstrassCurve.twoTorsionPolynomial_disc, IsUltrametricDist.nnnorm_natCast_le_one, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, Subring.closure_insert_one, ZMod.toCircle_natCast, FDRep.char_orthonormal, Matrix.invOf_submatrix_equiv_eq, CharP.pi', ZMod.orderOf_five, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, CochainComplex.HomComplex.Cochain.d_comp_ofHom_v, Polynomial.coeff_eq_esymm_roots_of_card, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Matrix.det_one_add_replicateCol_mul_replicateRow, Matrix.zero_zpow_eq, PositiveLinearMap.norm_apply_le_of_nonneg, HomologicalComplex.homologicalComplexToDGO_obj_obj, CochainComplex.HomComplex.Cochain.leftShift_units_smul, Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec, Rat.cast_inv_nat, stdSimplexEquivIcc_apply_coe, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_coe, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, Polynomial.Chebyshev.iterate_derivative_T_eval_one, Polynomial.smul_mem_rootSet_iff_of_isUnit, sbtw_lineMap_iff, ZMod.coe_mul_inv_eq_one, HomotopyCategory.homologyShiftIso_hom_app, Set.pairwise_disjoint_Ico_intCast, Int.divisorsAntidiag_ofNat, iter_deriv_inv_linear_sub, WeierstrassCurve.Jacobian.Point.zero_point, midpoint_sub_left, charP_of_card_eq_prime_pow, Quaternion.mul_coe_eq_smul, CochainComplex.shiftFunctorAdd_hom_app_f, WittVector.exists_frobenius_solution_fractionRing_aux, RingPreordering.neg_one_notMem, Algebra.norm_eq_one_of_not_module_finite, Nat.sub_one_lt_floor, lucas_primality_iff, ModularGroup.coe_T, midpoint_vsub, pow_eq_one_iff_cases, WeierstrassCurve.Jacobian.Point.toAffine_zero, rootsOfUnityEquivNthRoots_apply, MeasureTheory.lpNorm_natCast_mul, ZMod.invDFT_def, WittVector.iterate_verschiebung_mul_left, ComplexShape.instIsTruncLENatIntEmbeddingDownNat, Int.fract_eq_zero_or_add_one_sub_ceil, IsStarProjection.one_sub, DerivedCategory.Qh_obj_singleFunctors_obj, Polynomial.leadingCoeff_X_pow_sub_one, Matrix.J_det_mul_J_det, DoubleCentralizer.natCast_toProd, Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X, Quaternion.im_ratCast, Num.to_nat_to_int, legendreSym.eq_neg_one_iff', ZMod.injective_toCircle, nnnorm_sub_mul_le, ModP.v_p_lt_val, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, jacobiSum_mul_jacobiSum_inv, RatFunc.single_zpow, ArchimedeanClass.mk_one, iteratedDeriv_id, Quaternion.imJ_add, CochainComplex.HomComplex.δ_map, Ideal.Quotient.mk_eq_one_iff_sub_mem, exteriorPower.basis_repr, Finset.tendsto_Ico_neg, Num.ofZNum'_toNat, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, legendreSym.at_neg_two, Quaternion.im_sub, IsPrimitiveRoot.self_sub_one_pow_dvd_order, RootPairing.InvariantForm.apply_eq_or, spinGroup.star_mul_self_of_mem, CochainComplex.mappingCone.inl_v_descShortComplex_f, sum_Ioc_inv_sq_le_sub, hasStrictDerivAt_exp_zero_of_radius_pos, toIcoDiv_sub_natCast_mul, VectorFourier.fourierIntegral_comp_add_right, AddCircle.addOrderOf_period_div, UnitAddTorus.span_mFourier_closure_eq_top, IsAlgebraic.invOf_iff, Algebra.SubmersivePresentation.ofSubsingleton_σ', RingCon.coe_intCast, derivWithin_neg, AffineMap.lineMap_symm, Quaternion.imI_natCast, Algebra.discr_powerBasis_eq_prod'', WittVector.iterate_verschiebung_coeff, Polynomial.algEquivCMulXAddC_symm_apply, Polynomial.Chebyshev.T_eq_half_mul_C_comp_two_mul_X, CochainComplex.HomComplex.Cochain.d_comp_ofHoms_v, CochainComplex.HomComplex.Cochain.toSingleMk_postcomp, IsPrimitiveRoot.card_nthRoots_one, AddChar.zmod_zero, Matrix.disc_of_card_eq_two, hasDerivAt_single, IsCyclotomicExtension.norm_zeta_eq_one, CochainComplex.HomComplex.Cochain.ofHom_add, sub_half, QuaternionAlgebra.imJ_natCast, Finset.centroid_pair_fin, preNormEDS_odd, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_s, one_div_lt_one_div_of_neg, CochainComplex.mappingCone.inr_f_descShortComplex_f, orthonormal_iff_ite, DualNumber.exp_smul_eps, WeierstrassCurve.Jacobian.equation_zero, CochainComplex.HomComplex.Cochain.id_comp, Polynomial.coeff_eq_esymm_roots_of_splits, Rep.leftRegularHomEquiv_apply, Quaternion.snd_imI_dualNumberEquiv_symm, neg_one_lt_zero, QuaternionAlgebra.star_smul, round_eq_iff, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, CategoryTheory.ProjectiveResolution.instQuasiIsoIntπ', ZMod.addOrderOf_one, MvPolynomial.universalFactorizationMapPresentation_algebra_smul, CochainComplex.HomComplex.Cochain.single_v_eq_zero', round_sub_natCast, inner_self_eq_one_of_norm_one, round_one, ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_isCoprime, LieAlgebra.IsKilling.traceForm_coroot, Finset.centroidWeights_eq_const, DerivedCategory.exists_iso_Q_obj_of_isLE, ValuativeRel.inv_vle_one, EuclideanDomain.div_one, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, ZMod.coe_unitOfCoprime, DihedralGroup.r_one_pow_n, norm_commutator_units_sub_one_le, CochainComplex.shiftFunctorAdd'_hom_app_f, Fourier.fourierIntegral_def, IntermediateField.expChar', Matrix.SpecialLinearGroup.coe_neg, descPochhammer_succ_eval, DerivedCategory.instFullFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, Matrix.det_sum_smul_le, CochainComplex.HomComplex.Cochain.ofHom_zero, Ideal.Quotient.smulCommClass, Quaternion.add_im, FormalMultilinearSeries.ofScalars_comp_neg, CochainComplex.g_shortComplexTruncLEX₃ToTruncGE_assoc, Matrix.fromCols_one_isTotallyUnimodular_iff, FiniteField.card', CochainComplex.mappingCone.inr_f_triangle_mor₃_f_assoc, Matrix.TransvectionStruct.sumInl_toMatrix_prod_mul, WeierstrassCurve.Projective.nonsingular_zero, CochainComplex.HomComplex.leftHomologyData'_π, geom_series_mul_neg, LieModule.traceForm_eq_sum_finrank_nsmul_mul, div_sub_one, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add, WeierstrassCurve.Jacobian.Point.zero_def, WeierstrassCurve.Affine.evalEval_polynomialX, Mathlib.Tactic.Zify.Nat.cast_sub_of_lt, Int.preimage_ceil_singleton, quadraticChar_eq_pow_of_char_ne_two, IsCyclotomicExtension.Rat.associated_norm_zeta_sub_one, LinearMap.det_ring, Finset.tendsto_Ioc_neg, LieModule.genWeightSpace_chainTopCoeff_add_one_nsmul_add, convexHull_eq, PreTilt.instCharP, ZMod.natCast_eq_natCast_iff, geom_sum_mul_neg, WeierstrassCurve.Jacobian.dblU_of_Z_eq_zero, ordinaryHypergeometric_radius_top_of_neg_nat₁, CliffordAlgebra.ofBaseChange_tmul_one, ZNum.cast_to_int, Function.Periodic.sub_nat_mul_eq, HomogeneousLocalization.NumDenSameDeg.den_one, instSMulCommClassSubtypeMemSubalgebraIntegralClosure, RootPairing.pairingIn_neg_two_neg_two_iff, instCharZeroOfIsSemireal, Finset.disjoint_box_succ_prod, QuotSMulTop.map_apply_mk, Matrix.cramer_smul, ValuativeRel.not_rel_one_zero, MvPolynomial.universalFactorizationMapPresentation_val, IsCyclotomicExtension.norm_zeta_pow_sub_one_two, Int.floor_sub_natCast, Algebra.norm_smul_one_eq_norm, IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_one, IsDiscreteValuationRing.addVal_one, CochainComplex.HomComplex.Cochain.map_ofHom, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, Quaternion.sub_re, NormedSpace.norm_expSeries_div_summable, IsIdempotentElem.one_sub_iff, CoxeterSystem.lengthParity_eq_ofAdd_length, WeierstrassCurve.Δ_of_isCharThreeJNeZeroNF, WeierstrassCurve.c₄_of_isCharTwoJEqZeroNF, FractionalIdeal.spanSingleton_one, Quaternion.coe_intCast, IsLocalRing.ResidueField.residue_smul, GenContFract.get?_of_eq_some_of_succ_get?_intFractPair_stream, Ring.ord_one, ZMod.eq_one_or_isUnit_sub_one, Zsqrtd.re_natCast, Matrix.SpecialLinearGroup.coe_matrix_coe, ArithmeticFunction.coe_zeta_mul_moebius, FixedDetMatrices.smul_coe, RingEquiv.map_eq_neg_one_iff, PadicInt.norm_natCast_eq_one_iff, Matrix.SpecialLinearGroup.mapGL_coe_matrix, AddCircle.addOrderOf_div_of_gcd_eq_one', CStarAlgebra.norm_le_one_iff_of_nonneg, CochainComplex.shiftFunctorComm_hom_app_f, Matrix.coe_det_isEmpty, Profinite.NobelingProof.one_sub_e_mem_of_false, analyticAt_inverse_one_sub, Ring.descPochhammer_eq_factorial_smul_choose, toIocMod_add_natCast_mul, ZMod.toCircle_apply, CharP.isUnit_natCast_iff, autEquivRootsOfUnity_apply_rootOfSplit, IsLocalization.mul_toInvSubmonoid, Algebra.Norm.Transitivity.auxMat_toSquareBlock_ne, HahnSeries.coeff_toOrderTopSubOnePos_pow, deriv_fun_pow, unitary.norm_sub_one_lt_two_iff, one_le_div_of_neg, CyclotomicField.instCharZero, WeierstrassCurve.coeff_Ψ₃, Quaternion.re_smul, DirichletCharacter.delta_mul, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, FermatLastTheoremForThreeGen.Solution.associated_of_dvd_a_add_eta_mul_b_of_dvd_a_add_eta_sq_mul_b, ValuativeRel.inv_vlt_one, PosNum.cast_sub', CochainComplex.mappingCone.inl_v_snd_v, WeierstrassCurve.Jacobian.equation_some, Finset.prod_indicator_biUnion_sub_indicator, Quaternion.eq_re_iff_mem_range_coe, Polynomial.Chebyshev.S_eval_two, sq_dvd_add_pow_sub_sub, Affine.Triangle.prod_div_one_sub_eq_one_of_mem_line_point_lineMap, ZMod.χ₄_nat_mod_four, ZMod.natAbs_mod_two, deriv_descPochhammer_eval_eq_sum_prod_range_erase, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_f, analyticAt_inv_one_sub, derivWithin_id, Subring.smul_mem_pointwise_smul, CliffordAlgebra.ι_mem_evenOdd_one, IsStarProjection.one_sub_mul_self, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_symm_apply, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, dist_midpoint_midpoint_le', fwdDiff_addChar_eq, fromModuleCatToModuleCatLinearEquiv_apply, iteratedDeriv_fun_pow_zero, AbsoluteValue.apply_natAbs_eq, HomotopyCategory.Pretriangulated.rotate_distinguished_triangle, Quaternion.coe_add, dist_algebraMap, ZMod.cast_sub_one, CochainComplex.HomComplex.Cochain.rightShift_neg, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat, Matrix.mem_orthogonalGroup_iff', ZMod.coe_int_mul_inv_eq_one, zsmul_one, Projectivization.generalLinearGroup_smul_def, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, pow_eq_neg_one_iff, Quaternion.normSq_intCast, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, invOf_eq_of_coprime, HomotopyCategory.quotient_obj_singleFunctors_obj, Nat.Coprime.cast, iter_deriv_inv_linear, RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul, List.norm_prod, IsCyclotomicExtension.adjoin_roots, Summable.hasProdUniformlyOn_one_add, LieAlgebra.IsKilling.rootSpace_two_smul, DirichletCharacter.isMultiplicative_toArithmeticFunction, Quaternion.natCast_imK, tendsto_floor_left, PadicInt.ideal_eq_span_pow_p, convexHull_rangle_single_eq_stdSimplex, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃, Metric.unitClosedBall.coe_eq_one, DirichletCharacter.convolution_mul_moebius, WittVector.verschiebung_coeff_add_one, WithIdealFilter.mem_nhds_iff, EqualCharZero.of_algebraRat, odd_sub_one, FixedPoints.smul, dist_right_lineMap, DerivedCategory.instEssSurjCochainComplexIntQ, IsIdempotentElem.quasispectrum_subset, Polynomial.Chebyshev.leadingCoeff_T, ZMod.charZero, CochainComplex.HomComplex.Cochain.fromSingleMk_v_eq_zero, Nat.neg_cast_eq_cast, ZMod.toAddCircle_eq_zero, hasDerivWithinAt_id, WittVector.mul_polyOfInterest_aux5, Int.cast_le_neg_one_or_one_le_cast_of_ne_zero, Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero, HomologicalComplex.dgoEquivHomologicalComplex_inverse, tendsto_ceil_right, Subgroup.HasDetPlusMinusOne.abs_det, ModuleCat.FreeMonoidal.εIso_hom_one, DerivedCategory.singleFunctorsPostcompQIso_hom_hom, Mathlib.Meta.NormNum.isNat_neg_of_isNegNat, RCLike.nnnorm_natCast, Ring.choose_succ_succ, cfc_le_one_iff, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, instExpCharLinearMapSubtypeMemSubringCenterId, Quaternion.re_sub, IsCyclotomicExtension.Rat.inertiaDeg_of_not_dvd, WeierstrassCurve.Projective.Point.toAffine_zero, stdSimplexEquivIcc_symm_apply_coe, Padic.valuation_natCast, Matrix.det_fin_zero, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, WeierstrassCurve.Jacobian.neg_of_Z_ne_zero, AffineBasis.coe_coord_of_subsingleton_eq_one, AddChar.wInner_cWeight_eq_boole, Polynomial.qsmul_eq_C_mul, Matrix.TransvectionStruct.reverse_inv_prod_mul_prod, jacobiSym.list_prod_right, Padic.norm_p, Polynomial.Chebyshev.T_eval_neg_one, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, quadraticChar_neg_one, CochainComplex.shiftEval_inv_app, AffineBasis.toMatrix_self, Matrix.den_one, ZNum.dvd_to_int, Padic.norm_natCast_p_sub_one, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, EisensteinSeries.eisSummand_SL2_apply, IsPrimitiveRoot.zeta_sub_one_prime, CFC.abs_one, unitary.norm_sub_one_sq_eq, CFC.log_one, Polynomial.resultant_one_left, PosNum.to_nat_to_int, Polynomial.mirror_smul, NormedRing.inverse_one_sub_nth_order', abs_one, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, Quaternion.mul_imI, Rep.diagonalHomEquiv_apply, IsCyclotomicExtension.neZero', hasStrictFDerivAt_list_prod', BooleanRing.mul_one_add_self, right_sub_midpoint, PreTilt.pow_dvd_mul_untiltAux_sub_untiltAux_mul, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_acyclic, Int.mul_natCast_floor_div_cancel, WittVector.aeval_verschiebungPoly, FixedPoints.smulCommClass', WeierstrassCurve.b₄_of_isCharNeTwoNF, DualNumber.ideal_trichotomy, ProjectiveSpectrum.basicOpen_one, CategoryTheory.DifferentialObject.objEqToHom_d_assoc, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Asymptotics.IsEquivalent.listProd, Quaternion.re_ratCast, intCast_ofNat, Quaternion.intCast_re, IsInvariantSubfield.smul_mem, ContinuousLinearEquiv.coord_self, WittVector.verschiebung_isPoly, Quaternion.coe_im, Mathlib.Meta.NormNum.Rat.invOf_denom_swap, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_apply, WeierstrassCurve.Projective.dblX_eq, ZNum.cast_sub, pinGroup.coe_mul_star_self, MeasureTheory.lpNorm_one', Quaternion.zero_im, Ring.uniformContinuousConstSMul_op, KaehlerDifferential.DLinearMap_apply, CategoryTheory.DifferentialObject.d_squared_apply_assoc, CochainComplex.ConnectData.homologyMap_map_of_eq_neg_succ, complEDS'_one, RootPairing.pairing_one_four_iff, PadicInt.continuousAddCharEquiv_apply, CochainComplex.HomComplex.Cochain.equivHomotopy_symm_apply_hom, TwoSidedIdeal.coe_smul, localization_unit_isIso', IsAdjoinRootMonic.coeff_root, HomogeneousLocalization.NumDenSameDeg.num_zero, zpow_eq_one_iff_cases₀, CliffordAlgebra.ofProd_ι_mk, summable_norm_pow_mul_geometric_of_norm_lt_one, Int.preimage_fract, WeierstrassCurve.Jacobian.nonsingular_zero, CliffordAlgebra.GradedAlgebra.lift_ι_eq, ComplexShape.ε_up_ℤ, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, NormedSpace.expSeries_hasSum_exp_of_mem_ball', Quaternion.instNormOneClassReal, Quaternion.instIsScalarTower, CFC.spectrum_one_eq, IncidenceAlgebra.mu_prod_mu, FiniteField.sum_subgroup_units, CochainComplex.HomComplex.Cocycle.equivHomShift_comp_shift, HomotopyCategory.homologyFunctor_shiftMap, StandardEtalePresentation.toPresentation_relation, OrthonormalBasis.coe_singleton, MonoidHom.map_neg_one, ExteriorAlgebra.ι_mul_prod_list, ZMod.χ₈_nat_eq_if_mod_eight, ContinuousLinearMap.hasDerivWithinAt, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_symm_apply, abs_le_one_iff_mul_self_le_one, ArithmeticFunction.vonMangoldt_mul_zeta, Ring.descPochhammer_succ_succ_smeval, Matrix.SpecialLinearGroup.toLin'_symm_apply, prod_vanishing_of_summable_norm, iteratedDeriv_fun_mul, CharP.quotient_iff_le_ker_natCast, iUnion_Ioc_intCast, descPochhammer_zero_eval_zero, ModularGroup.coe_T_zpow, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, CochainComplex.mappingCone.lift_f_snd_v, toIcoDiv_add_natCast_mul', Matrix.GeneralLinearGroup.val_inv_swap, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, Matrix.intCast_mulVec, hasDerivAt_exp_zero, GenContFract.sub_convs_eq, descPochhammer_eval_zero, IsPrimitiveRoot.associated_sub_one_pow_sub_one_of_coprime, CochainComplex.isKProjective_shift_iff, ZMod.prod_Ico_one_prime, ComplexShape.embeddingDownIntUpInt_f, AddValuation.map_one, Int.instCharZero, LieAlgebra.Orthogonal.pb_inv, Quaternion.imJ_star, ModP.preVal_eq_zero, WittVector.mul_polyOfInterest_aux3, Matrix.invOf_eq, jacobiSym.at_neg_one, CochainComplex.instIsStrictlyLEObjIntSingleFunctor, Even.intCast, ComplexShape.embeddingUpIntGE_f, CochainComplex.mappingCone.triangle_obj₂, homothety_inv_two, sbtw_zero_one_iff, CochainComplex.instIsStrictlyGEObjIntSingleFunctor, IncidenceAlgebra.eulerChar_orderDual, Polynomial.shiftedLegendre_eval_symm, Matrix.TransvectionStruct.toMatrix_sumInl, Profinite.NobelingProof.list_prod_apply, OnePoint.equivProjectivization_apply_coe, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, Matrix.IsTotallyUnimodular.fromRows_one, IsCyclotomicExtension.union_right, ValuativeRel.one_srel_inv, ExpChar.exists_unique, IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_nth_roots, CochainComplex.mappingConeCompTriangle_mor₂, Zsqrtd.im_natCast, CFC.rpow_zero, Mathlib.Tactic.RingNF.int_rawCast_neg, ExpChar.exists, DerivedCategory.instLinearHomotopyCategoryIntUpQh, IsCyclotomicExtension.Rat.Three.cube_sub_one_eq_mul, isLittleO_pow_const_const_pow_of_one_lt, toIcoDiv_natCast_mul_add, Complex.re_nsmul, geom_sum_Ico, DirichletCharacter.modZero_eq_delta, exists_signed_sum, CochainComplex.cm5b.degreewiseEpiWithInjectiveKernel_p, hasStrictDerivAt_id, CochainComplex.HomComplex.Cochain.rightShift_v, CochainComplex.HomComplex.Cochain.rightUnshift_zero, AffineMap.lineMap_apply_one_sub, CochainComplex.mappingConeCompTriangleh_comm₁, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk, ValuativeRel.ValueGroupWithZero.lift_one, CochainComplex.HomComplex.Cocycle.leftShift_coe, Affine.Simplex.interior_eq_image_Ioo, Order.IsPredLimit.lt_sub_natCast, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, one_sub_div, deriv_neg, Matrix.invertibleEquivDetInvertible_symm_apply, bernsteinPolynomial.iterate_derivative_at_0, WeierstrassCurve.twoTorsionPolynomial_discr, FermatLastTheoremForThreeGen.Solution.associated_of_dvd_a_add_b_of_dvd_a_add_eta_sq_mul_b, dist_midpoint_left, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, NumberField.InfinitePlace.map_natCast, PowerSeries.binomialSeries_nat, WeierstrassCurve.Projective.add_of_Y_ne, LinearMap.hasDerivAt, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, Matrix.submatrixEquivInvertibleEquivInvertible_symm_apply, neg_one_pow_mul_eq_zero_iff, midpoint_vsub_midpoint_same_left, LinearMap.hasDerivAtFilter, Int.absNorm_under_eq_sInf, Ideal.IsLocal.mem_jacobson_or_exists_inv, Quaternion.sub_imK, CochainComplex.HomComplex.Cochain.shift_v', PreTilt.mk_untilt_eq_coeff_zero, PadicInt.unitCoeff_spec, IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvd, WeierstrassCurve.j_of_isShortNF, norm_sub_mul_le, FermatLastTheoremForThreeGen.lambda_sq_dvd_c, right_vsub_midpoint, Lagrange.eval_basis_self, Matrix.det_succ_row_zero, WeierstrassCurve.Projective.equation_zero, WeierstrassCurve.IsCharTwoJNeZeroNF.a₁, PadicInt.norm_natCast_zmodRepr_eq_iff, IntermediateField.forall_mem_adjoin_smul_eq_self_iff, Quaternion.im_sq, WeierstrassCurve.Projective.dblX_eq', CochainComplex.cm5b.instInjectiveXIntMappingConeIdI, reverse_lucas_primality, Ring.choose_zero_right', QuotSMulTop.map_id, div_lt_one_iff, one_div_le_one_div_of_neg_of_le, FirstOrder.Field.model_fieldOfChar_of_charP, ModuleCat.extendScalarsId_inv_app_apply, WittVector.mk_fontaineTheta, Polynomial.descPochhammer_smeval_eq_ascPochhammer, Mathlib.Meta.NormNum.isNat_intOfNat, Quaternion.imJ_natCast, Derivation.leibniz_invOf, PowerSeries.binomialSeries_constantCoeff, ordinaryHypergeometricSeries_norm_div_succ_norm, Int.cast_eq_one, WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero, Quaternion.natCast_imJ, Matrix.GeneralLinearGroup.coe_map_inv_mul_map, Mathlib.Meta.NormNum.isNat_ofScientific_of_false, nndist_right_midpoint, Matrix.mul_nonsing_inv, Polynomial.Chebyshev.S_eval_neg_two, IsPrimitiveRoot.eq_neg_one_of_two_right, preNormEDS_two, ModularGroup.coe_S, jacobiSym.list_prod_left, GradedTensorProduct.of_one, DerivedCategory.mem_distTriang_iff, Quaternion.coe_neg, inner_eq_one_iff_of_norm_one, EisensteinSeries.eisensteinSeries_slash_apply, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv_assoc, IsPrimitiveRoot.norm_of_cyclotomic_irreducible, isIdempotentElem_iff_mul_one_sub_self, nnnorm_sub_mul_le', AddChar.zmod_intCast, sbtw_one_zero_iff, CategoryTheory.Functor.instCommShiftCochainComplexIntMapMap₂CochainComplex, FDRep.scalar_product_char_eq_finrank_equivariant, tangentConeAt_eq_univ, IncidenceAlgebra.mu_toDual, FermatLastTheoremForThreeGen.Solution.lambda_sq_not_dvd_a_add_eta_mul_b, ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot, toBoolRing_top, Matrix.zpow_neg_mul_zpow_self, WeierstrassCurve.Jacobian.dblXYZ_of_Y_eq, CochainComplex.isKInjective_iff_rightOrthogonal, Quaternion.coeComplex_one, NormedSpace.expSeries_summable_of_mem_ball', IsPrimitiveRoot.associated_pow_sub_one_pow_of_coprime, CochainComplex.HomComplex.Cochain.rightShift_add, Int.cast_negOfNat, ZMod.instIsScalarTower, CochainComplex.ShiftSequence.shiftIso_inv_app, mem_finsuppAffineCoords_iff_linearCombination, Quaternion.hasSum_coe, Rep.free_ext_iff, LinearMap.detAux_id, ZMod.natCast_toNat, ZMod.euler_criterion, CochainComplex.HomComplex.Cochain.diff_v, HomologicalComplex.dgoEquivHomologicalComplexUnitIso_inv_app_f, ZMod.eq_unit_mul_divisor, WeierstrassCurve.b₄_of_isCharTwoJEqZeroNF, stdSimplexEquivIcc_one, isRoot_of_unity_iff, Quaternion.intCast_im, sub_one_dvd_pow_sub_one, DerivedCategory.instIsLEObjCochainComplexIntQOfIsLE, Int.lt_floor_iff, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, Matrix.GeneralLinearGroup.injective_upperRightHom, Quaternion.imI_coe, sub_self_div_two, CategoryTheory.Functor.instCommShiftCochainComplexIntMapFlipMap₂CochainComplex, DirichletCharacter.LSeries_eulerProduct, PEquiv.toMatrix_swap, Rat.natCast_lt_cast, Algebra.Norm.Transitivity.auxMat_toSquareBlock_eq, Quaternion.hom_ext_iff, PowerSeries.rescale_neg_one_invOneSubPow, zsmul_zero', CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk, MixedCharZero.reduce_to_maximal_ideal, CochainComplex.isGE_shift, PadicInt.unitCoeff_coe, ZMod.exists_sq_eq_neg_two_iff, Module.Presentation.tautologicalRelations_relation, FixedPoints.mem_intermediateField_iff, RCLike.normSq_one, Ideal.span_singleton_absNorm_le, AffineMap.deriv, fwdDiff_iter_sum_mul_pow_eq_zero, isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt, Subring.smul_mem_pointwise_smul_iff, CochainComplex.HomComplex.δ_neg_one_cochain, Summable.multipliableUniformlyOn_nat_one_add, CochainComplex.HomComplex.Cochain.ofHoms_zero, CongruenceSubgroup.Gamma_mem, DerivedCategory.Q_map_eq_of_homotopy, ArchimedeanClass.FiniteElement.mk_natCast, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_hom_app, ZMod.injective_stdAddChar, LinearMap.det_eq_one_of_subsingleton, smul_inv'', tendsto_pow_atTop_nhds_zero_iff, Int.instNormOneClass, ModularGroup.S_mul_S_eq, fderiv_list_prod', Quaternion.re_intCast, CochainComplex.mappingCone.triangleRotateShortComplex_f, HomogeneousLocalization.NumDenSameDeg.den_zero, ZMod.LFunction_dft, LieModule.coe_chainTop', PadicInt.coe_dpow_eq, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_exactAt, Matrix.SpecialLinearGroup.coe_mul, CochainComplex.HomComplex.Cocycle.rightUnshift_coe, RCLike.charZero_rclike, two_mul_le_add_mul_sq, WeierstrassCurve.Jacobian.add_of_Z_eq_zero, Matrix.adjugate_mul, toBoolAlg_one, Nat.infinite_setOf_prime_and_eq_mod, HahnSeries.mem_orderTopSubOnePos_iff, EuclideanDomain.gcd_one_left, AddChar.zmodAddEquiv_apply, gaussSum_mul_gaussSum_eq_card, rootsOfUnityEquivNthRoots_symm_apply, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, Quaternion.re_mul, Quaternion.normSq_div, Matrix.UnitaryGroup.star_mul_self, BoundedContinuousFunction.coe_npowRec, CFC.rpow_neg_mul_rpow, RootPairing.InvariantForm.two_mul_apply_root_root, TensorProduct.toMatrix_comm, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, ComplexShape.instIsRelIffIntEmbeddingUpIntDownInt, ZNum.to_int_inj, ZSpan.mem_fundamentalDomain, PadicInt.norm_natCast_p_sub_one, WeierstrassCurve.c₆_of_isShortNF, Ideal.Quotient.isScalarTower_right, CliffordAlgebra.evenOdd_isCompl, CochainComplex.mappingCone.lift_f, PowerSeries.mk_one_mul_one_sub_eq_one, PadicInt.prime_p, CochainComplex.HomComplex.Cochain.δ_leftShift, Nonneg.orderedSub, GenContFract.of_isSimpContFract, DerivedCategory.isIso_Q_map_iff_quasiIso, Algebra.Generators.comp_σ, neg_one_pow_expChar_pow, ZNum.mul_to_int, DerivedCategory.isIso_Qh_map_iff, Matrix.sub_scalar_sq_eq_discr, toIocDiv_add_natCast_mul, ContinuousLinearMap.hasStrictDerivAt, Function.Periodic.neg_nat_mul, CharP.quotient_iff, ZMod.eisenstein_lemma_aux, Quaternion.instFinite, GaussianInt.prime_iff_mod_four_eq_three_of_nat_prime, Finset.box_succ_union_prod, DoubleCentralizer.toProdHom_apply, WeierstrassCurve.Projective.equation_some, CStarRing.norm_one, IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two', CochainComplex.HomComplex.CohomologyClass.toHom_mk, ZMod.completedLFunction_modOne_eq, ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_sub_of_squarefree, Nat.abs_ceil_sub_le, logDeriv_pow, Set.Finite.convexHull_eq, derivWithin_pow, CochainComplex.HomComplex.Cochain.add_v, Sbtw.mem_image_Ioo, AddChar.zmod_injective, UnitAddCircle.integral_preimage, Int.fract_mul_natCast, WittVector.frobenius_verschiebung, WeierstrassCurve.j_of_isCharTwoJNeZeroNF_of_char_two, AlgebraicClosure.instCharZero, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_apply, CochainComplex.instIsMultiplicativeIntDegreewiseEpiWithInjectiveKernel, Complex.sum_div_factorial_le, WeierstrassCurve.Projective.eval_polynomialY, DerivedCategory.left_fac_of_isStrictlyGE, CochainComplex.mappingConeHomOfDegreewiseSplitIso_hom_f, CliffordAlgebra.contractLeft_one, CochainComplex.mappingCone.inl_v_fst_v_assoc, one_le_nnnorm_one, Quaternion.normSq_star, DihedralGroup.r_one_pow, Quaternion.imK_sub, NumberField.Embeddings.pow_eq_one_of_norm_eq_one, Matrix.invOf_fromBlocks₁₁_eq, nndist_self_homothety, Algebra.FormallyUnramified.iff_exists_tensorProduct, FermatLastTheoremForThreeGen.Solution'.multiplicity_lambda_c_finite, WeierstrassCurve.Jacobian.addMap_of_Y_eq, KaehlerDifferential.kerTotal_map', Padic.norm_p_zpow, RCLike.I_mul_I_of_nonzero, CategoryTheory.ProjectiveResolution.cochainComplex_d_assoc, IsPrimitiveRoot.norm_sub_one_two, zpow_eq_one_iff_of_ne_zero₀, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, ZMod.dft_def, Matrix.charpoly.univ_coeff_card, spectrum.vadd_eq, Finset.univ_of_card_le_two, IsStarProjection.mul_one_sub_self, Rep.barComplex.d_single, RCLike.span_one_I, Module.Presentation.tautological_relation, CFC.rpow_mul_rpow_neg, IsPrimitiveRoot.pow_sub_pow_eq_prod_sub_mul, RootPairing.forall_pairing_eq_swap_or, instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, Quaternion.normSq_ratCast, ZMod.coe_int_val_inv_mul, IncidenceAlgebra.zeta_prod_mk, Quaternion.imK_im, ModuleCat.ExtendScalars.hom_ext_iff, hasStrictDerivAt_exp_zero, HomotopyCategory.mappingConeCompTriangleh_distinguished, PerfectClosure.one_def, Quaternion.imK_add, wittPolynomial_eq_sum_C_mul_X_pow, CochainComplex.HomComplex.Cochain.leftShift_neg, Finset.sum_affineCombinationSingleWeights, NumberField.RingOfIntegers.instCharZero_1, Ring.choose_eq_nat_choose, Matrix.det_eq_sign_charpoly_coeff, 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CochainComplex.isLE_shift, CochainComplex.mappingCone.triangle_obj₁, Quaternion.imJ_intCast, ZMod.rootsOfUnityAddChar_val, wbtw_mul_sub_add_iff, HomologicalComplex.dgoEquivHomologicalComplexCounitIso_inv_app_f, FermatLastTheoremForThreeGen.Solution.lambda_dvd_a_add_eta_mul_b, Quaternion.smul_imJ, IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one, Subring.mem_inv_pointwise_smul_iff₀, Height.mulHeight₁_one, HomotopyCategory.instIsClosedUnderIsomorphismsIntUpSubcategoryAcyclic, ascPochhammer_eval_neg_eq_descPochhammer, Set.pairwise_disjoint_Ioo_intCast, PowerSeries.invOneSubPow_val_succ_eq_mk_add_choose, IsLocalRing.isUnit_one_sub_self_of_mem_nonunits, ZMod.toCircle_eq_circleExp, PadicInt.existsUnique_mem_range, CochainComplex.mappingCone.lift_f_snd_v_assoc, Profinite.NobelingProof.factors_prod_eq_basis, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, Polynomial.content_X_pow, ComplexShape.boundaryLE_embeddingUpIntLE_iff, homothety_one_half, RootPairing.pairingIn_same, UniformSpace.Completion.coe_one, CochainComplex.cm5b, RootPairing.EmbeddedG2.threeShortAddLongRoot_eq, Quaternion.one_re, Rep.FiniteCyclicGroup.resolution.π_f, ofBoolAlg_compl, WeierstrassCurve.Jacobian.neg_of_Z_eq_zero, Quaternion.exp_coe, Int.divisorsAntidiag_neg_natCast, AddChar.inv_mulShift, isUnit_one_sub_of_norm_lt_one, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, ZMod.stdAddChar_apply, Affine.Simplex.centroid_vsub_point_eq_smul_vsub, Module.Relations.Solution.π_single, WeierstrassCurve.leadingCoeff_Ψ₃, hasStrictDerivAt_pow, MixedCharZero.toCharZero, Quaternion.star_coe, Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul, Quaternion.smul_imI, Int.ceil_natCast_add, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom', convexHull_range_eq_exists_affineCombination, Quaternion.imI_one, IsLocalization.smul_toInvSubmonoid, WittVector.ghostComponentModPPow_map_mk, Matrix.det_one_add_mul_comm, Profinite.NobelingProof.factors_prod_eq_basis_of_eq, Module.presentationFinsupp_var, Quaternion.exp_eq, IsPrimitiveRoot.pow_add_pow_eq_prod_add_mul, HasFDerivAtFilter.hasDerivAtFilter, ZNum.of_to_int', CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_symm_apply, PadicInt.instCharZero, Ordinal.toGame_natCast, Int.ceil_one, CategoryTheory.InjectiveResolution.instInjectiveXIntCochainComplex, Subring.one_mem, pinGroup.mul_star_self_of_mem, Complex.coe_reAddGroupHom, CochainComplex.shiftFunctor_obj_d, WittVector.coeff_p_one, Matrix.det_invOf, Quaternion.imJ_sub, Subring.coe_one, Complex.instCharZero, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_two, EqualCharZero.of_not_mixedCharZero, PerfectClosure.natCast, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y, Quaternion.normSq_coe, Int.fract_div_intCast_eq_div_intCast_mod, PadicInt.zmodRepr_eq_zero_iff_dvd, PreTilt.coeff_iterate_frobenius', left_sub_midpoint, Subring.coe_natCast, TensorProduct.lidIsometry_symm_apply, CochainComplex.HomComplex.Cochain.toSingleMk_precomp, Matrix.SpecialLinearGroup.toLin'_apply, Valuation.one_rel_iff, neg_add_eq_mul_invOf_mul_same_iff, CochainComplex.HomComplex.Cocycle.rightShift_coe, Int.ceil_natCast, GenContFract.abs_sub_convs_le, midpoint_vsub_midpoint_same_right, CochainComplex.mappingCone.d_fst_v, Affine.Simplex.centroid_vsub_eq, toIcoMod_natCast_mul_add', FirstOrder.Field.charP_iff_model_fieldOfChar, Function.Antiperiodic.sub_nat_mul_eq, IsDedekindDomain.selmerGroup.valuation_ker_eq, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id_assoc, TrivSqZeroExt.eq_smul_exp_of_invertible, exteriorPower.basis_repr_self, GradedTensorProduct.of_symm_one, Subgroup.hasDetPlusMinusOne_iff_abs_det, Ring.choose_smul_choose, Convex.mem_Ioc, CochainComplex.HomComplex.Cochain.leftUnshift_zero, Quaternion.re_nnratCast, ModP.charP, FDRep.simple_iff_char_is_norm_one, Algebra.Extension.cotangentComplex_mk, Matrix.SpecialLinearGroup.mem_center_iff, CompleteOrthogonalIdempotents.bijective_pi, FreeCommRing.isSupported_one, zpow_eq_neg_one_iff₀, DerivedCategory.left_fac, WeierstrassCurve.c₆_of_isCharTwoJNeZeroNF_of_char_two, ZMod.χ₄_nat_eq_if_mod_four, IsPrimitiveRoot.toInteger_cube_eq_one, Height.mulHeight_one, LieAlgebra.Orthogonal.pd_inv, AddCircle.gcd_mul_addOrderOf_div_eq, CochainComplex.mappingCone.triangle_obj₃, Quaternion.natCast_imI, sub_one_mul, IsCyclotomicExtension.discr_prime_pow, CochainComplex.HomComplex.Cochain.map_neg, WeierstrassCurve.Jacobian.add_of_Y_ne, IsAdjoinRootMonic.coeff_root_pow, OrthonormalBasis.inner_eq_ite, CochainComplex.isZero_of_isLE, Ideal.mem_jacobson_bot, left_vsub_midpoint, dvd_geom_sum₂_iff_of_dvd_sub', WittVector.peval_polyOfInterest, Matrix.TransvectionStruct.mul_inv, CochainComplex.HomComplex_d_hom_apply, iter_deriv_pow, CochainComplex.instFaithfulIntSingleFunctor, Matrix.one_div_zpow, Quaternion.nnnorm_coe, Rat.cast_one, mul_self_sub_one, Finset.cast_card_inter, CochainComplex.HomComplex.CohomologyClass.homAddEquiv_apply, derivationQuotKerSq_mk, CochainComplex.mappingConeCompTriangle_obj₁, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two, OnePoint.equivProjectivization_apply_infinity, Convex.mem_Ico, CochainComplex.cm5b.I_X, LinearMap.BilinForm.apply_dualBasis_right, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, FermatLastTheoremForThreeGen.Solution.associated_of_dvd_a_add_b_of_dvd_a_add_eta_mul_b, FixedBy.subfield_mem_iff, IsFractionRing.charZero, Quaternion.mul_imJ, CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_apply, CliffordAlgebra.even.lift.aux_one, circleEquivGen_apply, Algebra.Generators.C_mul_X_sub_one_mem_ker, IsPrimitiveRoot.zeta_sub_one_prime', Polynomial.coeff_zero_eq_prod_roots_of_monic_of_splits, nsmul_zmod_val_inv_nsmul, CochainComplex.instAdditiveHomologicalComplexIntUpShiftFunctor, Matrix.mul_adjugate, bernsteinPolynomial.iterate_derivative_at_1, Ideal.eq_zero_of_polynomial_mem_map_range, ComplexShape.instIsTruncGENatIntEmbeddingUpNat, Quaternion.star_eq_self, Multiset.prod_X_sub_C_coeff, Nat.cast_eq_neg_cast, IsCyclotomicExtension.discr_prime_pow_ne_two', summable_indicator_mod_iff, Polynomial.coeff_freeMonic, Finpartition.IsEquipartition.card_interedges_sparsePairs_le', IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, PadicInt.addChar_of_value_at_one_def, WeierstrassCurve.ofJ1728_c₄, ArchimedeanClass.exists_nat_gt_of_mk_nonneg, Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_sup, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, IsPrimitiveRoot.pow_sub_one_mul_geom_sum_eq_pow_sub_one_mul_geom_sum, AddCircle.natCast_div_mul_eq_nsmul, LieAlgebra.SpecialLinear.sl_non_abelian, HasFDerivWithinAt.list_prod', NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, Quaternion.imK_snd_dualNumberEquiv, IsPrimitiveRoot.toInteger_sub_one_not_dvd_two, CongruenceSubgroup.Gamma0_mem, Module.Basis.traceDual_eq_iff, IsCyclotomicExtension.Rat.Three.lambda_dvd_mul_sub_one_mul_sub_eta_add_one, Quaternion.neg_imI, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f, FermatLastTheoremForThreeGen.lambda_sq_dvd_or_dvd_or_dvd, WeierstrassCurve.b₈_of_isCharTwoJNeZeroNF, TwoSidedIdeal.coe_mop_smul, ZMod.pow_div_two_eq_neg_one_or_one, SheafOfModules.unitHomEquiv_apply_coe, Quaternion.imI_ratCast, stdSimplexEquivIcc_zero, CochainComplex.ShiftSequence.shiftIso_hom_app, Matrix.permMatrix_l2_opNorm_eq, Valuation.HasExtension.instIsScalarTowerInteger, Quaternion.natCast_re, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, Polynomial.aeval_sumIDeriv_of_pos, Quaternion.ext_iff, Matrix.discr_fin_two, Int.fract_eq_iff, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_neg, abs_two, AlgHom.norm_apply_le_self_mul_norm_one, MvPolynomial.pderiv_inl_universalFactorizationMap_X, autEquivRootsOfUnity_smul, CochainComplex.HomComplex.Cochain.single_v_eq_zero, CategoryTheory.InjectiveResolution.cochainComplex_d, ZMod.eq_one_iff_odd, hasStrictDerivAt_neg, HomotopyCategory.instCommShiftHomologicalComplexIntUpHomFunctorMapHomotopyCategoryFactors, deriv_id', CochainComplex.mappingCone.map_δ, DerivedCategory.instIsLocalizationHomotopyCategoryIntUpQhTrWSubcategoryAcyclic, IsStarProjection.one_sub_nonneg, CochainComplex.HomComplex.Cochain.ofHom_comp, CochainComplex.HomComplex.Cochain.ofHomotopy_ofEq, RootPairing.pairing_neg_two_neg_two_iff, CochainComplex.ConnectData.restrictionGEIso_hom_f, tendsto_natCast_atTop_cobounded, PadicInt.norm_natCast_lt_one_iff, HasStrictDerivAt.fun_pow, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val, WeierstrassCurve.variableChange_b₄, Matrix.GeneralLinearGroup.fin_two_smul_prod, NormedSpace.exp_eq_ofScalarsSum, IntermediateField.coe_one, IsFractionRing.charZero_of_isFractionRing, DerivedCategory.instHasRightCalculusOfFractionsHomotopyCategoryIntUpQuasiIso
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toIntCast 📖 | CompOp | 714 mathmath: SetLike.intCast_mem_graded, Num.cast_to_int, legendreSym.eq_neg_one_iff, Int.ceil_lt_iff, ZMod.intCast_eq_intCast_iff_dvd_sub, continuousOn_ceil, sign_intCast, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two', Int.fract_intCast_add, Int.ceil_eq_self_iff_mem, RootPairing.GeckConstruction.h_def, toIocMod_intCast_mul_add, Int.mul_cast_floor_div_cancel_of_pos, Rat.intCast_lt_cast, DihedralGroup.r_one_zpow, Int.lt_succ_floor, ZMod.χ₈'_int_eq_if_mod_eight, Int.cast_neg, Int.lt_ceil, Algebra.TensorProduct.intCast_def', MvPolynomial.hom_C, Polynomial.Chebyshev.U_eval_zero, Int.smul_one_eq_cast, norm_zsmul, PadicInt.norm_int_lt_one_iff_dvd, exists_floor, PadicInt.norm_intCast_eq_padic_norm, toIcoDiv_mul_sub_self, Function.Periodic.int_mul, tendsto_ceil_right', quadraticChar_card_card, FreeCommRing.isSupported_int, Function.Antiperiodic.add_int_mul_eq, QuadraticAlgebra.im_intCast, abs_sub_round, ArchimedeanClass.mk_intCast, Int.cast_natCast, Odd.intCast_zmod_two, Padic.norm_intCast_eq_one_iff, Polynomial.Chebyshev.U_eval_one, IsCoprime.intCast, Algebra.adjoin_singleton_intCast, QuaternionAlgebra.intCast_imJ, Int.cast_one_le_of_pos, ArchimedeanClass.exists_int_gt_of_mk_nonneg, Mathlib.Tactic.ComputeDegree.coeff_intCast_ite, Int.preimage_Ioc, zsmul_eq_mul, one_le_pow_mul_abs_eval_div, ZMod.orderOf_one_add_mul_prime, DoubleCentralizer.intCast_snd, Int.cast_abs, eq_intCast', Rat.cast_intCast, Quaternion.intCast_imK, Matrix.det_permute, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, continuousOn_floor, PadicInt.norm_intCast_lt_one_iff, Int.ceil_div_ceil_inv_sub_one, AbsoluteValue.map_units_intCast, toIocMod_sub_self_eq_mul, Quaternion.im_intCast, IsUltrametricDist.norm_intCast_le_one, Subring.closure_singleton_intCast, toIcoDiv_add_intCast_mul', ContinuousLinearMap.intCast_apply, Int.cast_div_ofNat_charZero, Int.cast_le_neg_one_of_neg, Matrix.transpose_eq_intCast, TrivSqZeroExt.fst_intCast, Rat.cast_mk', Zsqrtd.exists_coprime_of_gcd_pos, Matrix.PosSemidef.intCast, inv_intCast_smul_eq, round_sub_intCast, tendsto_fract_left', toIcoDiv_sub_intCast_mul', Int.cast_le, intCast_mem, toIocDiv_add_intCast_mul', QuaternionAlgebra.imK_intCast, Function.Antiperiodic.int_even_mul_periodic, self_sub_toIocMod_eq_mul, Ideal.norm_dvd_iff, AddCommGroup.ModEq.intCast, ZMod.cast_intCast', GenContFract.of_partNum_eq_one_and_exists_int_partDen_eq, iter_deriv_zpow', QuaternionAlgebra.intCast_re, Int.cast_inj, Module.End.intCast_apply, toIcoDiv_mul_sub_toIcoMod, Int.floor_intCast, Surreal.zsmul_pow_two_powHalf, tendsto_floor_right_pure, ZMod.stdAddChar_coe, Function.Antiperiodic.int_odd_mul_antiperiodic, Polynomial.Chebyshev.T_eval_zero, toIcoDiv_intCast_mul_add, AbsoluteValue.eq_on_nat_iff_eq_on_int, Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence, continuousOn_fract, inv_intCast_smul_comm, QuadraticAlgebra.zsmul_val, Function.Antiperiodic.sub_int_mul_eq, AddSubgroup.intCast_mem_zmultiples_one, Commute.intCast_right, QuaternionAlgebra.imI_intCast, Int.preimage_Ioi, Padic.norm_int_le_one, BitVec.ofFin_intCast, LieAlgebra.IsKilling.apply_coroot_eq_cast', ZMod.intCast_eq_iff, RCLike.intCast_re, QuaternionAlgebra.imJ_intCast, Int.comap_cast_atTop, Matrix.conjTranspose_inv_intCast_smul, Int.fract_floor, Int.floor_intCast_add, NumberField.house_intCast, Polynomial.Chebyshev.T_eval_two_mul_zero, Polynomial.evalEval_intCast, AddMonoidAlgebra.intCast_def, GaussianInt.natCast_natAbs_norm, toIocMod_add_intCast_mul', toIcoMod_sub_self_eq_mul, Int.cast_sub, Equiv.Perm.prod_Ioi_comp_eq_sign_mul_prod, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two, ZMod.χ₄_int_mod_four, Int.ceil_sub_intCast, Int.cast_zero, AddAction.orbitZMultiplesEquiv_symm_apply', Int.cast_min, Int.coe_castRingHom, Int.cast_multiset_sum, Polynomial.Chebyshev.T_eval_neg, Rat.intCast_le_cast, Int.ceil_lt_two_mul, GenContFract.compExactValue_correctness_of_stream_eq_some_aux_comp, Int.cast_nonneg_iff, Int.cast_lt_zero, Int.le_ceil, IsSelfAdjoint.intCast, PadicInt.exists_mem_range_of_norm_rat_le_one, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_intCast_le_one, derivWithin_zpow, round_intCast_add, sub_half_lt_round, GenContFract.convs'_succ, WeierstrassCurve.coeff_preΨ, RootPairing.Base.exists_mem_span_pairingIn_ne_zero_and_pairwise_ne, Int.floor_lt, ZNum.of_intCast, Set.pairwise_disjoint_Ioo_add_intCast, ZMod.χ₈'_int_eq_χ₄_mul_χ₈, Polynomial.C_eq_intCast, BoundedContinuousFunction.coe_intCast, self_sub_toIocDiv_mul, SemiconjBy.intCast_mul_right, Int.commute_cast, tendsto_ceil_right_pure_add_one, toIocMod_sub_intCast_mul', Polynomial.Chebyshev.U_eval_neg_one, toIcoMod_add_intCast_mul, Int.cast_two, Prod.fst_intCast, self_sub_toIcoMod_eq_mul, Int.cast_dvd_cast, Int.cast_pow, Localization.mk_intCast, FloorRing.gc_ceil_coe, Int.cast_neg_natCast, Int.ceil_eq_iff, CharP.natCast_gcdA_mul_intCast_eq_gcd, Int.cast_negOnePow, Function.mulSupport_intCast, Polynomial.smeval_neg_nat, Rat.cast_inv_int, LucasLehmer.sZMod_eq_sMod, Module.End.intCast_def, Int.preimage_Iio, Int.floor_le_iff, toIocMod_add_intCast_mul, Surreal.dyadicMap_apply_pow', ArchimedeanClass.exists_int_ge_of_mk_nonneg, Int.cast_natAbs, Int.floor_le_sub_one_iff, tendsto_intCast_atBot_sup_atTop_cobounded, ZSpan.repr_ceil_apply, NonUnitalSubring.unitization_apply, Function.support_intCast, round_add_intCast, Int.cast_strictMono, Module.Basis.addSubgroupOfClosure_repr_apply, abs_sub_round_div_natCast_eq, Int.fract_intCast, descPochhammer_eval_cast, tendsto_fract_right', Int.floor_div_cast_of_nonneg, ArchimedeanClass.FiniteElement.mk_intCast, Mathlib.Meta.NormNum.isintCast, Tactic.ReduceModChar.CharP.intCast_eq_mod, iUnion_Icc_intCast, Int.cast_finsupp_sum, Int.nneg_mul_add_sq_of_abs_le_one, MeromorphicOn.divisor_intCast, natCast_floor_eq_intCast_floor, star_intCast, iUnion_Ioc_add_intCast, AddSubgroup.int_mul_mem, nnnorm_natAbs, Int.lt_floor_add_one, MonoidAlgebra.intCast_def, Int.fract_eq_fract, map_intCast, Nat.cast_natAbs, toIcoMod_add_intCast_mul', Int.sub_one_lt_floor, Int.ceil_intCast, iUnion_Ico_add_intCast, Zsqrtd.im_smul, Int.cast_add, Matrix.det_permutation, PadicInt.toZModPow_ofIntSeq_of_pow_dvd_sub, Set.pairwise_disjoint_Ico_add_intCast, Rat.cast_mkRat_of_ne_zero, natCast_ceil_eq_intCast_ceil_of_neg_one_lt, Zsqrtd.intCast_im, tendsto_ceil_left, Int.cast_lt, ZMod.coe_int_inv_mul_eq_one, Int.cast_mul_floor_div_cancel_of_pos, autEquivZmod_symm_apply_intCast, Int.cast_det, Int.cast_negSucc, iter_deriv_zpow, Rat.cast_lt_intCast, ZNum.neg_of_int, round_le, abs_sub_round_eq_min, Int.cast_multiset_prod, PosNum.cast_to_int, ZMod.coe_valMinAbs, DirectLimit.intCast_def, Zsqrtd.re_intCast, WeierstrassCurve.leadingCoeff_preΨ, Int.floor_add_fract, ZMod.nonsquare_of_jacobiSym_eq_neg_one, exists_int_lt, Odd.intCast, ZMod.intCast_abs_mod_two, ZMod.forall, Zsqrtd.lift_symm_apply_coe, Zsqrtd.re_smul, Mathlib.Tactic.Ring.natCast_int, iteratedDerivWithin_zpow, star_inv_intCast_smul, Int.cast_four, AddConstMapClass.map_add_int, Int.cast_max, Int.cast_sum, PadicInt.norm_int_le_pow_iff_dvd, toIcoMod_sub_intCast_mul, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, hasStrictDerivAt_zpow, LucasLehmer.X.closed_form, Int.ceil_eq_floor_add_one_iff_notMem, ZMod.lift_comp_coe, Function.Periodic.sub_int_mul_eq, QuaternionAlgebra.coe_intCast, norm_natAbs, Subring.mem_bot, PerfectClosure.intCast, GenContFract.IntFractPair.stream_succ_of_int, exists_int_ge, LieAlgebra.IsKilling.apply_coroot_eq_cast, Int.coe_castAddHom, eq_intCast, Polynomial.eval_intCast_map, tendsto_floor_right, legendreSym.eq_one_iff, Matrix.det_reindex, ArchimedeanClass.stdPart_intCast, Int.le_ceil_iff, ZSpan.coe_floor_self, ZMod.intCast_comp_cast, norm_intCast_abs, Int.cast_nonneg, toIocDiv_mul_sub_toIocMod, ZMod.χ₈_int_mod_eight, Int.cast_injOn_of_ringChar_ne_two, FiniteField.two_pow_card, Int.gc_coe_floor, QuadraticAlgebra.C_intCast, Quaternion.intCast_imI, CharP.intCast_injOn_Ico, Int.cast_nonpos, GenContFract.convs_succ, Int.floor_eq_self_iff_mem, Int.preimage_Iic, algebraMap_comp_intCast, iUnion_Icc_add_intCast, DihedralGroup.r_zpow, Int.cast_ofNat, ZMod.eq_zero_iff_gcd_ne_one, HomogeneousLocalization.val_intCast, LucasLehmer.sZMod_eq_s, Polynomial.Chebyshev.iterate_derivative_U_eval_one_dvd, Nat.ceil_intCast, intCast_negSucc, Polynomial.Chebyshev.iterate_derivative_T_eval_one_dvd, Polynomial.Chebyshev.derivative_U_eval_one, GenContFract.of_s_head_aux, Zsqrtd.ofInt_eq_intCast, Zsqrtd.smuld_val, nnnorm_intCast_abs, Subalgebra.intCast_mem, Quaternion.intCast_imJ, round_intCast, deriv_zpow', Matrix.conjTranspose_eq_intCast, GenContFract.convs'_of_int, CharP.intCast_eq_intCast, Zsqrtd.lift_apply_apply, Subgroup.quotientEquivSigmaZMod_apply, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, self_sub_toIcoDiv_mul, LucasLehmer.X.coe_natCast, Commute.self_intCast_mul_intCast_mul, AddConstMapClass.map_add_int', Polynomial.Chebyshev.derivative_U_eval_one_dvd, Polynomial.eval₂_at_intCast, Int.floor_eq_iff, PadicInt.limNthHom_spec, ArithmeticFunction.sum_eq_iff_sum_mul_moebius_eq_on, tendsto_ceil_left_pure, GenContFract.of_s_of_int, CharP.intCast_mul_natCast_gcdA_eq_gcd, ZMod.exists, ArithmeticFunction.sum_eq_iff_sum_mul_moebius_eq, tendsto_intCast_atTop_iff, Zsqrtd.norm_eq_mul_conj, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, Int.fract_sub_self, Algebra.adjoin_insert_intCast, tendsto_floor_left', ZMod.gauss_lemma, GenContFract.of_s_head, ZMod.orderOf_one_add_four_mul, Set.pairwise_disjoint_Ioc_intCast, Int.fract_add, Int.ceil_le_two_mul, IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic, ZMod.intCast_eq_intCast_iff', QuaternionAlgebra.re_intCast, ZMod.intCast_zmod_eq_zero_iff_dvd, toIcoMod_sub_intCast_mul', Int.comap_cast_atBot, Int.fract_ne_zero_iff, ZMod.coe_int_isUnit_iff_isCoprime, Polynomial.Chebyshev.U_eval_two_mul_zero, Polynomial.eval_intCast, isAlgebraic_int, Int.ceil_eq_add_one_sub_fract, SignType.intCast_cast, NumberField.discr_mem_differentIdeal, abs_unit_intCast, AddConstMapClass.map_sub_int', QuaternionAlgebra.intCast_im, Int.self_sub_floor, ZMod.intCast_eq_zero_iff_even, LucasLehmer.X.snd_intCast, GenContFract.exists_int_eq_of_partDen, SemiconjBy.intCast_mul_left, natCast_ceil_eq_intCast_ceil, ZMod.coe_int_mul_val_inv, ZMod.χ₄_int_three_mod_four, PadicInt.norm_intCast_eq_one_iff, Zsqrtd.norm_intCast, Zsqrtd.intCast_dvd_intCast, Zsqrtd.intCast_val, ZMod.intCast_eq_intCast_iff, Rat.cast_def, RootPairing.GeckConstruction.diagonal_elim_mem_span_h_iff, AddCommGroup.intCast_modEq_intCast', ZMod.cast_intCast, Padic.valuation_intCast, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, Int.cast_list_sum, legendreSym.eq_zero_iff, Padic.norm_intCast_lt_one_iff, RCLike.ofReal_intCast, Int.cast_mul, Rat.cast_divInt, ZMod.intCast_rightInverse, QuadraticAlgebra.norm_intCast, AddMonoidAlgebra.toDirectSum_intCast, ZMod.lift_coe, Int.cast_mul_eq_zsmul_cast, Set.pairwise_disjoint_Ioc_add_intCast, Int.self_sub_fract, Matrix.transpose_intCast, IntermediateField.intCast_mem, Int.cast_npow, ZMod.intCast_eq_one_iff_odd, exists_int_gt, iUnion_Ico_intCast, Int.ceil_le, deriv_zpow, Function.Periodic.int_mul_eq, Int.sub_floor_div_mul_nonneg, Int.ceil_lt_add_one, Int.image_fract, IntermediateField.adjoin_intCast, Int.cast_list_prod, ZMod.χ₄_int_one_mod_four, toIcoMod_add_toIcoDiv_mul, Polynomial.coeff_mul_intCast, Subring.coe_intCast, CharP.sq_add_sq, tendsto_intCast_atBot_iff, Matrix.posSemidef_intCast_iff, lp.infty_coeFn_intCast, Int.fract_add_intCast, Int.fract_eq_zero_iff, WeierstrassCurve.leadingCoeff_ΨSq, Polynomial.Chebyshev.U_eval_neg, AddConstMapClass.map_int_add, Quaternion.imK_intCast, ZMod.intCast_mod, GenContFract.of_h_eq_intFractPair_seq1_fst_b, CFC.abs_intCast, Polynomial.Chebyshev.iterate_derivative_U_eval_one, Int.fract_sub_intCast, Int.preimage_Ioo, Zsqrtd.mul_star, ZMod.toAddCircle_intCast, MulAction.orbitZPowersEquiv_symm_apply', tendsto_ceil_left', NumberField.linearDisjoint_of_isGalois_isCoprime_discr, CongruenceSubgroup.Gamma1_mem, Int.cast_comm, intCast_memℓp_infty, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow', Polynomial.Chebyshev.C_eval_neg_two, toIocDiv_add_intCast_mul, ZMod.val_intCast, AddSubgroup.intCast_mul_mem_zmultiples, ZNum.to_of_int, Matrix.map_mul_intCast, tendsto_fract_left, Int.cast_mono, legendreSym.eq_pow, Int.floor_add_intCast, Set.intCast_mem_center, Polynomial.Chebyshev.T_eval_zero_of_even, Int.preimage_Ici, hasDerivWithinAt_zpow, ZMod.orderOf_one_add_mul_prime_pow, Matrix.det_mul_aux, exists_int_le, mem_bot_iff_intCast, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_pow_ne_two, QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff, Matrix.conjTranspose_intCast_smul, quadraticChar_odd_prime, round_le_add_half, toIcoDiv_add_intCast_mul, Int.le_floor, PadicInt.norm_sub_modPart, Matrix.det_permute', ArchimedeanClass.mk_intCast_nonneg, ZMod.lift_injective, DirectSum.toAddMonoidAlgebra_intCast, IsIntegral.exists_int_iff_exists_rat, Zsqrtd.decompose, SL_reduction_mod_hom_val, AddConstMapClass.map_int_add', Int.preimage_Icc, Surreal.dyadicMap_apply, Quaternion.imI_intCast, DirectSum.of_intCast, toIocDiv_intCast_mul_add, legendreSym.card_sqrts, Int.ceil_sub_self_eq, PadicInt.pow_p_dvd_int_iff, ZMod.gauss_lemma_aux, Matrix.sum_single_intCast, QuadraticAlgebra.coe_intCast, Even.intCast_zmod_two, toIcoMod_intCast_mul_add, LucasLehmer.X.fst_intCast, ZMod.nonsquare_iff_jacobiSym_eq_neg_one, ZNum.of_to_int, Rat.cast_le_intCast, Int.preimage_floor_singleton, IsUltrametricDist.nnnorm_intCast_le_one, Matrix.map_intCast, CongruenceSubgroup.Gamma1_to_Gamma0_mem, Int.cast_commute, SkewMonoidAlgebra.intCast_def, GenContFract.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero, QuaternionAlgebra.intCast_imI, toIocDiv_sub_intCast_mul', AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div, Commute.intCast_mul_left, AddCommGroup.intCast_modEq_intCast, map_intCast_smul, Int.floor_lt_self_iff, Matrix.posDef_intCast_iff, Int.gc_ceil_coe, Zsqrtd.im_intCast, archimedean_iff_int_lt, Int.cast_subNatNat, norm_intCast_eq_abs_mul_norm_one, GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv, logDeriv_fun_zpow, Int.cast_three, Zsqrtd.smul_val, RootPairing.Base.eq_one_or_neg_one_of_mem_support_of_smul_mem_aux, Int.cast_eq_zero, Function.Antiperiodic.int_mul_eq_of_eq_zero, Polynomial.intCast_coeff_zero, uzpow_intCast, Int.floor_le, ZMod.toCircle_intCast, Int.fract_add_floor, Algebra.TensorProduct.intCast_def, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, FloorRing.gc_coe_floor, Polynomial.Chebyshev.iterate_derivative_T_eval_one, Set.pairwise_disjoint_Ico_intCast, Zsqrtd.intCast_dvd, Int.fract_eq_zero_or_add_one_sub_ceil, ZMod.χ₄_int_eq_if_mod_four, ZMod.intCast_zmod_cast, toIocMod_intCast_mul_add', ArchimedeanClass.exists_int_le_of_mk_nonneg, ZMod.isSquare_of_jacobiSym_eq_one, round_eq_iff, LucasLehmer.X.coe_mul, Int.mul_fract_eq_one_iff_exists_int, Int.preimage_ceil_singleton, GenContFract.IntFractPair.exists_succ_get?_stream_of_gcf_of_get?_eq_some, ZNum.cast_to_int, SetLike.GradeZero.coe_intCast, Quaternion.coe_intCast, GenContFract.get?_of_eq_some_of_succ_get?_intFractPair_stream, LucasLehmer.ω_pow_formula, AddCircle.addOrderOf_div_of_gcd_eq_one', quadraticChar_eq_pow_of_char_ne_two', QuotientAddGroup.mk_int_mul, Zsqrtd.smul_im, toIocDiv_sub_intCast_mul, SemiconjBy.intCast_mul_intCast_mul, Subring.coe_bot, Polynomial.Chebyshev.S_eval_two, ZMod.natAbs_mod_two, Module.Basis.ofZLatticeBasis_repr_apply, AbsoluteValue.apply_natAbs_eq, NumberField.InfinitePlace.map_intCast, ZMod.coe_int_mul_inv_eq_one, zsmul_one, GenContFract.of_h_eq_floor, Quaternion.normSq_intCast, invOf_eq_of_coprime, Mathlib.Tactic.Ring.intCast_zero, IsNonarchimedean.apply_intCast_le_one_of_isNonarchimedean, tendsto_floor_left, toIocMod_add_toIocDiv_mul, ZMod.coe_unitOfIsCoprime, Int.cast_le_neg_one_or_one_le_cast_of_ne_zero, tendsto_ceil_right, Matrix.intCast_apply, Int.ceil_add_intCast, CharP.intCast_eq_intCast_mod, QuaternionAlgebra.intCast_imK, Zsqrtd.toReal_apply, MvPolynomial.counit_C, Zsqrtd.dmuld, Polynomial.Chebyshev.T_eval_neg_one, ArchimedeanClass.exists_int_lt_of_mk_nonneg, DoubleCentralizer.intCast_fst, GenContFract.IntFractPair.exists_succ_nth_stream_of_fr_zero, atBot_hasCountableBasis_of_archimedean, meromorphicOrderAt_const_intCast, Filter.Eventually.intCast_atBot, toIcoDiv_sub_intCast_mul, AddCircle.intCast_div_mul_eq_zsmul, Zsqrtd.lift_injective, intCast_ofNat, Quaternion.intCast_re, QuaternionAlgebra.im_intCast, Matrix.PosDef.intCast, Mathlib.Meta.NormNum.Rat.invOf_denom_swap, tendsto_intCast_atTop_cobounded, Surreal.dyadic_aux, Int.preimage_fract, Int.div_two_lt_floor, Commute.self_intCast_mul, Matrix.det_apply', PadicInt.denseRange_intCast, iUnion_Ioc_intCast, Matrix.intCast_mulVec, Even.intCast, ZMod.coe_intCast, Zsqrtd.intCast_re, ZSpan.repr_floor_apply, TrivSqZeroExt.inl_intCast, CauSeq.Completion.ofRat_intCast, map_intCast', Polynomial.Chebyshev.derivative_U_eval_one_eq_div, Matrix.conjTranspose_intCast, tendsto_fract_right, tendsto_floor_left_pure_sub_one, AddConstMapClass.map_sub_int, WeierstrassCurve.coeff_ΨSq, Subfield.intCast_mem, Polynomial.toFinsupp_intCast, BitVec.toFin_intCast, Int.cast_eq_one, Int.cast_pos, Polynomial.Chebyshev.S_eval_neg_two, Matrix.isHermitian_intCast, tendsto_intCast_atTop_atTop, Matrix.vecMul_intCast, Int.cast_mem_ideal_iff, AddChar.zmod_intCast, hasDerivAt_zpow, RootPairing.GeckConstruction.h_eq_diagonal, Int.cast_negOfNat, ZMod.ringEquivCongr_intCast, Polynomial.coeff_intCast_mul, ZMod.natCast_toNat, tendsto_floor_right', PadicInt.intCast_eq, Quaternion.intCast_im, Int.lt_floor_iff, ArithmeticFunction.intCoe_apply, Mathlib.Meta.NormNum.isNat_intCast, Equiv.Perm.prod_Iio_comp_eq_sign_mul_prod, Function.Antiperiodic.int_mul_sub_eq, SubringClass.coe_intCast, CongruenceSubgroup.Gamma_mem, Int.cast_div_charZero, Commute.intCast_mul_intCast_mul, Quaternion.re_intCast, tendsto_intCast_atBot_cobounded, IsPrimitiveRoot.sum_eq_zero_iff_forall_eq_int, ZMod.intCast_cast, zsmul_eq_mul', Int.cast_div, PadicInt.coe_intCast, Zsqrtd.smul_re, archimedean_iff_int_le, Mathlib.Tactic.Ring.intCast_negOfNat_Int, ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_sub_of_squarefree, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_int, Int.fract_mul_natCast, Int.cast_smul_eq_zsmul, Padic.norm_int_le_pow_iff_dvd, CharP.intCast_eq_zero_iff, Rat.cast_divInt_of_ne_zero, Commute.intCast_mul_self, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, Commute.intCast_mul_right, Int.cast_prod, ZMod.coe_int_val_inv_mul, DoubleCentralizer.intCast_toProd, RCLike.intCast_im, Function.Periodic.int_mul_sub_eq, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, ZMod.valMinAbs_spec, ZMod.intCast_surjective, Int.add_one_le_ceil_iff, logDeriv_zpow, Polynomial.Chebyshev.derivative_T_eval_one, Subring.closure_insert_intCast, Int.cast_one, Int.cast_negOnePow_natCast, Quaternion.imJ_intCast, LinearMap.IsSymmetric.intCast, Set.pairwise_disjoint_Ioo_intCast, ZMod.eq_zero_of_gcd_ne_one, Int.cast_injective, Int.preimage_Ico, Mathlib.Meta.NormNum.IsInt.out, Int.cast_finsuppProd, Int.sub_floor_div_mul_lt, CharP.isUnit_intCast_iff, map_inv_intCast_smul, Polynomial.ofFinsupp_intCast, exists_div_btwn, Int.fract_div_intCast_eq_div_intCast_mod, Filter.Eventually.intCast_atTop, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow, Int.ceil_intCast_add, toIcoMod_intCast_mul_add', toIocDiv_mul_sub_self, Int.floor_sub_intCast, QuadraticAlgebra.re_intCast, Polynomial.Chebyshev.U_eval_zero_of_even, Derivation.map_intCast, TrivSqZeroExt.snd_intCast, Commute.intCast_left, ZMod.χ₈_int_eq_if_mod_eight, ZNum.ofInt'_eq, Prod.snd_intCast, CongruenceSubgroup.Gamma0_mem, Int.fract_eq_iff, star_intCast_smul, toIocMod_sub_intCast_mul
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