Defs

📁 Source: Mathlib/Data/Nat/Cast/Defs.lean

Statistics

Metric	Count
Definitions AddCommMonoidWithOne, toAddCommMonoid, toAddMonoidWithOne, AddMonoidWithOne, binary, toAddMonoid, toNatCast, toOne, unary, ofNat», binCast, unaryCast, instOfNatAtLeastTwo	13
Theorems add_comm, natCast_succ, natCast_zero, binCast_eq, cast_add, cast_add_one, cast_four, cast_ite, cast_ofNat, cast_one, cast_succ, cast_three, cast_two, cast_zero, nsmul_one, one_add_one_eq_two, three_add_one_eq_four, two_add_one_eq_three, two_add_two_eq_four	19
Total	32

AddCommMonoidWithOne

Definitions

Name	Category	Theorems
toAddCommMonoid 📖	CompOp	60 math math: CategoryTheory.DifferentialObject.shiftFunctor_obj_d, GradedTensorProduct.hom_ext_iff, Algebra.TensorProduct.natCast_def', AddCommGroup.ModEq.intCast, Ring.choose_eq_smul, Nat.cast_multiset_sum, GradedTensorProduct.auxEquiv_one, Int.cast_multiset_sum, Finset.natCast_card_filter, GradedTensorProduct.mul_def, FirstOrder.Language.presburger.realize_sum, AddCommGroupWithOne.ext_iff, GradedTensorProduct.auxEquiv_symm_one, GradedTensorProduct.auxEquiv_comm, Int.cast_finsupp_sum, AddConstMapClass.map_nat_add', PiTensorProduct.one_def, AddConstMapClass.map_nat_add, binomialSeries_apply, AddCommGroup.natCast_modEq_natCast, Int.cast_sum, Nat.cast_finsum, Matrix.sum_single_ofNat, AddConstMapClass.map_one_add, GradedTensorProduct.auxEquiv_mul, Nat.cast_finsum_mem, CategoryTheory.DifferentialObject.shiftFunctorAdd_hom_app_f, GradedTensorProduct.mulHom_apply, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, SetTheory.Game.isOrderedAddMonoid, GradedTensorProduct.auxEquiv_tmul, AddCommGroup.intCast_modEq_intCast', Nat.cast_sum, CategoryTheory.DifferentialObject.shiftFunctor_map_f, CategoryTheory.DifferentialObject.shiftFunctorAdd_inv_app_f, AddCommGroup.ModEq.natCast, AddConstMapClass.map_int_add, Nat.cast_finsupp_sum, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, SimpleGraph.degree_eq_sum_if_adj, AddConstMapClass.map_int_add', Matrix.trace_one, ext_iff, Matrix.sum_single_intCast, Algebra.TensorProduct.natCast_def, AddCommGroup.intCast_modEq_intCast, Matrix.trace_permutation, AddConstMapClass.map_ofNat_add, GradedTensorProduct.of_symm_of, Algebra.TensorProduct.intCast_def, Matrix.sum_single_natCast, AddConstMapClass.map_ofNat_add', ZNum.cast_sub, Matrix.one_kroneckerTMul_one, GradedTensorProduct.of_one, Finset.sum_boole, GradedTensorProduct.symm_of_of, Complex.ofReal_choose, GradedTensorProduct.of_symm_one, Algebra.TensorProduct.one_def
toAddMonoidWithOne 📖	CompOp	3814 math math: IsPrimitiveRoot.subOneIntegralPowerBasis_gen_prime, odd_add_one_self', Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, ENNReal.exists_nat_mul_gt, Matrix.frobenius_norm_replicateCol, MeasureTheory.L1.setToL1_eq_setToL1', OrderRingHom.coe_orderAddMonoidHom_apply, TangentBundle.continuousLinearMapAt_model_space, Finset.sum_pow_eq_sum_piAntidiag, Order.coheight_add_one_le, LinearGrowth.linearGrowthSup_zero, ProbabilityTheory.lintegral_exponentialPDF_eq_one, LinearGrowth.linearGrowthSup_top, odd_add_one_self, ENNReal.one_rpow, Finset.expect_ite_mem, Derivation.map_natCast, DirectSum.IsInternal.isometryL2OfOrthogonalFamily_symm_apply, PiLp.lipschitzWith_toLp, CoalgHom.ext_of_ring_iff, WithLp.prod_edist_eq_card, WithLp.prod_inner_apply, LSeries.convolution_one_eq_convolution_zeta, half_lt_self, Matrix.natCast_kronecker, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, PiLp.norm_toLp_const', instContMDiffVectorBundleOfNatWithTopENatTangentSpaceOfIsManifold, Submodule.rTensorOne_symm_apply, MvPowerSeries.WithPiTopology.tendsto_trunc_atTop, Matrix.toLinAlgEquiv_one, Bialgebra.comul_natCast, PMF.tsum_coe, Perfection.pthRoot_frobenius, PEquiv.vecMul_toMatrix_toPEquiv, EReal.one_lt_exp_iff, Polynomial.MonicDegreeEq.monic, Topology.RelCWComplex.skeletonLT_union_iUnion_closedCell_eq_skeletonLT_succ, Algebra.charP_iff, Module.Basis.equivFun_self, instLieAddGroupOfNatWithTopENat, MeasureTheory.condExpInd_of_measurable, Matrix.swap_mul_self, MeasureTheory.IsZeroOrProbabilityMeasure.measure_univ, Order.LTSeries.length_le_krullDim, ENat.floor_pos, ENNReal.one_lt_two, MeasureTheory.condExpL1_smul, ringChar.of_eq, Nat.cast_comm, PrimeSpectrum.isClopen_iff_mul_add, Polynomial.derivative_X_sq, Matrix.transposeInvertibleEquivInvertible_symm_apply, Polynomial.smeval_monomial_mul, SimpleGraph.vertexCoverNum_le_card_sub_one, Coalgebra.lTensor_counit_comul, exists_nat_one_div_lt, MeasureTheory.aestronglyMeasurable_condExpInd, ENNReal.iUnion_Iio_coe_nat, MeasureTheory.eLpNorm_condExp_le, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim, Mathlib.Tactic.RingNF.nnrat_rawCast, Real.toNNReal_lt_natCast', Nat.floor_add_one, Polynomial.eval₂_one_cyclotomic_prime, Submonoid.subsemiringClosure_toAddSubmonoid, ENNReal.HolderConjugate.instOneInfty, MvPowerSeries.weightedOrder_monomial, RingHom.map_add', MvPowerSeries.eq_iff_frequently_trunc'_eq, PolyEquivTensor.toFunBilinear_apply_eq_sum, Polynomial.lcoeff_comp_mapAlgHom_eq, selfZPow_of_nonpos, Submodule.isScalarTower, Perfection.perfectRing, Nat.commute_cast, PMF.toMeasure_pure_apply, Ideal.Quotient.map_ker_stabilizer_subtype, Real.dimH_of_mem_nhds, Even.one_add, EReal.natCast_mul, ProbabilityTheory.measure_limsup_eq_one, ExpGrowth.eventually_le_exp, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, Polynomial.coeff_derivative, ENat.lt_add_one_iff', TensorProduct.AlgebraTensorModule.rid_symm_apply, Subsemiring.closure_addSubmonoid_closure, IsHilbertSum.surjective_isometry, MvPowerSeries.trunc'_trunc', MeasureTheory.L1.setToL1_indicatorConstLp, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left, ENNReal.coe_eq_one, ringKrullDim_succ_le_ringKrullDim_polynomial, UnitAddTorus.coe_mFourierBasis, ModularFormClass.hasFPowerSeries_cuspFunction, Num.cast_lt, RCLike.tendsto_inverse_atTop_nhds_zero_nat, Submodule.orthogonalDecomposition_symm_apply, ModularFormClass.qExpansionFormalMultilinearSeries_radius, ENNReal.exists_inv_two_pow_lt, OrthogonalFamily.linearIsometry_apply_single, AbsoluteValue.isEquiv_trivial_iff_eq_trivial, MvPolynomial.rTensor_apply_tmul_apply, instIsContMDiffRiemannianBundleOfNatWithTopENat_1, Finset.card_mul_cast_addConst, AddMonoidAlgebra.liftNC_mul, dotProductEquiv_symm_apply, sum_col_of_mem_doublyStochastic, MvPolynomial.rTensorAlgEquiv_apply, MvPolynomial.one_def, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, PiTensorProduct.isEmptyEquiv_apply_tprod, SchwartzMap.inner_fourier_toL2_eq, SchwartzMap.toLp_fourierTransformInv_eq, Matrix.kronecker_natCast, Subsemiring.closure_insert_natCast, EuclideanSpace.orthonormal_single, Order.krullDim_lt_coe_iff, Finset.sum_boole_mul, Nat.cast_factorial, MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral, ENat.toNat_one, Nat.cast_choose_eq_ascPochhammer_div, SkewMonoidAlgebra.coeff_single_one_mul, LinearGrowth.linearGrowthInf_add_le', tendsto_const_div_atTop_nhds_zero_nat, ENNReal.ofNNReal_add_natCast, MvPolynomial.weightedDegree_eq_zero_iff, MeasureTheory.tendsto_condExpL1_of_dominated_convergence, EuclideanSpace.closedBall_zero_eq, Finset.dens_cons, MvPolynomial.universalFactorizationMap_comp_map, WithLp.prod_nndist_eq_of_L2, MvPolynomial.isScalarTower_right, Submodule.toLinearEquiv_orthogonalDecomposition_symm, OrthonormalBasis.repr_injective, algebraMap.coe_one, PEquiv.single_mul_single_of_ne, ENat.coe_one, SimpleGraph.adjMatrix_mulVec_apply, Ideal.relNorm_smul, contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt, Polynomial.coeff_one, LinearGrowth.le_linearGrowthSup_add, IncidenceAlgebra.zeta_mul_kappa, MeasureTheory.Measure.hausdorffMeasure_zero_singleton, selfZPow_zero, ENNReal.toNNReal_eq_one_iff, Ideal.isHomogeneous_iff_subset_iInter, Matrix.spectrum_toEuclideanLin, ProbabilityTheory.Kernel.borelMarkovFromReal_apply', Ring.multichoose_two, PerfectClosure.mk_mul_mk, MeasureTheory.norm_condExpL2_le, Matrix.cstar_nnnorm_def, PrimeSpectrum.isClopen_iff_mul_add_zeroLocus, parallelogram_law_with_nnnorm, AlgHom.coe_addMonoidHom_injective, Ideal.rank_prime_pow_ramificationIdx, NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnreal, lp.inner_eq_tsum, Matrix.mul_mul_left, ContinuousLinearMap.continuous_integral_comp_L1, Algebra.algebraMap_eq_smul_one', DividedPowers.factorial_mul_dpow_eq_pow, ContractingWith.edist_le_of_fixedPoint, Matrix.l2_opNorm_mulVec, one_div_add_one_div, MvPolynomial.X_pow_eq_monomial, Polynomial.MonicDegreeEq.degree, MeasureTheory.L1.norm_setToL1_le, thickenedIndicatorAux_tendsto_indicator_closure, CategoryTheory.injectiveDimension_le_iff, Algebra.IsPushout.equiv_symm_algebraMap_left, PMF.toOuterMeasure_pure_apply, LinearGrowth.linearGrowthSup_add_le, Subalgebra.coe_toAddSubmonoid, MeasureTheory.inner_condExpL2_left_eq_right, ProbabilityTheory.lintegral_gaussianPDF_eq_one, AddMonoidAlgebra.isScalarTower_self, Polynomial.nnqsmul_eq_C_mul, ascPochhammer_succ_eval, SkewMonoidAlgebra.coeff_single_mul_of_not_exists_mul, Set.Icc.coe_zero, Holor.cprankMax_upper_bound, PiLp.norm_toLp_one, LinearMap.IsSymmetric.diagonalization_apply_self_apply, PartENat.ofENat_one, Even.add_one, Submodule.toLinearEquiv_orthogonalDecomposition, Finset.sum_antidiagonal_choose_succ_mul, SimpleGraph.sum_incMatrix_apply, Polynomial.leadingCoeff_one, TensorProduct.piScalarRight_symm_algebraMap, Polynomial.C_1, Matroid.eRk_singleton_le, Nat.floor_eq_iff, Polynomial.homogenize_smul, Algebra.to_smulCommClass, LieModule.traceForm_eq_sum_finrank_nsmul', MvPolynomial.divMonomial_add_modMonomial, Polynomial.sum_smul_index', cfc_const_one, Polynomial.charZero, MeasureTheory.norm_setToFun_le_mul_norm', LinearMap.ext_ring_op_iff, ENNReal.ofNNReal_natCast_sub, Ideal.natCast_eq_top, MvPowerSeries.trunc'_expand_trunc', Algebra.TensorProduct.natCast_def', ENNReal.log_lt_zero_iff, Ring.krullDimLE_iff, EuclideanSpace.inner_single_left, ascPochhammer_eval_one, EuclideanSpace.basisFun_toBasis, ENNReal.finset_card_const_le_le_of_tsum_le, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, Ideal.smul_closure, Odd.exists_bit1, ringKrullDim_eq_one_iff_of_isLocalRing_isDomain, Finset.mulConst_mul_card, spectrum.units_smul_resolvent_self, EReal.coe_coe_eq_natCast, SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, Coalgebra.sum_map_tmul_counit_eq, Algebra.IsPushout.cancelBaseChange_tmul, SimplexCategory.toTopObj_one_coe_add_coe_eq_one, DiffeologicalSpace.CorePlotsOn.isOpen_iff_preimages_plots, algebraRat.charP_zero, frobenius_one, Finset.card_mul_divConst, Matrix.mul_invOf_eq_iff_eq_mul_right, contMDiff_addInvariantVectorField, Cardinal.one_eq_ofENat, SkewMonoidAlgebra.mapDomain_one, HahnSeries.embDomain_smul, Finset.card_mul_dens, EuclideanSpace.norm_sq_eq, WithLp.prod_norm_eq_idemFst_of_L1, PowerSeries.order_expand, Int.enorm_natCast, MeasureTheory.Measure.haarMeasure_closure_self, Coalgebra.sum_tmul_counit_eq, ENNReal.exists_nat_pos_mul_gt, LinearMap.toMatrix_one, Complex.nndist_self_conj, SkewMonoidAlgebra.smul_of, Finsupp.weight_single_one_apply, MeasureTheory.L1.ofReal_norm_eq_lintegral, NNRat.coe_natCast, Monovary.sum_mul_sum_le_card_mul_sum, MeasureTheory.condExpIndL1Fin_smul, Ideal.isHomogeneous_iff_forall_subset, nnnorm_nsmul_le, geom_sum₂_self, SimpleGraph.dotProduct_mulVec_adjMatrix, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, Polynomial.coeff_one_add_X_pow, MvPowerSeries.coeff_X_pow, CentroidHom.starCenterIsoCentroid_symm_apply_coe, RingHomClass.toAddMonoidHomClass, ENat.natCast_le_of_coe_top_le_withTop, MvPolynomial.monomial_finsupp_sum_index, Finset.card_mul_subConst, WithLp.instCompleteSpace, NumberField.FinitePlace.norm_def', ArithmeticFunction.sum_Ioc_mul_zeta_eq_sum, Nat.cast_pos, Ideal.mem_pointwise_smul_iff_inv_smul_mem, Mathlib.Meta.NormNum.Finset.prod_empty, ExpGrowth.expGrowthInf_exp, Subsemiring.mem_smul_pointwise_iff_exists, contMDiff_neg_sphere, segment_eq_image₂, MeasureTheory.lintegral_indicator_one_le, instFaithfulSMulNatOfCharZero, Polynomial.derivative_pow_succ, MulChar.map_ringChar, sum_div_card_sq_le_sum_sq_div_card, stdSimplex_fin_two, two_mul_le_add_sq, Monotone.expGrowthInf_comp_mul, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, Submodule.top_eq_ofList_cons_smul_iff, BoxIntegral.unitPartition.mem_smul_span_iff, PartENat.toWithTop_natCast, RingAut.smul_def, Ideal.exists_smul_eq_of_isGaloisGroup, Function.Antiperiodic.periodic_two_mul, fact_one_le_two_ennreal, NNReal.sqrt_mul_lt_half_add_of_ne, Polynomial.monomial_one_one_eq_X, MeasureTheory.L1.SimpleFunc.setToL1SCLM_const, IsHilbertSum.linearIsometryEquiv_symm_apply, SmoothBumpCovering.exists_immersion_euclidean, Fintype.expect_dite_eq, Module.Basis.isScalarTower_of_nonempty, cfc_apply_one, MonoidAlgebra.liftNC_mul, Order.height_add_one_le, Polynomial.isMonicOfDegree_iff, IsGaloisGroup.fixingSubgroup_top, Matrix.detp_neg_one_one, EuclideanHalfSpace.ext_iff, Nat.floor_div_natCast, add_pow_prime_pow_eq, EuclideanSpace.basisFun_apply, ENat.one_lt_card_iff_nontrivial, invOf_pos, NNRat.den_natCast, MvPowerSeries.X_pow_eq, Nat.preimage_Ioi, ENat.map_one, AlgEquiv.apply_smulCommClass', NNRat.cast_one, tsum_geometric_lt_top, Finset.one_le_mulConst_self, Finsupp.le_weight_of_ne_zero', Ideal.subset_pointwise_smul_iff, mem_doublyStochastic_iff_sum, IsGaloisGroup.fixedPoints_top, MvPolynomial.algHom_ext'_iff, Polynomial.natDegree_smul, ENNReal.natCast_lt_top, TensorPower.gMul_eq_coe_linearMap, MeasureTheory.Integrable.toL1_zero, IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply, RingCon.comap_bot, Polynomial.iterate_derivative_eq_factorial_smul_sum, Matrix.le_one_of_mem_colStochastic, HahnSeries.ofPowerSeries_X_pow, LinearMap.BilinForm.toMatrix'_apply, PEquiv.toMatrix_toPEquiv_mulVec, Metric.ediam_closedEBall_le, ENNReal.HolderConjugate.one_sub_inv, Commute.ofNat_left, PartENat.withTopEquiv_one, Subsemiring.smul_mem_pointwise_smul_iff, convexComboPair_one, Behrend.sphere_subset_preimage_metric_sphere, Matrix.map_swap, Matrix.mulVec_single_one, Real.volume_closedEBall, NNRat.cast_listProd, contMDiff_mulInvariantVectorField, frobenius_natCast, TrivSqZeroExt.inv_one, ExpGrowth.expGrowthInf_le_iff, Module.Basis.mk_coord_apply_eq, CFC.abs_nnrpow_two, NNRat.cast_def, ENat.coe_top_add_one, MvPowerSeries.ext_trunc', Order.krullDim_le_one_iff, PerfectClosure.frobenius_mk, IsScalarTower.right, Matrix.swap_mulVec_apply, Polynomial.eval₂_one, Matrix.permMatrix_mem_rowStochastic, Nat.preimage_Iio, tendsto_nat_floor_mul_atTop, MeasureTheory.withDensity_one, Algebra.TensorProduct.algebraMap_apply, Polynomial.dvd_iterate_derivative_pow, uzpow_natCast, Subsemiring.mem_bot, SimpleGraph.extremalNumber_le_iff_of_nonneg, Module.supportDim_add_length_eq_supportDim_of_isRegular, PartENat.lt_find_iff, Ideal.ne_top_iff_one, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, MeasureTheory.condExpIndL1_add, Nat.le_of_ceil_le, Submodule.span_pow, MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM, Dynamics.coverMincard_univ, contDiff_one_iff_fderiv, CompactlySupportedContinuousMap.nnrealPart_smul_neg, Matrix.IsHermitian.eigenvalues_eq, MeasureTheory.MemLp.norm_rpow, Set.Ioo.lt_one, LinearMap.intrinsicStar_toSpanSingleton, contMDiff_equivTangentBundleProd_symm, PMF.binomial_apply_zero, ENNReal.lintegral_rpow_funMulInvSnorm_eq_one, mulRightLinearMap_one, PreTilt.instPerfectRing, Ideal.LiesOver.smul, AddMonoidHom.coe_smul', NNReal.agmSequences_zero, Module.Basis.repr_self_apply, LinearGrowth.le_linearGrowthSup_add', MeasureTheory.L1.integral_smul, Matrix.exists_right_inverse_iff_isUnit, inv_natCast_smul_eq, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, Polynomial.C_mul', ENNReal.tendsto_pow_atTop_nhds_zero_iff, IsPrimitiveRoot.subOneIntegralPowerBasis_gen, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, two_inv_lt_one, MeasureTheory.Lp.instFourierInvSMul, ProbabilityTheory.uniformOn_of_univ, Real.contDiffAt_rpow_const_of_le, PartENat.coe_lt_coe, Algebra.adjoin_insert_natCast, Set.Icc.nonneg, Subalgebra.coe_one, Module.Basis.toMatrix_smul, Matrix.map_mul_natCast, ConditionallyCompleteLinearOrderedField.toZeroLEOneClass, Matrix.conjTranspose_natCast_smul, ENat.ceil_add_natCast, MeasureTheory.prob_compl_eq_one_iff₀, SkewMonoidAlgebra.support_one, Polynomial.derivative_monomial, Algebra.TensorProduct.basis_apply, geom_sum_two, MvPolynomial.pderiv_one, LinearMap.liftBaseChange_one_tmul, Matrix.toMvPolynomial_one, OrthonormalBasis.repr_self, Matrix.smul_one_eq_diagonal, Num.cast_le, invOf_nonneg, Submodule.one_mem_div, LinearGrowth.linearGrowthInf_bot, MeasureTheory.L2.inner_def, Nat.cast_ascFactorial, add_halves, Icc_isBoundaryPoint_bot, LinearMap.IsSymmetric.directSum_decompose_apply, Metric.ediam_thickening_le, Nat.preimage_Ici, ProbabilityTheory.evariance_lt_top_iff_memLp, Finset.divConst_mul_card, EuclideanSpace.nndist_eq, MeasureTheory.Measure.haarMeasure_self, Nat.one_div_le_one_div, ContractingWith.one_sub_K_pos', SkewMonoidAlgebra.support_one_subset, conjneg_one, IsOrderedRing.toZeroLEOneClass, MeasureTheory.condExpIndL1Fin_add, Fintype.expect_ite_eq, MeasureTheory.Measure.count_singleton', MulSemiringActionHom.map_smulₛₗ, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup_atTop, stereographic'_source, MvPolynomial.schwartz_zippel_totalDegree, Polynomial.leadingCoeff_X_pow_add_C, contMDiff_infty, ContinuousLinearMap.toSpanSingleton_apply_one, ProbabilityTheory.Kernel.measure_eq_zero_or_one_of_indepSet_self', Nat.cast_multiset_sum, ProbabilityTheory.Kernel.rnDeriv_eq_one_iff_eq, MvPolynomial.le_weightedTotalDegree, contDiffOn_nat_iff_continuousOn_differentiableOn_deriv, stdSimplexHomeomorphUnitInterval_zero, IsArithFrobAt.mul_inv_mem_inertia, finsuppTensorFinsupp'_symm_single_eq_tmul_single_one, Subalgebra.coe_pointwise_smul, MeasureTheory.condExpL1_measure_zero, OrthonormalBasis.measurePreserving_repr, ENat.floor_add_one, Order.le_krullDim_iff, Set.Ioc.coe_pow, Coalgebra.sum_counit_tmul_eq, PMF.toMeasure_ofMultiset_apply, Submonoid.subsemiringClosure_coe, AddMonoidAlgebra.divOfHom_apply_apply, SchwartzMap.inner_toL2_toL2_eq, IncidenceAlgebra.zeta_mul_zeta, MeasureTheory.AEEqFun.integrable_iff_mem_L1, instIsSemirealOfIsStrictOrderedRingOfExistsAddOfLE, PMF.uniformOfFinset_apply_of_mem, edist_le_of_edist_le_geometric_of_tendsto, MulSemiringActionHom.coe_fn_coe', PiLp.nnnorm_eq_of_L2, Finset.mulConst_le_card, half_pos, NNReal.half_le_self, charP_of_injective_algebraMap, ProbabilityTheory.cond_apply_self, ProbabilityTheory.Kernel.bound_le_one, Polynomial.X_pow_eq_monomial, Polynomial.trunc_toLaurent, LaurentSeries.ofPowerSeries_powerSeriesPart, Matrix.IsHermitian.eigenvectorUnitary_col_eq, Metric.PiNatEmbed.edist_def, AddChar.sum_eq_ite, QuadraticAlgebra.nsmul_mk, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_snd, MeasureTheory.L1.SimpleFunc.norm_setToL1S_le, Subalgebra.inclusion.isScalarTower_left, LaurentSeries.single_order_mul_powerSeriesPart, Finsupp.linearCombination_smul, lt_one_div, Fintype.expect_ite_zero, RingEquiv.toAddMonoidHom_refl, IsNonarchimedean.apply_natCast_le_one_of_isNonarchimedean, CharTwo.two_nsmul, Nat.lt_succ_floor, PowerSeries.binomialSeries_coeff, Num.cast_bit0, ENat.map_coe_nnreal, Mathlib.Tactic.NoncommRing.nat_lit_mul_eq_nsmul, MeasureTheory.L1.SimpleFunc.setToL1S_neg, SchwartzMap.toLp_fourierInv_eq, PartENat.lt_coe_iff, IsFoelner.mean_univ_eq_one, ordinaryHypergeometricSeries_radius_eq_one, LinearGrowth.linearGrowthSup_bot, Matrix.toEuclideanLin_apply, Finset.expect_ite_zero, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.Measure.rnDeriv_eq_one_iff_eq, Nat.floor_sub_one, Matrix.permMatrixHom_apply, MeasureTheory.Measure.addHaarMeasure_closure_self, MeasureTheory.continuous_condExpIndL1, LinearMap.toMatrixAlgEquiv'_id, IsHilbertSum.hasSum_linearIsometryEquiv_symm, MvPowerSeries.smul_eq_C_mul, ENat.floor_add_natCast, MeasureTheory.memLp_two_iff_integrable_sq_norm, mfderivWithin_projIcc_one, WithBot.lt_add_one_iff, Mathlib.Tactic.Linarith.zero_lt_one, MvPowerSeries.trunc_C, ENNReal.toReal_one, Polynomial.eval₂_reflect_eq_zero_iff, PEquiv.map_toMatrix, contDiffWithinAt_nat, MvPolynomial.coe_one, Polynomial.monic_of_isUnit_leadingCoeff_inv_smul, Finset.card_mul_addConst, MeasureTheory.dominatedFinMeasAdditive_condExpInd, MeasureTheory.L1.SimpleFunc.integral_add, Nat.floor_add_natCast, EuclideanSpace.norm_single, Matrix.conjTranspose_natCast, instSMulCommClassMatrixFinOfNatNatProd, Metric.coveringNumber_two_mul_le_externalCoveringNumber, MonoidAlgebra.lift_symm_apply, PowerSeries.le_order_smul, AddMonoidAlgebra.uniqueRingEquiv_apply, Positive.val_one, MeasureTheory.Integrable.edist_toL1_zero, Polynomial.eval₂_ofFinsupp, Nat.cast_nonneg, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobson, Euclidean.closedBall_eq_image, LinearGrowth.linearGrowthInf_biInf, Polynomial.integralNormalization_coeff_natDegree, ProbabilityTheory.Kernel.measure_eq_zero_or_one_of_indepSet_self, Matroid.IsNonloop.eRk_eq, EReal.tendsto_exp_nhds_zero_nhds_one, MonoidAlgebra.uniqueRingEquiv_apply, Matrix.op_smul_one_eq_diagonal, AdjoinRoot.evalEval_apply, Submodule.coe_orthogonalDecomposition_symm, QuadraticAlgebra.omega_mul_coe_mul_mk, MonoidAlgebra.coe_liftNCAlgHom, OrderRingHom.coe_orderAddMonoidHom_id, MeasureTheory.aestronglyMeasurable_condExpL2, DualNumber.lift_apply_eps, TensorProduct.gradedMul_def, selfZPow_neg_mul, ENNReal.one_le_inv, AlternatingMap.ext_ring_iff, MeasureTheory.L1.setToL1_smul_left, Algebra.TensorProduct.includeRight_apply, MvPowerSeries.coeff_X, Fintype.expect_dite_eq', MeasureTheory.L1.setToL1_zero_left, Quaternion.linearIsometryEquivTuple_symm_apply, Int.self_le_zpow_clog, Finsupp.linearCombination_one_tmul, exists_add_pow_prime_pow_eq, binomialSeries_radius_eq_one, add_sq, ofNat_eq_one, Pi.counit_eq_adjoint, WithLp.unitization_algebraMap, Polynomial.eval_natCast_map, WithLp.prod_dist_eq_of_L2, LinearMap.BilinForm.coeFnAddMonoidHom_apply, Finset.card_div_choose_le_card_shadow_div_choose, MeasureTheory.condExpInd_nonneg, Polynomial.ofFinsupp_natCast, le_one_of_mem_doublyStochastic, MulSemiringAction.toRingEquiv_apply, Icc_isInteriorPoint_interior, ringKrullDim_succ_le_ringKrullDim_powerseries, PerfectClosure.instPerfectRing, Ideal.smul_sup, MonoidAlgebra.smulCommClass_self, Matrix.toLinearMapₛₗ₂'_single, LDL.lowerInv_orthogonal, ArithmeticFunction.IsMultiplicative.natCast, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, contDiffOn_infty, MonoidAlgebra.instIsPushout, Cardinal.nsmul_lt_aleph0_iff_of_ne_zero, Ideal.Quotient.stabilizerHom_surjective, ENNReal.half_lt_self, Polynomial.height_eq_height_add_one, NNReal.natCast_iInf, HahnSeries.single_zero_mul_eq_smul, MeasureTheory.condExpL1_of_aestronglyMeasurable', Polynomial.derivative_eval, Dynamics.one_le_coverMincard_iff, GradedTensorProduct.auxEquiv_one, Algebra.TensorProduct.basis_repr_tmul, ExpGrowth.expGrowthSup_def, NormedField.exists_one_lt_enorm, ENNReal.top_rpow_def, segment_single_subset_stdSimplex, tangentBundle_model_space_coe_chartAt, ENat.ceil_sub_one, ENat.ceil_lt_add_one, MvPolynomial.coeffs_one, MeasureTheory.L1.continuous_integral, Submodule.FG.restrictScalars, Subsemiring.smul_mem_pointwise_smul, ContinuousMultilinearMap.ext_ring_iff, ENNReal.iInter_Ici_coe_nat, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, Subalgebra.list_prod_mem, one_div_strictAntiOn, CharP.existsUnique, MeasureTheory.L1.integrable_coeFn, MvPolynomial.coeffs_one_of_nontrivial, MeasureTheory.condExpL2_indicator_ae_eq_smul, AbsoluteValue.isEquiv_iff_lt_one_iff, SkewPolynomial.φ_iterate_apply, mfderivWithin_comp_projIcc_one, Real.enorm_natCast, contDiff_iff_forall_nat_le, Ideal.pointwise_smul_subset_iff, MonoidAlgebra.distribMulActionHom_ext'_iff, Polynomial.X_pow_smul_rTensor_monomial, uzpow_one, Subsemiring.pointwise_smul_toAddSubmonoid, instIsPushoutFractionRingPolynomial_1, Finset.local_lubell_yamamoto_meshalkin_inequality_div, contDiffWithinAt_euclidean, SkewPolynomial.monomial_def, MvPolynomial.monomial_mul_mem_coeffsIn, LinearMap.toMatrix_id, Real.dimH_univ_eq_finrank, one_geom_sum, contDiff_succ_iff_fderiv, Matrix.mul_reindexLinearEquiv_one, WithLp.prod_nndist_eq_of_L1, SubsemiringClass.toAddSubmonoidClass, contMDiffAt_mulInvariantVectorField, AddMonoidAlgebra.singleZeroRingHom_apply, Finset.natCast_card_filter, TrivSqZeroExt.fst_invOf, ProbabilityTheory.IsMarkovKernel.bound_eq_one, Ideal.instCovariantClassHSMulLe, MvPowerSeries.weightedOrder_monomial_of_ne_zero, SimpleGraph.mul_adjMatrix_apply, LinearIndependent.repr_eq_single, IsContDiffImplicitAt.one_le, TensorProduct.gradedComm_algebraMap_tmul, Nat.preimage_Ioc, Finset.divConst_le_card, Finset.one_le_mulConst, UnitAddTorus.mFourierCoeff_toLp, MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero, WeakDual.toStrongDual_inj, Representation.leftRegular_norm_eq_zero_iff, PiCountable.min_edist_le_edist_pi, Finsupp.supported_eq_span_single, EuclideanSpace.volume_closedBall_fin_three, ContinuousMultilinearMap.mkPiAlgebraFin_apply, RingHom.toAddMonoidHom_eq_coe, Submodule.instSMulCommClass, Matrix.conjTranspose_permMatrix, IccLeftChart_extend_interior_pos, MvPolynomial.sumAlgEquiv_comp_rename_inr, PowerSeries.coe_smul, MvPolynomial.aevalTower_toAlgHom, PreTilt.coeff_frobeniusEquiv_symm, PiCountable.edist_eq_tsum, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, Real.dimH_univ, MeasureTheory.exists_isSigmaFiniteSet_measure_ge, HopfAlgebra.sum_mul_antipode_eq_smul, MvPolynomial.coe_eq_one_iff, Algebra.TensorProduct.basisAux_map_smul, ProbabilityTheory.IsGaussian.memLp_two_id, Pi.basis_repr_single, algebraMap_apply, Hamming.nndist_eq_hammingDist, Matrix.IsHermitian.eigenvectorUnitary_mulVec, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left', FiniteMultiplicity.emultiplicity_self, LinearMap.isIdempotentElem_map_one_iff, Algebra.IsInvariant.exists_smul_of_under_eq, Matrix.det_kroneckerMapBilinear, PartENat.get_natCast, MvPolynomial.X_mul_pderiv_monomial, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, Polynomial.eval₂_list_prod, Subsemiring.closure_insert_one, NNRat.mul_den_eq_num, indicator_le_thickenedIndicatorAux, Subring.coe_matrix, MvPowerSeries.coeff_index_single_X, Polynomial.aeval_one, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim, MeasureTheory.continuous_setToFun, IsOfFinOrder.eq_one, Matrix.toLinearMap₂'Aux_single, Matrix.frobenius_nnnorm_one, mulVec_one_of_mem_doublyStochastic, Nat.preimage_Icc, MeasureTheory.L1.dist_eq_integral_dist, ENNReal.instCharZero, NeZero.of_faithfulSMul, ProbabilityTheory.Kernel.bound_eq_one, EReal.one_le_exp_iff, Matrix.instSMulCommClassForall_1, MeasureTheory.L1.norm_def, OrthonormalBasis.prod_apply, PiLp.nnnorm_toLp_one, MvPolynomial.totalDegree_list_prod, Topology.RelCWComplex.iUnion_openCell_eq_skeleton, RingEquiv.moduleEndSelf_symm_apply, Dynamics.netMaxcard_zero, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, Nat.two_pow_sub_pow, MeasureTheory.integral_condExpL2_eq, SimpleGraph.dotProduct_mulVec_degMatrix, Ideal.range_mul, LocalizedModule.equivTensorProduct_apply_mk, mdifferentiableAt_addInvariantVectorField, StdSimplex.ext_iff, PowerSeries.coeff_zero_one, DirectSum.algebraMap_toAddMonoid_hom, FirstOrder.Language.presburger.realize_sum, ENNReal.exists_nat_gt, EReal.exists_nat_ge_mul, PosNum.cast_mul, HomogeneousIdeal.toAddSubmonoid_irrelevant_le, Polynomial.sum_smul_index, isGroupLikeElem_iff, MvPowerSeries.trunc'_trunc'_pow, DividedPowers.OfInvertibleFactorial.dpow_zero, Finset.cast_subConst_mul_card, ENNReal.holderConjugate_iff, Algebra.directSumGAlgebra_toFun_apply, ContractingWith.apriori_edist_iterate_efixedPoint_le', Nat.le_floor_iff', EuclideanSpace.dist_single_same, ENat.one_le_card_iff_nonempty, MeasureTheory.Integrable.tendsto_eLpNorm_condExp, StarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar, Module.Basis.coe_toOrthonormalBasis_repr, contDiffAt_one_iff, IsAddFoelner.mean_univ_eq_zero, DividedPowers.dpow_comp, Algebra.TensorProduct.includeLeft_apply, WeakDual.coe_toStrongDual, Order.coheight_eq_coe_add_one_iff, gc_floorDiv_mul, orthonormal_fourier, Polynomial.C_eq_natCast, ProbabilityTheory.measure_eq_zero_or_one_of_indepSet_self, Nat.cast_div_charZero, MeasureTheory.setIntegral_condExpL2_indicator, Polynomial.coeff_X_pow, contMDiff_coe_sphere, Polynomial.smul_eq_C_mul, ENNReal.natCast_le_ofNNReal, Nat.preimage_Ioo, MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub, ArithmeticFunction.one_smul', Mathlib.Tactic.Ring.one_mul, PartENat.le_coe_iff, MeasureTheory.Integrable.norm_toL1, Nat.preimage_floor_of_ne_zero, Ideal.under_smul, single_mem_stdSimplex, Module.FinitePresentation.linearEquivMap_symm_apply, MvPolynomial.expand_zero, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, CFC.abs_nnrpow, Finsupp.coe_pointwise_smul, LinearGrowth.linearGrowthInf_top, Algebra.TensorProduct.right_algebraMap_apply, VitaliFamily.ae_tendsto_measure_inter_div_of_measurableSet, MeasureTheory.L1.setToL1_mono_left', ascPochhammer_eval_zero, CompactlySupportedContinuousMap.exists_add_of_le, Polynomial.sum_X_index, ENat.card_le_one_iff_subsingleton, IsLocalization.mk'_eq_mul_mk'_one, SemimoduleCat.MonoidalCategory.rightUnitor_inv_apply, Submodule.mul_mem_smul_iff, MeasureTheory.Integrable.toL1_eq_mk, tendsto_one_div_add_atTop_nhds_zero_nat, stdSimplex.eq_one_of_unique, Polynomial.eval₂_natCast, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, summable_const_div_iff, CFC.nnrpow_sqrt_two, LinearMap.toMatrixAlgEquiv_id, AddMonoidAlgebra.of_apply, ENNReal.iUnion_Iic_coe_nat, Metric.externalCoveringNumber_le_one_of_ediam_le, NNRat.toNNRat_coe_nat, MvPowerSeries.trunc_one, Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_symm_apply, PEquiv.mul_toMatrix_apply, one_lt_div, Matrix.permanent_one, NNReal.natCast_natAbs, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen_prime, instIsPushoutPolynomial_1, IsClosed.measure_eq_one_iff_eq_univ, Polynomial.eval_natCast, PiLp.volume_preserving_toLp, ENNReal.div_self_le_one, Subsemiring.coe_one, InnerProductGeometry.norm_toLp_symm_crossProduct, Finset.pluennecke_ruzsa_inequality_nsmul_add, Nat.ofDigits_one_cons, MeasureTheory.condExpIndSMul_empty, MeasureTheory.prob_le_one, MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass, MeasureTheory.charFun_eq_prod_iff, Polynomial.UniversalFactorizationRing.jacobian_resentation, SimpleGraph.eccent_le_one_iff, invOf_lt_zero, Finsupp.weight_single, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, Int.zpow_le_iff_le_log, ENat.lift_one, odd_add_self_one', MeasureTheory.Measure.coeAddHom_apply, AbsoluteValue.apply_nat_le_self, MvPolynomial.coeff_X, Ideal.span_singleton_one, EReal.coe_natCast, contDiff_all_iff_nat, Mathlib.Tactic.Bound.Nat.one_le_cast_of_le, contDiffOn_succ_of_fderivWithin, NonUnitalSubsemiring.unitization_apply, IsPrincipalIdealRing.height_eq_one_of_isMaximal, DirectSum.toAddMonoidAlgebra_one, IsLocalization.mk'_self, MeasureTheory.setIntegral_condExpInd, RingCon.ker_comp, Derivation.instAddMonoidHomClass, RingHom.charP_iff_charP, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1, LinearGrowth.linearGrowthInf_const_mul_self, Finset.sum_choose_succ_mul, Ideal.span_single_eq_top, Hamming.nnnorm_eq_hammingNorm, DualNumber.fst_eq_zero_iff_eps_dvd, Submodule.le_one_toAddSubmonoid, MeasureTheory.eLpNorm_one_eq_lintegral_enorm, OrthonormalBasis.coe_ofRepr, Function.Periodic.nat_mul, TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf, PartENat.not_isMax_natCast, Algebra.adjoin_insert_one, Polynomial.aevalTower_toAlgHom, MatrixEquivTensor.toFunBilinear_apply, EuclideanSpace.nnnorm_single, MonoidAlgebra.basis_apply, Matrix.permMatrix_mul, NNReal.hasLipschitzAdd, NNRat.one_le_cast, LinearMap.toBilin'Aux_toMatrixAux, SkewMonoidAlgebra.coeff_mul_single_of_not_exists_mul, Derivation.map_one_eq_zero, Complex.orthonormalBasisOneI_repr_apply, MeasureTheory.lpNorm_one_eq_integral_norm, MeasureTheory.L1.setToL1_eq_setToL1SCLM, ENat.add_one_le_iff, Real.volume_emetric_closedBall, Commute.exists_add_pow_prime_pow_eq, RingHom.charZero, Stream'.Seq.length'_cons, MeasureTheory.norm_condExpL2_coe_le, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, SimpleGraph.edist_top, PolynomialLaw.one_smul, Real.toNNReal_ofNat, MeasureTheory.prob_compl_eq_one_sub₀, MonomialOrder.span_leadingTerm_eq_span_monomial, MeasureTheory.Measure.addHaarMeasure_eq_iff, TensorPower.algebraMap₀_one, MvPowerSeries.one_le_order_iff_constCoeff_eq_zero, MonomialOrder.span_leadingTerm_eq_span_monomial₀, Nat.Partition.hasProd_powerSeriesMk_card_countRestricted, SimpleGraph.vertexCoverNum_top, IsAbsoluteValue.abv_one, Ideal.card_stabilizer_eq, MeasureTheory.aestronglyMeasurable_condExpL1, Matrix.conjTranspose_inv_natCast_smul, ENNReal.iSup_natCast, NeZero.nat_of_injective, AbsoluteValue.IsEquiv.le_one_iff, IsLocalization.tensorProduct_isLocalizedModule, Polynomial.smeval_smul, MeasureTheory.prob_compl_eq_one_iff, map_ofNat, mdifferentiable_mulInvariantVectorField, SchwartzMap.norm_fourier_toL2_eq, Real.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, HahnSeries.embDomain_one, ENNReal.smul_top, Submodule.mem_smul_iff_inv_mul_mem, MonoidAlgebra.singleAddHom_apply, Matroid.eRk_insert_le_add_one, ENNReal.div_eq_one_iff, MatrixEquivTensor.invFun_algebraMap, Algebra.TensorProduct.productMap_left_apply, PowerSeries.coeff_derivativeFun, Polynomial.instCharP, Subalgebra.lTensorBot_one_tmul, FractionalIdeal.coe_nsmul, StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_span, Polynomial.MonicDegreeEq.freeMonic_coe, Polynomial.hasseDeriv_comp, ENNReal.one_lt_top, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, MeasureTheory.Lp.instFourierPair, MvPowerSeries.coeff_index_single_self_X, NNReal.rpow_sum_le_const_mul_sum_rpow, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff', Real.dimH_univ_pi_fin, ENNReal.tsum_set_one, SkewMonoidAlgebra.coeff_mul_right, OrderedSemiring.toPosSMulMonoNat, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, MeasureTheory.Measure.dirac_apply', NeZero.nat_of_neZero, MeasureTheory.L1.integral_def, QuadraticAlgebra.im_ofNat, MvPolynomial.bind₂_monomial, Matrix.toEuclideanCLM_toLp, spectrum.spectralRadius_one, hasSum_fourier_series_L2, MvPowerSeries.le_weightedOrder_pow, DualNumber.lift_inlAlgHom_eps, MvPolynomial.monomialOneHom_apply, Commute.add_pow_prime_pow_eq, MeasureTheory.L1.SimpleFunc.setToL1S_smul_real, Real.dimH_ball_pi, Module.End.hasUnifEigenvalue_iff_mem_spectrum, ENNReal.inv_le_iff_le_mul, CategoryTheory.injectiveDimension_ge_iff, AddMonoidAlgebra.smulCommClass_symm_self, GradedTensorProduct.auxEquiv_symm_one, FractionalIdeal.coe_natCast, two_smul, Ideal.IsPrime.smul_iff, SkewMonoidAlgebra.of_apply, toBilin'Aux_toMatrixAux, Matrix.detp_one_one, Perfection.charP, contDiffOn_nat_iff_continuousOn_differentiableOn, Module.Basis.isScalarTower_finsupp, CharP.exists, Ideal.height_le_height_add_one_of_mem, ContinuousLinearMap.toSpanSingleton_apply_map_one, two_mul, Finset.dens_le_one, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup, MeasureTheory.eLpNorm_one_le_of_le', egauge_le_one, LinearGrowth.linearGrowthInf_zero, DirectSum.decompose_symm_one, Semiring.toGrindSemiring_ofNat, Metric.packingNumber_two_mul_le_externalCoveringNumber, RingHom.expChar_iff, PiLp.nnnorm_toLp_const', ite_eq_mem_stdSimplex, MvPolynomial.IsSymmetric.one, MeasureTheory.L1.SimpleFunc.setToL1S_eq_setToSimpleFunc, MeasureTheory.Measure.toSphere_apply_univ, Nat.floor_natCast, IsGaloisGroup.fixedPoints_fixingSubgroup, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_maximalIdeal, HilbertBasis.hasSum_repr, Matroid.exists_eRk_insert_eq_add_one_of_lt, Module.End.Eigenvalues.mk_val, Module.Basis.reindexRange_repr_self, ENNReal.orderIsoIicOneBirational_apply_coe, Nat.one_le_floor_iff, LinearMap.toSpanSingleton_one_eq_algebraLinearMap, WithLp.prod_edist_eq_of_L2, MeasureTheory.condExpIndSMul_smul, MeasureTheory.Measure.haar.addHaarContent_self, AddConstMapClass.map_nat_add', Int.lt_zpow_iff_log_lt, AlgEquiv.smul_def, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_fst, MeasureTheory.eLpNorm_one_smul_measure, MeasureTheory.lintegral_nnnorm_condExpL2_le, SkewMonoidAlgebra.lift_unique, Nat.cast_dvd_cast, star_natCast_smul, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff, Fintype.card_mul_expect, MeasureTheory.L1.setToFun_eq_setToL1, Module.Basis.repr_eq_iff, MvPolynomial.coeff_X_pow, SchwartzMap.norm_fourierTransformCLM_toL2_eq, RingEquiv.map_one, TensorProduct.tmul_eq_smul_one_tmul, EuclideanSpace.volume_closedBall_fin_two, Pi.orthonormalBasis_apply, Matrix.piLp_ofLp_toEuclideanLin, ENNReal.tsum_schlomilch_le, LinearMap.IsSymmetric.diagonalization_symm_apply, exists_spanning_measurableSet_le, MvPolynomial.pow_idealOfVars_eq_span, DualNumber.isNilpotent_iff_eps_dvd, Polynomial.addHom_ext'_iff, PiTensorProduct.one_def, stereographic'_target, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, PerfectClosure.mk_add_mk, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, MeasureTheory.memLp_two_iff_integrable_sq, WeakDual.isCompact_closedBall, MeasureTheory.L1.integral_eq_setToL1, Polynomial.derivative_X_pow_succ, spinGroup.conjAct_smul_range_ι, MeasureTheory.Integrable.toL1_smul, Behrend.norm_of_mem_sphere, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, Nat.lt_one_of_floor_lt_one, IsSelfAdjoint.inr, MvPolynomial.weightedHomogeneousSubmodule_eq_finsupp_supported, Finset.card_mul_mulConst, MulSemiringAction.toAlgEquiv_symm_apply, div_nat_lt_self_of_pos_of_two_le, Ideal.Quotient.smul_top, OrthonormalBasis.tensorProduct_repr_tmul_apply', PiLp.dist_eq_of_L1, charP_of_injective_ringHom, Ideal.IsPrime.one_notMem, exists_nat_ge, PowerSeries.constantCoeff_one, IsGaloisGroup.fixingSubgroup_le_of_le, one_div_mul_add_mul_one_div_eq_one_div_add_one_div, ENNReal.toNNReal_one, Submodule.FG.restrictScalars_iff, MvPolynomial.bind₂_monomial_one, RingHom.map_one, contMDiff_vectorSpace_iff_contDiff, IsSumSq.natCast, LinearMap.liftBaseChangeEquiv_symm_apply, MeasureTheory.condExpL1CLM_indicatorConstLp, LinearGrowth.linearGrowthSup_le_of_eventually_le, MeasureTheory.prob_compl_lt_one_sub_of_lt_prob, UnitAddCircle.measure_univ, IsAddTorsionFree.of_isCancelMulZero_charZero, Polynomial.eval₂_reflect_mul_pow, Matrix.l2_opNNNorm_mulVec, EMetric.diam_ball, lp.inner_single_right, Commute.add_pow, frontier_range_modelWithCornersEuclideanHalfSpace, Polynomial.toFinsupp_nsmul, TensorProduct.gradedComm_algebraMap, ringKrullDim_succ_le_of_surjective, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup, Matrix.invOf_mul_eq_iff_eq_mul_left, MeasureTheory.L1.setToL1_add_left', Complex.antilipschitz_equivRealProd, Besicovitch.exist_finset_disjoint_balls_large_measure, Set.Ico.coe_zero, Nat.cast_finsetSup', MvPolynomial.instCharZero, EuclideanSpace.instIsManifoldSphere, DualNumber.lift_smul, Module.Basis.dualBasis_apply_self, LaurentPolynomial.T_apply, ENat.top_sub_one, Finset.card_mul_cast_subConst, MvPolynomial.C_1, RingEquiv.map_eq_one_iff, MvPolynomial.eval₂_one, MvPolynomial.rTensor_apply_X_tmul, MvPolynomial.pderiv_X, MeasureTheory.L1.SimpleFunc.coe_negPart, Nat.one_div_cast_pos, MeasureTheory.L1.setToL1_mono_left, TangentBundle.coordChange_model_space, LinearMap.toSpanSingleton_apply_one, MeasureTheory.condExpInd_disjoint_union, IsStrictOrderedRing.toIsStrictOrderedModule, one_div_lt, ProbabilityTheory.Kernel.withDensity_one', Cardinal.one_le_ofENat, Polynomial.toFinsupp_X_pow, DirectSum.algebraMap_apply, LinearMap.restrictScalars_self, Finset.prod_one_add_ordered, Nat.ceil_lt_add_one, Subsemiring.one_mem, natCast_eq_one, instContMDiffInv₀OfNatWithTopENat, CategoryTheory.projectiveDimension_lt_iff, Finset.expect_eq_single_of_mem, Function.Antiperiodic.nat_even_mul_periodic, Matrix.conjTranspose_swap, MeasureTheory.setIntegral_condExpIndSMul, Metric.coveringNumber_eq_one_of_ediam_le, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, Nat.cast_add_choose, Nat.cast_max, SubsemiringClass.noZeroDivisors, add_thirds, RingEquiv.toAddMonoidMom_commutes, Polynomial.leadingCoeff_pow_X_add_C, OrthonormalBasis.equiv_apply, MulSemiringActionHom.map_smul, Nat.comap_cast_atTop, Commute.natCast_mul_right, add_pow_le, AddConstMapClass.map_nat_add, MeasureTheory.norm_setToFun_le', Set.Icc.coe_mul, SimpleGraph.chromaticNumber_eq_iff_colorable_not_colorable, traceForm_dualSubmodule_adjoin, Topology.RelCWComplex.openCell_subset_skeletonLT, TensorPower.galgebra_toFun_def, div_two_lt_of_pos, Metric.ediam_cthickening_le, NNRat.mk_natCast, SkewMonoidAlgebra.single_mul_single, Polynomial.divX_hom_toFun, Matrix.toMatrix₂Aux_toLinearMap₂'Aux, Topology.RelCWComplex.closedCell_subset_skeletonLT, ENNReal.tendsto_pow_atTop_nhds_top_iff, Real.toNNReal_le_natCast, MonovaryOn.sum_mul_sum_le_card_mul_sum, MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_spec, ENNReal.tsum_geometric_add_one, Algebra.adjoin_nonUnitalSubalgebra_eq_span, WittVector.frobenius_eq_map_frobenius, hasSum_const_div_iff, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, Module.Basis.coe_toOrthonormalBasis_repr_symm, MvPolynomial.isWeightedHomogeneous_one, MvPowerSeries.constantCoeff_smul, Finset.card_mul_expect, ContractingWith.edist_efixedPoint_le', Subsemiring.noZeroDivisors, Matrix.one_vecMul, Finset.dens_eq_card_div_card, ENat.ceil_lt, MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval, SimplexCategory.toTopObj_one_add_eq_one, Matrix.mulVecLin_one, Polynomial.charP, Ideal.Quotient.stabilizerHom_surjective_of_profinite, MonoidAlgebra.ofMagma_apply, contMDiff_subtype_coe_Icc, Finsupp.finite_of_nat_weight_le, IsTopologicalSemiring.toIsModuleTopology, Int.log_one_right, RingHom.charZero_iff, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen, sup_eq_half_smul_add_add_abs_sub', Nat.floor_div_eq_div, mem_Icc_of_mem_stdSimplex, MeasureTheory.IsProbabilityMeasure.measure_univ, tendsto_natCast_div_add_atTop, MvPolynomial.tensorEquivSum_one_tmul_C, Int.zpow_pred_clog_lt_self, ENNReal.toReal_natCast, ENNReal.zero_lt_log_iff, AddMonoidAlgebra.toDirectSum_natCast, MvPolynomial.rTensor_apply_tmul, OrthonormalBasis.volume_parallelepiped, MeasureTheory.condExpL1_undef, MeasureTheory.eLpNorm_smul_measure_of_ne_top, Ideal.inertia_le_stabilizer, MeasureTheory.OuterMeasure.dirac_apply, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul, MeasureTheory.charFun_pi, contDiffOn_succ_iff_fderiv_of_isOpen, PointwiseConvergenceCLM.equivWeakDual_apply, one_half_lt_one, QuadraticAlgebra.C_natCast, MeasureTheory.L1.SimpleFunc.setToL1S_sub, ascPochhammer_nat_eq_natCast_descFactorial, Polynomial.natCast_coeff_zero, ENNReal.log_eq_one_iff, ProbabilityTheory.evariance_eq_top_iff, LinearGrowth.linearGrowthSup_biSup, ProbabilityTheory.lintegral_betaPDF_eq_one, OrthonormalBasis.repr_apply_apply, SkewPolynomial.monomial_zero_one, hasProd_one_add_of_hasSum_prod, WithLp.prod_nnnorm_eq_of_L2, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, Set.Icc.coe_nonneg, pi_eq_sum_univ', ENNReal.HolderConjugate.div_conj_eq_sub_one, sup_eq_half_smul_add_add_abs_sub, Nat.floor_lt', PMF.uniformOfFintype_apply, Matrix.conjTranspose_inv_ofNat_smul, Subsemiring.closure_singleton_one, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, ENat.map_natCast_mul, hasFTaylorSeriesUpToOn_succ_iff_right, four_mul_le_sq_add, MonoidAlgebra.lift_unique, Nat.cast_finprod, uniformity_basis_edist_inv_nat, IsGaloisGroup.faithful, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, TensorProduct.algebraMap_gradedMul, Function.Periodic.nat_mul_eq, Polynomial.MonicDegreeEq.coeff_of_ge, Num.cast_bit1, WithLp.prod_nnnorm_eq_of_L1, NNRat.natCast_le_cast, MeasureTheory.L2.inner_indicatorConstLp_one, MvPolynomial.mkDerivationₗ_monomial, RCLike.tendsto_add_mul_div_add_mul_atTop_nhds, NNReal.lipschitzWith_sub, ENNReal.sub_half, Finsupp.le_weight, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, LinearMap.toMatrixAlgEquiv'_apply, IsDiscreteValuationRing.addVal_uniformizer, contDiff_nat_iff_iteratedDeriv, GroupLike.val_one, MeasureTheory.L1.setToL1_smul_left', SubMulAction.algebraMap_mem, Matrix.fin_two_smul_prod, EuclideanSpace.edist_single_same, Nat.cast_npow, Nat.preimage_Iic, Nat.preimage_ceil_of_ne_zero, CFC.sqrt_eq_nnrpow, Submodule.coe_orthogonalDecomposition, MeasureTheory.L1.SimpleFunc.toLp_one_eq_toL1, TensorProduct.lid_symm_apply, Unitization.inrNonUnitalStarAlgHom_apply, NNRat.num_one, IsSMulRegular.submodule, Polynomial.trinomial_monic, EuclideanHalfSpace.convex, MvPolynomial.IsWeightedHomogeneous.sum_weight_X_mul_pderiv, instIsManifoldMinSmoothnessOfNatWithTopENat_1, Algebra.IsInvariant.orbit_eq_primesOver, fact_one_le_top_ennreal, Finset.nonneg_addConst, exists_sum_eq_one_iff_pairwise_coprime', MeasureTheory.condExpIndSMul_add, RingHom.applyFaithfulSMul, LinearGrowth.linearGrowthSup_inv, MeasureTheory.Lp.norm_fourier_eq, MvPolynomial.pderiv_def, AnalyticAt.analyticOrderAt_deriv_add_one, LinearGrowth.linearGrowthInf_const, SzemerediRegularity.coe_stepBound, Nat.ceil_add_one, Polynomial.coeff_natCast_ite, Matrix.mem_range_scalar_iff_commute_single, Subsemiring.sInf_toAddSubmonoid, Module.ringKrullDim_quotient_add_one_of_mem_nonZeroDivisors, stdSimplex.vertex_coe, PreTilt.coeff_frobenius, EuclideanSpace.sphere_zero_eq, Order.krullDim_WithTop, Submodule.smul_le_smul, SimpleGraph.IsSRGWith.matrix_eq, contDiffPointwiseHolderAt_iff, IsLocalizedModule.map_linearCombination, MvPolynomial.coeff_single_X, ENNReal.exists_nat_pos_inv_mul_lt, MeasureTheory.Lp.instFourierSMul, AddCommGroup.natCast_modEq_natCast, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left, Finset.dens_eq_one, HopfAlgebra.sum_antipode_mul_eq_smul, PEquiv.toMatrix_toPEquiv_mul, MeasureTheory.OuterMeasure.mkMetric'.tendsto_pre_nat, Module.charP_end, LinearMap.toMatrix_innerₛₗ_apply, Nat.Partition.powerSeriesMk_card_restricted_eq_tprod, Nat.le_floor_iff, PointwiseConvergenceCLM.equivWeakDual_symm_apply, MeasureTheory.norm_condExpIndL1_le, EReal.nsmul_eq_mul, TensorProduct.gradedComm_one, RCLike.wInner_one_eq_inner, Set.Ico.nonneg, Set.Icc.coe_pow, ringKrullDim_le_ringKrullDim_quotient_add_card, finsuppTensorFinsupp'_symm_single_eq_single_one_tmul, Dynamics.coverMincard_zero, MvPolynomial.modMonomial_add_divMonomial, Submodule.setLike.coe_galgebra_toFun, TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf, Nat.floor_lt_one, NumberField.RingOfIntegers.mk_add_mk, LinearGrowth.linearGrowthSup_le_iff, star_lt_one_iff, IsLocalization.mk'_self'', Coalgebra.sum_counit_tmul_map_eq, NNReal.HolderConjugate.two_two, Ideal.exact_mulQuot_quotOfMul, Polynomial.eval_list_prod, IsGaloisGroup.fixingSubgroup_fixedPoints, IsGaloisGroup.mulEquivAlgEquiv_apply_apply, IsFractionRing.stabilizerHom_surjective, MeasureTheory.condExpL1_add, CFC.abs_nnrpow_two_mul, NNRat.instCharZero, geom_sum_one, ENat.natCast_lt_succ, PreTilt.coeff_iterate_frobeniusEquiv_symm, Matrix.mul_mul_right, MultilinearMap.freeDFinsuppEquiv_single, MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul, WeakDual.isSeqCompact_closedBall, MvPowerSeries.coeff_one, PowerSeries.one_le_order_iff_constCoeff_eq_zero, Matrix.convex_colStochastic, selfZPow_of_neg, MeasureTheory.norm_condExpInd_apply_le, PartENat.withTopEquiv_symm_ofNat, MvPolynomial.coeff_single_X_pow, HahnModule.instIsScalarTowerHahnSeries_1, Polynomial.smul_X, Nat.cast_finsum, Ideal.height_le_ringKrullDim_quotient_add_one, SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet, Polynomial.coeff_X_one, IsSelfAdjoint.natCast, PadicAlgCl.valuation_p, tsub_one_mul, MvPolynomial.monomial_one_mul_cancel_left_iff, ENNReal.coe_one, Matrix.conjTranspose_eq_natCast, Polynomial.integralNormalization_coeff_degree, contDiffAt_euclidean, PadicComplex.valuation_p, single_one_dotProduct, TrivSqZeroExt.mul_inv_cancel, ENat.toENNRealOrderEmbedding_apply, NNRat.natCast_lt_cast, NNRat.tendsto_inv_atTop_nhds_zero_nat, RingEquiv.map_list_prod, OrthogonalFamily.hasSum_linearIsometry, Polynomial.coe_smul, IsLocalization.away_snd, MvPolynomial.coe_basisMonomials, Unitization.val_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe, LinearGrowth.linearGrowthSup_const_mul_self, PMF.toOuterMeasure_ofMultiset_apply, Mathlib.Tactic.Ring.natCast_nat, sum_row_of_mem_doublyStochastic, Matrix.sum_single_ofNat, MeasureTheory.dirac_eq_one_iff_mem, Nat.lt_of_floor_lt, finrank_euclideanSpace, SimpleGraph.adjMatrix_pow_apply_eq_card_walk, Subsemiring.closure_singleton_natCast, SimpleGraph.dotProduct_adjMatrix, MeasureTheory.FiniteMeasure.testAgainstNN_add, LinearMap.toMatrix'_apply, NNRat.cast_le_one, Ideal.Quotient.stabilizerHom_apply, Set.Ico.coe_eq_zero, PartENat.ofENat_ofNat, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', TrivSqZeroExt.inv_mul_cancel, Submodule.fst_orthogonalDecomposition_apply, DividedPowers.RatAlgebra.dpow_apply, Polynomial.smul_eq_map, expChar_of_injective_ringHom, Subsemiring.smul_mem_pointwise_smul_iff₀, MultilinearMap.freeDFinsuppEquiv_def, instContMDiffVectorBundleOfNatWithTopENat, MeasureTheory.condExpL1_neg, EReal.tendsto_const_div_atTop_nhds_zero_nat, LinearMap.ext_ring_iff, Polynomial.eval₂_at_natCast, Filter.Eventually.natCast_atTop, Unitization.isSelfAdjoint_inr, MeasureTheory.L1.nnnorm_integral_le, trivializationAt_model_space_apply, hasFTaylorSeriesUpToOn_top_iff, HomogeneousIdeal.mem_irrelevant_iff, Ideal.homogeneousHull_eq_iSup, Representation.asAlgebraHom_single_one, IsNonarchimedean.nmul_le, Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe, MvPolynomial.smulCommClass_right, Polynomial.coeff_natCast_mul, Finsupp.degree_eq_weight_one, ENNReal.HolderConjugate.one_le, SkewMonoidAlgebra.domCongr_refl, ENNReal.add_thirds, ENNReal.rpow_add_le_mul_rpow_add_rpow, inv_natCast_smul_comm, ProbabilityTheory.lintegral_paretoPDF_eq_one, MonoidAlgebra.ringHom_ext_iff, ENNReal.ofReal_eq_natCast, AddConstMapClass.map_one_add, MvPowerSeries.le_weightedOrder_smul, mfderiv_coe_sphere_injective, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, IsLocalization.isInteger_one, ENNReal.tendsto_nat_nhds_top, ENNReal.ofNNReal_le_natCast, Finsupp.isCompl_range_lmapDomain_span, GradedTensorProduct.auxEquiv_mul, RingEquiv.coe_addMonoidHom_refl, MeasureTheory.pdf.IsUniform.pdf_toReal_ae_eq, contDiffOn_euclidean, SimpleGraph.ediam_top, HahnSeries.ofPowerSeries_apply_coeff, one_le_kstar, Module.FinitePresentation.linearEquivMap_apply, Finset.addConst_le_card, Ideal.mul_homogeneous_element_mem_of_mem, PiLp.volume_preserving_ofLp, Finset.dens_mul_card, MeasureTheory.Measure.haar.haarContent_self, MvPolynomial.rTensorAlgHom_toLinearMap, Finset.prod_one_add, Submodule.rTensorOne'_tmul_one, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul', IsGaloisGroup.fixedPoints_bot, Subsemiring.add_mem', ENat.ceil_natCast_add, TrivSqZeroExt.invOf_eq_inv, Finset.expect_boole_mul', hasFTaylorSeriesUpTo_succ_nat_iff_right, DirectSum.toAddMonoidAlgebra_natCast, Order.coheight_coe_withTop, Polynomial.smul_eval_smul, Nat.floor_lt, MeasureTheory.lintegral_indicator_one₀, atTop_hasCountableBasis_of_archimedean, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, MvPowerSeries.le_weightedOrder_subst, MeasureTheory.Measure.count_singleton, Subsemiring.isHomogeneous_iff_subset_iInter, Finset.one_le_divConst, MeasureTheory.smul_extend, PartENat.instCanLiftNatCastDom, MvPowerSeries.trunc'_expand, MeasureTheory.setIntegral_condExpL1, ENNReal.HolderConjugate.sub_one_mul_inv, Module.Basis.coe_singleton, Algebra.TensorProduct.basisAux_tmul, Polynomial.UniversalFactorizationRing.monicDegreeEq_coe, Topology.RelCWComplex.skeleton_union_iUnion_closedCell_eq_skeleton_succ, InnerProductGeometry.norm_ofLp_crossProduct, Orthonormal.linearIsometryEquiv_symm_apply_single_one, MvPolynomial.algebraTensorAlgEquiv_symm_X, Perfection.coeff_iterate_frobenius, ENNReal.HolderConjugate.eq_top_iff_eq_one, Nat.ofDigits_eq_foldr, SkewMonoidAlgebra.coe_algebraMap, MonomialOrder.monic_monomial, Mathlib.Tactic.Ring.atom_pf', MeasureTheory.condExpIndL1_smul, Submodule.baseChange_eq_span, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, UnitAddTorus.orthonormal_mFourier, MeasureTheory.Measure.addHaarMeasure_self, Polynomial.leadingCoeff_X, EReal.natCast_lt_iff, Matrix.ofLp_toEuclideanCLM, Ideal.coe_restrictScalars, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Fintype.expect_one, ENNReal.tsum_two_zpow_neg_add_one, SemiconjBy.natCast_mul_right, instExpCharProd, Cardinal.ofENat_eq_one, Coalgebra.rTensor_counit_comp_comul, MeasureTheory.Measure.ae_smul_measure_iff, Polynomial.instExpChar, add_pow_two, ENat.one_le_iff_ne_zero_withTop, CompleteOrthogonalIdempotents.single, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces', SkewMonoidAlgebra.liftNC_one, AddMonoidAlgebra.instIsPushout, Finset.sum_pow_of_commute, toMatrix_dualTensorHom, Metric.ediam_eball_le, MeasureTheory.Integrable.enorm_toL1, Order.height_eq_iSup_lt_height, Order.height_eq_coe_add_one_iff, MeasureTheory.continuous_integral_integral, fourierCoeff_toLp, SimpleGraph.eccent_eq_one_iff, SimpleGraph.incMatrix_mul_transpose, Nat.choose_lt_pow_div, Nat.cast_prod, MeasureTheory.L1.SimpleFunc.setToL1S_indicatorConst, OrthogonalFamily.summable_of_lp, coe_fourierBasis, NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat, completeOrthogonalIdempotents_iff, gc_mul_ceilDiv, ENat.floor_sub_natCast, map_inv_natCast_smul, ENNReal.HolderConjugate.conj_eq, LinearMap.pi_apply_eq_sum_univ, ENNReal.coe_le_one_iff, Matrix.conjTranspose_eq_ofNat, Algebra.IsInvariant.exists_smul_of_under_eq_of_profinite, ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank, Real.toNNReal_eq_natCast, Bound.div_lt_one_of_pos_of_lt, MvPolynomial.psum_zero, inr_comp_cfcₙHom_eq_cfcₙAux, Mathlib.Tactic.Bound.Nat.cast_pos_of_pos, Cardinal.instCharZero, HahnSeries.ofPowerSeries_X, Polynomial.smeval_at_natCast, LinearGrowth.linearGrowthSup_sup, MeasureTheory.Integrable.toL1_sub, PartENat.toWithTop_one, contDiffWithinAt_succ_iff_hasFDerivWithinAt', NNReal.coe_natCast, Pi.sum_nnnorm_apply_le_nnnorm, range_two_mul, contDiffOn_succ_iff_hasFDerivWithinAt, Matrix.vecMul_ofNat, instIsContMDiffRiemannianBundleOfNatWithTopENat_2, differentiableWithinAt_euclidean, Order.height_eq_coe_iff, AddMonoidAlgebra.instIsPushout', LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', LinearAlgebra.FreeProduct.identify_one, Mathlib.Tactic.Ring.natCast_zero, Finsupp.smul_single', Localization.mkAddMonoidHom_apply, MvPowerSeries.trunc_map, Finsupp.weight_single_index, Ideal.isMaximal_iff, Ideal.Quotient.stabilizerQuotientInertiaEquiv_mk, Matrix.isPositive_toEuclideanLin_iff, SimpleGraph.ediam_eq_one, MonoidAlgebra.smul_of, IsLocalization.mk'_mul_mk'_eq_one', Module.Basis.baseChange_apply, Subalgebra.nsmul_mem, AddMonoidHom.ENatMap_apply, AbsoluteValue.IsEquiv.lt_one_iff, PiLp.norm_sq_eq_of_L2, Polynomial.hasseDeriv_coeff, PMF.toMeasure_uniformOfFintype_apply, Nat.cast_div_div_div_cancel_right, ENNReal.inv_mul_le_one, Matrix.toBilin'Aux_single, Finset.cast_mulConst_mul_card, ENat.floor_one, Polynomial.monomial_zero_one, ProbabilityTheory.Kernel.continuous_integral_integral, WittVector.dvd_sub_sum_teichmuller_iterateFrobeniusEquiv_coeff, PiLp.norm_eq_of_L1, MonomialOrder.monic_monomial_one, EuclideanQuadrant.convex, RingHom.codomain_trivial_iff_map_one_eq_zero, Set.Icc.mul_le_left, Matrix.eRank_subsingleton, ENNReal.coe_two, ExpGrowth.expGrowthSup_exp, Real.dimH_of_nonempty_interior, LinearGrowth.linearGrowthInf_inf, MeasureTheory.L2.real_inner_indicatorConstLp_one_indicatorConstLp_one, MultilinearMap.freeFinsuppEquiv_def, ENat.ceil_sub_natCast, ENNReal.HolderConjugate.instTwoTwo, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, PartENat.natCast_get, Finset.expect_dite_eq', Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, Polynomial.aeval_smul, Nat.cast_finsum_mem, TensorProduct.gradedMul_one, ENNReal.natCast_le_ofReal, MvPowerSeries.coeff_trunc', SkewMonoidAlgebra.coeff_mul, tangentBundle_model_space_coe_chartAt_symm, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, ProbabilityTheory.uniformOn_eq_one_of, EuclideanSpace.toLp_single, Mathlib.Tactic.Ring.one_pow, tangentBundleModelSpaceHomeomorph_coe, ENNReal.ofReal_le_one, NNReal.agm_eq_agm_gm_am, MeasureTheory.prob_compl_eq_zero_iff, ENNReal.half_le_self, IsLocalization.Away.mul_invSelf, Polynomial.toFinsupp_natCast, Submodule.mul_smul_mul_eq_smul_mul_smul, ENNReal.toNNReal_natCast, Set.equitableOn_singleton, Polynomial.iterate_derivative_X_pow_eq_smul, IsTopologicalSemiring.toOppositeIsModuleTopology, Set.one_le_encard_insert, IsManifold.instLEInftyOfNatWithTopENat_1, MeasureTheory.mem_ae_iff_prob_eq_one, MeasureTheory.memL1_smul_of_L1_withDensity, amenable_of_maxFoelner_neBot, MeasureTheory.condExp_ae_eq_condExpL1, MeasureTheory.Measure.toSphere_apply', Polynomial.monomial_one_eq_iff, AddMonoidAlgebra.lift_symm_apply, PartENat.dom_natCast, Polynomial.smeval_C_mul, Subsemiring.nsmul_mem, NormedField.exists_enorm_lt_one, IsBaseChange.equiv_symm_apply, Matrix.transpose_invOf, NNRat.num_natCast, Polynomial.TrailingMonic.trailingCoeff, Ideal.add_eq_one_iff, Matrix.one_submatrix_mul, MvPowerSeries.coeff_weightedHomogeneousComponent, Matrix.smul_eq_mul_diagonal, Subsemiring.center.smulCommClass_right, charP_of_injective_algebraMap', geom_sum₂_with_one, ENNReal.one_le_ofReal, MeasureTheory.condExpIndL1_smul', Submodule.singleton_smul, ENNReal.ofReal_lt_natCast, NNReal.le_gm_and_am_le, DividedPowers.mul_dpow, Nat.Prime.emultiplicity_self, Real.nnnorm_two, range_euclideanHalfSpace, SimpleGraph.adjMatrix_mulVec_const_apply, MonoidAlgebra.liftNC_single, tprod_one_add, MvPolynomial.psumPart_zero, Bialgebra.counit_natCast, Ring.ascPochhammer_succ_succ, Algebra.TensorProduct.mul_one, CFC.nnrpow_sqrt, invOf_two_smul_add_invOf_two_smul, instIsInvariantSubtypeMemSubalgebraSubalgebraSubgroupQuotient, tangentBundleCore_coordChange_model_space, Module.length_eq_one, ENNReal.tsum_geometric_two, Metric.externalCoveringNumber_eq_one_of_ediam_le, ENat.epow_one, IsLocalization.mk'_self', Subalgebra.noZeroDivisors, Finset.nonneg_addConst_self, Nat.gc_ceil_coe, TensorProduct.finsuppScalarRight_symm_apply_single, ProbabilityTheory.Kernel.isProper_iff_restrict_eq_indicator_smul, PMF.toOuterMeasure_uniformOfFinset_apply, Subsemiring.mem_inv_pointwise_smul_iff₀, Module.End.genEigenspace_one, AddSubmonoid.pow_eq_closure_pow_set, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, NumberField.RingOfIntegers.mk_zero, contDiffOn_all_iff_nat, Subalgebra.coe_matrix, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower_1, enorm_one, Nat.ceil_one, WithLp.prod_lipschitzWith_toLp, ENNReal.toNNReal_natCast_eq_toNNReal, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, PolynomialLaw.one_tmul_ground, Dynamics.IsDynCoverOf.coverEntropyEntourage_le_log_card_div, instIsManifoldMinSmoothnessOfNatWithTopENat, IccLeftChart_extend_bot, LinearGrowth.linearGrowthSup_eventually_monotone, Matrix.sum_col_of_mem_colStochastic, Ideal.span_one, Matrix.l2_opNNNorm_def, ENNReal.ofReal_one, ENNReal.one_eq_coe, ringKrullDim_add_length_eq_ringKrullDim_of_isRegular, MeasureTheory.L1.SimpleFunc.setToL1S_const, MvPowerSeries.coeff_trunc, Order.krullDim_le_one_iff_of_boundedOrder, Module.Basis.addHaar_eq_iff, MvPolynomial.mkDerivation_monomial, SubMulAction.ENat_card_ofStabilizer_add_one_eq, Algebra.adjoin_singleton_one, FloorSemiring.gc_ceil, ENNReal.one_sub_inv_two, Ideal.coe_smul_primesOver_mk, PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopen, contDiffOn_succ_iff_deriv_of_isOpen, Polynomial.iterate_derivative_eq_sum, VitaliFamily.ae_tendsto_measure_inter_div, MvPolynomial.schwartz_zippel_sup_sum, Module.Basis.reindexFinsetRange_repr_self, Set.Icc.le_one, LinearGrowth.linearGrowthSup_const, MeasureTheory.condExpL2_indicator_of_measurable, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, WittVector.exists_frobenius_solution_fractionRing, GradedTensorProduct.mulHom_apply, ENNReal.iUnion_Icc_coe_nat, MonoidAlgebra.smul_single', MulSemiringAction.toRingEquiv_symm_apply, Polynomial.wronskianBilin_apply, MeasureTheory.condExp_ae_eq_condExpL1CLM, TensorAlgebra.algebraMap_eq_one_iff, instContMDiffMulOfNatWithTopENat, Nat.ceil_sub_natCast, PartENat.find_le, Nat.ceil_add_natCast, Ideal.isCoprime_tfae, Pi.sum_nnnorm_apply_le_nnnorm', EuclideanSpace.basisFun_repr, Module.Basis.repr_symm_single_one, ProbabilityTheory.indepFun_iff_charFun_prod, Finset.le_card_falling_div_choose, WithLp.prod_norm_eq_of_L1, Polynomial.leadingCoeff_X_pow, MeasureTheory.Integrable.toL1_smul', one_div_le_one_div, QuadraticAlgebra.lift_symm_apply_coe, Nat.Partition.hasProd_powerSeriesMk_card_restricted, Matrix.mem_range_scalar_iff_commute_single', Module.Flat.linearIndependent_one_tmul, ProbabilityTheory.measure_eq_zero_or_one_or_top_of_indepSet_self, Submodule.sndL_comp_coe_orthogonalDecomposition, OrthonormalBasis.equiv_apply_euclideanSpace, Polynomial.sylvesterDeriv_updateRow, Algebra.algebraMap_eq_smul_one, Cubic.monic_of_a_eq_one', ContractingWith.exists_fixedPoint, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, WithLp.unitization_nnnorm_inr, PMF.coe_le_one, MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le', MeasureTheory.condExpL1CLM_indicatorConst, NumberField.FinitePlace.norm_def_int, Polynomial.expand_zero, Complex.orthonormalBasisOneI_repr_symm_apply, MvPolynomial.coeff_one, MeasureTheory.L1.nnnorm_Integral_le_one, Holor.slice_unitVec_mul, MeasureTheory.L1.SimpleFunc.integrable, Manifold.riemannianEDist_def, NNReal.coe_two, NNReal.coe_nsmul, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, AddMonoidAlgebra.singleAddHom_apply, SkewMonoidAlgebra.coeff_mul_antidiagonal_finsum, ProbabilityTheory.uniformOn_self, LinearGrowth.linearGrowthInf_natCast_nonneg, MeasureTheory.L1.integral_eq_norm_posPart_sub, MeasureTheory.Lp.instContinuousFourierInv, uniformity_basis_edist_inv_two_pow, AddMonoidAlgebra.coe_liftNCAlgHom, add_one_pow_unbounded_of_pos, MulSemiringActionHom.map_one', Module.End.natCast_def, pinGroup.conjAct_smul_range_ι, Subalgebra.rTensorBot_tmul_one, Matrix.mul_invOf_cancel_right, UnitAddTorus.hasSum_mFourier_series_L2, Polynomial.eval_one_map, MvPolynomial.msymm_zero, Ideal.primeHeight_add_one_le_of_lt, modelWithCornersEuclideanHalfSpace_zero, Matrix.swap_mul_apply_right, Set.one_le_chainHeight_iff, LinearMap.isIdempotentElem_apply_one_iff, tangentBundleCore.isContMDiff, OrderRingHom.toOrderAddMonoidHom_eq_coe, Nat.cast_min, MonomialOrder.Monic.leadingCoeff_eq_one, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, TensorPower.toTensorAlgebra_gOne, PiTensorProduct.tprod_eq_tprodCoeff_one, Algebra.adjoin_inl_union_inr_eq_prod, MulSemiringAction.smul_mul, MeasureTheory.laverage_one, AddMonoidAlgebra.natCast_def, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_nonZeroDivisors, contDiffOn_iff_forall_nat_le, WeakDual.isClosed_closedBall, contDiff_succ_iff_fderiv_apply, ENat.add_one_eq_coe_top_iff, MeasureTheory.setLIntegral_one, ENat.le_ceil, DirectSum.GAlgebra.map_mul, LinearGrowth.linearGrowthSup_comp_nonneg, QuadraticMap.half_moduleEnd_apply_eq_half_smul, PartENat.toWithTop_natCast', Finset.pluennecke_ruzsa_inequality_pow_div, Besicovitch.ae_tendsto_measure_inter_div, emultiplicity_geom_sum₂_eq_one, PartENat.eq_top_iff_forall_le, MvPolynomial.divMonomial_mul_monomial, EReal.exp_le_one_iff, PowerSeries.X_eq, TangentBundle.contMDiffVectorBundle, MeasureTheory.Measure.one_le_hausdorffMeasure_zero_of_nonempty, Module.supportDim_quotSMulTop_succ_eq_supportDim, Matroid.IsCircuit.eRk_add_one_eq, half_lt_self_iff, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, EReal.natCast_eq_iff, TrivSqZeroExt.snd_invOf, PartENat.natCast_lt_top, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, WithLp.unitization_norm_def, PosNum.cast_le, ENNReal.coe_inv_two, div_nat_le_self_of_nonnneg, one_lt_star_iff, MeasureTheory.pdf.IsUniform.pdf_eq, EuclideanSpace.norm_eq, star_inv_natCast_smul, LinearMap.toMatrixRight'_id, nnnorm_pow_le_mul_norm, sq_sum_le_card_mul_sum_sq, Matrix.IsHermitian.eigenvectorUnitary_apply, Matrix.mem_rowStochastic_iff_sum, MvPolynomial.prod_X_pow_eq_monomial, ENNReal.coe_lt_natCast, Subalgebra.smul_mem_pointwise_smul, add_pow_prime_eq, PartENat.withTopEquiv_symm_one, matrixEquivTensor_apply_single, stdSimplex.sum_eq_one, contDiffAt_succ_iff_hasFDerivAt, ringChar.Nat.cast_ringChar, MeasureTheory.L2.eLpNorm_inner_lt_top, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', ENat.epow_eq_one_iff, Set.Subsingleton.equitableOn, SemiconjBy.natCast_mul_left, ENNReal.log_pow, Algebra.TensorProduct.cancelBaseChange_symm_tmul, PartENat.withTopEquiv_natCast, MvPolynomial.degrees_one, PiLp.antilipschitzWith_ofLp, PartENat.coe_le_coe, MeasureTheory.condExpL1CLM_lpMeas, Matrix.frobenius_nnnorm_replicateRow, ContinuousLinearEquiv.unitsEquivAut_symm_apply, MvPolynomial.coeff_rTensorAlgHom_tmul, MeasureTheory.L1.SimpleFunc.negPart_toSimpleFunc, Submodule.rTensorOne_tmul_one, Nat.cast_div, MeasureTheory.Measure.count_apply_finset', sign_one, AbsoluteValue.trivial_apply, Int.zpow_log_le_self, Matrix.le_one_of_mem_rowStochastic, EuclideanSpace.inner_eq_star_dotProduct, AlgEquiv.algHomUnitsEquiv_apply_symm_apply, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, Dynamics.coverEntropyEntourage_le_log_coverMincard_div, MeasureTheory.setLAverage_one, ENNReal.zero_rpow_def, PartENat.eq_top_iff_forall_lt, Cubic.monic_of_b_eq_one', OrthonormalBasis.sum_repr_symm, Set.encard_singleton_inter, MeasureTheory.one_le_prob_iff, Localization.mk_natCast, MvPolynomial.divMonomial_monomial, PartENat.coe_succ_le_iff, MvPolynomial.frobenius_zmod, Finset.sum_card_slice_div_choose_le_one, PartENat.coe_lt_iff, MeasureTheory.L1.setToL1_apply_coeToLp, MeasureTheory.MemLp.enorm_rpow, Polynomial.derivative_sq, conjneg_eq_one, ringKrullDim_quotient_succ_le_of_nonZeroDivisor, Module.DualBases.eval_same, Matrix.conjTranspose_one, MvPowerSeries.coeff_zero_one, one_div_le_one_div_of_le, MatrixEquivTensor.invFun_smul, Matrix.frobenius_nnnorm_replicateCol, contDiffWithinAt_infty, Pi.orthonormalBasis.toBasis, contMDiffWithinAt_comp_projIcc_iff, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_jacobson, PartENat.get_eq_iff_eq_coe, tangentBundle_model_space_chartAt, Cubic.monic_of_c_eq_one', NNRat.addSubmonoid_closure_range_pow, CharP.subsemiring, NNReal.natCast_iSup, Subalgebra.inclusion.isScalarTower_right, tendsto_add_mul_div_add_mul_atTop_nhds, Polynomial.hasseDeriv_monomial, Module.length_eq_one_iff, Polynomial.degree_smul_of_isRightRegular_leadingCoeff, cfc_one, ENat.one_le_epow, Odd.natCast, Set.Ioc.coe_pos, ContinuousLinearMap.toSpanSingleton_one, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, tendsto_one_div_atTop_nhds_zero_nat, Finset.addConst_mul_card, ENNReal.tsum_condensed_le, contMDiffAt_iff_nat, Ideal.quotOfMul_surjective, map_natCast_smul, ENNReal.iUnion_Ico_coe_nat, Function.Antiperiodic.add_nat_mul_eq, MeasureTheory.L1.setToL1_congr_left', nsmul_eq_mul', ENNReal.mul_inv_cancel, LinearMap.IsSymmetric.direct_sum_isInternal, toAddMonoidWithOne_injective, LinearMap.toSpanSingleton_eq_algebra_linearMap, Function.Antiperiodic.nat_mul_eq_of_eq_zero, Finsupp.llift_symm_apply, WeakDual.CharacterSpace.eq_set_map_one_map_mul, Algebra.adjoin_singleton_natCast, tendsto_natCast_atTop_iff, Polynomial.eval₂_at_one, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, MeasureTheory.Lp.instFourierPairInv, MeasureTheory.Measure.dirac_apply_ne_zero_iff_eq_one, Ideal.pointwise_smul_eq_comap, div_le_one, WithLp.prod_dist_eq_of_L1, Matroid.eRk_eq_one_iff, Int.log_natCast, Set.Icc.coe_eq_zero, Monotone.linearGrowthInf_nonneg, dotProduct_single_one, PowerSeries.coeff_smul, ContinuousAlgHom.ext_ring_iff, MeasureTheory.OuterMeasure.coeFnAddMonoidHom_apply, EuclideanSpace.volume_ball_fin_three, matrixEquivTensor_apply_symm, Complex.nnnorm_ofNat, MeasureTheory.AddSubgroup.index_mul_measure, LieModule.traceForm_eq_sum_finrank_nsmul, Metric.externalCoveringNumber_singleton, PiCountable.edist_le_two, Int.lt_zpow_succ_log_self, IsPrincipalIdealRing.ringKrullDim_eq_one, QuadraticAlgebra.coe_natCast, Real.contDiffAt_rpow_const, Subalgebra.coe_eq_one, add_sq_le, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, ENNReal.inv_lt_one, RestrictScalars.ringEquiv_map_smul, Finset.sum_pow_eq_sum_piAntidiag_of_commute, IsUnit.natCast_factorial_of_algebra, MonomialOrder.degree_one, Submodule.one_eq_span_one_set, MvPolynomial.isHomogeneous_one, Matrix.exists_left_inverse_iff_isUnit, Commute.natCast_mul_left, Ideal.eq_top_iff_one, ContinuousMapZero.toContinuousMapHom_toNNReal, ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial, CompleteOrthogonalIdempotents.unique_iff, instZeroLEOneClass, ArithmeticFunction.zeta_pmul, Matrix.toLin'_one, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, IsDomain.instIsAddTorsionFreeOfCharZero, MeasureTheory.prob_compl_le_one_sub_of_le_prob, DualNumber.coe_lift_symm_apply, ExpGrowth.le_expGrowthInf_iff, MultilinearMap.freeFinsuppEquiv_apply, Matrix.vecMul_surjective_iff_exists_left_inverse, Commute.exists_add_pow_prime_eq, StrictOrderedSemiring.toSMulPosStrictMonoNat, ENNReal.orderIsoUnitIntervalBirational_apply_coe, IsDiscreteValuationRing.addVal_pow, TensorProduct.isBaseChange, MeasureTheory.Lp.instFourierInvAdd, LinearEquiv.algEquivOfRing_symm_apply, Matrix.frobenius_nnnorm_diagonal, MeasureTheory.L1.setToL1_congr_left, MulSemiringActionHom.map_mul', even_two_mul, MeasureTheory.Measure.dirac_apply_eq_zero_or_one, NNReal.rpow_add_le_mul_rpow_add_rpow, Subsemiring.isHomogeneous_iff_forall_subset, Module.Basis.smul_eq_map, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, SkewMonoidAlgebra.support_mul_single_subset, Real.Convex.dimH_eq_finrank_vectorSpan, instIsPushoutPolynomial, MonoidAlgebra.instIsPushout', Nat.coe_ofDigits, Ideal.isCoprime_iff_exists, QuadraticAlgebra.coe_ofNat, AddMonoidAlgebra.liftNC_smul, WithLp.unitizationAlgEquiv_symm_apply_ofLp, MeasureTheory.L1.setToL1_smul, Polynomial.MonicDegreeEq.map_coe, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_apply_eq, GradedTensorProduct.auxEquiv_tmul, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_paramSet_exp, QuadraticAlgebra.omega_mul_omega_eq_mk, Derivation.map_one_eq_zero', Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, thickenedIndicatorAux_one, Representation.ker_leftRegular_norm_eq, Subalgebra.lTensorBot_symm_apply, AddMonoidAlgebra.of'_apply, MeasureTheory.L1.SimpleFunc.posPart_toSimpleFunc, EReal.coe_ennreal_eq_one, Diffeology.isPlot_iff_contDiff, ContractingWith.edist_inequality, Nat.cast_sum, multipliable_one_add_of_summable_prod, ENNReal.mul_eq_left, PMF.binomial_apply, SubsemiringClass.addSubmonoidWithOneClass, MeasureTheory.condExpIndSMul_nonneg, OrthonormalBasis.measurePreserving_repr_symm, AddMonoidAlgebra.liftNC_single, OrderRingHom.coe_coe_orderAddMonoidHom, Polynomial.coe_basisMonomials, lp.summable_inner, RingHom.one_notMem_ker, Finset.expect_boole_mul, Subalgebra.inclusion.faithfulSMul, Real.volume_eball, EuclideanSpace.piLpCongrLeft_single, NumberField.RingOfIntegers.mk_one, ENNReal.div_self, Ring.smeval_ascPochhammer_nat_cast, OrthonormalBasis.enorm_eq_one, MvPowerSeries.le_order_smul, DividedPowers.dpow_zero, SkewMonoidAlgebra.coeff_mul_single, PEquiv.single_mul_single_right, Algebra.charZero_of_charZero, IsLocalization.smul_mk'_one, oneTangentSpaceIcc_def, Matrix.mul_submatrix_one, ENNReal.tendsto_inv_nat_nhds_zero, IsGroupLikeElem.antipode_mul_cancel, MvPolynomial.hsymmPart_zero, MeasureTheory.L1.dist_def, Finsupp.coe_basisSingleOne, Module.Basis.sumCoords_self_apply, AbsoluteValue.not_isNontrivial_iff, PowerSeries.le_order_pow, analyticOrderAt_pow, ExpGrowth.frequently_le_exp, SkewMonoidAlgebra.support_mul, div_add_one, Order.one_le_krullDim_iff, MeasureTheory.OuterMeasure.mkMetric'.mono_pre_nat, IccRightChart_extend_top_mem_frontier, Commute.add_sq, SubsemiringClass.instCharZero, CompactlySupportedContinuousMap.toReal_add, Module.FinitePresentation.linearEquivMapExtendScalars_apply, ENNReal.log_le_zero_iff, hasFDerivWithinAt_euclidean, MeasureTheory.mem_ae_iff_prob_eq_one₀, squarefree_iff_emultiplicity_le_one, nsmul_eq_self, NNRat.one_lt_cast, TensorProduct.piScalarRight_symm_single, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, Set.encard_eq_one, Matrix.scalar_comm_iff, stabilizer_isOpen_of_isIntegral, Algebra.TensorProduct.one_mul, MeasureTheory.tendsto_eLpNorm_condExp, hasFPowerSeriesOnBall_inv_one_sub, PiLp.dist_sq_eq_of_L2, MeasureTheory.Measure.dirac_apply_of_mem, SymAlg.sym_mul_self, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, LinearGrowth.linearGrowthInf_eventually_monotone, AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj, Metric.coveringNumber_subset_le, ENat.toENNReal_one, ENNReal.HolderConjugate.inv_add_inv_eq_one, MvPolynomial.monomial_sum_index, AddMonoidAlgebra.smul_single', MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left', MeasureTheory.diracProba_toMeasure_apply', AbsoluteValue.exists_one_lt_lt_one_of_not_isEquiv, MeasureTheory.L1.norm_integral_le, AddMonoidAlgebra.ofMagma_apply, hasFPowerSeriesOnBall_inverse_one_sub, MvPolynomial.monic_monomial_eq, SkewMonoidAlgebra.liftNC_mul, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, Polynomial.comp_one, Polynomial.coeffs_one, Matrix.IsHermitian.eigenvectorUnitary_coe, Asymptotics.IsBigO.natCast_atTop, PowerSeries.coeff_X, ENNReal.ofNNReal_sub_natCast, MvPolynomial.pderiv_monomial_single, ProbabilityTheory.Kernel.isProper_iff_inter_eq_indicator_mul, Finset.cast_subConst, Nat.cast_finsuppProd, Polynomial.coeff_X_pow_self, smulAddHom_apply, ProbabilityTheory.Kernel.continuous_integral_integral_comp, MultilinearMap.mkPiAlgebraFin_apply, PolyEquivTensor.toFunBilinear_apply_apply, Commute.add_pow', Ideal.IsPrime.smul, Module.End.instSMulCommClass', MeasureTheory.isProbabilityMeasure_iff, Real.dimH_univ_pi, CompleteOrthogonalIdempotents.iff_ortho_complete, Matrix.ofNat_mulVec, ringKrullDim_le_ringKrullDim_add_card, PolyEquivTensor.toFunLinear_tmul_apply, ArithmeticFunction.coe_zeta_smul_apply, Matrix.toEuclideanLin_eq_toLin, Finset.nnratCast_dens, Polynomial.coeff_iterate_derivative, Num.cast_inj, Module.End.instIsScalarTower, analyticOrderAt_id, Euclidean.closedBall_eq_preimage, Matrix.isHermitian_iff_isSymmetric, Set.encard_eq_add_one_iff, Polynomial.toFinsupp_X, Nat.cast_mul, one_div_le, PowerSeries.order_pow, MultilinearMap.freeFinsuppEquiv_single, CategoryTheory.projectiveDimension_le_iff, Finset.subConst_le_card, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, map_natCast, MvPowerSeries.weightedOrder_eq_nat, MeasureTheory.L1.aemeasurable_coeFn, ExpGrowth.frequently_exp_le, SimpleGraph.chromaticNumber_le_one_of_subsingleton, EuclideanSpace.basisFun_inner, MvPowerSeries.totalDegree_trunc', Matrix.mul_swap_of_ne, ENNReal.natCast_lt_ofReal, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, Polynomial.eval_natCast_mul, Real.HolderConjugate.inv_add_inv_ennreal, Nat.Partition.powerSeriesMk_card_countRestricted_eq_tprod, Ideal.restrictScalars_mul, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, Monotone.expGrowthInf_comp_le, NNReal.half_lt_self, InnerProductSpace.toMatrix_rankOne, pi_eq_sum_univ, contMDiffAt_vectorSpace_iff_contDiffAt, MvPolynomial.rTensor_symm_apply_single, EuclideanSpace.ofLp_single, differentiableAt_euclidean, Module.Basis.toMatrix_mul_toMatrix_flip, Nat.cast_multiset_prod, lp.inner_single_left, ProbabilityTheory.Kernel.IsProper.setLIntegral_eq_indicator_mul_lintegral, ENNReal.toReal_nsmul, FractionalIdeal.den_mul_self_eq_num, MeasureTheory.condExpIndL1Fin_disjoint_union, MvPowerSeries.order_expand, AlgEquiv.subalgebraMap_apply_coe, MulSemiringActionHom.map_one, MvPolynomial.pderiv_monomial, Complex.enorm_exp_I_mul_ofReal, Module.Basis.apply_eq_iff, skewAdjointPart_apply_coe, Matrix.mul_right_eq_iff_eq_mul_invOf, Module.Basis.mk_coord_apply, WithLp.prod_norm_sq_eq_of_L2, SkewMonoidAlgebra.coeff_mul_single_one, ENNReal.ofReal_nsmul, HahnSeries.ofPowerSeriesAlg_apply_coeff, ringChar.spec, tendsto_natCast_atTop_atTop, convex_stdSimplex, ENat.recTopCoe_one, MonoidAlgebra.GroupSMul.linearMap_apply, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, Ideal.smul_mem_pointwise_smul, Polynomial.derivative_pow, QuadraticAlgebra.omega_mul_algebraMap_mul_mk, Set.encard_ne_add_one, LinearMap.mulRight_one, Matrix.stdBasis_eq_single, one_half_pos, kstar_one, Module.supportDim_le_supportDim_quotSMulTop_succ, SymmetricAlgebra.algebraMap_eq_one_iff, ContinuousLinearMap.integral_comp_L1_comm, PMF.apply_eq_one_iff, LinearMap.toMatrix'_id, WithLp.prod_edist_eq_of_L1, CategoryTheory.projectiveDimension_ge_iff, MvPolynomial.esymmAlgHomMonomial_single_one, selfAdjointPartL_apply_coe, Nat.cast_finsetInf', Even.two_dvd, nndist_midpoint_midpoint_le, QuadraticAlgebra.C_ofNat, mdifferentiable_addInvariantVectorField, Complex.conjCLE_enorm, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, Polynomial.smeval_at_zero, Probability.lintegral_cauchyPDF_eq_one, PowerSeries.constantCoeff_smul, MeasureTheory.L1.measurable_coeFn, MeasureTheory.aestronglyMeasurable_condExpL1CLM, ENat.lt_add_one_iff, Matrix.conjTranspose_eq_one, Module.supportDim_quotSMulTop_succ_eq_supportDim_mem_jacobson, Matrix.mul_swap_apply_left, SchwartzMap.inner_fourierTransformCLM_toL2_eq, mdifferentiableWithinAt_comp_projIcc_iff, IsStrictOrderedRing.toCharZero, MeasureTheory.continuous_integral, LinearAlgebra.FreeProduct.rel_id, Submodule.mem_smul_top_iff, ProbabilityTheory.IsZeroOrMarkovKernel.bound_le_one, MemHolder.nnHolderNorm_nsmul, MeasureTheory.Measure.count_apply_finset, Module.Basis.coe_ofRepr, MultilinearMap.mkPiRing_apply_one_eq_self, QuadraticMap.weightedSumSquares_apply, half_le_self, PiLp.norm_toLp_const, DualNumber.range_inlAlgHom_sup_adjoin_eps, Submodule.smul_one_eq_span, Diffeology.isOpen_iff_preimages_plots, AddCommGroup.ModEq.natCast, differentiableOn_euclidean, Dvd.dvd.natCast, contDiffAt_infty, floorDiv_one, Real.hasFPowerSeriesOnBall_linear_zero, HasStrictFDerivAt.approximates_deriv_on_open_nhds, LSeries.one_convolution_eq_zeta_convolution, Odd.one_add, MultilinearMap.ext_ring_iff, fact_one_le_one_ennreal, MonoidAlgebra.scalarTensorEquiv_symm_single, TangentBundle.symmL_model_space, IsGaloisGroup.intermediateField, MeasureTheory.integrable_condExpL2_indicator, MvPowerSeries.constantCoeff_one, one_le_star_iff, Algebra.TensorProduct.tmul_one_eq_one_tmul, Diffeology.IsContDiffCompatible.isPlot_iff, NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral, LinearGrowth.linearGrowthInf_iInf, CategoryTheory.injectiveDimension_lt_iff, Finset.cast_mulConst, EuclideanSpace.ball_zero_eq, Real.fib_isSol_fibRec, Int.clog_zpow, MvPolynomial.instCharP, PowerSeries.coeff_one, LinearIsometry.enorm_toContinuousLinearMap, range_mfderiv_coe_sphere, div_lt_one, Diffeology.IsPlot.continuous, SimpleGraph.adjMatrix_mul_apply, add_mul_self_eq, MeasureTheory.eLpNorm'_add_le_of_le_one, Subalgebra.coe_zero, PosNum.cast_pos, Subsemiring.coe_pointwise_smul, Nat.cast_finsupp_sum, AddSubmonoid.pow_subset_pow, LinearGrowth.linearGrowthInf_monotone, Finset.subConst_mul_card, Matrix.instIsScalarTowerForall, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, PMF.toMeasure_apply_eq_one_iff, dividedPowersBot_dpow_eq, MvPowerSeries.exists_coeff_ne_zero_and_weightedOrder, NNRat.nsmul_coe, ENNReal.le_tsum_condensed, PolyEquivTensor.invFun_monomial, Matrix.ofLp_toEuclideanLin_apply, Matrix.invOf_diagonal_eq, Polynomial.ringKrullDim_le, Nat.cast_list_prod, Matrix.swap_mulVec, MultilinearMap.freeDFinsuppEquiv_apply, EuclideanSpace.volume_ball_fin_two, Polynomial.map_smul, SimpleGraph.incMatrix_mul_transpose_diag, Matrix.isHermitian_natCast, CompleteOrthogonalIdempotents.complete, QuadraticAlgebra.algHom_ext_iff, Finset.card_mul_cast_mulConst, Complex.nnnorm_natCast, one_vecMul_of_mem_doublyStochastic, EuclideanSpace.inner_basisFun_real, DividedPowers.OfInvertibleFactorial.dpow_eq_of_mem, Matrix.swap_mul_of_ne, PartENat.ofENat_coe, MvPolynomial.rTensor_apply_monomial_tmul, Nat.one_div_cast_nonneg, iccLeftChart_extend_zero, AddSubmonoid.closure_pow, Complex.nndist_conj_self, MeasureTheory.eLpNorm_one_le_of_le, Polynomial.mirror_eval_one, MvPolynomial.coeff_X', Set.Ioc.coe_eq_one, MvPolynomial.pderiv_pow, Euclidean.ball_eq_preimage, contDiff_nat_iff_continuous_differentiable, PolyEquivTensor.toFunLinear_one_tmul_one, NNRat.ofNat_le_cast, Set.Ioc.coe_le_one, ENat.le_sub_one_of_lt, ContractingWith.exists_fixedPoint', differentiableWithinAt_localInvariantProp, invOf_nonpos, ceilDiv_one, MonoidAlgebra.uniqueRingEquiv_symm_apply, Ideal.card_inertia_eq_ramificationIdxIn, FaithfulSMul.algebraMap_eq_one_iff, Submodule.coe_smul, EuclideanSpace.volume_ball, Subsemiring.mem_closure_iff_exists_list, Matrix.mul_left_eq_iff_eq_invOf_mul, OrthonormalBasis.repr_symm_single, MvPolynomial.vars_one, Mathlib.Meta.NormNum.Finset.sum_empty, le_floorDiv_iff_mul_le, interior_range_modelWithCornersEuclideanHalfSpace, WeakDual.CharacterSpace.norm_le_norm_one, DualNumber.commute_eps_left, Subsemiring.mem_toAddSubmonoid, Matrix.vecMul_natCast, MeasureTheory.L1.stronglyMeasurable_coeFn, MulSemiringAction.toAlgEquiv_apply, ExpGrowth.eventually_exp_le, EReal.exp_zero, Real.dimH_ball_pi_fin, RingHom.smul_def, Polynomial.coeff_X_add_one_pow, MeasureTheory.L1.norm_setToL1_le_mul_norm', MvPowerSeries.weightedOrder_le, Set.Icc.coe_one, ProbabilityTheory.lintegral_gaussianPDFReal_eq_one, RingHom.charP, contDiffWithinAt_iff_forall_nat_le, Matrix.smul_eq_mulVec, MvPolynomial.degreeOf_one, LinearGrowth.linearGrowthSup_iSup, Nat.cast_div_le, ENNReal.half_pos, mulLeftLinearMap_one, OrderedSemiring.toSMulPosMonoNat, Module.Basis.toDual_apply, stdSimplexHomeomorphUnitInterval_one, formalMultilinearSeries_geometric_radius, CFC.nnrpow_three, LinearGrowth.linearGrowthInf_comp_nonneg, PerfectClosure.mk_eq_iff, Unitization.instIsStarNormal, ProbabilityTheory.condVar_of_sigmaFinite, Finset.dens_singleton, ENNReal.zero_le_log_iff, Polynomial.iterate_derivative_X_pow_eq_C_mul, DualNumber.algHom_ext_iff, ENat.add_one_pos, MvPolynomial.support_smul_eq, isCoprime_one_right, Polynomial.derivative_X_pow, Subsemiring.list_prod_mem, Real.natCastle_toNNReal', ENNReal.add_halves, OrthogonalFamily.range_linearIsometry, hasFPowerSeriesOnBall_cuspFunction, SeminormedAddCommGroup.lipschitzWith_sub, ProbabilityTheory.Kernel.withDensity_one, TensorAlgebra.tprod_apply, FixedPoints.linearIndependent_smul_of_linearIndependent, TensorProduct.gradedComm_tmul_algebraMap, MvPolynomial.C_eq_coe_nat, Units.add_eq_mul_one_add_div, RCLike.nnnorm_two, NNReal.summable_one_div_rpow, MvPolynomial.tensorEquivSum_X_tmul_X, MeasureTheory.L1.SimpleFunc.integral_smul, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, Nat.one_div_pos_of_nat, PiTensorProduct.smul_tprodCoeff', ENNReal.rpow_zero, ENNReal.iUnion_Ioo_coe_nat, add_pow_prime_pow_eq', IsAddTorsionFree.of_isDomain_charZero, Mathlib.Tactic.Ring.mul_one, SimpleGraph.eq_top_iff_forall_eccent_eq_one, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, AddMonoidAlgebra.uniqueRingEquiv_symm_apply, FreeAlgebra.charZero, Matrix.mem_colStochastic, Module.Projective.exists_dual_eq_one, Cardinal.one_lt_ofENat, Even.add_pow_le, Topology.CWComplex.iUnion_openCell_eq_skeleton, toMatrix_innerSL_apply, MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le, isGroupLikeElem_self, ENat.ceil_one, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, Ideal.Quotient.ker_stabilizerHom, Ideal.rank_pow_quot, ArithmeticFunction.coe_mul_zeta_apply, Finset.nonneg_subConst_self, PerfectClosure.r_iff, MvPolynomial.esymmAlgHomMonomial_add, two_mul_le_add_of_sq_eq_mul, MvPolynomial.algebraTensorAlgEquiv_symm_map, TensorProduct.rid_symm_apply, Matrix.mem_colStochastic_iff_sum, Ideal.map_height_le_one_of_mem_minimalPrimes, LinearMap.intrinsicStar_smulRight, Algebra.TensorProduct.productMap_right_apply, odd_one, MvPolynomial.weightedDecomposition.decompose'_eq, ProbabilityTheory.uniformOn_univ, Module.End.instSMulCommClass, Pi.basisFun_apply, ProjectiveSpectrum.basicOpen_eq_union_of_projection, MvPolynomial.tensorEquivSum_C_tmul_one, Submodule.restrictScalars.isScalarTower, Finsupp.le_weight_of_ne_zero, Diffeology.IsPlot.contDiff, tangentBundleModelSpaceHomeomorph_coe_symm, Nat.ceil_sub_one, Submodule.pow_eq_span_pow_set, MeasureTheory.L1.integral_of_fun_eq_integral, MeasureTheory.L1.integral_zero, Polynomial.factorial_smul_hasseDeriv, WeakDual.instContinuousSMul, PiLp.edist_eq_card, Subsemiring.coe_closure_eq, PartENat.toWithTop_one', PowerSeries.coe_X, lp.hasSum_inner, Submodule.torsionBy_one, MvPolynomial.hsymm_zero, Submodule.eq_span_singleton_of_surjective, contDiff_one_iff_hasFDerivAt, AddMonoidAlgebra.algHom_ext_iff, SchwartzMap.toLp_fourierTransform_eq, Nat.lt_of_ceil_lt, MeasureTheory.setLIntegral_nnnorm_condExpIndSMul_le, Polynomial.eval₂AddMonoidHom_apply, Algebra.TensorProduct.basis_repr_symm_apply, SimpleGraph.degree_eq_sum_if_adj, pow_sum_le_card_mul_sum_pow, Int.two_pow_sub_pow, PiLp.nnnorm_eq_of_L1, ZMod.frobenius_zmod, MeasureTheory.condExpIndL1_of_not_measurableSet, AddCommMonoid.nat_isScalarTower, MeasureTheory.stoppedProcess_eq', MeasureTheory.L1.norm_setToL1_le', MeasureTheory.withDensitySMulLI_apply, ContinuousMapZero.toContinuousMapHom_apply, SimpleGraph.incMatrix_transpose_mul_diag, Finsupp.single_mem_span_single, Nat.cast_finsetSup, DirectSum.ringHom_ext'_iff, AbsoluteValue.IsEquiv.one_lt_iff, ProbabilityTheory.Kernel.deterministic_apply', polyEquivTensor_apply, MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq, NNReal.bddAbove_natCast_image_iff, PolyEquivTensor.toFunBilinear_apply_eq_smul, ENNReal.log_one, Order.krullDim_le_one_iff_forall_isMax, MonoidAlgebra.singleOneRingHom_apply, Nat.coe_castRingHom, UnitAddTorus.hasSum_prod_mFourierCoeff, Order.krullDim_withBot, IsLocalization.mk'_mul_mk'_eq_one, MvPolynomial.totalDegree_one, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem, CharZero.of_isAddTorsionFree, Cardinal.ofENat_le_one, Metric.packingNumber_singleton, contMDiff_equivTangentBundleProd, Matrix.instSMulCommClassForall, geom_sum_mul_add, instIsManifoldOfNatWithTopENatOfMinSmoothness_1, Finset.natCast_card_mul_nnratCast_dens, Ideal.smul_bot, Module.Invertible.rTensorEquiv_symm_apply_apply, Int.le_zpow_iff_clog_le, SubAddAction.ENat_card_ofStabilizer_add_zero_eq, cfcₙAux_mem_range_inr, Algebra.TensorProduct.algebraMap_apply', Polynomial.MonicDegreeEq.mk_coe, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, NNRat.coe_one, Set.Ico.coe_mul, MeasureTheory.L1.norm_of_fun_eq_integral_norm, MonoidAlgebra.smulCommClass_symm_self, selfAdjointPart_apply_coe, MeasureTheory.L1.integral_add, Finset.expect_univ, AddMonoidAlgebra.basis_apply, AlgEquiv.moduleEndSelfOp_symm_apply, MeasureTheory.aestronglyMeasurable_condExpIndSMul, MeasureTheory.Egorov.mem_notConvergentSeq_iff, skewAdjointPartL_apply_coe, Nat.floor_sub_natCast, Subsemiring.toAddSubmonoid_mono, TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, Finset.one_le_divConst_self, ringKrullDim_nat, one_add_cpow_hasFPowerSeriesOnBall_zero, IsCoprime.exists, PowerSeries.X_pow_eq, ContinuousAlternatingMap.ext_ring_iff, PartENat.ne_top_iff, ProbabilityTheory.iIndepFun_iff_charFun_pi, MeasureTheory.L2.mem_L1_inner, Multiset.pow_smul_esymm, Finset.cast_addConst_mul_card, MvPolynomial.esymm_eq_sum_monomial, Subsemiring.one_mem_toNonUnitalSubsemiring, MeasureTheory.L1.integral_eq_integral, Matrix.trace_one, Subalgebra.rTensorBot_symm_apply, div_add_same, Cardinal.nsmul_lt_aleph0_iff, openSegment_eq_image₂, DirectSum.GAlgebra.smul_def, MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc', Matrix.invOf_mul_cancel_right, DualNumber.commute_eps_right, PreErgodic.prob_eq_zero_or_one, MeasureTheory.Integrable.coeFn_toL1, LinearEquiv.isScalarTower, instIsPushoutFractionRingPolynomial, Perfection.coeff_frobeniusEquiv_symm, IsGroupLikeElem.counit_eq_one, NNReal.tendsto_inverse_atTop_nhds_zero_nat, ENNReal.mul_eq_right, Module.End.mem_genEigenspace_one, FreeAlgebra.charP, LinearGrowth.le_linearGrowthInf_iff, AbsoluteValue.IsEquiv.eq_one_iff, hasFTaylorSeriesUpToOn_succ_iff_left, SkewMonoidAlgebra.isScalarTower_self, isConjRoot_iff_orbitRel, Matroid.eRk_insert_eq_add_one, MvPolynomial.aevalTower_comp_toAlgHom, Ideal.pointwise_smul_le_pointwise_smul_iff, one_div_lt_one_div, MeasureTheory.condExpIndL1_disjoint_union, contDiffOn_succ_iff_fderivWithin, ext_iff, MeasureTheory.Lp.inner_fourier_eq, Matrix.mul_invOf_cancel_left, Commute.ofNat_right, MeasureTheory.Integrable.norm_toL1_eq_lintegral_norm, two_mul_le_add_pow_two, mem_doublyStochastic, MeasureTheory.Measure.le_count_apply, DividedPowers.RatAlgebra.dpow_eq_of_mem, Polynomial.MonicDegreeEq.natDegree, MeasureTheory.L1.aestronglyMeasurable_coeFn, HilbertBasis.repr_self, Set.one_lt_encard_iff, nnnorm_commutator_sub_one_le, Coalgebra.rTensor_counit_comul, IsGaloisGroup.fixingSubgroup_bot, Nat.cast_smul_eq_nsmul, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Real.contDiff_rpow_const_of_le, Mathlib.Meta.NormNum.IsNNRat.to_isNat, LinearMap.trace_tensorProduct, Polynomial.derivative_monomial_succ, MeasureTheory.condExpInd_smul', PreTilt.coeff_iterate_frobenius, HahnSeries.C_mul_eq_smul, EReal.exp_lt_one_iff, LaurentPolynomial.single_zero_one_eq_one, MvPowerSeries.WithPiTopology.tendsto_trunc'_atTop, MeasureTheory.L1.setToL1_add_left, add_pow, ContDiffPointwiseHolderAt.contDiffAt, MvPolynomial.pderiv_inr_universalFactorizationMap_X, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup_atBot, Algebra.TensorProduct.natCast_def, NNReal.summable_rpow_inv, NNRat.smul_one_eq_cast, Matrix.natCast_mulVec, PowerSeries.coeff_X_pow_self, IsCyclic.mulAutMulEquiv_symm_apply_symm_apply, Matrix.convex_rowStochastic, MeasureTheory.L2.integrable_inner, RatFunc.single_one_eq_pow, MvPowerSeries.coeff_smul, Subsemiring.coe_matrix, PadicInt.limNthHom_one, hasFTaylorSeriesUpTo_top_iff, TensorProduct.gradedMul_algebraMap, Polynomial.monomial_one_right_eq_X_pow, Matrix.conjTranspose_ofNat_smul, RingHom.map_zero', stdSimplex.add_eq_one, IsGaloisGroup.subgroup, MonomialOrder.leadingCoeff_X, MulSemiringAction.smul_one, Ideal.card_stabilizer_eq_card_inertia_mul_finrank, Finsupp.lift_symm_apply, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, MeasureTheory.isZeroOrProbabilityMeasure_iff, MvPolynomial.instIsPushout_1, Module.End.genEigenspace_div, CompactlySupportedContinuousMap.toReal_smul, Int.log_zpow, PreTilt.untilt_iterate_frobeniusEquiv_symm_pow, ascPochhammer_zero_eval_zero, LinearMap.ringLmapEquivSelf_apply, Submodule.lTensorOne_symm_apply, ascPochhammer_nat_eq_natCast_ascFactorial, ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_add_of_squarefree, AddMonoidAlgebra.liftNC_one, MvPolynomial.mul_monomial_mem_coeffsIn, MeasureTheory.condExp_of_sigmaFinite, AddMonoidAlgebra.scalarTensorEquiv_symm_single, MonoidAlgebra.one_def, Subalgebra.coe_eq_zero, ExpGrowth.expGrowthInf_def, DirectSum.liftRingHom_symm_apply_coe, mdifferentiableAt_mulInvariantVectorField, Polynomial.eval_one, CompleteOrthogonalIdempotents.pair_iff'ₛ, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, MeasureTheory.norm_setToFun_le_mul_norm, pos_invOf_of_invertible_cast, contDiffOn_succ_iff_fderiv_apply, same_add_div, ArithmeticFunction.ppow_zero, Nat.choose_le_pow_div, MeasureTheory.L1.SimpleFunc.norm_eq_integral, MvPolynomial.esymmPart_zero, Algebra.baseChange_lmul, Polynomial.Monic.coeff_natDegree, MeasureTheory.condExpIndL1_of_measure_eq_top, RingHom.charP_iff, MonoidAlgebra.liftNC_smul, edist_le_of_edist_le_geometric_of_tendsto₀, ENNReal.nhdsGT_ofNat_neBot, Subsemiring.toAddSubmonoid_injective, Matrix.toEuclideanLin_apply_piLp_toLp, SemimoduleCat.MonoidalCategory.leftUnitor_inv_apply, LinearGrowth.linearGrowthInf_le_of_eventually_le, add_pow_prime_eq', Set.Ioo.pos, Subalgebra.instIsScalarTowerSubtypeMem, AddAut.mulLeft_apply_apply, LinearGrowth.linearGrowthInf_le_iff, Matrix.trace_permutation, TensorProduct.toLinearMap_symm_lid, Polynomial.coeff_mul_natCast, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, PerfectionMap.surjective, MeasureTheory.L1.SimpleFunc.norm_integral_le_norm, ascPochhammer_eval_succ, ENNReal.exists_inv_nat_lt, contMDiffWithinAt_infty, SkewMonoidAlgebra.support_single_mul_subset, Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson, ENat.floor_natCast_add, contDiff_succ_iff_deriv, SimpleGraph.adjMatrix_mulVec_const_apply_of_regular, IsManifold.instOfNatWithTopENat_1, Module.End.HasUnifEigenvalue.of_mem_spectrum, TensorProduct.tmul_of_gradedMul_of_tmul, LinearGrowth.linearGrowthSup_comp_le, AbsoluteValue.not_isNontrivial_apply, ENat.toENNReal_coe, Monotone.linearGrowthInf_comp_le, Dual.apply_one_mul_eq, Polynomial.TrailingMonic.def, even_iff_two_dvd, EuclideanSpace.dist_eq, ProbabilityTheory.Kernel.measure_eq_zero_or_one_or_top_of_indepSet_self, MeasureTheory.L1.norm_setToL1_le_mul_norm, Submodule.lTensorOne'_one_tmul, Matrix.diagonal_const_mulVec, contDiffOn_succ_iff_derivWithin, Int.clog_natCast, ProbabilityTheory.Kernel.IsProper.setLIntegral_inter_eq_indicator_mul_setLIntegral, MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_weight, ENat.card_eq_one_iff_unique, Commute.natCast_mul_self, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left', Finset.cast_divConst_mul_card, MeasureTheory.Measure.count_apply_finite', MeasureTheory.Measure.dirac_apply, CFC.sqrt_nnrpow_two, AlgEquiv.moduleEndSelf_symm_apply, Unitization.inrRangeEquiv_apply_coe, Dynamics.netMaxcard_univ, exists_add_pow_prime_eq, Monotone.linearGrowthInf_comp_mul, nsmul_eq_mul, Real.toNNReal_coe_nat, Int.nnnorm_natCast, MeasureTheory.lintegral_indicator_one, contMDiffOn_comp_projIcc_iff, Matrix.permMatrix_mem_colStochastic, expChar_of_injective_algebraMap, Real.dimH_segment, EReal.exp_nmul, HahnSeries.C_one, MeasureTheory.diracProba_toMeasure_apply, Bialgebra.comul_one, Int.clog_one_right, Module.End.Eigenvalues.val_mk, SkewMonoidAlgebra.coeff_mul_antidiagonal_of_finset, ENNReal.HolderTriple.one_div_eq, Nat.floor_le, volume_euclideanSpace_eq_dirac, PowerSeries.coe_orderHom, Ideal.pointwise_central_scalar, NNRat.cast_divNat_of_ne_zero, Subsemiring.coe_zero, Nat.preimage_floor_zero, Module.Basis.finTwoProd_zero, StarSubalgebra.one_mem_toNonUnitalStarSubalgebra, PowerSeries.coeff_derivative, instContMDiffAddOfNatWithTopENat, PartENat.some_eq_natCast, ArithmeticFunction.pdiv_zeta, Finset.max_abv_sum_one_le_of_isNonarchimedean, Polynomial.derivative_C_mul_X_pow, Matrix.frobenius_norm_diagonal, QuadraticAlgebra.mk_eq_add_smul_omega, MeasureTheory.norm_condExpInd_le, CFC.sqrt_nnrpow, Metric.lipschitz_infDist, nnnorm_commutator_units_sub_one_le, Matrix.conjTranspose_list_prod, QuadraticAlgebra.re_natCast, MeasureTheory.setToFun_mono_left, ProbabilityTheory.Kernel.eLpNorm_density_le, MvPolynomial.instIsPushout, Matroid.eRk_singleton_eq, Polynomial.hasseDeriv_apply, IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen, PMF.hasSum_coe_one, Pi.linearIndependent_single_one, Polynomial.addSubmonoid_closure_setOf_eq_monomial, height_le_ringKrullDim_quotient_add_spanFinrank, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower, Nat.floor_eq_zero, Matrix.toLinAlgEquiv'_one, OrthonormalBasis.coe_toBasis_repr, IsManifold.instOfNatWithTopENat_2, MeasureTheory.Measure.hausdorffMeasure_le_one_of_subsingleton, Mathlib.Tactic.Ring.pow_prod_atom, Algebra.mem_adjoin_of_map_mul, Matrix.toLin_one, Order.coheight_eq_coe_iff, CategoryTheory.Mat.id_apply, Rat.toNNRat_one, ENNReal.one_lt_coe_iff, SimpleGraph.lt_extremalNumber_iff_of_nonneg, inf_eq_half_smul_add_sub_abs_sub, FreeAlgebra.algebraMap_eq_one_iff, PowerSeries.coeff_X_pow, Ideal.pointwise_smul_toAddSubgroup, geom_sum_succ, ENNReal.nhdsGT_nat_neBot, MulSemiringAction.toAlgHom_apply, Submodule.span_singleton_mul, Mathlib.Tactic.Linarith.natCast_nonneg, MeasureTheory.Measure.rnDeriv_restrict_self, LaurentPolynomial.counit_T, Representation.leftRegular_norm_apply, Odd.add_one, contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn, Finsupp.weight_sub_single_add, ENNReal.tsum_geometric_two_encode_le_two, OrthonormalBasis.sum_repr, ContinuousLinearMap.toSpanSingleton_one_eq_algebraMapCLM, one_div_lt_one_div_of_lt, CharP.of_ringHom_of_ne_zero, Coalgebra.TensorProduct.rid_symm_apply, star_le_one_iff, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, Algebra.TensorProduct.intCast_def, Subsemiring.zero_mem', TensorProduct.mk_surjective, Int.zpow_lt_iff_lt_clog, Nat.lt_ceil, SimpleGraph.adjMatrix_vecMul_apply, hasSum_sq_fourierCoeff, Real.nnnorm_natCast, MvPolynomial.support_esymm'', MeasureTheory.condExpInd_disjoint_union_apply, DirectSum.GAlgebra.commutes, MvPolynomial.instExpChar, ascPochhammer_eval_cast, SkewMonoidAlgebra.single_eq_algebraMap_mul_of, ENat.one_lt_top, convex_doublyStochastic, MvPolynomial.divMonomial_monomial_mul, ENat.floor_sub_one, Submodule.fstL_comp_coe_orthogonalDecomposition, Matrix.mulVec_surjective_iff_exists_right_inverse, NumberField.toNNReal_valued_eq_adicAbv, Finset.expect_dite_eq, PiLp.dist_eq_of_L2, PrimeSpectrum.zeroLocus_singleton_one, Antivary.card_mul_sum_le_sum_mul_sum, odd_iff_exists_bit1, MeasureTheory.L1.setToL1_simpleFunc_indicatorConst, isQuasiregular_iff_isUnit', FiniteField.frobenius_pow, Asymptotics.IsLittleO.natCast_atTop, IsHilbertSum.linearIsometryEquiv_symm_apply_single, WittVector.exists_frobenius_solution_fractionRing_aux, ENat.lt_floor, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left, Set.Icc.coe_eq_one, exists_embedding_euclidean_of_compact, UnitAddTorus.mFourierBasis_repr, MeasureTheory.condExpIndL1Fin_ae_eq_condExpIndSMul, Mathlib.Tactic.RingNF.nat_rawCast_2, Polynomial.Monic.def, Finset.cast_divConst, Subalgebra.natCast_mem, Matrix.isHermitian_one, PMF.uniformOfFinset_apply, Module.Basis.singleton_apply, Matrix.sum_single_natCast, MonomialOrder.Monic.coeff_degree, Nat.le_ceil, fourierBasis_repr, Bialgebra.TensorProduct.rid_symm_apply, PartENat.coe_le_iff, NNRat.cast_lt_one, MeasureTheory.L1.setToL1_zero_left', MeasureTheory.BoundedContinuousFunction.inner_toLp, inf_eq_half_smul_add_sub_abs_sub', MvPolynomial.mem_ideal_span_monomial_image_iff_dvd, NNReal.mk_natCast, ConvexSpace.assoc, emultiplicity_pow_prime_sub_pow_prime, SymAlg.unsym_mul_self, Bialgebra.counit_one, amenable_of_maxAddFoelner_neBot, MeasureTheory.condExpL1_mono, MeasureTheory.L1.norm_Integral_le_one, ContinuousLinearMap.toSpanSingletonLE_symm_apply, MeasureTheory.OuterMeasure.mkMetric'.eq_iSup_nat, LinearMap.toMatrix_singleton, MvPolynomial.aeval_one_tmul, one_add_div, MeasureTheory.Integrable.uniformIntegrable_condExp_filtration, Nat.smul_one_eq_cast, AlgEquiv.apply_faithfulSMul, Submodule.pow_subset_pow, Complex.imCLM_enorm, MonoidAlgebra.isScalarTower_self, MvPowerSeries.monomial_zero_one, MvPowerSeries.monomial_one_eq, Polynomial.UniversalFactorizationRing.factor₁_mul_factor₂, Matrix.ofNat_kronecker, Set.encard_insert_le, NNRat.instIsScalarTowerRight, Nat.pow_le_choose, OrthonormalBasis.coe_toBasis_repr_apply, TensorProduct.lid'_symm_apply, SimpleGraph.radius_top, MvPolynomial.counitNat_C, Polynomial.integralNormalization_coeff, Matrix.mul_one, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRing, DistribMulActionHom.ext_ring_iff, PosNum.one_le_cast, NNReal.summable_schlomilch_iff, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, RingAut.apply_faithfulSMul, ENNReal.lintegral_Lp_add_le_of_le_one, ArithmeticFunction.coe_zeta_mul_comm, Basis.multilinearMap_apply, LinearGrowth.linearGrowthInf_add_le, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atTop, Set.encard_le_one_iff, Cardinal.toENat_le_one, Set.encard_diff_singleton_add_one, OrthonormalBasis.coe_equiv_euclideanSpace, ENNReal.mul_inv_le_one, CompactlySupportedContinuousMap.nnrealPart_smul_pos, SkewMonoidAlgebra.coeff_mul_left, Polynomial.UniversalCoprimeFactorizationRing.factor₁_mul_factor₂, ENNReal.iUnion_Ioc_coe_nat, Matrix.instIsScalarTowerMulOppositeForallOfSMulCommClass, add_comm, PartENat.withTopEquiv_symm_coe, Nat.ceil_natCast, Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, MvPolynomial.IsHomogeneous.sum_X_mul_pderiv, essSup_smul_measure, EuclideanSpace.dist_sq_eq, DirectSum.GAlgebra.map_one, IsCyclic.mulAutMulEquiv_symm_apply_apply, Polynomial.derivative_X_add_C_sq, Commute.add_pow_prime_eq, Order.krullDim_eq_length_of_finiteDimensionalOrder, Complex.ofRealCLM_enorm, Real.toNNReal_lt_natCast, MvPolynomial.monomial_one_dvd_monomial_one, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, MvPolynomial.mul_monomial_modMonomial, MvPolynomial.eval₂_natCast, MvPolynomial.tensorEquivSum_one_tmul_X, ExpGrowth.expGrowthSup_le_iff, PartENat.lt_find, Set.encard_tsub_one_le_encard_diff_singleton, ProbabilityTheory.uniformOn_compl, MvPolynomial.coeffAddMonoidHom_apply, HahnSeries.ofPowerSeries_apply, Coalgebra.lTensor_counit_comp_comul, EuclideanSpace.inner_toLp_toLp, UnitAddTorus.hasSum_sq_mFourierCoeff, GroupAlgebra.mul_average_left, EReal.coe_ennreal_one, ENat.ceil_add_one, Int.toNat_add_toNat_neg_eq_nnnorm, Matrix.vecMul_swap_apply, MvPolynomial.one_coeffsIn, LaurentPolynomial.leftInverse_trunc_toLaurent, contDiff_infty, contMDiffAt_addInvariantVectorField, AbsoluteValue.IsEquiv.one_le_iff, contMDiff_tangentBundleModelSpaceHomeomorph, CategoryTheory.Mat.id_apply_self, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, Order.KrullDimLE.krullDim_le, Set.one_lt_encard_iff_nontrivial, EReal.natCast_div_le, CanonicallyOrderedAdd.list_prod_pos, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, NNReal.exists_nat_pos_inv_lt, Bound.one_lt_div_of_pos_of_lt, IsGaloisGroup.fixedPoints_le_of_le, ENNReal.inv_mul_cancel, Unitization.antilipschitzWith_addEquiv, PEquiv.toMatrix_mul_apply, LocalizedModule.smul_eq_iff_of_mem, ENNReal.natCast_lt_coe, PowerSeries.coe_one, FloorSemiring.gc_floor, SimpleGraph.adjMatrix_mul_self_apply_self, Set.Icc.coe_le_one, Submodule.setSemiring_smul_def, Subsemiring.nonneg_toAddSubmonoid, MeasureTheory.lintegral_nnnorm_condExpIndSMul_le, Subsemiring.toAddSubmonoid_strictMono, Algebra.IsPushout.equiv_symm_algebraMap_right, ringKrullDim_le_ringKrullDim_add_spanFinrank, ProbabilityTheory.measure_condCDF_univ, LaurentPolynomial.smul_eq_C_mul, RingEquiv.unop_map_list_prod, DualNumber.lift_op_smul, ENat.succ_def, AbsoluteValue.IsNontrivial.exists_abv_lt_one, Polynomial.leadingCoeff_X_pow_add_one, PowerSeries.order_X, ENNReal.ofReal_eq_one, MeasureTheory.integrable_condExpIndSMul, DirectSum.decompose_one, ContinuousLinearMap.smulRight_one_one, Finset.prod_natCast, stereographic'_symm_apply, IsFractional.nsmul, Polynomial.evalEval_list_prod, Ring.multichoose_one, tendsto_add_one_pow_atTop_atTop_of_pos, Mathlib.Tactic.RingNF.nat_rawCast_1, SkewMonoidAlgebra.coeff_mul_single_aux, MeasureTheory.Measure.le_dirac_apply, LinearMap.toSpanSingleton_one, MvPolynomial.monomial_sum_one, Nat.cast_pow, Submodule.snd_orthogonalDecomposition_apply, SimpleGraph.adjMatrix_dotProduct, LinearMap.mulLeft_one, ENNReal.one_half_lt_one, Num.cast_mul, IsStarNormal.one_add, MvPolynomial.schwartz_zippel_sum_degreeOf, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, MeasureTheory.eLpNorm'_measure_zero_of_exponent_zero, Polynomial.eval₂_one_cyclotomic_prime_pow, convexComboPair_zero, MeasureTheory.prob_compl_eq_one_sub, AlgHom.toRingHom_toAddMonoidHom, ENNReal.coe_nsmul, MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv, mul_self_tsub_one, Nat.cast_finprod_mem, ceilDiv_le_iff_le_mul, MvPolynomial.totalDegree_smul_le, MeasureTheory.condExpL1_zero, RingEquiv.coe_addMonoidHom_trans, Polynomial.eval₂_reverse_mul_pow, MeasureTheory.Measure.exists_null_set_measure_lt_of_disjoint, Commute.natCast_mul_natCast_mul, EuclideanSpace.coe_measurableEquiv, Polynomial.Monic.nextCoeff_pow, IsNonarchimedean.apply_intCast_le_one_of_isNonarchimedean, Ideal.ncard_primesOver_mul_card_inertia_mul_finrank, SubMulAction.mem_one', ProbabilityTheory.uniformOn_singleton, ProbabilityTheory.IsGaussian.memLp_two_fun_id, AddAut.mulLeft_apply_symm_apply, NNRat.cast_le_natCast, WeakDual.toStrongDual_apply, tendsto_inverse_atTop_nhds_zero_nat, NumberField.mixedEmbedding.euclidean.finrank, PadicInt.nthHomSeq_one, contMDiffAt_infty, Set.Icc.mul_le_right, Polynomial.scaleRoots_zero, Polynomial.derivative_X_add_C_pow, Order.krullDim_eq_one_iff_of_boundedOrder, Set.encard_le_one_iff_eq, Matroid.eRk_le_one_iff, Orthonormal.enorm_eq_one, Fintype.expect_ite_eq', MeasureTheory.L1.SimpleFunc.setToL1S_add, Polynomial.smul_eval, BoxIntegral.unitPartition.volume_box, Basis.equivFun_symm_single, Finset.pluennecke_ruzsa_inequality_pow_mul, WithLp.unitization_mul, MeasureTheory.L1.norm_sub_eq_lintegral, NNRat.addSubmonoid_closure_range_mul_self, ENNReal.HolderConjugate.lt_top_iff_one_lt, SimpleGraph.degMatrix_mulVec_apply, MonoidAlgebra.lift_def, MvPolynomial.scalarRTensor_symm_apply_single, IsLocalization.away_fst, ENNReal.one_lt_ofReal, ENat.floor_eq_zero, ProbabilityTheory.lintegral_gammaPDF_eq_one, Matrix.permanent_eq_one_of_card_eq_zero, EuclideanSpace.nnnorm_eq, selfZPow_neg_natCast, Polynomial.Monic.leadingCoeff, RCLike.nnnorm_natCast, ENNReal.tendsto_nhds_top_iff_nat, PiLp.inner_apply, IsLocalization.invertible_mk'_one_invOf, Module.End.natCast_apply, Perfection.coeff_iterate_frobeniusEquiv_symm, AddMonoidAlgebra.addHom_ext'_iff, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, contMDiff_tangentBundleModelSpaceHomeomorph_symm, Finsupp.range_lmapDomain, MeasureTheory.Measure.pi_empty_univ, Submodule.orthogonalDecomposition_apply, range_modelWithCornersEuclideanHalfSpace, ContinuousMapZero.toNNReal_neg_smul, MeasureTheory.integrable_condExpL1, contDiffOn_succ_of_fderiv_apply, Submodule.instSMulCommClass_1, Monotone.linearGrowthSup_nonneg, Matroid.eRk_singleton_eq_one_iff, PerfectClosure.iterate_frobenius_mk, Submonoid.subsemiringClosure_mem, LinearMap.toMatrix_basis_equiv, MeasureTheory.Integrable.toL1_add, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, Nat.inv_pos_of_nat, RingHom.expChar, SimpleGraph.sum_incMatrix_apply_of_notMem_edgeSet, Nat.Prime.emultiplicity_factorial_mul_succ, exists_sum_eq_one_iff_pairwise_coprime, Mathlib.Tactic.Ring.atom_pf, Nat.floor_one, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left, Nat.lt_of_lt_floor, NNReal.agmSequences_succ', NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne, Set.Ioc.coe_one, MvPolynomial.mem_ideal_span_monomial_image, EuclideanSpace.inner_single_right, Monotone.linearGrowthSup_comp_mul, Finset.pluennecke_ruzsa_inequality_nsmul_sub, Nat.floor_eq_iff', MeasureTheory.LpAddConst_zero, Module.Basis.opNNNorm_le, Polynomial.evalEval_smul, kstar_eq_self, MeasureTheory.setIntegral_condExpL1CLM, MeasureTheory.L1.hasFiniteIntegral_coeFn, CharP.pi, LaurentPolynomial.trunc_C_mul_T, contDiff_norm_rpow, Matrix.single_one_vecMul, DualNumber.algHom_ext'_iff, ENNReal.HolderConjugate.top_one, Monotone.le_linearGrowthSup_comp, tsum_sq_fourierCoeff, Subsemiring.coe_toAddSubmonoid, ENNReal.one_le_coe_iff, Ring.multichoose_succ_succ, MeasureTheory.eLpNorm_condExpL2_le, MeasureTheory.Measure.count_apply_finite, selfZPow_mul_neg, BialgHom.ext_of_ring_iff, four_mul_le_pow_two_add, MonomialOrder.monic_one, LinearMap.trace_comp_comm, ENNReal.inv_three_add_inv_three, WeakSpace.instIsScalarTower, exists_nat_gt, MvPolynomial.coeff_weightedHomogeneousComponent, Submodule.one_le, NNRat.floor_natCast_div_natCast, Nat.cast_choose, charZero_of_expChar_one', MeasureTheory.L1.integral_eq', Matrix.toEuclideanLin_eq_toLin_orthonormal, Order.krullDim_le_one_iff_forall_isMin, MvPolynomial.esymm_zero, Matrix.mem_rowStochastic, DualNumber.eps_mul_eps, Commute.self_natCast_mul_natCast_mul, MvPolynomial.rTensor_apply, ENNReal.iInter_Ioi_coe_nat, AntivaryOn.card_mul_sum_le_sum_mul_sum, MeasureTheory.eLpNorm_one_add_measure, DirectSum.liftRingHom_apply, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, NNReal.summable_condensed_iff, MeasureTheory.Measure.tprod_tprod, star_natCast, RingHom.map_dfinsuppSumAddHom, birkhoffAverage_apply_sub_birkhoffAverage, TensorPower.toTensorAlgebra_galgebra_toFun, AddMonoidAlgebra.lift_unique, Finset.sum_pow, ArithmeticFunction.natCoe_mul, CFC.spectrum_one_eq, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, Nat.cast_tsub, AddMonoidAlgebra.lift_def, EuclideanSpace.measurableEquiv_toEquiv, SemiconjBy.natCast_mul_natCast_mul, ProbabilityTheory.Kernel.trajContent_eq_lmarginalPartialTraj, Polynomial.ringKrullDim_of_isNoetherianRing, Order.height_coe_withBot, stdSimplex.le_one, PMF.pure_apply_self, Matrix.swap_mul_apply_left, ContinuousMapZero.toNNReal_smul, IsGroupLikeElem.one, Matrix.natCast_kronecker_natCast, Submodule.mem_set_smul, Polynomial.eval₂_smul, Subsemiring.smul_closure, EReal.coe_ennreal_nsmul, Submodule.lTensorOne_one_tmul, MvPowerSeries.rescale_one, ENNReal.tsum_geometric, LinearMap.toMatrix'_one, mul_tsub_one, Matrix.one_kroneckerTMul_one, MeasureTheory.eLpNorm_smul_measure_of_ne_zero, NNRat.cast_divNat, MvPolynomial.ringKrullDim_of_isNoetherianRing, PowerSeries.rescale_one, Matrix.cstar_norm_def, Submodule.baseChange_span, MvPolynomial.pderiv_X_self, Set.one_le_encard_iff_nonempty, Set.Ioc.coe_mul, PerfectClosure.eq_iff, ContMDiff.codRestrict_sphere, NNReal.sqrt_mul_le_half_add, Commute.add_pow_prime_eq', MvPowerSeries.trunc'_one, one_le_div, Bialgebra.TensorProduct.lid_symm_apply, Mathlib.Tactic.Ring.toProd_pf, Set.Ico.coe_lt_one, PartENat.natCast_inj, Matrix.vec_mul_eq_vecMul, IsQuasiregular.isUnit_one_add, algebraMap.coe_natCast, ENNReal.add_rpow_le_two_rpow_mul_rpow_add_rpow, MonomialOrder.leadingCoeff_one, inner_matrix_row_row, MeasureTheory.condExpIndSMul_ae_eq_smul, Quaternion.linearIsometryEquivTuple_apply, MeasureTheory.withDensity_indicator_one, LinearMap.toMatrixₛₗ₂'_apply, Polynomial.isScalarTower_right, MvPowerSeries.trunc_C_mul, odd_two_mul_add_one, LinearMap.transvection.baseChange, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, MeasureTheory.Measure.rnDeriv_self, Unitization.lipschitzWith_addEquiv, Module.Basis.coe_ofEquivFun, PolynomialLaw.ground_apply, Matrix.toLinearMapRight'_one, MvPolynomial.restrictSupport_eq_span, RCLike.nnnorm_nsmul, NNRat.cast_lt_natCast, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, MeasureTheory.prob_add_prob_compl, MonoidAlgebra.addHom_ext'_iff, Set.encard_insert_of_notMem, ENNReal.zero_zpow_def, NNRat.cast_natCast, Monotone.expGrowthSup_comp_mul, MeasureTheory.L1.setToL1'_eq_setToL1SCLM, Metric.coveringNumber_singleton, PartENat.lt_coe_succ_iff_le, mfderiv_subtype_coe_Icc_one, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_jacobson, MeasureTheory.condExpIndSMul_smul', permMatrix_mem_doublyStochastic, TensorProduct.one_gradedMul, kstar_zero, WithLp.unitizationAlgEquiv_apply, NNReal.HolderConjugate.inv_add_inv_ennreal, Polynomial.leadingCoeff_X_add_C, ContDiffPointwiseHolderAt.zero_exponent_iff, ENNReal.ofReal_lt_one, SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, TensorProduct.finsuppScalarLeft_symm_apply_single, QuadraticAlgebra.omega_mul_mk, ProbabilityTheory.Kernel.rnDeriv_self, Nat.cast_mul_floor_div_cancel, MeasureTheory.condExpL1_sub, PiLp.norm_eq_of_L2, Nat.mul_cast_floor_div_cancel, Subalgebra.pointwise_smul_toSubmodule, AddMonoidAlgebra.distribMulActionHom_ext'_iff, DividedPowers.prod_dpow, ENNReal.inv_le_one, Bialgebra.mul_compr₂_comul, Matroid.one_le_eRank, Set.encard_diff_singleton_of_mem, ENNReal.natCast_sub, PEquiv.mul_toMatrix_toPEquiv, IsGaloisGroup.card_fixingSubgroup_eq_finrank, Mathlib.Meta.NormNum.NNRat.invOf_denom_swap, DualNumber.snd_mul, AlgEquiv.subalgebraMap_symm_apply_coe, RingHom.coe_addMonoidHom_id, IsManifold.instLEInftyCastWithTopENat, SkewMonoidAlgebra.coeff_single_mul_aux, Subalgebra.one_mem, Polynomial.aeval_natCast, MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le, IsAbsoluteValue.abv_one', Polynomial.aevalTower_comp_toAlgHom, Matrix.vec_mul_eq_mulVec, MvPolynomial.X_divMonomial, Complex.enorm_exp_ofReal_mul_I, MeasureTheory.memLp_one_iff_integrable, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, QuadraticAlgebra.im_natCast, StrictOrderedSemiring.toPosSMulStrictMonoNat, Numbering.dens_prefixed, SetLike.GradeZero.coe_natCast, Pi.mem_span_range_single_inl_iff, Set.Ioc.le_one, tendsto_algebraMap_inv_atTop_nhds_zero_nat, PowerSeries.coeff_one_pow, ENNReal.le_inv_iff_mul_le, pow_sum_div_card_le_sum_pow, Ideal.map_pointwise_smul, Ideal.smul_mem_pointwise_smul_iff, MeasureTheory.L1.integral_sub, MeasureTheory.L1.ofReal_norm_sub_eq_lintegral, Polynomial.coeff_X, TensorProduct.toLinearMap_symm_rid, MvPowerSeries.trunc'_map, MeasureTheory.ContinuousMap.inner_toLp, PiLp.nnnorm_toLp_const, IsStrictOrderedRing.toZeroLEOneClass, Polynomial.evalEval_natCast, PowerSeries.smul_eq_C_mul, MvPolynomial.tensorEquivSum_X_tmul_one, exists_continuous_add_one_of_isCompact_nnreal, Polynomial.smul_X_eq_monomial, PMF.toOuterMeasure_apply_eq_one_iff, Finset.expect_eq_sum_div_card, MonoidAlgebra.liftNC_one, PrimeSpectrum.basicOpen_one, MeasureTheory.L1.SimpleFunc.integral_L1_eq_integral, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_univ_le_one, CharP.charP_iff_prime_eq_zero, contMDiffOn_vectorSpace_iff_contDiffOn, EuclideanSpace.single_eq_zero_iff, Matrix.IsHermitian.mulVec_eigenvectorBasis, Finset.sum_boole, Matrix.l2_opNorm_def, PEquiv.toMatrix_trans, RingHom.codomain_trivial_iff_range_trivial, Subsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMul, MvPowerSeries.le_order_pow, OrthogonalFamily.linearIsometry_apply, matrixEquivTensor_apply, Matrix.toEuclideanLin_toLp, Ideal.toIdeal_homogeneousHull_eq_iSup, TensorProduct.lift_mk_compr₂, MatrixEquivTensor.toFunAlgHom_apply, LinearAlgebra.FreeProduct.lof_map_one, MeasureTheory.Lp.instContinuousFourier, Module.Basis.repr_eq_iff', ENNReal.coe_lt_one_iff, stdSimplexEquivIcc_one, ArithmeticFunction.pmul_zeta, Set.Ico.coe_nonneg, Complex.reCLM_enorm, MeasureTheory.condExpInd_empty, MeasureTheory.condExpL1CLM_smul, add_div_two_lt_right, Manifold.exists_lt_of_riemannianEDist_lt, IsFoelner.amenable, Nat.ceil_eq_iff, Perfection.coeff_iterate_frobenius', Ideal.coe_smul_primesOver, Module.Basis.toMatrix_self, OrthonormalBasis.measurePreserving_measurableEquiv, Matrix.scalar_commute_iff, MeasureTheory.L1.edist_def, ENNReal.coe_natCast, Finset.expect_ite_eq, MeasureTheory.continuous_setIntegral, ENNReal.ofReal_natCast, atTop_hasAntitoneBasis_of_archimedean, SkewMonoidAlgebra.lift_def, Ideal.exists_map_eq_of_isGalois, Ideal.IsMaximal.exists_inv, CharZero.of_module, ENat.one_lt_card, Nat.ofNat_nsmul_eq_mul, MeasureTheory.L1.SimpleFunc.integral_eq_integral, Order.coheight_eq_iSup_gt_coheight, AnalyticAt.analyticOrderAt_sub_eq_one_of_deriv_ne_zero, PMF.toOuterMeasure_uniformOfFintype_apply, LinearGrowth.linearGrowthSup_monotone, Polynomial.isMonicOfDegree_monomial_one, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, QuadraticAlgebra.omega_mul_omega_eq_add, Finset.sum_mul_boole, LinearGrowth.linearGrowthInf_le_linearGrowthSup_of_frequently_le, Ideal.instNormalSubtypeMemSubgroupStabilizerSubgroupOfInertia, EuclideanSpace.nndist_single_same, inTangentCoordinates_model_space, Nat.add_one_le_ceil_iff, SimpleGraph.edist_top_of_ne, ENNReal.HolderConjugate.one_top, mul_two, Algebra.isEpi_iff_forall_one_tmul_eq, LinearGrowth.le_linearGrowthInf_comp, EuclideanSpace.edist_eq, EuclideanSpace.single_apply, ContinuousMapZero.coe_toContinuousMapHom, Pi.orthonormalBasis_repr, MonomialOrder.C_mul_leadingCoeff_monomial_degree, Algebra.TensorProduct.lid_symm_apply, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, MeasureTheory.Measure.rnDeriv_le_one_of_le, LinearMap.toMatrix₂'_apply, Submodule.toSubMulAction_one, Order.krullDim_of_isSimpleOrder, Set.natCast_mem_center, MeasureTheory.condExpIndL1Fin_smul', even_iff_exists_two_mul, Ideal.one_notMem, add_sq', Unitization.unitsFstOne_val_val_fst, pow_add_pow_le', ringKrullDim_le_ringKrullDim_quotSMulTop_succ, WithLp.unitization_norm_inr, Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes, MeasureTheory.charFun_eq_pi_iff, WithLp.unitization_nnnorm_def, NNReal.tendsto_const_div_atTop_nhds_zero_nat, AbsoluteValue.IsNontrivial.exists_abv_gt_one, Nat.cast_pow_eq_one, Matrix.mul_adjp_add_detp, WithLp.prod_norm_eq_of_L2, MvPolynomial.tensorEquivSum_C_tmul_C, Finset.cast_card, Mathlib.Tactic.ENatToNat.coe_one, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, ENNReal.tsum_one, Cardinal.ofENat_one, NNRat.cast_le_ofNat, instCharZeroEReal, PiTensorProduct.algebraMap_apply, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀, Mathlib.Tactic.RingNF.nat_rawCast_0, Matrix.mulVec_one, Matrix.mul_swap_apply_right, contMDiffWithinAt_iff_nat, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atBot, MeasureTheory.L1.integral_eq, Polynomial.coeff_one_zero, Finset.nnratCast_dens_mul_natCast_card, ContractingWith.apriori_edist_iterate_efixedPoint_le, IccRightChart_extend_top, RingHom.coe_addMonoidHom_injective, MvPolynomial.coeff_zero_one, LinearGrowth.le_linearGrowthSup_iff, ExpGrowth.le_expGrowthSup_iff, eq_natCast, half_le_self_iff, IsScalarTower.nnrat, NNRat.den_mul_eq_num, IsGroupLikeElem.mul_antipode_cancel, ENNReal.ofNNReal_natCast_add, Matrix.one_mulVec, MeasureTheory.Lp.fourier_toTemperedDistribution_eq, LaurentPolynomial.instIsScalarTowerPolynomial, IsAddFoelner.amenable, RingEquiv.prodProdProdComm_toAddEquiv, Unitization.inrRangeEquiv_symm_apply, PMF.pure_apply, PartENat.instCharZero, boundary_Icc, ENat.ceil_le_floor_add_one, ringChar.eq_iff, ENNReal.one_lt_inv, Matrix.frobenius_norm_replicateRow, MeasureTheory.charFun_prod, MeasureTheory.L1.setToL1'_apply_coeToLp, Antivary.sum_mul_lt_sum_mul_comp_perm_iff, range_two_mul_add_one, PiLp.edist_eq_of_L1, ENat.natCast_lt_of_coe_top_le_withTop, SchwartzMap.toLp_fourier_eq, Polynomial.UniversalCoprimeFactorizationRing.isCoprime_factor₁_factor₂, Commute.one_div_add_one_div, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, isUnit_two_iff_forall_even, FormalMultilinearSeries.radius_eq_liminf, Finsupp.weight_eq_zero_iff_eq_zero, ContractingWith.edist_efixedPoint_le, Module.Basis.addHaar_self, RingQuot.one_quot, isCoprime_one_left, IsArithFrobAt.conj, SimpleGraph.chromaticNumber_eq_one_iff, Polynomial.scaleRoots_one, MeasureTheory.L1.setToL1_const, EReal.natCast_le_iff, ENNReal.top_zpow_def, Matrix.one_mul, Polynomial.ofFinsupp_nsmul, ENNReal.ofReal_le_natCast, PolynomialLaw.one_tmul_ground_apply', instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, Dynamics.one_le_netMaxcard_iff, MonoidAlgebra.natCast_def, MeasureTheory.norm_condExpIndL1Fin_le, MeasureTheory.prob_compl_eq_zero_iff₀, Matrix.diagonal_comp_single, NNReal.dist_gm_am_le, Polynomial.eval_smul', MeasureTheory.continuous_L1_toL1, Algebra.TensorProduct.rid_symm_apply, Coalgebra.TensorProduct.lid_symm_apply, Module.Basis.repr_self, hasFTaylorSeriesUpToOn_top_iff_add, DiffeologicalSpace.CorePlotsOn.isPlotOn_univ, charZero_of_injective_ringHom, EuclideanSpace.volume_closedBall, MvPolynomial.monomial_one_mul_cancel_right_iff, finrank_euclideanSpace_fin, Commute.add_pow_prime_pow_eq', MeasureTheory.Integrable.edist_toL1_toL1, Nat.cast_inv_le_one, CStarAlgebra.nnnorm_le_natCast_iff_of_nonneg, WithLp.unitization_isometry_inr, charZero_of_injective_algebraMap, one_add_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.L1.setToL1_lipschitz, Algebra.forall_mem_adjoin_smul_eq_self_iff, boundary_product, MeasureTheory.Integrable.toL1_neg, Manifold.exists_lt_locally_constant_of_riemannianEDist_lt, MeasureTheory.norm_condExpL2_le_one, AddMonoidAlgebra.smulCommClass_self, Nat.lt_floor_add_one, ProbabilityTheory.HasGaussianLaw.memLp_two, SkewPolynomial.smul_monomial, Subsemiring.mem_closure_iff, SimpleGraph.edist_eq_one_iff_adj, Polynomial.IsMonicOfDegree.leadingCoeff_eq, MeasureTheory.setToFun_eq, Function.Antiperiodic.nat_odd_mul_antiperiodic, Set.encard_le_one_iff_subsingleton, OrthonormalBasis.repr_reindex, NNRat.cast_lt_ofNat, Nat.one_div_lt_one_div, MeasureTheory.condExpL2_comp_continuousLinearMap, Set.encard_singleton, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, Polynomial.eval₂_list_prod_noncomm, InnerProductSpace.symm_toEuclideanLin_rankOne, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, inCoordinates_tangent_bundle_core_model_space, Polynomial.derivative_apply, Algebra.Extension.Cotangent.ker_mk, tendsto_inv_atTop_nhds_zero_nat, EuclideanSpace.coe_measurableEquiv_symm, HopfAlgebra.antipode_one, Finset.card_mul_cast_divConst, Matrix.op_smul_eq_vecMul, IsGaloisGroup.commutes, Mathlib.Tactic.NoncommRing.mul_nat_lit_eq_nsmul, PosNum.cast_lt, Matrix.one_vecMul_of_mem_colStochastic, Finset.expect_ite_eq', polyEquivTensor_symm_apply_tmul_eq_smul, ENat.lt_coe_add_one_iff, Finset.dens_univ, Finset.cast_addConst, Finset.prod_add_one, IsOrderedRing.toIsOrderedModule, NNReal.agmSequences_succ, Matrix.conjTranspose_ofNat, binomialSeries_radius_ge_one, ENat.card_le_one, Polynomial.le_trailingDegree_X, Subalgebra.one_mem_toNonUnitalSubalgebra, ENNReal.orderIsoIicOneBirational_symm_apply, Finsupp.weight_apply, thickenedIndicatorAux_one_of_mem_closure, le_one_div, lipschitzGroup.conjAct_smul_range_ι, RCLike.wInner_cWeight_eq_smul_wInner_one, AddMonoidAlgebra.toDirectSum_one, Matrix.transposeInvertibleEquivInvertible_apply, AddMonoidAlgebra.one_def, ArithmeticFunction.coe_zeta_mul_apply, NNRat.ofNat_lt_cast, AlgHom.coe_toAddMonoidHom, contMDiff_snd_tangentBundle_modelSpace, MeasureTheory.condExpL2_const_inner, Matrix.transpose_list_prod, CategoryTheory.Mat.id_def, PMF.toMeasure_uniformOfFinset_apply, ringChar.charP, MvPolynomial.weightedHomogeneousComponent_apply, one_dotProduct_one, IsLocalization.mem_span_iff, Polynomial.evalEval_one, BoundedContinuousFunction.nndist_le_two_nnnorm, ContinuousMapZero.coeFnAddMonoidHom_apply, lt_two_mul_self, Subsemiring.mem_inv_pointwise_smul_iff, ContinuousLinearMap.ext_ring_iff, left_lt_add_div_two, Matrix.vecMul_swap, LinearGrowth.le_linearGrowthInf_add, Finsupp.linearIndependent_single_one, Nat.ceil_le, ENNReal.inv_two_add_inv_two, Subsemiring.coe_nonneg, MeasureTheory.Lp.instFourierAdd, one_le_formalMultilinearSeries_geometric_radius, instPerfectRingProd, contDiff_euclidean, IccLeftChart_extend_bot_mem_frontier, PiLp.nndist_eq_of_L2, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, NNRat.den_one, Module.Basis.finTwoProd_one, ProbabilityTheory.Kernel.swap_apply', Ideal.mem_inv_pointwise_smul_iff, instLieGroupOfNatWithTopENat, OrthonormalBasis.tensorProduct_repr_tmul_apply, ENNReal.nhdsGT_one_neBot, RingCon.comap_eq, GradedRing.proj_apply, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, MeasureTheory.lintegral_one, CommSemiring.comul_apply, AddChar.expect_eq_ite, Perfection.frobenius_pthRoot, Quaternion.norm_toLp_equivTuple, Icc_isBoundaryPoint_top, Ideal.pointwise_smul_def, MeasureTheory.Subgroup.index_mul_measure, Nat.cast_commute, MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff, Order.one_lt_height_iff, stdSimplex_eq_inter, Polynomial.card_mahlerMeasure_le_prod, Real.natCast_le_toNNReal, MeasureTheory.norm_setToFun_le, RCLike.inner_eq_wInner_one, Unitization.mem_unitsFstOne, Orientation.measure_orthonormalBasis, Algebra.TensorProduct.lift_includeLeft_includeRight, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, MeasureTheory.measure_sigmaFiniteSetGE_ge, Matrix.invOf_mul_cancel_left, Nat.cast_descFactorial, MeasureTheory.Measure.toSphere_apply_univ', Polynomial.trailingDegree_X, Polynomial.emultiplicity_le_one_of_separable, NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPart, CompleteOrthogonalIdempotents.pair_iffₛ, stdSimplex_unique, Polynomial.coeff_X_add_C_pow, MeasureTheory.condExpL1_eq, MonoidAlgebra.of_apply, MeasureTheory.L1.SimpleFunc.coe_posPart, contMDiffOn_infty, SkewMonoidAlgebra.coeff_single_mul, SimplexCategory.toTopObj_zero_apply_zero, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, PreTilt.coeff_iterate_frobenius', Real.cast_natAbs_eq_nnabs_cast, Polynomial.coeff_list_prod_of_natDegree_le, DualNumber.isNilpotent_eps, ENNReal.le_tsum_schlomilch, MvPolynomial.C_eq_smul_one, Nat.preimage_Ico, PiLp.edist_eq_of_L2, MeasureTheory.Measure.haarMeasure_eq_iff, GradedRing.proj_recompose, HilbertBasis.hasSum_repr_symm, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', ENat.one_le_iff_ne_zero, Algebra.TensorProduct.adjoin_one_tmul_image_eq_top, contDiff_succ_iff_hasFDerivAt, Module.End.hasUnifEigenvalue_iff_hasUnifEigenvalue_one, Submodule.restrictScalars_self, Polynomial.derivative_C_mul_X_sq, MeasureTheory.setToFun_toL1, Unitization.unitsFstOne_val_inv_val_fst, MeasureTheory.condExpL2_indicator_nonneg, AbsoluteValue.exists_lt_one_one_le_of_not_isEquiv, SkewMonoidAlgebra.liftNC_smul, NNReal.bddAbove_range_natCast_iff, instIsManifoldIcc, Unitization.isStarNormal_inr, ENNReal.inv_eq_one, MvPolynomial.monomial_modMonomial, ENat.lt_one_iff_eq_zero, Polynomial.taylor_one, invOf_add_invOf, MeasureTheory.eLpNorm'_exponent_zero, Nonneg.existsAddOfLE, invOf_two_add_invOf_two, ENat.floor_le, MeasureTheory.L1.integral_neg, EMetric.diam_closedBall, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, Matrix.permanent_isEmpty, Polynomial.derivativeFinsupp_X, contDiff_one_iff_deriv, inner_matrix_col_col, instIsPushoutFractionRingMvPolynomial_1, Algebra.TensorProduct.one_def, MeasureTheory.Integrable.uniformIntegrable_condExp, GroupAlgebra.mul_average_right, NNRat.natCast_eq_divNat, Order.krullDimLE_iff, contMDiffOn_projIcc, Cardinal.toENat_eq_one, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left', zero_geom_sum, algebraMap_comp_natCast, DiffeologicalSpace.isOpen_iff_preimages_plots, PMF.ofMultiset_apply, NNReal.summable_rpow, Commute.self_natCast_mul, Finset.max_abv_sum_one_le, Set.Ioo.coe_mul, MeasureTheory.ae_iff_prob_eq_one, BoxIntegral.unitPartition.tag_mem_smul_span, NNRat.num_div_den, ENat.epow_zero, Matrix.sum_row_of_mem_rowStochastic, Algebra.TensorProduct.includeLeftRingHom_apply, contMDiff_circleExp, MeasureTheory.Measure.rnDeriv_le_one_iff_le, contDiffWithinAt_succ_iff_hasFDerivWithinAt, PEquiv.single_mul_single, CFC.nnrpow_two, ENat.one_epow, Matrix.conjTranspose_invOf, SimpleGraph.eccent_top, MeasureTheory.Measure.ae_smul_measure_eq, RingEquiv.moduleEndSelfOp_symm_apply, Mathlib.Tactic.Ring.pow_zero, MvPowerSeries.trunc'_C, ENNReal.rpow_sum_le_const_mul_sum_rpow, Real.natCast_lt_toNNReal, PiLp.nndist_eq_of_L1, ENNReal.toReal_eq_one_iff, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, Polynomial.eval₂_reverse_eq_zero_iff, MvPowerSeries.prod_smul_X_eq_smul_monomial_one, PowerSeries.coeff_one_X, Finset.nonneg_subConst, Submodule.instIsScalarTower, LipschitzWith.dist, SimpleGraph.chromaticNumber_bot, WithLp.prod_antilipschitzWith_ofLp, ProbabilityTheory.Kernel.IsProper.inter_eq_indicator_mul, Submodule.span_smul_of_span_eq_top, AbsoluteValue.map_one, SimpleGraph.edist_le_one_iff_adj_or_eq, MvPowerSeries.trunc'_C_mul, MeasureTheory.eLpNorm_nsmul, MvPolynomial.expand_zero_apply, LinearMap.toLinearMap₂'Aux_toMatrix₂Aux, MeasureTheory.diracProba_toMeasure_apply_of_mem, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', kstar_eq_one, AlgEquiv.apply_smulCommClass, Matrix.toBilin'_single, thickenedIndicatorAux_le_one, Subsemiring.coe_bot, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, Submodule.one_eq_span, Real.volume_emetric_ball, AbsoluteValue.eq_trivial_of_isEquiv_trivial, Perfection.coeff_frobenius, TensorProduct.includeRight_lid, add_self_div_two, IsField.mul_inv_cancel, factorial_mul_ascPochhammer, LinearGrowth.EReal.eventually_atTop_exists_nat_between, MvPolynomial.coe_mapEquivMonic_comp, stdSimplexEquivIcc_zero, Holor.sum_unitVec_mul_slice, instIsPushoutFractionRingMvPolynomial, WithBot.add_one_le_iff, SimpleGraph.incMatrix_mul_transpose_apply_of_adj, Set.Icc.instZeroLEOneClass, MvPolynomial.monomial_mul_modMonomial, LinearGrowth.linearGrowthInf_neg, Metric.coveringNumber_le_one_of_ediam_le, MeasureTheory.L1.SimpleFunc.setToL1S_smul, MvPolynomial.pderiv_inl_universalFactorizationMap_X, LinearEquiv.piRing_apply, SkewMonoidAlgebra.lift_symm_apply, Matrix.one_vecMul_of_mem_rowStochastic, Monotone.le_expGrowthSup_comp, ENNReal.HolderTriple.one_div_add_one_div, LinearMap.IsSymmetric.eigenvectorBasis_def, Matrix.vecMul_one, IsAlgClosed.perfectRing, hasStrictFDerivAt_euclidean, MeasureTheory.L1.norm_eq_integral_norm, Polynomial.toSubring_one, Fintype.expect_eq_sum_div_card, Nat.floor_pos, Ideal.mulQuot_injective, Subsemiring.center.smulCommClass_left, Mathlib.Tactic.Ring.pow_atom, MvPolynomial.rTensorAlgHom_apply_eq

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
add_comm 📖	mathematical	—	AddSemigroup.toAdd AddMonoid.toAddSemigroup AddMonoidWithOne.toAddMonoid toAddMonoidWithOne	—	—

AddMonoidWithOne

Definitions

Name	Category	Theorems
binary 📖	CompOp	—
toAddMonoid 📖	CompOp	1253 math math: OrderRingHom.coe_orderAddMonoidHom_apply, Finset.sum_Ico_add_eq_sum_Ico_add_one, Num.cast_to_int, ZMod.addOrderOf_coe, Matrix.natCast_kronecker, MvPowerSeries.WithPiTopology.tendsto_trunc_atTop, CharP.cast_eq_zero, RingHom.compLeftContinuousBounded_apply_apply, CategoryTheory.DifferentialObject.shiftFunctor_obj_d, Polynomial.smeval_monomial_mul, IntermediateField.aeval_gen_minpoly, RootPairing.four_nsmul_coPolarization_compl_polarization_apply_root, Submonoid.subsemiringClosure_toAddSubmonoid, MvPowerSeries.weightedOrder_monomial, RingHom.map_add', MvPowerSeries.eq_iff_frequently_trunc'_eq, RootPairing.linearIndepOn_root_baseOf', PolyEquivTensor.toFunBilinear_apply_eq_sum, Polynomial.lcoeff_comp_mapAlgHom_eq, Submodule.isScalarTower, Ideal.Quotient.map_ker_stabilizer_subtype, Subsemiring.closure_addSubmonoid_closure, MvPowerSeries.trunc'_trunc', Subring.center.smulCommClass_right, MvPolynomial.rTensor_apply_tmul_apply, AddMonoidAlgebra.liftNC_mul, PowerSeries.heval_C, MvPolynomial.rTensorAlgEquiv_apply, LieAlgebra.IsKilling.restrict_killingForm_eq_sum, Matrix.kronecker_natCast, Nat.cast_succ, AddSubmonoidWithOneClass.toAddSubmonoidClass, SkewMonoidAlgebra.coeff_single_one_mul, Quaternion.star_smul, MvPolynomial.weightedDegree_eq_zero_iff, ZMod.LFunction_stdAddChar_eq_expZeta, Subgroup.HasDetPlusMinusOne.isParabolic_iff_of_upperTriangular, MvPolynomial.universalFactorizationMap_comp_map, MvPolynomial.isScalarTower_right, Ideal.relNorm_smul, Ideal.isHomogeneous_iff_subset_iInter, Polynomial.smul_mem_rootSet, WittVector.verschiebung_zmod, AlgHom.coe_addMonoidHom_injective, Ideal.rank_prime_pow_ramificationIdx, RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraCartanSubalgebra, three_pos, Matrix.mul_mul_left, AddChar.exists_divisor_of_not_isPrimitive, Matrix.transpose_ofNat, WithTop.untop₀_ofNat, NumberField.RingOfIntegers.instSMulDistribClass, Subalgebra.coe_toAddSubmonoid, LieAlgebra.LoopAlgebra.twoCochainOfBilinear_apply_apply, Matrix.natCast_apply, ArithmeticFunction.coe_moebius_mul_coe_zeta, AddMonoidAlgebra.isScalarTower_self, Polynomial.nnqsmul_eq_C_mul, SkewMonoidAlgebra.coeff_single_mul_of_not_exists_mul, Holor.cprankMax_upper_bound, zero_le_three, ZMod.invDFT_apply, AddConstMapClass.map_add_one, Polynomial.homogenize_smul, Algebra.to_smulCommClass, LieModule.traceForm_eq_sum_finrank_nsmul', Polynomial.sum_smul_index', WittVector.eq_iterate_verschiebung, MvPowerSeries.trunc'_expand_trunc', WithTop.untop₀_natCast, Ideal.smul_closure, SkewMonoidAlgebra.single_algebraMap_eq_algebraMap_mul_of, natCast_zero, descPochhammer_succ_comp_X_sub_one, HahnSeries.embDomain_smul, PowerSeries.order_expand, SkewMonoidAlgebra.smul_of, Finsupp.weight_single_one_apply, QuotSMulTop.equivTensorQuot_naturality, Ideal.isHomogeneous_iff_forall_subset, AddSubmonoid.mem_one, RingHomClass.toAddMonoidHomClass, Polynomial.aeval_iterate_derivative_of_ge, ArithmeticFunction.sum_Ioc_mul_zeta_eq_sum, Ideal.mem_pointwise_smul_iff_inv_smul_mem, AddChar.sum_mulShift, Subsemiring.mem_smul_pointwise_iff_exists, instFaithfulSMulNatOfCharZero, stdSimplex_fin_two, Submodule.top_eq_ofList_cons_smul_iff, BoxIntegral.unitPartition.mem_smul_span_iff, RingAut.smul_def, Ideal.exists_smul_eq_of_isGaloisGroup, Module.Basis.isScalarTower_of_nonempty, CategoryTheory.DifferentialObject.d_squared_apply, MonoidAlgebra.liftNC_mul, IsGaloisGroup.fixingSubgroup_top, AlgEquiv.apply_smulCommClass', ZeroLEOneClass.neZero.two, ZNum.of_natCast, SkewMonoidAlgebra.toFinsupp_eq_single_one_one_iff, Finsupp.le_weight_of_ne_zero', Ideal.subset_pointwise_smul_iff, IsGaloisGroup.fixedPoints_top, MvPolynomial.algHom_ext'_iff, Polynomial.natDegree_smul, TensorPower.gMul_eq_coe_linearMap, IsGaloisGroup.mulEquivAlgEquiv_apply_symm_apply, RingCon.comap_bot, Polynomial.iterate_derivative_eq_factorial_smul_sum, Subring.mk_eq_zero, Subsemiring.smul_mem_pointwise_smul_iff, RatFunc.mk_smul, Finset.prod_Ico_mul_eq_prod_Ico_add_one, WittVector.verschiebung_coeff_succ, MvPowerSeries.ext_trunc', IsScalarTower.right, CompactlySupportedContinuousMap.nnrealPart_smul_neg, LinearMap.intrinsicStar_toSpanSingleton, Ideal.LiesOver.smul, AddMonoidHom.coe_smul', PresheafOfModules.Derivation.d_map, Polynomial.C_mul', CategoryTheory.DifferentialObject.shiftFunctor_obj_obj, Matrix.det_le, CharZero.NeZero.two, Module.Basis.toMatrix_smul, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe, SkewMonoidAlgebra.support_one, Matrix.smul_one_eq_diagonal, Polynomial.aeval_sumIDeriv, LieModule.trace_toEnd_genWeightSpace, ZMod.stdAddChar_coe, four_pos, SkewMonoidAlgebra.support_one_subset, Polynomial.aeval_iterate_derivative_self, IntermediateField.isScalarTower, KaehlerDifferential.quotKerTotalEquiv_symm_comp_D, MulSemiringActionHom.map_smulₛₗ, QuotSMulTop.equivTensorQuot_naturality_mk, Subring.mem_pointwise_smul_iff_inv_smul_mem, MvPolynomial.le_weightedTotalDegree, Nonneg.canonicallyOrderedAdd, IsArithFrobAt.mul_inv_mem_inertia, Subalgebra.coe_pointwise_smul, ZMod.completedLFunction_def_even, Submonoid.subsemiringClosure_coe, AddChar.IsPrimitive.zmod_char_eq_one_iff, AddMonoidAlgebra.divOfHom_apply_apply, MulSemiringActionHom.coe_fn_coe', CategoryTheory.DifferentialObject.shiftZero_hom_app_f, Polynomial.trunc_toLaurent, WittVector.iterate_verschiebung_mul, Subalgebra.inclusion.isScalarTower_left, Finsupp.linearCombination_smul, zero_lt_three, Subring.mem_pointwise_smul_iff_inv_smul_mem₀, RingEquiv.toAddMonoidHom_refl, CharTwo.two_nsmul, Mathlib.Tactic.NoncommRing.nat_lit_mul_eq_nsmul, QuotSMulTop.map_comp_mkQ, WittVector.verschiebung_nonzero, LieAlgebra.IsKilling.rootSpace_neg_nsmul_add_chainTop_of_lt, even_two, AddConstMapClass.map_nat, MvPowerSeries.smul_eq_C_mul, MvPowerSeries.trunc_C, Algebra.trace_algebraMap, ZMod.minOrder_of_prime, Polynomial.monic_of_isUnit_leadingCoeff_inv_smul, instSMulCommClassMatrixFinOfNatNatProd, PowerSeries.le_order_smul, AddMonoidAlgebra.uniqueRingEquiv_apply, Polynomial.eval₂_ofFinsupp, AdjoinRoot.smul_mk, MonoidAlgebra.uniqueRingEquiv_apply, CharP.ofNat_eq_zero, AdjoinRoot.evalEval_apply, NonarchimedeanRing.left_mul_subset, MonoidAlgebra.coe_liftNCAlgHom, HomologicalComplex.dgoToHomologicalComplex_obj_d, OrderRingHom.coe_orderAddMonoidHom_id, IsAlgebraic.nsmul, TensorProduct.gradedMul_def, gaussSum_mul, LieAlgebra.SpecialLinear.singleSubSingle_add_singleSubSingle, Finsupp.linearCombination_one_tmul, LinearMap.BilinForm.coeFnAddMonoidHom_apply, DualNumber.inv_eps, MulSemiringAction.toRingEquiv_apply, Ideal.smul_sup, MonoidAlgebra.smulCommClass_self, MonoidAlgebra.instIsPushout, Cardinal.nsmul_lt_aleph0_iff_of_ne_zero, Ideal.Quotient.stabilizerHom_surjective, HahnSeries.single_zero_mul_eq_smul, ZMod.LFunction_def_odd, GradedTensorProduct.auxEquiv_one, Algebra.TensorProduct.basis_repr_tmul, ENat.map_natCast_eq_zero, segment_single_subset_stdSimplex, Submodule.FG.restrictScalars, Subsemiring.smul_mem_pointwise_smul, NeZero.charZero_ofNat, PresheafOfModules.Derivation.postcomp_d_apply, SkewPolynomial.φ_iterate_apply, Ideal.pointwise_smul_subset_iff, MonoidAlgebra.distribMulActionHom_ext'_iff, Polynomial.X_pow_smul_rTensor_monomial, PresheafOfModules.Derivation.d_one, Subsemiring.pointwise_smul_toAddSubmonoid, DoubleCentralizer.norm_def, instIsPushoutFractionRingPolynomial_1, ArithmeticFunction.moebius_mul_coe_zeta, SkewPolynomial.monomial_def, NormMulClass.toNormSMulClass_op, SubsemiringClass.toAddSubmonoidClass, AddMonoidAlgebra.singleZeroRingHom_apply, Finset.natCast_card_filter, Ideal.instCovariantClassHSMulLe, SkewMonoidAlgebra.one_def, MvPowerSeries.weightedOrder_monomial_of_ne_zero, UInt16.toBitVec_nsmul, AddConstMapClass.map_add_nat, TensorProduct.gradedComm_algebraMap_tmul, WeakDual.toStrongDual_inj, ZMod.minOrder, RingHom.toAddMonoidHom_eq_coe, Submodule.instSMulCommClass, MvPolynomial.sumAlgEquiv_comp_rename_inr, NeZero.charZero_one, PowerSeries.coe_smul, MvPolynomial.aevalTower_toAlgHom, Algebra.TensorProduct.basisAux_map_smul, Nat.binCast_eq, Algebra.IsInvariant.exists_smul_of_under_eq, PresheafOfModules.Derivation.d_mul, MvPolynomial.X_mul_pderiv_monomial, WittVector.verschiebung_injective, Subring.coe_matrix, Matrix.instSMulCommClassForall_1, instSMulDistribClassSubtypeMemSubalgebraIntegralClosure, Matrix.GeneralLinearGroup.upperRightHom_apply, two_nsmul_lie_lmul_lmul_add_add_eq_zero, Ideal.range_mul, ZNum.of_intCast, Complex.exp_nsmul, CentroidHom.toEnd_smul, DirectSum.algebraMap_toAddMonoid_hom, FirstOrder.Language.presburger.realize_sum, HomogeneousIdeal.toAddSubmonoid_irrelevant_le, Polynomial.sum_smul_index, MvPowerSeries.trunc'_trunc'_pow, Algebra.directSumGAlgebra_toFun_apply, WeakDual.coe_toStrongDual, gc_floorDiv_mul, QuotSMulTop.map_surjective, FreeLieAlgebra.liftAux_map_smul, Polynomial.smul_eq_C_mul, ZNum.cast_succ, Ideal.under_smul, Module.FinitePresentation.linearEquivMap_symm_apply, AddSubmonoid.natCast_mem_one, Finsupp.coe_pointwise_smul, AddChar.zmod_add, Subfield.coe_zero, CompactlySupportedContinuousMap.exists_add_of_le, DoubleCentralizer.nnnorm_def, Submodule.mul_mem_smul_iff, Matrix.natCast_fin_three, CliffordAlgebra.evenOdd.gradedMonoid, AddGroupWithOne.sub_eq_add_neg, UInt64.toBitVec_nsmul, MvPowerSeries.trunc_one, Subring.coe_pointwise_smul, Finset.cast_card_union, instIsPushoutPolynomial_1, Polynomial.cauchyBound_smul, IsInvariantSubring.smul_mem, MulSemiringActionSemiHomClass.toDistribMulActionSemiHomClass, Finsupp.weight_single, FixedPoints.instSMulCommClassSubtypeMemSubfieldSubfield, MeasureTheory.Measure.coeAddHom_apply, gaussSum_frob, Nat.cast_add_one_pos, CharTwo.two_eq_zero, Matrix.transpose_eq_ofNat, RingCon.ker_comp, Derivation.instAddMonoidHomClass, Ring.uniformContinuousConstSMul, Polynomial.aevalTower_toAlgHom, MatrixEquivTensor.toFunBilinear_apply, NNReal.hasLipschitzAdd, SkewMonoidAlgebra.coeff_mul_single_of_not_exists_mul, QuaternionAlgebra.star_smul', ArchimedeanClass.orderHom_zero, AddGroupWithOne.ext_iff, Ideal.card_stabilizer_eq, Polynomial.smeval_smul, ENNReal.smul_top, Submodule.mem_smul_iff_inv_mul_mem, MonoidAlgebra.singleAddHom_apply, IsNilpotent.exp_smul, FractionalIdeal.coe_nsmul, Polynomial.hasseDeriv_comp, ZMod.toAddCircle_inj, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, ext_iff, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff', ZMod.completedLFunction_def_odd, SkewMonoidAlgebra.coeff_mul_right, OrderedSemiring.toPosSMulMonoNat, prodXSubSMul.smul, QuadraticAlgebra.im_ofNat, AddMonoid.End.smul_apply, MvPowerSeries.le_weightedOrder_pow, isSMulRegular_submodule_iff_right_eq_zero_of_smul, AddMonoidAlgebra.smulCommClass_symm_self, GradedTensorProduct.auxEquiv_symm_one, Ideal.IsPrime.smul_iff, Module.Basis.isScalarTower_finsupp, Ordinal.smul_eq_mul, two_pos, IsGaloisGroup.fixedPoints_fixingSubgroup, Matrix.natCast_fin_two, AlgEquiv.smul_def, UInt32.toBitVec_nsmul, AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.mem_carrier_iff, NeZero.of_not_dvd, DualNumber.isNilpotent_iff_eps_dvd, Polynomial.addHom_ext'_iff, Matrix.det_sum_le, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, WeakDual.isCompact_closedBall, spinGroup.conjAct_smul_range_ι, IsSelfAdjoint.inr, Order.succ_iterate, MvPolynomial.weightedHomogeneousSubmodule_eq_finsupp_supported, MulSemiringAction.toAlgEquiv_symm_apply, Ideal.Quotient.smul_top, three_add_one_eq_four, IsGaloisGroup.fixingSubgroup_le_of_le, Submodule.FG.restrictScalars_iff, Matrix.isAddUnit_mul, charP_iff, PosNum.cast_succ, UInt8.toBitVec_nsmul, IsAddTorsionFree.of_isCancelMulZero_charZero, Finset.card_nsmul_lt_card_nsmul_of_lt_of_le', Polynomial.toFinsupp_nsmul, CategoryTheory.DifferentialObject.d_squared, mul_gaussSum_inv_eq_gaussSum, TensorProduct.gradedComm_algebraMap, Mathlib.Meta.Positivity.pos_of_isNat', ZNum.cast_add, DualNumber.lift_smul, Fin.addRothNumber_eq_rothNumberNat, AddGroupWithOne.zsmul_succ', MvPolynomial.rTensor_apply_X_tmul, Subring.mem_inv_pointwise_smul_iff, IsStrictOrderedRing.toIsStrictOrderedModule, DirectSum.algebraMap_apply, LinearMap.restrictScalars_self, MulSemiringAction.charpoly_eq_prod_smul, Int.cast_add, MulSemiringAction.smul_coeff_charpoly, SubsemiringClass.noZeroDivisors, IsDivSequence.smul, RingEquiv.toAddMonoidMom_commutes, MulSemiringActionHom.map_smul, AddChar.mulShift_unit_eq_one_iff, AddConstMapClass.map_nat_add, traceForm_dualSubmodule_adjoin, TensorPower.galgebra_toFun_def, SkewMonoidAlgebra.single_mul_single, FirstOrder.Language.presburger.realize_natCast, Polynomial.divX_hom_toFun, AddChar.pow_mulShift, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descAddMonoidHom_quotMk, CategoryTheory.DifferentialObject.Hom.comm_assoc, MvPowerSeries.constantCoeff_smul, Subsemiring.noZeroDivisors, MvPolynomial.algebraTensorAlgEquiv_symm_comp_aeval, Ideal.Quotient.stabilizerHom_surjective_of_profinite, PresheafOfModules.Derivation.congr_d, Finsupp.finite_of_nat_weight_le, IsTopologicalSemiring.toIsModuleTopology, MvPolynomial.tensorEquivSum_one_tmul_C, MvPolynomial.rTensor_apply_tmul, AddChar.to_mulShift_inj_of_isPrimitive, Ideal.inertia_le_stabilizer, Polynomial.smul_mem_rootSet_iff, PointwiseConvergenceCLM.equivWeakDual_apply, QuadraticAlgebra.C_natCast, Finset.centerMass_smul_left, instSMulDistribClassAlgEquiv, MulSemiringAction.smul_charpoly, KaehlerDifferential.ker_map, Nat.cast_nonpos, IsGaloisGroup.faithful, IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite, TensorProduct.algebraMap_gradedMul, LinearOrderedField.inducedOrderRingHom_toFun, CategoryTheory.DifferentialObject.shiftZero_inv_app_f, SkewMonoidAlgebra.coeff_one_one, Finsupp.le_weight, Matrix.fin_two_smul_prod, PosNum.cast_to_int, Unitization.inrNonUnitalStarAlgHom_apply, AddChar.zmodChar_apply', IsSMulRegular.submodule, MvPolynomial.IsWeightedHomogeneous.sum_weight_X_mul_pderiv, Algebra.IsInvariant.orbit_eq_primesOver, RingHom.applyFaithfulSMul, Order.IsSuccPrelimit.add_natCast_lt, ZMod.algebraOfModule.proof, Subsemiring.sInf_toAddSubmonoid, DualNumber.exists_mul_left_or_mul_right, Mathlib.Tactic.Ring.smul_eq_cast, Submodule.smul_le_smul, SimpleGraph.IsSRGWith.matrix_eq, IsLocalizedModule.map_linearCombination, Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_det, trace_eq_trace_adjoin, Nat.cast_nonneg', PointwiseConvergenceCLM.equivWeakDual_symm_apply, TensorProduct.gradedComm_one, Submodule.setLike.coe_galgebra_toFun, NumberField.RingOfIntegers.mk_add_mk, ArithmeticFunction.coe_zeta_mul_coe_moebius, AddConstMapClass.map_add_int, Ideal.exact_mulQuot_quotOfMul, ZMod.lift_castAddHom, Subring.mem_smul_pointwise_iff_exists, IsGaloisGroup.fixingSubgroup_fixedPoints, IsGaloisGroup.mulEquivAlgEquiv_apply_apply, IsFractionRing.stabilizerHom_surjective, CharP.addOrderOf_one, AdjoinRoot.smul_of, WithBot.succ_one, Matrix.mul_mul_right, MultilinearMap.freeDFinsuppEquiv_single, WeakDual.isSeqCompact_closedBall, Matrix.convex_colStochastic, HahnModule.instIsScalarTowerHahnSeries_1, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, Polynomial.smul_X, Matrix.ofNat_fin_three, Matrix.GeneralLinearGroup.continuous_upperRightHom, sum_embeddings_eq_finrank_mul, ZMod.lift_comp_coe, Polynomial.coe_smul, Matrix.sum_single_ofNat, Num.cast_succ, MeasureTheory.FiniteMeasure.testAgainstNN_add, Ideal.Quotient.stabilizerHom_apply, Polynomial.smul_eq_map, Subsemiring.smul_mem_pointwise_smul_iff₀, MultilinearMap.freeDFinsuppEquiv_def, CoxeterSystem.lengthParity_comp_simple, Unitization.isSelfAdjoint_inr, HomogeneousIdeal.mem_irrelevant_iff, Ideal.homogeneousHull_eq_iSup, Num.cast_to_nat, MvPolynomial.smulCommClass_right, SkewMonoidAlgebra.domCongr_refl, addRothNumber_le_ruzsaSzemerediNumber, Int.coe_castAddHom, MvPowerSeries.le_weightedOrder_smul, Matrix.transpose_natCast, SymAlg.invOf_sym, GradedTensorProduct.auxEquiv_mul, RingEquiv.coe_addMonoidHom_refl, Matrix.ofNat_fin_two, AddChar.mulShift_apply, Module.FinitePresentation.linearEquivMap_apply, Ideal.mul_homogeneous_element_mem_of_mem, MvPolynomial.rTensorAlgHom_toLinearMap, RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra', ArithmeticFunction.natCoe_one, IsGaloisGroup.fixedPoints_bot, Finset.card_nsmul_lt_card_nsmul_of_le_of_lt', Subsemiring.add_mem', QuotSMulTop.equivQuotTensor_naturality, zero_le_four, Polynomial.smul_eval_smul, MvPowerSeries.le_weightedOrder_subst, Subsemiring.isHomogeneous_iff_subset_iInter, MeasureTheory.smul_extend, MvPowerSeries.trunc'_expand, Algebra.TensorProduct.basisAux_tmul, KaehlerDifferential.derivationQuotKerTotal_apply, AdicCompletion.transitionMap_comp_reduceModIdeal, Num.cast_sub', Subring.smul_closure, SkewMonoidAlgebra.coe_algebraMap, natCast_succ, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, Ideal.coe_restrictScalars, Num.cast_ofZNum, MeasureTheory.Measure.ae_smul_measure_iff, ZMod.toAddCircle_natCast, SkewMonoidAlgebra.liftNC_one, AddMonoidAlgebra.instIsPushout, gc_mul_ceilDiv, IsScalarTower.rat, Algebra.IsInvariant.exists_smul_of_under_eq_of_profinite, ZMod.dft_apply, inr_comp_cfcₙHom_eq_cfcₙAux, bijective_rootsOfUnityAddChar, AddChar.mulShift_mul, CharP.ofNat_eq_zero', Pi.sum_nnnorm_apply_le_nnnorm, Polynomial.eval_iterate_derivative_rootMultiplicity, PosNum.cast_add, AddMonoidAlgebra.instIsPushout', Finsupp.smul_single', Localization.mkAddMonoidHom_apply, MvPowerSeries.trunc_map, Finsupp.weight_single_index, Ideal.Quotient.stabilizerQuotientInertiaEquiv_mk, WittVector.iterate_verschiebung_coeff_eq_zero, MonoidAlgebra.smul_of, Subalgebra.nsmul_mem, AddMonoidHom.ENatMap_apply, AddMonoid.End.isCentralScalar, MultilinearMap.freeFinsuppEquiv_def, Order.IsSuccLimit.add_natCast_lt, Submodule.quotOfListConsSMulTopEquivQuotSMulTopInner_naturality, Polynomial.aeval_smul, LieModule.trace_comp_toEnd_genWeightSpace_eq, TensorProduct.gradedMul_one, MvPowerSeries.coeff_trunc', SkewMonoidAlgebra.coeff_mul, Finset.weightedVSub_const_smul, Submodule.mul_smul_mul_eq_smul_mul_smul, Polynomial.iterate_derivative_X_pow_eq_smul, trace_eq_sum_roots, CategoryTheory.DifferentialObject.shiftFunctorAdd_hom_app_f, WittVector.verschiebung_coeff_zero, IsTopologicalSemiring.toOppositeIsModuleTopology, RatFunc.div_smul, one_add_one_eq_two, WithVal.instIsScalarTower_1, Polynomial.smeval_C_mul, Subsemiring.nsmul_mem, Subring.coe_eq_zero_iff, MvPowerSeries.coeff_weightedHomogeneousComponent, Matrix.smul_eq_mul_diagonal, Subsemiring.center.smulCommClass_right, Submodule.singleton_smul, KaehlerDifferential.kerTotal_map, MonoidAlgebra.liftNC_single, Ring.ascPochhammer_succ_succ, two_nsmul_lie_lmul_lmul_add_eq_lie_lmul_lmul_add, instIsInvariantSubtypeMemSubalgebraSubalgebraSubgroupQuotient, Subalgebra.noZeroDivisors, Complex.ofReal_nsmul, Subsemiring.mem_inv_pointwise_smul_iff₀, AddSubmonoid.pow_eq_closure_pow_set, NumberField.RingOfIntegers.mk_zero, Subalgebra.coe_matrix, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower_1, MvPowerSeries.coeff_trunc, Ideal.coe_smul_primesOver_mk, Polynomial.iterate_derivative_eq_sum, GradedTensorProduct.mulHom_apply, MonoidAlgebra.smul_single', MulSemiringAction.toRingEquiv_symm_apply, Polynomial.wronskianBilin_apply, WittVector.iterate_verschiebung_iterate_frobenius, surjective_rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar, Pi.sum_nnnorm_apply_le_nnnorm', prodXSubSMul.coeff, zero_lt_three', AddConstMapClass.map_add_int', Polynomial.sylvesterDeriv_updateRow, RatFunc.instIsScalarTowerPolynomial, WittVector.verschiebung_mul_frobenius, Holor.slice_unitVec_mul, NNReal.coe_nsmul, AddMonoidAlgebra.singleAddHom_apply, SkewMonoidAlgebra.coeff_mul_antidiagonal_finsum, AddMonoidAlgebra.coe_liftNCAlgHom, MulSemiringActionHom.map_one', IntermediateField.coe_zero, AddChar.mulShift_spec', pinGroup.conjAct_smul_range_ι, QuotSMulTop.map_exact, Equiv.Perm.toList_formPerm_nontrivial, OrderRingHom.toOrderAddMonoidHom_eq_coe, AddChar.zmodChar_apply, AddChar.starComp_apply, MulSemiringAction.smul_mul, WeakDual.isClosed_closedBall, DirectSum.GAlgebra.map_mul, ZMod.LFunction_def_even, ZMod.lift_comp_castAddHom, Subring.smul_mem_pointwise_smul_iff₀, ZMod.exponent, PresheafOfModules.Derivation'.d_app, IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite, Subalgebra.smul_mem_pointwise_smul, SkewMonoidAlgebra.toFinsupp_one, WittVector.ghostComponent_verschiebung, MvPolynomial.coeff_rTensorAlgHom_tmul, PosNum.cast_to_nat, Nat.cast_add, Nat.coe_castAddMonoidHom, AlgEquiv.algHomUnitsEquiv_apply_symm_apply, AddConstMapClass.map_nat', MatrixEquivTensor.invFun_smul, NNRat.addSubmonoid_closure_range_pow, Subalgebra.inclusion.isScalarTower_right, LieAlgebra.toEnd_pow_apply_mem, Polynomial.degree_smul_of_isRightRegular_leadingCoeff, Ideal.quotOfMul_surjective, nsmul_eq_mul', Mathlib.Meta.NormNum.isNat_zero, Ideal.pointwise_smul_eq_comap, PowerSeries.coeff_smul, MeasureTheory.OuterMeasure.coeFnAddMonoidHom_apply, matrixEquivTensor_apply_symm, LieModule.traceForm_eq_sum_finrank_nsmul, QuadraticAlgebra.coe_natCast, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, CategoryTheory.DifferentialObject.objEqToHom_d, RestrictScalars.ringEquiv_map_smul, ContinuousMapZero.toContinuousMapHom_toNNReal, LieModule.exists_genWeightSpace_smul_add_eq_bot, IsDomain.instIsAddTorsionFreeOfCharZero, MultilinearMap.freeFinsuppEquiv_apply, StrictOrderedSemiring.toSMulPosStrictMonoNat, WithBot.succ_zero, IsDiscreteValuationRing.addVal_pow, LinearPMap.map_smul, ZeroLEOneClass.neZero.three, MulSemiringActionHom.map_mul', AddConstMapClass.map_ofNat', Subsemiring.isHomogeneous_iff_forall_subset, Module.Basis.smul_eq_map, SkewMonoidAlgebra.support_mul_single_subset, WittVector.map_verschiebung, instIsPushoutPolynomial, WittVector.verschiebung_frobenius, MonoidAlgebra.instIsPushout', QuadraticAlgebra.coe_ofNat, AddMonoidAlgebra.liftNC_smul, Ring.choose_add_smul_choose, SemiRingCat.FilteredColimits.colimitCoconeIsColimit.descMonoidHom_apply_eq, IsEllDivSequence.smul, GradedTensorProduct.auxEquiv_tmul, Complex.expMonoidHom_apply, Complex.coe_imAddGroupHom, MulSemiringAction.charpoly_eq, Num.cast_succ', AddMonoidAlgebra.liftNC_single, OrderRingHom.coe_coe_orderAddMonoidHom, Int.cast_list_sum, Subalgebra.inclusion.faithfulSMul, MvPowerSeries.le_order_smul, SkewMonoidAlgebra.coeff_mul_single, Matrix.detp_smul_adjp, PowerSeries.le_order_pow, analyticOrderAt_pow, SkewMonoidAlgebra.support_mul, Num.cast_add, CompactlySupportedContinuousMap.toReal_add, Module.FinitePresentation.linearEquivMapExtendScalars_apply, ZMod.lift_coe, nsmul_eq_self, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, PolyEquivTensor.toFunAlgHom_apply_tmul_eq_smul, Matrix.scalar_comm_iff, stabilizer_isOpen_of_isIntegral, AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj, AddMonoid.End.smulCommClass, AddMonoidAlgebra.smul_single', exteriorPower.presentation_relation, SkewMonoidAlgebra.liftNC_mul, CategoryTheory.DifferentialObject.shiftFunctor_map_f, Algebra.trace_algebraMap_of_basis, smulAddHom_apply, AddSubmonoid.one_eq_mrange, FixedPoints.smul_polynomial, AddChar.mulShift_zero, PolyEquivTensor.toFunBilinear_apply_apply, Commute.add_pow', Ideal.IsPrime.smul, Module.End.instSMulCommClass', Complex.instIsAddTorsionFree, Matrix.ofNat_mulVec, PolyEquivTensor.toFunLinear_tmul_apply, ArithmeticFunction.coe_zeta_smul_apply, CoxeterSystem.lengthParity_simple, Polynomial.coeff_iterate_derivative, Module.End.instIsScalarTower, PowerSeries.order_pow, MultilinearMap.freeFinsuppEquiv_single, SkewMonoidAlgebra.coeff_one, MvPowerSeries.weightedOrder_eq_nat, Nat.cast_eq_zero, LieModule.chainTopCoeff_add_one, MvPowerSeries.totalDegree_trunc', ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, HomologicalComplex.dgoToHomologicalComplex_map_f, Ideal.restrictScalars_mul, MvPolynomial.rTensor_symm_apply_single, WittVector.ghostComponent_zero_verschiebung, SkewMonoidAlgebra.single_one_one, Complex.im_nsmul, ENNReal.toReal_nsmul, FractionalIdeal.den_mul_self_eq_num, MvPowerSeries.order_expand, Surreal.nat_toGame, AlgEquiv.subalgebraMap_apply_coe, AddSubmonoid.one_eq_closure, SkewMonoidAlgebra.coeff_mul_single_one, ENNReal.ofReal_nsmul, AddChar.starComp_eq_inv, convex_stdSimplex, Ideal.smul_mem_pointwise_smul, IsSemisimpleModule.exists_end_algEquiv, QuotSMulTop.equivQuotTensor_naturality_mk, CategoryTheory.DifferentialObject.shiftFunctorAdd_inv_app_f, Rat.instIsScalarTowerRight, ZMod.addOrderOf_coe', QuadraticAlgebra.C_ofNat, ZeroLEOneClass.neZero.four, Polynomial.smeval_at_zero, Polynomial.eval_sumIDeriv_of_pos, PowerSeries.constantCoeff_smul, AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div, ValuationSubring.ofPrime_scalar_tower, ZNum.cast_bit0, Submodule.mem_smul_top_iff, MemHolder.nnHolderNorm_nsmul, QuadraticMap.weightedSumSquares_apply, ZNum.cast_bitm1, Submodule.smul_one_eq_span, BitVec.toFin_nsmul, AddConstMapClass.map_int_add, IsGaloisGroup.intermediateField, CategoryTheory.Functor.mapDifferentialObject_obj_d, KaehlerDifferential.derivationQuotKerTotal_lift_comp_linearCombination, AddSubmonoid.one_eq_closure_one_set, Subalgebra.coe_zero, MatrixModCat.isScalarTower_toModuleCat, Subsemiring.coe_pointwise_smul, AddSubmonoid.pow_subset_pow, ZMod.toAddCircle_intCast, Matrix.instIsScalarTowerForall, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, MvPowerSeries.exists_coeff_ne_zero_and_weightedOrder, NNRat.nsmul_coe, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, MultilinearMap.freeDFinsuppEquiv_apply, Polynomial.map_smul, Nat.ofNat_pos', LieAlgebra.LoopAlgebra.residuePairing_apply_apply, SkewMonoidAlgebra.ofFinsupp_eq_one, KaehlerDifferential.kerTotal_mkQ_single_smul, PresheafOfModules.Derivation.d_app, MvPolynomial.rTensor_apply_monomial_tmul, IsIntegral.nsmul, HahnSeries.SummableFamily.binomialFamily_apply, AddSubmonoid.closure_pow, ZMod.toAddCircle_apply, FirstOrder.Language.presburger.realize_nsmul, MonoidAlgebra.uniqueRingEquiv_symm_apply, Ideal.card_inertia_eq_ramificationIdxIn, Submodule.coe_smul, FixedBy.intermediateField_mem_iff, le_floorDiv_iff_mul_le, WeakDual.CharacterSpace.norm_le_norm_one, DualNumber.commute_eps_left, Subsemiring.mem_toAddSubmonoid, MulSemiringAction.toAlgEquiv_apply, RingHom.smul_def, MvPowerSeries.weightedOrder_le, Mathlib.Meta.Positivity.nonneg_of_isNat', LieModule.eventually_genWeightSpace_smul_add_eq_bot, Matrix.smul_eq_mulVec, WittVector.iterate_verschiebung_mul_coeff, Matrix.detp_smul_add_adjp, ZMod.ker_intCastAddHom, OrderedSemiring.toSMulPosMonoNat, Unitization.instIsStarNormal, integralClosure.coe_smul, Subring.coe_zero, AddChar.IsPrimitive.compMulHom_of_isPrimitive, MvPolynomial.support_smul_eq, Ideal.natAbs_det_equiv, ArchimedeanClass.mk_map_of_archimedean, FixedPoints.linearIndependent_smul_of_linearIndependent, TensorProduct.gradedComm_tmul_algebraMap, zero_lt_two', MvPolynomial.tensorEquivSum_X_tmul_X, PiTensorProduct.smul_tprodCoeff', IsNilpotent.exp_eq_sum, IsAddTorsionFree.of_isDomain_charZero, AddMonoidAlgebra.uniqueRingEquiv_symm_apply, Fin.addRothNumber_le_rothNumberNat, MvPolynomial.coeff_rTensorAlgHom_monomial_tmul, Ideal.Quotient.ker_stabilizerHom, Ideal.rank_pow_quot, AddGroupWithOne.neg_add_cancel, ArithmeticFunction.coe_mul_zeta_apply, PresheafOfModules.Derivation'.app_apply, LinearMap.intrinsicStar_smulRight, MvPolynomial.weightedDecomposition.decompose'_eq, Module.End.instSMulCommClass, ProjectiveSpectrum.basicOpen_eq_union_of_projection, MvPolynomial.tensorEquivSum_C_tmul_one, Submodule.restrictScalars.isScalarTower, Finsupp.le_weight_of_ne_zero, Polynomial.factorial_smul_hasseDeriv, WeakDual.instContinuousSMul, QuotientAddGroup.zmultiples_zsmul_eq_zsmul_iff, Subsemiring.coe_closure_eq, Matrix.isAddUnit_detp_smul_mul_adjp, Module.Finite.toModuleEnd_moduleEnd_surjective, Polynomial.eval₂AddMonoidHom_apply, SimpleGraph.degree_eq_sum_if_adj, AddCommMonoid.nat_isScalarTower, ContinuousMapZero.toContinuousMapHom_apply, DirectSum.ringHom_ext'_iff, PolyEquivTensor.toFunBilinear_apply_eq_smul, SkewMonoidAlgebra.natCast_def, MonoidAlgebra.singleOneRingHom_apply, Subring.center.smulCommClass_left, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem, Matrix.instSMulCommClassForall, Ideal.smul_bot, ZMod.lift_injective, cfcₙAux_mem_range_inr, MonoidAlgebra.smulCommClass_symm_self, WithBot.succ_natCast, QuotSMulTop.map_first_exact_on_four_term_exact_of_isSMulRegular_last, Subsemiring.toAddSubmonoid_mono, Surreal.dyadicMap_apply, Multiset.pow_smul_esymm, FreeLieAlgebra.Rel.smulOfTower, Matrix.trace_one, Cardinal.nsmul_lt_aleph0_iff, CategoryTheory.DifferentialObject.Hom.comm, DirectSum.GAlgebra.smul_def, USize.toBitVec_nsmul, MvPowerSeries.coeff_mul_eq_coeff_trunc'_mul_trunc', DualNumber.commute_eps_right, Finset.weightedVSubOfPoint_const_smul, LinearEquiv.isScalarTower, instIsPushoutFractionRingPolynomial, SkewMonoidAlgebra.isScalarTower_self, isConjRoot_iff_orbitRel, AlgebraicClosure.instIsScalarTower, MvPolynomial.aevalTower_comp_toAlgHom, Ideal.pointwise_smul_le_pointwise_smul_iff, ENat.map_natCast_nonneg, WittVector.verschiebung_shift, IsGaloisGroup.fixingSubgroup_bot, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end, LinearMap.trace_tensorProduct, HahnSeries.C_mul_eq_smul, Complex.ofReal_comp_nsmul, HahnSeries.SummableFamily.powerSeriesFamily_of_orderTop_pos, MvPowerSeries.WithPiTopology.tendsto_trunc'_atTop, ZMod.toAddCircle_injective, MvPolynomial.pderiv_inr_universalFactorizationMap_X, Matrix.natCast_mulVec, ZNum.cast_bit1, IsCyclic.mulAutMulEquiv_symm_apply_symm_apply, Matrix.convex_rowStochastic, MvPowerSeries.coeff_smul, Subsemiring.coe_matrix, TensorProduct.gradedMul_algebraMap, RingHom.map_zero', IsGaloisGroup.subgroup, Ideal.Quotient.smulCommClass', MulSemiringAction.smul_one, Ideal.card_stabilizer_eq_card_inertia_mul_finrank, MvPolynomial.instIsPushout_1, CompactlySupportedContinuousMap.toReal_smul, LieModule.traceForm_genWeightSpace_eq, Surreal.zero_toGame, SkewMonoidAlgebra.intCast_def, AddMonoidAlgebra.liftNC_one, Subalgebra.coe_eq_zero, DirectSum.liftRingHom_symm_apply_coe, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, KaehlerDifferential.mvPolynomialBasis_repr_D, MonoidAlgebra.liftNC_smul, Subsemiring.toAddSubmonoid_injective, Even.natCast, AddSubgroup.zsmul_mem_zmultiples_iff_exists_sub_div, Subalgebra.instIsScalarTowerSubtypeMem, AddAut.mulLeft_apply_apply, Matrix.trace_permutation, SkewMonoidAlgebra.support_single_mul_subset, SkewMonoidAlgebra.single_nat, IsEllSequence.smul, TensorProduct.tmul_of_gradedMul_of_tmul, zero_lt_four, Matrix.diagonal_const_mulVec, Subgroup.mem_strictPeriods_iff, MvPowerSeries.ne_zero_iff_exists_coeff_ne_zero_and_weight, Unitization.inrRangeEquiv_apply_coe, nsmul_eq_mul, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, Polynomial.fwdDiff_iter_degree_eq_factorial, AddConstMapClass.map_add_nat', SkewMonoidAlgebra.coeff_mul_antidiagonal_of_finset, QuotSMulTop.map_comp, AddConstMapClass.map_ofNat_add, PowerSeries.coe_orderHom, Ideal.pointwise_central_scalar, FreeLieAlgebra.instIsCentralScalar, Subsemiring.coe_zero, Subring.instNoZeroDivisorsSubtypeMem, Polynomial.rootSet.coe_smul, rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val, MvPolynomial.instIsPushout, Polynomial.addSubmonoid_closure_setOf_eq_monomial, Matrix.instSMulCommClassMulOppositeForallOfIsScalarTower, zero_le_two, Ideal.univ_eq_iUnion_image_add, WittVector.verschiebung_frobenius_comm, MulSemiringAction.toAlgHom_apply, Submodule.span_singleton_mul, ZMod.toCircle_intCast, ZMod.toCircle_natCast, Finsupp.weight_sub_single_add, AddMonoid.End.isScalarTower, Subsemiring.zero_mem', DirectSum.GAlgebra.commutes, SkewMonoidAlgebra.single_eq_algebraMap_mul_of, Polynomial.smul_mem_rootSet_iff_of_isUnit, convex_doublyStochastic, zero_lt_four', RingCon.coe_natCast, ZMod.invDFT_def, WittVector.iterate_verschiebung_mul_left, Matrix.sum_single_natCast, ZMod.injective_toCircle, VectorFourier.fourierIntegral_comp_add_right, RingCon.coe_intCast, Nat.smul_one_eq_cast, WittVector.iterate_verschiebung_coeff, AlgEquiv.apply_faithfulSMul, MonoidAlgebra.isScalarTower_self, AddChar.zmod_zero, Matrix.ofNat_kronecker, NNRat.instIsScalarTowerRight, DistribMulActionHom.ext_ring_iff, RingAut.apply_faithfulSMul, ArithmeticFunction.coe_zeta_mul_comm, CompactlySupportedContinuousMap.nnrealPart_smul_pos, SkewMonoidAlgebra.coeff_mul_left, Matrix.instIsScalarTowerMulOppositeForallOfSMulCommClass, AddCommMonoidWithOne.add_comm, QuaternionAlgebra.star_smul, ZMod.addOrderOf_one, MvPolynomial.IsHomogeneous.sum_X_mul_pderiv, essSup_smul_measure, LieAlgebra.IsKilling.traceForm_coroot, DirectSum.GAlgebra.map_one, IsCyclic.mulAutMulEquiv_symm_apply_apply, Fourier.fourierIntegral_def, Matrix.det_sum_smul_le, Ideal.Quotient.smulCommClass, MvPolynomial.tensorEquivSum_one_tmul_X, LieModule.traceForm_eq_sum_finrank_nsmul_mul, MvPolynomial.coeffAddMonoidHom_apply, LieModule.genWeightSpace_chainTopCoeff_add_one_nsmul_add, AddConstMapClass.map_ofNat, LaurentPolynomial.leftInverse_trunc_toLaurent, PosNum.cast_inj, ZNum.cast_to_int, instSMulCommClassSubtypeMemSubalgebraIntegralClosure, QuotSMulTop.map_apply_mk, Matrix.cramer_smul, IsGaloisGroup.fixedPoints_le_of_le, CoxeterSystem.lengthParity_eq_ofAdd_length, Submodule.setSemiring_smul_def, Subsemiring.nonneg_toAddSubmonoid, Subsemiring.toAddSubmonoid_strictMono, IsLocalRing.ResidueField.residue_smul, ArithmeticFunction.coe_zeta_mul_moebius, LaurentPolynomial.smul_eq_C_mul, DualNumber.lift_op_smul, Ring.descPochhammer_eq_factorial_smul_choose, ZMod.toCircle_apply, autEquivRootsOfUnity_apply_rootOfSplit, Nat.cast_zero, IsFractional.nsmul, SkewMonoidAlgebra.coeff_mul_single_aux, PosNum.cast_sub', SimpleGraph.one_add_adjMatrix_add_compl_adjMatrix_eq_allOnes, Subring.smul_mem_pointwise_smul, fromModuleCatToModuleCatLinearEquiv_apply, CategoryTheory.DifferentialObject.d_squared_assoc, AlgHom.toRingHom_toAddMonoidHom, ENNReal.coe_nsmul, ceilDiv_le_iff_le_mul, MvPolynomial.totalDegree_smul_le, Projectivization.generalLinearGroup_smul_def, fromModuleCatToModuleCatLinearEquiv_symm_apply_coe, RingEquiv.coe_addMonoidHom_trans, Polynomial.Monic.nextCoeff_pow, RootPairing.four_smul_rootForm_sq_eq_coxeterWeight_smul, Ideal.ncard_primesOver_mul_card_inertia_mul_finrank, AddAut.mulLeft_apply_symm_apply, LieAlgebra.IsKilling.rootSpace_two_smul, WeakDual.toStrongDual_apply, Polynomial.scaleRoots_zero, WittVector.verschiebung_coeff_add_one, WithIdealFilter.mem_nhds_iff, Polynomial.smul_eval, FixedPoints.smul, NNRat.addSubmonoid_closure_range_mul_self, MonoidAlgebra.lift_def, nsmul_one, ZMod.toAddCircle_eq_zero, ArithmeticFunction.natCoe_apply, AddMonoidAlgebra.addHom_ext'_iff, CharP.cast_eq_zero_iff, AddConstMapClass.map_add_ofNat, Nonneg.coe_natCast, ContinuousMapZero.toNNReal_neg_smul, Submodule.instSMulCommClass_1, Polynomial.qsmul_eq_C_mul, Submonoid.subsemiringClosure_mem, AddMonoid.End.coe_smul, Num.of_natCast, Module.Basis.opNNNorm_le, Polynomial.evalEval_smul, Polynomial.mirror_smul, LaurentPolynomial.trunc_C_mul_T, WittVector.aeval_verschiebungPoly, FixedPoints.smulCommClass', Subsemiring.coe_toAddSubmonoid, Nat.cast_list_sum, CategoryTheory.DifferentialObject.objEqToHom_d_assoc, IsInvariantSubfield.smul_mem, SkewMonoidAlgebra.ofFinsupp_one, WittVector.verschiebung_isPoly, LinearMap.trace_comp_comm, WeakSpace.instIsScalarTower, MvPolynomial.coeff_weightedHomogeneousComponent, zero_lt_two, Ring.uniformContinuousConstSMul_op, CategoryTheory.DifferentialObject.d_squared_apply_assoc, Finset.card_nsmul_lt_card_nsmul_of_lt_of_le, DualNumber.eps_mul_eps, MvPolynomial.rTensor_apply, TwoSidedIdeal.coe_smul, HomogeneousLocalization.NumDenSameDeg.num_zero, DirectSum.liftRingHom_apply, CliffordAlgebra.GradedAlgebra.lift_ι_eq, RingHom.map_dfinsuppSumAddHom, TensorPower.toTensorAlgebra_galgebra_toFun, ArithmeticFunction.natCoe_mul, AddMonoidAlgebra.lift_def, ArithmeticFunction.vonMangoldt_mul_zeta, Ring.descPochhammer_succ_succ_smeval, ContinuousMapZero.toNNReal_smul, Submodule.mem_set_smul, Polynomial.eval₂_smul, Subsemiring.smul_closure, EReal.coe_ennreal_nsmul, Matrix.intCast_mulVec, Matrix.one_kroneckerTMul_one, Even.intCast, MvPowerSeries.trunc'_one, Polynomial.isScalarTower_right, MvPowerSeries.trunc_C_mul, Complex.re_nsmul, RCLike.nnnorm_nsmul, MonoidAlgebra.addHom_ext'_iff, Nat.cast_add_one, two_add_one_eq_three, TensorProduct.one_gradedMul, IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_mod_eq, Nat.ofNat_nonneg', SymmetricAlgebra.IsSymmetricAlgebra.mvPolynomial, Subalgebra.pointwise_smul_toSubmodule, AddMonoidAlgebra.distribMulActionHom_ext'_iff, Bialgebra.mul_compr₂_comul, IsGaloisGroup.card_fixingSubgroup_eq_finrank, DualNumber.snd_mul, AlgEquiv.subalgebraMap_symm_apply_coe, RingHom.coe_addMonoidHom_id, SkewMonoidAlgebra.coeff_single_mul_aux, MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le, Polynomial.aevalTower_comp_toAlgHom, IntermediateField.forall_mem_adjoin_smul_eq_self_iff, AddConstMapClass.map_add_ofNat', QuotSMulTop.map_id, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, QuadraticAlgebra.im_natCast, StrictOrderedSemiring.toPosSMulStrictMonoNat, Ideal.map_pointwise_smul, Ideal.smul_mem_pointwise_smul_iff, MvPowerSeries.trunc'_map, two_add_two_eq_four, PowerSeries.smul_eq_C_mul, Finset.card_nsmul_lt_card_nsmul_of_le_of_lt, MvPolynomial.tensorEquivSum_X_tmul_one, exists_continuous_add_one_of_isCompact_nnreal, Polynomial.smul_X_eq_monomial, Ideal.quotTorsionOfEquivSpanSingleton_apply_mk, MonoidAlgebra.liftNC_one, AddChar.zmod_intCast, tangentConeAt_eq_univ, Finset.sum_boole, ZMod.instIsScalarTower, MvPowerSeries.le_order_pow, Ideal.toIdeal_homogeneousHull_eq_iSup, TensorProduct.lift_mk_compr₂, MatrixEquivTensor.toFunAlgHom_apply, CliffordAlgebra.GradedAlgebra.ι_sq_scalar, Matrix.GeneralLinearGroup.injective_upperRightHom, Ideal.coe_smul_primesOver, PEquiv.toMatrix_swap, Matrix.scalar_commute_iff, AddGroupWithOne.zsmul_zero', Module.Presentation.tautologicalRelations_relation, FixedPoints.mem_intermediateField_iff, SkewMonoidAlgebra.lift_def, Ideal.exists_map_eq_of_isGalois, Subring.smul_mem_pointwise_smul_iff, ZMod.injective_stdAddChar, smul_inv'', Nat.ofNat_nsmul_eq_mul, NeZero.charZero, ZMod.LFunction_dft, LieModule.coe_chainTop', Ideal.instNormalSubtypeMemSubgroupStabilizerSubgroupOfInertia, AddChar.zmodAddEquiv_apply, gaussSum_mul_gaussSum_eq_card, ContinuousMapZero.coe_toContinuousMapHom, Ideal.Quotient.isScalarTower_right, Order.lt_one_iff_nonpos, Nonneg.orderedSub, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, Nat.cast_pos', Matrix.mul_adjp_add_detp, MvPolynomial.tensorEquivSum_C_tmul_C, DoubleCentralizer.toProdHom_apply, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀, RingHom.coe_addMonoidHom_injective, AddChar.zmod_injective, WittVector.frobenius_verschiebung, IsScalarTower.nnrat, LaurentPolynomial.instIsScalarTowerPolynomial, RingEquiv.prodProdProdComm_toAddEquiv, Unitization.inrRangeEquiv_symm_apply, KaehlerDifferential.kerTotal_map', Antivary.sum_mul_lt_sum_mul_comp_perm_iff, Finset.card_nsmul_le_card_nsmul', Finsupp.weight_eq_zero_iff_eq_zero, Surreal.dyadicMap_apply_pow, ZMod.dft_def, spectrum.vadd_eq, IsArithFrobAt.conj, Rep.barComplex.d_single, Module.Presentation.tautological_relation, Polynomial.ofFinsupp_nsmul, instSMulCommClassQuotientSubgroupSubtypeMemSubalgebraSubalgebra, Matrix.diagonal_comp_single, Polynomial.eval_smul', Nonneg.mk_natCast, exteriorPower.presentation.relations_relation, Fourier.fourierIntegral_comp_add_right, Algebra.forall_mem_adjoin_smul_eq_self_iff, ArithmeticFunction.zeta_mul_vonMangoldt, AddMonoidAlgebra.smulCommClass_self, SkewPolynomial.smul_monomial, Subsemiring.mem_closure_iff, CategoryTheory.Functor.mapDifferentialObject_map_f, Algebra.Extension.Cotangent.ker_mk, Surreal.one_toGame, Matrix.op_smul_eq_vecMul, IsGaloisGroup.commutes, Mathlib.Tactic.NoncommRing.mul_nat_lit_eq_nsmul, polyEquivTensor_symm_apply_tmul_eq_smul, IsOrderedRing.toIsOrderedModule, Finsupp.weight_apply, ZMod.rootsOfUnityAddChar_val, Order.one_le_iff_pos, lipschitzGroup.conjAct_smul_range_ι, Matrix.transpose_eq_natCast, Subring.mem_inv_pointwise_smul_iff₀, ArithmeticFunction.coe_zeta_mul_apply, AlgHom.coe_toAddMonoidHom, MvPolynomial.weightedHomogeneousComponent_apply, ZMod.toCircle_eq_circleExp, ContinuousMapZero.coeFnAddMonoidHom_apply, Subsemiring.mem_inv_pointwise_smul_iff, Matrix.isAddUnit_detp_mul_detp, WithBot.one_le_iff_pos, WithBot.succ_ofNat, Subsemiring.coe_nonneg, AddChar.inv_mulShift, ZMod.stdAddChar_apply, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, Ideal.mem_inv_pointwise_smul_iff, RingCon.comap_eq, Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul, GradedRing.proj_apply, Ideal.pointwise_smul_def, MonovaryOn.sum_mul_comp_perm_lt_sum_mul_iff, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, Complex.coe_reAddGroupHom, SkewMonoidAlgebra.coeff_single_mul, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, DualNumber.isNilpotent_eps, GradedRing.proj_recompose, IsDedekindDomain.selmerGroup.valuation_ker_eq, Submodule.restrictScalars_self, Ring.choose_smul_choose, SkewMonoidAlgebra.liftNC_smul, Unitization.isStarNormal_inr, Nonneg.existsAddOfLE, Polynomial.derivativeFinsupp_X, instIsPushoutFractionRingMvPolynomial_1, BoxIntegral.unitPartition.tag_mem_smul_span, MeasureTheory.Measure.ae_smul_measure_eq, Finset.cast_card_inter, MvPowerSeries.trunc'_C, FixedBy.subfield_mem_iff, Function.support_natCast, IsCyclotomicExtension.Rat.galEquivZMod_smul_of_pow_eq, Finset.card_nsmul_le_card_nsmul, Submodule.instIsScalarTower, Submodule.span_smul_of_span_eq_top, MvPowerSeries.trunc'_C_mul, Ideal.eq_zero_of_polynomial_mem_map_range, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', AlgEquiv.apply_smulCommClass, Module.FinitePresentation.linearEquivMapExtendScalars_symm_apply, LieAlgebra.SpecialLinear.sl_non_abelian, TwoSidedIdeal.coe_mop_smul, Holor.sum_unitVec_mul_slice, instIsPushoutFractionRingMvPolynomial, Valuation.HasExtension.instIsScalarTowerInteger, Polynomial.aeval_sumIDeriv_of_pos, MvPolynomial.pderiv_inl_universalFactorizationMap_X, autEquivRootsOfUnity_smul, Matrix.GeneralLinearGroup.fin_two_smul_prod, Ideal.mulQuot_injective, Subsemiring.center.smulCommClass_left, MvPolynomial.rTensorAlgHom_apply_eq
toNatCast 📖	CompOp	2767 math math: ArithmeticFunction.vonMangoldt.residueClass_eq, Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, ENNReal.exists_nat_mul_gt, Matrix.frobenius_norm_replicateCol, TangentBundle.continuousLinearMapAt_model_space, ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_one, Finset.sum_pow_eq_sum_piAntidiag, LinearGrowth.linearGrowthSup_zero, LinearGrowth.linearGrowthSup_top, Finset.expect_ite_mem, ZMod.addOrderOf_coe, Derivation.map_natCast, DirectSum.IsInternal.isometryL2OfOrthogonalFamily_symm_apply, PiLp.lipschitzWith_toLp, vsub_midpoint, WithLp.prod_inner_apply, LSeries.convolution_one_eq_convolution_zeta, RootPairing.pairing_two_two_iff, ZMod.isUnit_iff_coprime, half_lt_self, Ordinal.lt_omega0_opow_succ, WeierstrassCurve.coeff_Ψ₂Sq, Matrix.natCast_kronecker, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two', PiLp.norm_toLp_const', IsCyclotomicExtension.neZero_of_mem, Bialgebra.comul_natCast, CharP.cast_eq_zero, WittVector.RecursionMain.succNthDefiningPoly_degree, Polynomial.degree_pow_le_of_le, LucasLehmer.X.fst_natCast, ONote.repr_one, AddCircle.exists_gcd_eq_one_of_isOfFinAddOrder, Order.LTSeries.length_le_krullDim, ENNReal.one_lt_two, Nat.cast_comm, ordinaryHypergeometric_sum_eq, Polynomial.derivative_X_sq, QuaternionAlgebra.natCast_re, RootPairing.pairing_smul_root_eq_of_not_linearIndependent, exists_nat_one_div_lt, ENNReal.iUnion_Iio_coe_nat, MeasureTheory.eLpNorm_condExp_le, QuaternionAlgebra.self_add_star, LinearMap.IsSymmetric.inner_map_polarization, Real.toNNReal_lt_natCast', Polynomial.eval₂_one_cyclotomic_prime, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, AddMonoid.End.natCast_apply, Nat.commute_cast, PadicInt.lift_sub_val_mem_span, Real.dimH_of_mem_nhds, EReal.natCast_mul, ExpGrowth.eventually_le_exp, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, Polynomial.coeff_derivative, IsHilbertSum.surjective_isometry, SimpleGraph.deleteFar_iff, SimpleGraph.lapMatrix_toLinearMap₂', dist_midpoint_right, NormedSpace.expSeries_eq_ofScalars, UnitAddTorus.coe_mFourierBasis, RootPairing.coroot_eq_polarizationEquiv_apply_root, RCLike.tendsto_inverse_atTop_nhds_zero_nat, Submodule.orthogonalDecomposition_symm_apply, ENNReal.exists_inv_two_pow_lt, OrthogonalFamily.linearIsometry_apply_single, Finset.card_mul_cast_addConst, Fin.isAddFreimanIso_Iio, Quaternion.coe_natCast, PadicInt.valuation_p, quadraticChar_card_card, SchwartzMap.inner_fourier_toL2_eq, SchwartzMap.toLp_fourierTransformInv_eq, Matrix.kronecker_natCast, Subsemiring.closure_insert_natCast, EuclideanSpace.orthonormal_single, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, Order.krullDim_lt_coe_iff, Nat.cast_factorial, MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral, Nat.cast_descFactorial_two, meromorphicOrderAt_const_ofNat, abs_sub_round, Nat.cast_succ, round_neg_two_inv, Int.cast_natCast, Ordinal.card_le_ofNat, Nat.cast_choose_eq_ascPochhammer_div, LinearGrowth.linearGrowthInf_add_le', tendsto_const_div_atTop_nhds_zero_nat, ENNReal.ofNNReal_add_natCast, WeierstrassCurve.c_relation, Polynomial.coe_lt_degree, EuclideanSpace.closedBall_zero_eq, CharP.cast_eq_mod, Finset.dens_cons, Algebra.normalizedTrace_eq_of_finiteDimensional, WithLp.prod_nndist_eq_of_L2, Submodule.toLinearEquiv_orthogonalDecomposition_symm, OrthonormalBasis.repr_injective, WeierstrassCurve.toCharNeTwoNF_t, Zsqrtd.nonneg_smul, CFC.posPart_natCast, DirichletCharacter.LSeries_eulerProduct_tprod, contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt, LinearGrowth.le_linearGrowthSup_add, round_add_natCast, IncidenceAlgebra.zeta_mul_kappa, ENat.some_eq_coe, SimpleGraph.DeleteFar.le_card_sub_card, Matrix.spectrum_toEuclideanLin, WeierstrassCurve.coeff_preΨ', Ring.multichoose_two, MeasureTheory.lpNorm_fun_div_natCast, MeasureTheory.norm_condExpL2_le, Matrix.cstar_nnnorm_def, parallelogram_law_with_nnnorm, PreTilt.valAux_eq, hasSum_choose_mul_geometric_of_norm_lt_one, NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnreal, tsum_coe_mul_geometric_of_norm_lt_one', lp.inner_eq_tsum, three_pos, norm_natCast_eq_mul_norm_one, HasStrictDerivAt.pow, AddChar.exists_divisor_of_not_isPrimitive, DividedPowers.factorial_mul_dpow_eq_pow, Matrix.l2_opNorm_mulVec, Matrix.transpose_ofNat, not_isUnit_prime_of_dvd_card, ZMod.orderOf_one_add_mul_prime, pow_four_add_four_mul_pow_four', ENat.map_natCast_inj, RootPairing.root_coroot_two, Surreal.nsmul_pow_two_powHalf, Polynomial.MonicDegreeEq.degree, Ordinal.add_right_cancel, CategoryTheory.injectiveDimension_le_iff, ordinaryHypergeometric_radius_top_of_neg_nat₃, aeval_wittPolynomial, WittVector.ghostComponent_verschiebungFun, LinearGrowth.linearGrowthSup_add_le, MeasureTheory.inner_condExpL2_left_eq_right, Matrix.natCast_apply, CharP.natCast_eq_natCast_mod, ascPochhammer_succ_eval, ONote.nf_repr_split', zero_le_three, Polynomial.degree_quadratic_lt, PiLp.norm_toLp_one, LinearMap.IsSymmetric.diagonalization_apply_self_apply, QuaternionAlgebra.star_eq_two_re_sub, PadicInt.appr_spec, IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_pow, Submodule.toLinearEquiv_orthogonalDecomposition, Finset.sum_antidiagonal_choose_succ_mul, SimpleGraph.sum_incMatrix_apply, RCLike.sub_conj, WeierstrassCurve.ofJNe0Or1728_Δ, Nat.floor_eq_iff, Ordinal.succ_one, MeasureTheory.smul_le_stoppedValue_hittingBtwn, DirichletCharacter.LSeries_modOne_eq, WithBot.map_eq_natCast_iff, ENNReal.ofNNReal_natCast_sub, Ideal.natCast_eq_top, FiniteField.isSquare_two_iff, Algebra.TensorProduct.natCast_def', Ring.krullDimLE_iff, WithTop.untop₀_natCast, EuclideanSpace.inner_single_left, ascPochhammer_eval_one, EuclideanSpace.basisFun_toBasis, ENNReal.finset_card_const_le_le_of_tsum_le, Odd.exists_bit1, Finset.mulConst_mul_card, EReal.coe_coe_eq_natCast, sum_hom_units, natCast_zero, Quaternion.normSq_natCast, DiffeologicalSpace.CorePlotsOn.isOpen_iff_preimages_plots, IsCyclotomicExtension.discr_odd_prime, dist_left_midpoint, Finset.card_mul_divConst, contMDiff_addInvariantVectorField, Finset.card_mul_dens, EuclideanSpace.norm_sq_eq, Quaternion.imK_natCast, Int.enorm_natCast, ENNReal.exists_nat_pos_mul_gt, ZMod.exists_sq_eq_prime_iff_of_mod_four_eq_three, toIcoDiv_sub_natCast_mul', Complex.nndist_self_conj, Polynomial.Sequence.degree_eq', ZNum.of_nat_toZNumNeg, NNRat.coe_natCast, Monovary.sum_mul_sum_le_card_mul_sum, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, nnnorm_nsmul_le, geom_sum₂_self, round_two_inv, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, Polynomial.coeff_one_add_X_pow, LinearMap.IsReflective.apply_self_mul_coroot_apply, AddSubmonoid.mem_one, DirichletCharacter.LSeriesSummable_of_one_lt_re, WeierstrassCurve.variableChange_a₁, ENat.natCast_le_of_coe_top_le_withTop, Finset.box_succ_disjUnion, Finset.card_mul_subConst, NumberField.FinitePlace.norm_def', ArithmeticFunction.sum_Ioc_mul_zeta_eq_sum, Nat.cast_pos, AddChar.sum_mulShift, ExpGrowth.expGrowthInf_exp, contMDiff_neg_sphere, Polynomial.derivative_pow_succ, MulChar.map_ringChar, PadicInt.sub_zmodRepr_mem, sum_div_card_sq_le_sum_sq_div_card, tsum_choose_mul_geometric_of_norm_lt_one', two_mul_le_add_sq, Monotone.expGrowthInf_comp_mul, WeierstrassCurve.leadingCoeff_preΨ', PartENat.toWithTop_natCast, Int.cast_div_ofNat_charZero, Function.Antiperiodic.periodic_two_mul, Order.pred_iterate, fact_one_le_two_ennreal, NNReal.sqrt_mul_lt_half_add_of_ne, IsHilbertSum.linearIsometryEquiv_symm_apply, SmoothBumpCovering.exists_immersion_euclidean, Fintype.expect_dite_eq, iteratedDeriv_pow, hasSum_coe_mul_geometric_of_norm_lt_one', RCLike.conj_nat_cast, EuclideanHalfSpace.ext_iff, Nat.floor_div_natCast, PowerSeries.degree_weierstrassMod_lt, Polynomial.degree_eq_natDegree, isUltrametricDist_iff_forall_norm_natCast_le_one, add_pow_prime_pow_eq, EuclideanSpace.basisFun_apply, Rat.cast_mk', NNRat.den_natCast, tsum_coe_mul_geometric_of_norm_lt_one, Nat.preimage_Ioi, WeierstrassCurve.Projective.polynomial_relation, ZeroLEOneClass.neZero.two, ZNum.of_natCast, ENNReal.natCast_lt_top, Finpartition.IsEquipartition.card_biUnion_offDiag_le', HahnSeries.ofPowerSeries_X_pow, MeasureTheory.StronglyAdapted.isStoppingTime_upperCrossingTime, ZMod.natCast_natAbs_valMinAbs, WittVector.factorPowSucc_comp_fontaineThetaModPPow, PadicInt.norm_p_pow, Metric.ediam_closedEBall_le, Commute.ofNat_left, Polynomial.Chebyshev.S_eq_U_comp_half_mul_X, SetTheory.Game.birthday_natCast, Behrend.sphere_subset_preimage_metric_sphere, Real.volume_closedEBall, ZMod.wilsons_lemma, DihedralGroup.r_pow, contMDiff_mulInvariantVectorField, frobenius_natCast, ExpGrowth.expGrowthInf_le_iff, PreTilt.coeff_pow_p, CFC.abs_nnrpow_two, NNRat.cast_def, WeierstrassCurve.ofJ_1728_of_two_ne_zero, Hyperreal.coe_ofNat, WeierstrassCurve.Δ_of_isCharTwoJEqZeroNF, NormedSpace.exp_series_hasSum_exp', Nat.preimage_Iio, Function.Antiperiodic.int_even_mul_periodic, tendsto_nat_floor_mul_atTop, Polynomial.dvd_iterate_derivative_pow, uzpow_natCast, Subsemiring.mem_bot, SimpleGraph.extremalNumber_le_iff_of_nonneg, summable_norm_mul_geometric_of_norm_lt_one, Module.supportDim_add_length_eq_supportDim_of_isRegular, PartENat.lt_find_iff, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, sub_sq, Nat.le_of_ceil_le, DirichletCharacter.LSeries_twist_vonMangoldt_eq, Order.IsSuccLimit.natCast_lt, WittVector.mul_polyOfInterest_aux2, autEquivZmod_symm_apply_natCast, Matrix.IsHermitian.eigenvalues_eq, nndist_midpoint_right, WeierstrassCurve.Jacobian.eval_polynomialY, Nat.WithBot.add_eq_two_iff, RootPairing.coxeterWeightIn_eq_four_iff_not_linearIndependent, iter_deriv_zpow', IsSl2Triple.lie_lie_smul_f, QuaternionAlgebra.natCast_im, lineMap_inv_two, NNReal.agmSequences_zero, LinearGrowth.le_linearGrowthSup_add', inv_natCast_smul_eq, quadraticChar_two, CStarAlgebra.norm_le_natCast_iff_of_nonneg, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, two_inv_lt_one, MeasureTheory.Lp.instFourierInvSMul, round_eq_div, Real.contDiffAt_rpow_const_of_le, DirichletCharacter.LFunction_eq_LSeries, PartENat.coe_lt_coe, Algebra.adjoin_insert_natCast, CharZero.NeZero.two, RingOfIntegers.exponent_eq_sInf, WeierstrassCurve.ofJNe0Or1728_c₄, Matrix.map_mul_natCast, Prod.fst_natCast, Matrix.PosSemidef.natCast, Matrix.conjTranspose_natCast_smul, ENat.ceil_add_natCast, Polynomial.derivative_monomial, OrthonormalBasis.repr_self, IntermediateField.natCast_mem, toIocMod_sub_natCast_mul', PadicComplex.coe_natCast, LinearGrowth.linearGrowthInf_bot, ZMod.val_natCast_of_lt, DirichletCharacter.norm_LSeries_product_ge_one, Ring.choose_eq_smul, Surreal.zsmul_pow_two_powHalf, PairReduction.card_pairSetSeq_le_logSizeRadius_mul, MeasureTheory.L2.inner_def, GenContFract.succ_nth_fib_le_of_nth_den, Nat.cast_ascFactorial, div_two_sub_self, add_halves, Icc_isBoundaryPoint_bot, Metric.ediam_thickening_le, Nat.preimage_Ici, ProbabilityTheory.evariance_lt_top_iff_memLp, Function.Antiperiodic.int_odd_mul_antiperiodic, four_pos, Finset.divConst_mul_card, PadicInt.irreducible_p, EuclideanSpace.nndist_eq, WeierstrassCurve.leadingCoeff_preΨ₄, Nat.one_div_le_one_div, IsPrimitiveRoot.prod_one_sub_pow_eq_order, WittVector.factorPowSucc_fontaineThetaModPPow_eq, Fintype.expect_ite_eq, WeierstrassCurve.b₂_of_isCharThreeJNeZeroNF, stereographic'_source, MvPolynomial.schwartz_zippel_totalDegree, contMDiff_infty, AbsoluteValue.eq_on_nat_iff_eq_on_int, Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence, jacobiSum_trivial_trivial, Nat.cast_multiset_sum, contDiffOn_nat_iff_continuousOn_differentiableOn_deriv, ZMod.natCast_eq_one_iff_odd, toIcoMod_add_natCast_mul, OrthonormalBasis.measurePreserving_repr, Matrix.charpoly_natCast, FirstOrder.Field.realize_eqZero, Order.le_krullDim_iff, PMF.toMeasure_ofMultiset_apply, dvd_geom_sum₂_iff_of_dvd_sub, Nat.cast_withTop, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, SchwartzMap.inner_toL2_toL2_eq, IncidenceAlgebra.zeta_mul_zeta, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, PMF.uniformOfFinset_apply_of_mem, ZMod.natCast_self, PiLp.nnnorm_eq_of_L2, Cardinal.preAleph_nat, Finset.mulConst_le_card, Nat.abs_cast, half_pos, NNReal.half_le_self, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, DirichletCharacter.LFunction_changeLevel, Matrix.IsHermitian.eigenvectorUnitary_col_eq, Metric.PiNatEmbed.edist_def, AddChar.sum_eq_ite, QuadraticAlgebra.nsmul_mk, zero_lt_three, Fintype.expect_ite_zero, IsNonarchimedean.apply_natCast_le_one_of_isNonarchimedean, NormedSpace.expSeries_apply_eq_div', SimpleGraph.farFromTriangleFree_iff, Nat.lt_succ_floor, Num.cast_bit0, ENat.map_coe_nnreal, ArchimedeanClass.mk_natCast, SchwartzMap.toLp_fourierInv_eq, PartENat.lt_coe_iff, ZMod.not_isUnit_of_mem_primeFactors, LinearGrowth.linearGrowthSup_bot, ZMod.cast_eq_val, Matrix.toEuclideanLin_apply, WeierstrassCurve.b₈_of_isCharNeTwoNF, Finset.expect_ite_zero, even_two, IsHilbertSum.hasSum_linearIsometryEquiv_symm, AddConstMapClass.map_nat, WeierstrassCurve.Projective.dblU_eq, ENat.floor_add_natCast, MeasureTheory.memLp_two_iff_integrable_sq_norm, mfderivWithin_projIcc_one, WithBot.lt_add_one_iff, Nat.cast_sub, SetTheory.PGame.quot_natCast, contDiffWithinAt_nat, ZMod.natCast_zmod_surjective, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, PadicInt.maximalIdeal_eq_span_p, Finset.card_mul_addConst, Nat.floor_add_natCast, EuclideanSpace.norm_single, Matrix.conjTranspose_natCast, Metric.coveringNumber_two_mul_le_externalCoveringNumber, Nat.cast_nonneg, CHSH_inequality_of_comm, Euclidean.closedBall_eq_image, LinearGrowth.linearGrowthInf_biInf, PadicInt.norm_lt_one_iff_dvd, MeromorphicOn.divisor_natCast, Submodule.coe_orthogonalDecomposition_symm, MeasureTheory.aestronglyMeasurable_condExpL2, ZMod.eq_zero_iff_even, Ideal.absNorm_mem, Ordinal.one_add_ofNat, Fintype.expect_dite_eq', FiniteField.cast_card_eq_zero, Quaternion.linearIsometryEquivTuple_symm_apply, Int.self_le_zpow_clog, exists_add_pow_prime_pow_eq, add_sq, GaussianInt.natCast_natAbs_norm, Pi.counit_eq_adjoint, Polynomial.eval_natCast_map, WithLp.prod_dist_eq_of_L2, ZMod.LFunction_eq_LSeries, Finset.card_div_choose_le_card_shadow_div_choose, Polynomial.ofFinsupp_natCast, round_natCast, Icc_isInteriorPoint_interior, Ordinal.nat_nadd, PosNum.of_to_nat, IsPrimitiveRoot.not_exists_int_prime_dvd_sub_of_prime_ne_two, monotoneOn_descPochhammer_eval, LDL.lowerInv_orthogonal, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, contDiffOn_infty, ENNReal.half_lt_self, NNReal.natCast_iInf, FloorSemiring.tendsto_mul_pow_div_factorial_sub_atTop, Lagrange.eq_interpolate_iff, Polynomial.derivative_eval, AddConstMapClass.map_sub_nat', WeierstrassCurve.ofJ0_Δ, ENat.map_natCast_eq_zero, ExpGrowth.expGrowthSup_def, tangentBundle_model_space_coe_chartAt, toIocMod_sub_natCast_mul, WithBot.ofNat_eq_map_iff, LieAlgebra.Orthogonal.jb_transform, NormedSpace.exp_eq_tsum, DirichletCharacter.mul_delta, NeZero.charZero_ofNat, ENNReal.iInter_Ici_coe_nat, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, Finset.sum_indicator_mod, MeasureTheory.condExpL2_indicator_ae_eq_smul, mfderivWithin_comp_projIcc_one, Real.enorm_natCast, Int.floor_natCast, contDiff_iff_forall_nat_le, LucasLehmer.X.ofNat_fst, PadicInt.exists_mem_range, Finset.local_lubell_yamamoto_meshalkin_inequality_div, contDiffWithinAt_euclidean, Polynomial.degree_X_pow_add_C, PreTilt.mk_comp_untilt_eq_coeff_zero, Real.dimH_univ_eq_finrank, one_geom_sum, DirichletCharacter.eval_modulus_sub, even_neg_two, Real.not_summable_indicator_one_div_natCast, contMDiffAt_mulInvariantVectorField, Finset.natCast_card_filter, ENat.map_natCast_strictMono, NormedSpace.exp_eq_tsum_div, AddConstMapClass.map_add_nat, toIocDiv_natCast_mul_add, sub_half_lt_round, Nat.preimage_Ioc, Polynomial.Chebyshev.leadingCoeff_U_natCast, Finset.divConst_le_card, WittVector.mk_pow_fontaineTheta, UnitAddTorus.mFourierCoeff_toLp, PowerSeries.degree_trunc_lt, PiCountable.min_edist_le_edist_pi, EuclideanSpace.volume_closedBall_fin_three, IccLeftChart_extend_interior_pos, Polynomial.card_roots_map_le_degree, PreTilt.coeff_frobeniusEquiv_symm, PiCountable.edist_eq_tsum, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, MeasureTheory.exists_isSigmaFiniteSet_measure_ge, ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, ProbabilityTheory.IsGaussian.memLp_two_id, Nat.binCast_eq, Hamming.nndist_eq_hammingDist, Matrix.IsHermitian.eigenvectorUnitary_mulVec, ZMod.exists_sq_eq_two_iff, Cubic.degree_of_a_eq_zero', toIocMod_natCast_mul_add, PartENat.get_natCast, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, NNRat.mul_den_eq_num, MvPolynomial.degree_optionEquivLeft, RootPairing.Base.cartanMatrixIn_apply_same, Matrix.frobenius_nnnorm_one, Nat.preimage_Icc, NeZero.of_faithfulSMul, HasDerivAt.pow, OrthonormalBasis.prod_apply, PiLp.nnnorm_toLp_one, ContinuousMap.HomotopyRel.trans_apply, Nat.ceil_lt_add_one_of_gt_neg_one, ZMod.χ₈'_nat_eq_if_mod_eight, MeasureTheory.integral_condExpL2_eq, SimpleGraph.dotProduct_mulVec_degMatrix, Int.floor_div_natCast, mdifferentiableAt_addInvariantVectorField, QuadraticForm.polarBilin_tmul, ENNReal.exists_nat_gt, EReal.exists_nat_ge_mul, Ordinal.natCast_mul_omega0, archimedean_iff_nat_le, Nat.mono_cast, Finset.cast_subConst_mul_card, Subring.closure_singleton_natCast, Nat.le_floor_iff', WeierstrassCurve.b₂_of_isCharTwoJNeZeroNF, EuclideanSpace.dist_single_same, PairReduction.pow_logSizeRadius_le_card_le_logSizeRadius, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_ne_two, Module.Basis.coe_toOrthonormalBasis_repr, DividedPowers.dpow_comp, orthonormal_fourier, Polynomial.C_eq_natCast, Nat.cast_div_charZero, MeasureTheory.setIntegral_condExpL2_indicator, contMDiff_coe_sphere, AddChar.sum_eq_card_of_eq_one, Polynomial.derivative_X_sub_C_sq, DirichletCharacter.sum_characters_eq, ENNReal.natCast_le_ofNNReal, Nat.preimage_Ioo, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, WeierstrassCurve.b₂_of_isCharNeTwoNF, PartENat.le_coe_iff, HasDerivAt.fun_pow, ArithmeticFunction.vonMangoldt.residueClass_apply, Polynomial.Splits.degree_eq_card_roots, Nat.preimage_floor_of_ne_zero, WeierstrassCurve.Jacobian.polynomialY_eq, logDeriv_fun_pow, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, AddSubmonoid.natCast_mem_one, ZMod.natCast_self', CFC.abs_nnrpow, MeasureTheory.lpNorm_mul_natCast, LinearGrowth.linearGrowthInf_top, Ring.choose_neg, LinearMap.trace_one, Ordinal.natCast_sub, QuadraticMap.associated_apply, WeierstrassCurve.Jacobian.eval_polynomialX, NormedSpace.expSeries_sum_eq, Cubic.degree_of_a_ne_zero', WeierstrassCurve.c₆_of_isCharThreeJNeZeroNF, Int.cast_two, ZMod.natCast_rightInverse, FloorSemiring.tendsto_pow_div_factorial_atTop, Matrix.natCast_fin_three, Padic.valuation_p, tendsto_one_div_add_atTop_nhds_zero_nat, WeierstrassCurve.Projective.eval_polynomialX, Polynomial.eval₂_natCast, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, CFC.nnrpow_sqrt_two, Matrix.PosDef.natCast, ENNReal.iUnion_Iic_coe_nat, PowerSeries.mk_add_choose_mul_one_sub_pow_eq_one, WeierstrassCurve.toCharNeTwoNF_s, NNRat.toNNRat_coe_nat, Finset.cast_card_union, NNReal.natCast_natAbs, IsPrimitiveRoot.coe_autToPow_apply, WeierstrassCurve.variableChange_b₈, Polynomial.eval_natCast, Nat.cast_pred, PiLp.volume_preserving_toLp, InnerProductGeometry.norm_toLp_symm_crossProduct, Finset.pluennecke_ruzsa_inequality_nsmul_add, Nat.ofDigits_one_cons, MeasureTheory.condExpIndSMul_empty, zmod_val_inv_nsmul_nsmul, MeasureTheory.charFun_eq_prod_iff, Polynomial.degree_quadratic, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, PadicInt.norm_natCast_zmodRepr_eq_one_iff_ne, Int.zpow_le_iff_le_log, midpoint_eq_smul_add, Int.cast_neg_natCast, AbsoluteValue.apply_nat_le_self, CharP.natCast_gcdA_mul_intCast_eq_gcd, minpoly.degree_le, DirichletCharacter.LSeriesSummable_mul, EReal.coe_natCast, contDiff_all_iff_nat, midpoint_sub_right, Mathlib.Tactic.Bound.Nat.one_le_cast_of_le, Mathlib.Tactic.Zify.Nat.cast_sub_of_add_le, Nat.cast_add_one_pos, Ordinal.iSup_add_nat, WeierstrassCurve.Affine.slope_of_Y_ne, NonUnitalSubsemiring.unitization_apply, CharTwo.two_eq_zero, RCLike.ofReal_natCast, Matrix.transpose_eq_ofNat, IsCyclotomicExtension.Rat.p_mem_span_zeta_sub_one, Int.ceil_sub_natCast, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1, xInTermsOfW_eq, LinearGrowth.linearGrowthInf_const_mul_self, Finset.sum_choose_succ_mul, Hamming.nnnorm_eq_hammingNorm, WeierstrassCurve.c₄_of_isCharThreeJNeZeroNF, IsSl2Triple.HasPrimitiveVectorWith.exists_nat, OrthonormalBasis.coe_ofRepr, PowerSeries.IsWeierstrassDivisionAt.degree_lt, Function.Periodic.nat_mul, PartENat.not_isMax_natCast, Polynomial.smeval_neg_nat, EuclideanSpace.nnnorm_single, PairReduction.card_le_logSizeRadius_le_pow_logSizeRadius, Quaternion.star_eq_two_re_sub, Complex.orthonormalBasisOneI_repr_apply, PadicInt.mahlerSeries_apply_nat, Real.volume_emetric_closedBall, Commute.exists_add_pow_prime_pow_eq, WeierstrassCurve.Affine.slope_of_Y_ne', MeasureTheory.norm_condExpL2_coe_le, WeierstrassCurve.b₆_of_isCharTwoJNeZeroNF, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, Real.toNNReal_ofNat, Ordinal.nat_le_card, Polynomial.degree_cubic_lt, IsCyclotomicExtension.Rat.inertiaDegIn_of_not_dvd, Nat.Partition.hasProd_powerSeriesMk_card_countRestricted, SimpleGraph.farFromTriangleFree.le_card_sub_card, WeierstrassCurve.leadingCoeff_Ψ₂Sq, Quaternion.im_natCast, Matrix.conjTranspose_inv_natCast_smul, ZMod.natCast_pow_eq_zero_of_le, WeierstrassCurve.Δ_of_char_three, PowerSeries.mk_one_pow_eq_mk_choose_add, ENNReal.iSup_natCast, NeZero.nat_of_injective, map_ofNat, Quaternion.star_add_self, mdifferentiable_mulInvariantVectorField, RootPairing.EmbeddedG2.twoShortAddLongRoot_eq, DirichletCharacter.LSeries_changeLevel, SchwartzMap.norm_fourier_toL2_eq, WeierstrassCurve.Jacobian.polynomial_relation, Int.cast_natAbs, Asymptotics.isEquivalent_nat_ceil, PowerSeries.coeff_derivativeFun, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, Path.Homotopy.hcomp_apply, MeasureTheory.Lp.instFourierPair, NNReal.rpow_sum_le_const_mul_sum_rpow, IsUnit.natCast_factorial_iff_of_charP, Real.dimH_univ_pi_fin, Nat.one_le_cast, norm_natCast, IsPrimitiveRoot.sub_one_norm_isPrimePow, NeZero.nat_of_neZero, Odd.natCast_zmod_two, Ordinal.natCast_opow, Matrix.toEuclideanCLM_toLp, abs_sub_round_div_natCast_eq, hasSum_fourier_series_L2, Matrix.charpoly_degree_eq_dim, natCast_mem, Commute.add_pow_prime_pow_eq, one_le_two', Real.dimH_ball_pi, CategoryTheory.injectiveDimension_ge_iff, Fin.isAddFreimanIso_Iic, FractionalIdeal.coe_natCast, deriv_pow, two_smul, Nat.castOrderEmbedding_apply, contDiffOn_nat_iff_continuousOn_differentiableOn, Padic.norm_natCast_lt_one_iff, BoundedContinuousFunction.coe_natCast, two_mul, Ordinal.smul_eq_mul, MeasureTheory.eLpNorm_one_le_of_le', LinearGrowth.linearGrowthInf_zero, WeierstrassCurve.Projective.polynomialZ_eq, Semiring.toGrindSemiring_ofNat, Metric.packingNumber_two_mul_le_externalCoveringNumber, PiLp.nnnorm_toLp_const', Polynomial.eval_monomial_one_add_sub, CharP.natCast_injOn_Iio, two_pos, Num.to_of_nat, tsum_pow_div_one_sub_eq_tsum_sigma, MeasureTheory.Measure.toSphere_apply_univ, Nat.floor_natCast, Matrix.natCast_fin_two, ZMod.val_inv_mul, HilbertBasis.hasSum_repr, Finpartition.IsEquipartition.sum_nonUniforms_lt', meromorphicOrderAt_const_natCast, WithLp.prod_edist_eq_of_L2, ZMod.valMinAbs_natCast_of_le_half, MeasureTheory.condExpIndSMul_smul, AddConstMapClass.map_nat_add', toIocMod_add_natCast_mul', hasDerivWithinAt_pow, Int.lt_zpow_iff_log_lt, Padic.norm_p_pow, MeasureTheory.lintegral_nnnorm_condExpL2_le, Padic.norm_p_lt_one, PadicInt.norm_ascPochhammer_le, Nat.cast_dvd_cast, star_natCast_smul, Ideal.iInf_span_singleton_natCast, Fintype.card_mul_expect, SchwartzMap.norm_fourierTransformCLM_toL2_eq, natCast_floor_eq_intCast_floor, ZMod.valMinAbs_natCast_of_half_lt, QuaternionAlgebra.im_natCast, EuclideanSpace.volume_closedBall_fin_two, NormedSpace.norm_expSeries_summable_of_mem_ball', NeZero.of_not_dvd, Pi.orthonormalBasis_apply, Matrix.piLp_ofLp_toEuclideanLin, ENNReal.tsum_schlomilch_le, Polynomial.Chebyshev.degree_T, LinearMap.IsSymmetric.diagonalization_symm_apply, exists_spanning_measurableSet_le, MeasureTheory.stoppedValue_lowerCrossingTime, stereographic'_target, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, Int.fract_natCast, Subring.closure_insert_natCast, MeasureTheory.memLp_two_iff_integrable_sq, Polynomial.derivative_X_pow_succ, Polynomial.degree_X_pow_le, Commute.sub_sq, Num.of_to_nat, Behrend.norm_of_mem_sphere, AddCircle.addOrderOf_div_of_gcd_eq_one, Order.succ_iterate, Finset.card_mul_mulConst, div_nat_lt_self_of_pos_of_two_le, OrthonormalBasis.tensorProduct_repr_tmul_apply', nnnorm_natAbs, three_add_one_eq_four, WeierstrassCurve.variableChange_b₂, Ordinal.eq_nat_or_omega0_le, exists_nat_ge, dist_right_midpoint, Ordinal.nat_lt_card, ZMod.val_cast_of_lt, ordinaryHypergeometricSeries_apply_eq', charP_iff, Polynomial.degree_monomial_le, contMDiff_vectorSpace_iff_contDiff, IsSumSq.natCast, LinearGrowth.linearGrowthSup_le_of_eventually_le, Polynomial.natDegree_lt_iff_degree_lt, Polynomial.derivative_X_sub_C_pow, Matrix.l2_opNNNorm_mulVec, EMetric.diam_ball, lp.inner_single_right, Lagrange.degree_interpolate_erase_lt, Commute.add_pow, frontier_range_modelWithCornersEuclideanHalfSpace, Ordinal.iSup_mul_nat, Complex.antilipschitz_equivRealProd, Besicovitch.exist_finset_disjoint_balls_large_measure, Nat.cast_finsetSup', EuclideanSpace.instIsManifoldSphere, Finset.tendsto_Ioo_neg, complEDS₂_zero, Finset.card_mul_cast_subConst, Polynomial.descPochhammer_smeval_eq_descFactorial, FDRep.average_char_eq_finrank_invariants, wittPolynomial_one, WeierstrassCurve.variableChange_b₆, WeierstrassCurve.Δ_of_isShortNF, Nat.one_div_cast_pos, IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two, IsPrimitiveRoot.prod_pow_sub_one_eq_order, Ideal.Quotient.index_eq_zero, TangentBundle.coordChange_model_space, Nat.cast_natAbs, Nat.ceil_lt_add_one, Nat.cast_card_eq_zero, natCast_eq_one, RootPairing.EmbeddedG2.long_eq_three_mul_short, Polynomial.degree_quadratic_le, CategoryTheory.projectiveDimension_lt_iff, Finset.expect_eq_single_of_mem, Function.Antiperiodic.nat_even_mul_periodic, MeasureTheory.setIntegral_condExpIndSMul, round_natCast_add, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, WeierstrassCurve.b₆_of_isShortNF, Nat.cast_add_choose, Lagrange.degree_interpolate_lt, Nat.cast_max, add_thirds, OrthonormalBasis.equiv_apply, Nat.comap_cast_atTop, inner_eq_sum_norm_sq_div_four, Rat.cast_lt_natCast, Commute.natCast_mul_right, add_pow_le, AddConstMapClass.map_nat_add, WithBot.map_natCast, Ordinal.natCast_mod, Polynomial.preHilbertPoly_eq_choose_sub_add, WittVector.mul_polyOfInterest_aux4, div_two_lt_of_pos, Polynomial.Sequence.degree_eq, Metric.ediam_cthickening_le, NNRat.mk_natCast, tendsto_nat_floor_mul_div_atTop, FirstOrder.Language.presburger.realize_natCast, AddChar.pow_mulShift, DirichletCharacter.LSeries.mul_mu_eq_one, Real.toNNReal_le_natCast, MonovaryOn.sum_mul_sum_le_card_mul_sum, MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_spec, Module.Basis.coe_toOrthonormalBasis_repr_symm, Rat.cast_mkRat_of_ne_zero, Finset.card_mul_expect, IsSl2Triple.lie_h_e_smul, Finset.dens_eq_card_div_card, MulChar.sum_one_eq_card_units, Rat.valuation_le_one_iff_den, contMDiff_subtype_coe_Icc, DirichletCharacter.sum_char_inv_mul_char_eq, natCast_ceil_eq_intCast_ceil_of_neg_one_lt, sup_eq_half_smul_add_add_abs_sub', Nat.floor_div_eq_div, RCLike.add_conj, DirectLimit.natCast_def, tendsto_natCast_div_add_atTop, ArchimedeanClass.mk_natCast_nonneg, CFC.abs_natCast, Int.zpow_pred_clog_lt_self, ENNReal.toReal_natCast, RCLike.im_eq_conj_sub, AddMonoidAlgebra.toDirectSum_natCast, Nat.cast_lt_one, Polynomial.exists_approx_polynomial_aux, MeasureTheory.charFun_pi, MeasureTheory.lpNorm_fun_mul_natCast, one_half_lt_one, QuadraticAlgebra.C_natCast, PerfectClosure.natCast_eq_iff, Ordinal.omega0_le, Char.card_pow_card, one_add_mul_sub_le_pow, ascPochhammer_nat_eq_natCast_descFactorial, Polynomial.degree_freeMonic, Polynomial.natCast_coeff_zero, Int.cast_negSucc, ProbabilityTheory.evariance_eq_top_iff, LinearGrowth.linearGrowthSup_biSup, PowerBasis.mem_span_pow', OrthonormalBasis.repr_apply_apply, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow', WithLp.prod_nnnorm_eq_of_L2, iter_deriv_zpow, sup_eq_half_smul_add_add_abs_sub, RootPairing.pairing_neg_one_neg_four_iff, Nat.floor_lt', Ordinal.iSup_add_natCast, PMF.uniformOfFintype_apply, Matrix.conjTranspose_inv_ofNat_smul, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, ENat.map_natCast_mul, Int.fract_add_natCast, Nat.cast_nonpos, nndist_left_midpoint, four_mul_le_sq_add, Nat.cast_finprod, uniformity_basis_edist_inv_nat, AffineIsometryEquiv.dist_pointReflection_self, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, Function.Periodic.nat_mul_eq, trace_eq_finrank_mul_minpoly_nextCoeff, NormedSpace.expSeries_summable', Nat.range_mul_add, Num.cast_bit1, toIcoMod_sub_natCast_mul', NNRat.natCast_le_cast, MeasureTheory.L2.inner_indicatorConstLp_one, MvPolynomial.mkDerivationₗ_monomial, RCLike.tendsto_add_mul_div_add_mul_atTop_nhds, NNReal.lipschitzWith_sub, ENNReal.sub_half, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, WithTop.map_eq_natCast_iff, contDiff_nat_iff_iteratedDeriv, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, EuclideanSpace.edist_single_same, Nat.cast_npow, Nat.preimage_Iic, Nat.preimage_ceil_of_ne_zero, Polynomial.degree_derivative_eq, CFC.sqrt_eq_nnrpow, Submodule.coe_orthogonalDecomposition, Function.Antiperiodic.nat_mul_sub_eq, AddChar.zmodChar_apply', Rat.natCast_le_cast, EuclideanHalfSpace.convex, summable_prod_mul_pow, dist_right_pointReflection, MeasureTheory.condExpIndSMul_add, QuadraticMap.associated_toQuadraticMap, QuaternionAlgebra.star_add_self, LinearGrowth.linearGrowthSup_inv, LinearMap.isPositive_natCast, quadratic_eq_zero_iff_discrim_eq_sq, Algebra.normalizedTrace_eq_of_fininteDimensional, MeasureTheory.Lp.norm_fourier_eq, LinearGrowth.linearGrowthInf_const, SzemerediRegularity.coe_stepBound, Order.IsSuccPrelimit.add_natCast_lt, Polynomial.coeff_natCast_ite, Int.fract_sub_natCast, FiniteField.isSquare_neg_two_iff, Zsqrtd.le_arch, PreTilt.coeff_frobenius, Nimber.add_nat, EuclideanSpace.sphere_zero_eq, legendreSym.at_two, contDiffPointwiseHolderAt_iff, Polynomial.degree_le_of_natDegree_le, ENNReal.exists_nat_pos_inv_mul_lt, MeasureTheory.Lp.instFourierSMul, AddCommGroup.natCast_modEq_natCast, MeasureTheory.OuterMeasure.mkMetric'.tendsto_pre_nat, LinearMap.toMatrix_innerₛₗ_apply, NormedSpace.expSeries_div_hasSum_exp_of_mem_ball, Nat.Partition.powerSeriesMk_card_restricted_eq_tprod, Nat.cast_nonneg', Nat.le_floor_iff, EReal.nsmul_eq_mul, NumberField.Ideal.liesOver_primesOverSpanEquivMonicFactorsMod_symm, RCLike.wInner_one_eq_inner, Ordinal.card_lt_nat, ringKrullDim_le_ringKrullDim_quotient_add_card, QuaternionAlgebra.imK_natCast, Int.ceil_add_natCast, LinearGrowth.linearGrowthSup_le_iff, iteratedDerivWithin_zpow, Nat.castEmbedding_apply, Int.cast_four, NNReal.HolderConjugate.two_two, ZMod.mul_val_inv, PadicInt.coe_natCast, MeasureTheory.lpNorm_fun_natCast_mul, PowerSeries.exp_pow_sum, CFC.abs_nnrpow_two_mul, ZMod.cast_natCast', ContinuousMap.HomotopyWith.trans_apply, quadratic_eq_zero_iff_of_discrim_eq_zero, PreTilt.coeff_iterate_frobeniusEquiv_symm, WithBot.succ_one, Nat.WithBot.add_eq_three_iff, ExpGrowth.le_expGrowthInf_comp, WittVector.bind₁_wittMulN_wittPolynomial, Polynomial.Chebyshev.iterate_derivative_T_eval_zero_recurrence, ArchimedeanClass.exists_nat_ge_of_mk_nonneg, NormedSpace.expSeries_apply_eq, PartENat.withTopEquiv_symm_ofNat, PadicInt.denseRange_natCast, WeierstrassCurve.b₆_of_isCharThreeJNeZeroNF, Int.natCast_mul_floor_div_cancel, Nat.cast_finsum, toIocDiv_sub_natCast_mul, SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet, IsSelfAdjoint.natCast, PadicAlgCl.valuation_p, Matrix.conjTranspose_eq_natCast, tendsto_nat_floor_div_atTop, PowerBasis.degree_minpoly, Nat.cast_lt_ofNat, contDiffAt_euclidean, Zsqrtd.natCast_im, PadicComplex.valuation_p, ENat.toENNRealOrderEmbedding_apply, NNRat.natCast_lt_cast, NNRat.tendsto_inv_atTop_nhds_zero_nat, OrthogonalFamily.hasSum_linearIsometry, LinearGrowth.linearGrowthSup_const_mul_self, PMF.toOuterMeasure_ofMultiset_apply, Mathlib.Tactic.Ring.natCast_nat, Nat.lt_of_floor_lt, finrank_euclideanSpace, xInTermsOfW_aux, Ring.descPochhammer_smeval_add, SimpleGraph.adjMatrix_pow_apply_eq_card_walk, Subsemiring.closure_singleton_natCast, norm_natAbs, ascPochhammer_eval_eq_zero_iff, PartENat.ofENat_ofNat, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', Submodule.fst_orthogonalDecomposition_apply, DividedPowers.RatAlgebra.dpow_apply, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, EReal.tendsto_const_div_atTop_nhds_zero_nat, Polynomial.degree_hermite, Ordinal.preOmega_ofNat, Polynomial.eval₂_at_natCast, Filter.Eventually.natCast_atTop, nndist_midpoint_left, trivializationAt_model_space_apply, hasFTaylorSeriesUpToOn_top_iff, Num.cast_to_nat, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_natCast_le_one, Finset.centroidWeights_apply, RCLike.natCast_re, IsNonarchimedean.nmul_le, Polynomial.coeff_natCast_mul, ENNReal.add_thirds, ENNReal.rpow_add_le_mul_rpow_add_rpow, inv_natCast_smul_comm, WeierstrassCurve.variableChange_def, ENNReal.ofReal_eq_natCast, ZMod.natCast_eq_natCast_iff', mfderiv_coe_sphere_injective, Matrix.transpose_natCast, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, ENNReal.tendsto_nat_nhds_top, Function.Periodic.nat_mul_sub_eq, SymAlg.invOf_sym, ZMod.natCast_eq_iff, ENNReal.ofNNReal_le_natCast, Lagrange.degree_nodal, contDiffOn_euclidean, HahnSeries.ofPowerSeries_apply_coeff, ZMod.natCast_val, Finset.addConst_le_card, summable_choose_mul_geometric_of_norm_lt_one, PiLp.volume_preserving_ofLp, Finset.dens_mul_card, QuadraticAlgebra.norm_natCast, ENat.map_natCast_injective, WittVector.mul_polyOfInterest_vars, ENat.ceil_natCast_add, jacobiSym.at_neg_two, Finset.expect_boole_mul', hasFTaylorSeriesUpTo_succ_nat_iff_right, DirectSum.toAddMonoidAlgebra_natCast, MeasureTheory.StronglyAdapted.isStoppingTime_crossing, ordinaryHypergeometric_radius_top_of_neg_nat₂, zero_le_four, Nat.floor_lt, atTop_hasCountableBasis_of_archimedean, PartENat.instCanLiftNatCastDom, ZMod.natCast_comp_val, ZMod.natCast_eq_zero_iff, WeierstrassCurve.Affine.addPolynomial_eq, ModP.preVal_mk, InnerProductGeometry.norm_ofLp_crossProduct, Orthonormal.linearIsometryEquiv_symm_apply_single_one, nndist_midpoint_midpoint_le', WeierstrassCurve.variableChange_a₂, ModP.v_p_lt_preVal, Nat.ofDigits_eq_foldr, Polynomial.degree_X_pow_sub_C, MeasureTheory.stoppedValue_upperCrossingTime, odd_sq_dvd_geom_sum₂_sub, IsPrimitiveRoot.norm_pow_sub_one_eq_prime_pow_of_ne_zero, sum_Ioo_inv_sq_le, Nat.ofNat_le_cast, natCast_succ, WeierstrassCurve.variableChange_a₃, UnitAddTorus.orthonormal_mFourier, Polynomial.degree_le_natDegree, WithBot.natCast_eq_map_iff, Nat.cast_inj, EReal.natCast_lt_iff, Matrix.ofLp_toEuclideanCLM, Num.cast_ofZNum, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Nat.cast_le_pow_sub_div_sub, ENNReal.tsum_two_zpow_neg_add_one, summable_pow_div_add, SemiconjBy.natCast_mul_right, NormedSpace.expSeries_div_summable, mahler_natCast_eq, FiniteField.two_pow_card, add_pow_two, ZMod.toAddCircle_natCast, summable_descFactorial_mul_geometric_of_norm_lt_one, tsum_choose_mul_geometric_of_norm_lt_one, ordinaryHypergeometric_eq_tsum, Finset.sum_pow_of_commute, quadraticChar_neg_two, NormedSpace.expSeries_apply_eq_div, Metric.ediam_eball_le, Order.IsPredPrelimit.lt_sub_natCast, fourierCoeff_toLp, SimpleGraph.incMatrix_mul_transpose, Nat.choose_lt_pow_div, Nat.cast_prod, OrthogonalFamily.summable_of_lp, Padic.norm_natCast_eq_one_iff, coe_fourierBasis, NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat, ENat.floor_sub_natCast, map_inv_natCast_smul, iteratedDerivWithin_one_div, Nat.Partition.powerSeriesMk_card_restricted_eq_powerSeriesMk_card_countRestricted, Matrix.conjTranspose_eq_ofNat, Nat.abs_sub_ceil_le, ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank, Real.toNNReal_eq_natCast, IsCyclotomicExtension.discr_prime_pow_ne_two, Polynomial.exists_multiset_roots, Ideal.mem_leadingCoeffNth, WithBot.bot_lt_natCast, QuaternionAlgebra.re_natCast, Nat.cast_choose_eq_descPochhammer_div, MvPolynomial.psum_zero, Mathlib.Tactic.Bound.Nat.cast_pos_of_pos, Pell.pellZd_succ_succ, IsCyclotomicExtension.Rat.inertiaDeg_eq, Polynomial.smeval_at_natCast, LinearGrowth.linearGrowthSup_sup, WeierstrassCurve.ofJ1728_j, SimpleGraph.not_isUniform_iff, NNReal.coe_natCast, WeierstrassCurve.c₆_of_isCharTwoJEqZeroNF, IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two, range_two_mul, Matrix.vecMul_ofNat, instIsContMDiffRiemannianBundleOfNatWithTopENat_2, Nat.div_two_lt_floor, differentiableWithinAt_euclidean, IsCyclotomicExtension.neZero_of_mem', Affine.Simplex.smul_faceOppositeCentroid_vsub_point_eq_sum_vsub, WithTop.natCast_eq_map_iff, Mathlib.Tactic.Ring.natCast_zero, Matrix.isPositive_toEuclideanLin_iff, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, QuaternionAlgebra.star_add_self', MeasureTheory.smul_le_stoppedValue_hitting, PiLp.norm_sq_eq_of_L2, Polynomial.hasseDeriv_coeff, RCLike.re_eq_add_conj, PMF.toMeasure_uniformOfFintype_apply, Nat.cast_div_div_div_cancel_right, Finset.cast_mulConst_mul_card, Polynomial.degree_C_mul_X_pow_le, sub_pow, Nat.forall_exists_prime_gt_and_eq_mod, Polynomial.Chebyshev.C_eval_two, EuclideanQuadrant.convex, Matrix.discr_of_card_eq_two, ENNReal.coe_two, odd_add_two, Int.absNorm_under_mem, ExpGrowth.expGrowthSup_exp, Real.dimH_of_nonempty_interior, LinearGrowth.linearGrowthInf_inf, MeasureTheory.L2.real_inner_indicatorConstLp_one_indicatorConstLp_one, PadicInt.zmodRepr_spec, ENat.ceil_sub_natCast, ENNReal.HolderConjugate.instTwoTwo, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, PartENat.natCast_get, Finset.expect_dite_eq', Order.IsSuccLimit.add_natCast_lt, Nat.cast_finsum_mem, Cardinal.ord_ofNat, WittVector.ker_map_le_ker_mk_comp_ghostComponent, ENNReal.natCast_le_ofReal, tangentBundle_model_space_coe_chartAt_symm, Padic.valuation_p_lt_one, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, Path.Homotopy.trans_apply, EuclideanSpace.toLp_single, tangentBundleModelSpaceHomeomorph_coe, SimpleGraph.DeleteFar.le_card_edgeFinset, NNReal.agm_eq_agm_gm_am, ENNReal.half_le_self, Polynomial.toFinsupp_natCast, round_eq, IsCyclotomicExtension.Rat.inertiaDegIn_eq_of_not_dvd, ENNReal.toNNReal_natCast, Polynomial.Chebyshev.iterate_derivative_U_eval_one_dvd, Polynomial.eval_one_cyclotomic_prime_pow, WittVector.fontaineThetaModPPow_teichmuller, Polynomial.iterate_derivative_X_pow_eq_smul, AddGroupWithOne.intCast_negSucc, one_sub_invOf_two, WeierstrassCurve.Projective.eval_polynomialZ, Polynomial.Chebyshev.iterate_derivative_T_eval_one_dvd, Polynomial.Chebyshev.derivative_U_eval_one, DirichletCharacter.LSeriesSummable_twist_vonMangoldt, derivWithin_pow_field, one_add_one_eq_two, LinearMap.trace_id, midpoint_vsub_left, MeasureTheory.Measure.toSphere_apply', Mathlib.Meta.NormNum.isNat_natCast, PartENat.dom_natCast, Ordinal.natCast_add_of_omega0_le, Ordinal.one_add_natCast, LinearMap.IsSymmetric.natCast, NNRat.num_natCast, PadicInt.norm_natCast_zmodRepr_eq_one_iff, ENNReal.ofReal_lt_natCast, HomogeneousLocalization.val_natCast, NNReal.le_gm_and_am_le, DividedPowers.mul_dpow, Matrix.charmatrix_natCast, Real.nnnorm_two, toIcoDiv_add_natCast_mul, range_euclideanHalfSpace, NatOrdinal.toOrdinal_natCast, SimpleGraph.adjMatrix_mulVec_const_apply, DirichletCharacter.modOne_eq_one, DirichletCharacter.convolution_twist_vonMangoldt, Bialgebra.counit_natCast, CFC.nnrpow_sqrt, invOf_two_smul_add_invOf_two_smul, Zsqrtd.nsmul_val, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two', Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_eval, tangentBundleCore_coordChange_model_space, ENNReal.tsum_geometric_two, Nat.gc_ceil_coe, ContinuousMap.Homotopy.trans_apply, PMF.toOuterMeasure_uniformOfFinset_apply, Finpartition.coe_energy, contDiffOn_all_iff_nat, Polynomial.Chebyshev.degree_U_of_ne_neg_one, WithLp.prod_lipschitzWith_toLp, ENNReal.toNNReal_natCast_eq_toNNReal, binomialSeries_radius_eq_top_of_nat, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, Dynamics.IsDynCoverOf.coverEntropyEntourage_le_log_card_div, CharZero.cast_injective, instIsManifoldMinSmoothnessOfNatWithTopENat, IccLeftChart_extend_bot, Ideal.natCast_mem_of_charP_quotient, LinearGrowth.linearGrowthSup_eventually_monotone, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, Matrix.l2_opNNNorm_def, ringKrullDim_add_length_eq_ringKrullDim_of_isRegular, ONote.repr_opow_aux₁, PeriodPair.order_weierstrassP, MvPolynomial.mkDerivation_monomial, Ordinal.iSup_mul_natCast, Polynomial.degreeLT_succ_eq_degreeLE, FloorSemiring.gc_ceil, ENNReal.one_sub_inv_two, Quaternion.normSq_add, Nat.setOf_prime_and_eq_mod_infinite, MvPolynomial.schwartz_zippel_sup_sum, LinearGrowth.linearGrowthSup_const, MeasureTheory.condExpL2_indicator_of_measurable, MvPolynomial.mul_esymm_eq_sum, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, WittVector.exists_frobenius_solution_fractionRing, WittVector.ghostComponentModPPow_teichmuller_coeff, ENNReal.iUnion_Icc_coe_nat, iter_deriv_pow', Nat.ceil_sub_natCast, PartENat.find_le, Nat.ceil_add_natCast, ordinaryHypergeometricSeries_apply_eq, ZMod.χ₄_nat_one_mod_four, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, EuclideanSpace.basisFun_repr, pow_zmod_val_inv_pow, ProbabilityTheory.indepFun_iff_charFun_prod, Finset.le_card_falling_div_choose, zero_lt_three', Polynomial.Chebyshev.derivative_U_eval_one_dvd, jacobiSym.neg, Nat.Partition.hasProd_powerSeriesMk_card_restricted, Polynomial.degree_eq_iff_natDegree_eq_of_pos, SimpleGraph.unreduced_edges_subset, Submodule.sndL_comp_coe_orthogonalDecomposition, OrthonormalBasis.equiv_apply_euclideanSpace, Ordinal.lift_natCast, RootPairing.pairing_same, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow, NumberField.FinitePlace.norm_def_int, TrivSqZeroExt.inl_natCast, Complex.orthonormalBasisOneI_repr_symm_apply, Manifold.riemannianEDist_def, NNReal.coe_two, WeierstrassCurve.b₄_of_isShortNF, WeierstrassCurve.Projective.polynomialX_eq, WeierstrassCurve.c₄_of_isShortNF, LinearGrowth.linearGrowthInf_natCast_nonneg, MeasureTheory.Lp.instContinuousFourierInv, uniformity_basis_edist_inv_two_pow, Module.End.natCast_def, Ideal.is_fg_degreeLE, AddChar.mulShift_spec', UnitAddTorus.hasSum_mFourier_series_L2, CharP.intCast_mul_natCast_gcdA_eq_gcd, WeierstrassCurve.c₆_of_isCharTwoJNeZeroNF, modelWithCornersEuclideanHalfSpace_zero, Nat.abs_sub_floor_le, Equiv.Perm.toList_formPerm_nontrivial, not_summable_indicator_mod_of_antitone_of_neg, Ordinal.natCast_pow, Ordinal.natCast_mul, Nat.cast_min, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, IsCyclotomicExtension.neZero, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, AddMonoidAlgebra.natCast_def, Ordinal.natCast_succ, contDiffOn_iff_forall_nat_le, Quaternion.star_add_self', LinearGrowth.linearGrowthSup_comp_nonneg, SimpleGraph.lapMatrix_mulVec_apply, LucasLehmer.X.mul_fst, QuadraticMap.half_moduleEnd_apply_eq_half_smul, RootPairing.coxeterWeightIn_le_four, PartENat.toWithTop_natCast', Finset.pluennecke_ruzsa_inequality_pow_div, PartENat.eq_top_iff_forall_le, ZMod.gauss_lemma, WeierstrassCurve.b₈_of_isCharThreeJNeZeroNF, AffineBasis.coord_apply_centroid, RootPairing.EmbeddedG2.pairing_long_short, WeierstrassCurve.Projective.polynomialY_eq, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, half_lt_self_iff, IsCyclotomicExtension.norm_zeta_sub_one_of_prime_ne_two, EReal.natCast_eq_iff, ZMod.orderOf_one_add_four_mul, WeierstrassCurve.Projective.negDblY_eq, PartENat.natCast_lt_top, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, quadratic_eq_zero_iff, Matrix.sub_scalar_sq_eq_disc, ENNReal.coe_inv_two, div_nat_le_self_of_nonnneg, isUnit_iff_not_dvd_char, EuclideanSpace.norm_eq, star_inv_natCast_smul, nnnorm_pow_le_mul_norm, sq_sum_le_card_mul_sum_sq, Matrix.IsHermitian.eigenvectorUnitary_apply, Matrix.disc_fin_two, AddMonoid.End.natCast_def, ENNReal.coe_lt_natCast, add_pow_prime_eq, contDiffAt_succ_iff_hasFDerivAt, RootPairing.coroot_root_two, ringChar.Nat.cast_ringChar, MeasureTheory.L2.eLpNorm_inner_lt_top, PreTilt.pow_dvd_untiltAux_sub_untiltAux, DirichletCharacter.LSeriesSummable_iff, SemiconjBy.natCast_mul_left, Nat.prime_iff_fac_equiv_neg_one, ENNReal.log_pow, PartENat.withTopEquiv_natCast, WittVector.ghostComponent_verschiebung, PiLp.antilipschitzWith_ofLp, PartENat.coe_le_coe, Matrix.frobenius_nnnorm_replicateRow, PosNum.cast_to_nat, Nat.cast_div, MeasureTheory.Measure.count_apply_finset', toIcoMod_add_natCast_mul', ZMod.cast_natCast, Nat.cast_add, ONote.split_add_lt, Nat.coe_castAddMonoidHom, Int.zpow_log_le_self, EuclideanSpace.inner_eq_star_dotProduct, IsPrimitiveRoot.neZero', MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, ZMod.cast_neg_one, Dynamics.coverEntropyEntourage_le_log_coverMincard_div, PartENat.eq_top_iff_forall_lt, ZMod.χ₈_nat_mod_eight, OrthonormalBasis.sum_repr_symm, Localization.mk_natCast, PartENat.coe_succ_le_iff, Finset.sum_card_slice_div_choose_le_one, Ordinal.natCast_opow_omega0, QuaternionAlgebra.self_add_star', PartENat.coe_lt_iff, AddConstMapClass.map_nat', Polynomial.derivative_sq, archimedean_iff_nat_lt, Matrix.frobenius_nnnorm_replicateCol, contDiffWithinAt_infty, Pi.orthonormalBasis.toBasis, contMDiffWithinAt_comp_projIcc_iff, PadicInt.mem_span_pow_iff_le_valuation, NormedSpace.norm_expSeries_summable', PartENat.get_eq_iff_eq_coe, tangentBundle_model_space_chartAt, PreTilt.pow_dvd_one_untiltAux_sub_one, Polynomial.degree_cubic, toIocMod_natCast_mul_add', NNReal.natCast_iSup, tendsto_add_mul_div_add_mul_atTop_nhds, NormedSpace.norm_expSeries_div_summable_of_mem_ball, ZMod.natCast_zmod_val, Polynomial.hasseDeriv_monomial, hasSum_coe_mul_geometric_of_norm_lt_one, Cubic.degree_of_a_eq_zero, QuaternionGroup.a_one_pow, Odd.natCast, tendsto_one_div_atTop_nhds_zero_nat, IsCyclotomicExtension.norm_zeta_sub_one_of_isPrimePow, Finset.addConst_mul_card, ENNReal.tsum_condensed_le, Ordinal.card_le_nat, contMDiffAt_iff_nat, map_natCast_smul, ENNReal.iUnion_Ico_coe_nat, Function.Antiperiodic.add_nat_mul_eq, nsmul_eq_mul', SimpleGraph.FarFromTriangleFree.lt_half, Affine.Simplex.centroid_eq_smul_vsub_vadd_point, ZMod.isUnit_prime_iff_not_dvd, Function.Antiperiodic.nat_mul_eq_of_eq_zero, round_eq_zero_iff, Polynomial.degree_X_pow, Algebra.adjoin_singleton_natCast, Quaternion.self_add_star', tendsto_natCast_atTop_iff, ArchimedeanClass.stdPart_natCast, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, MeasureTheory.Lp.instFourierPairInv, RootPairing.RootPositiveForm.two_mul_apply_root_root, NormedSpace.expSeries_apply_eq', hasSum_choose_mul_geometric_of_norm_lt_one', Int.log_natCast, Monotone.linearGrowthInf_nonneg, Cubic.equiv_symm_apply_b, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two, Ring.choose_natCast, EuclideanSpace.volume_ball_fin_three, toIcoMod_sub_natCast_mul, Complex.nnnorm_ofNat, ascPochhammer_eval_neg_coe_nat_of_lt, Ordinal.type_fintype, MeasureTheory.AddSubgroup.index_mul_measure, PiCountable.edist_le_two, Nat.cast_le_ofNat, Int.lt_zpow_succ_log_self, QuadraticAlgebra.coe_natCast, Real.contDiffAt_rpow_const, QuotientAddGroup.mk_nat_mul, natCast_ceil_eq_intCast_ceil, Ring.multichoose_succ_neg_natCast, add_sq_le, CHSH_id, Int.floor_natCast_add, ZMod.coe_int_mul_val_inv, Lagrange.degree_basis, Finset.sum_pow_eq_sum_piAntidiag_of_commute, IsUnit.natCast_factorial_of_algebra, Commute.natCast_mul_left, ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, EqualCharZero.pnatCast_eq_natCast, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, summable_norm_pow_mul_geometric_div_one_sub, DirichletCharacter.absicssaOfAbsConv_eq_one, CentroidHom.toEnd_natCast, ExpGrowth.le_expGrowthInf_iff, ExpGrowth.expGrowthSup_comp_le, Asymptotics.isEquivalent_nat_floor, Commute.exists_add_pow_prime_eq, WeierstrassCurve.variableChange_a₄, MeasureTheory.Lp.instFourierInvAdd, Matrix.frobenius_nnnorm_diagonal, ZeroLEOneClass.neZero.three, Quaternion.re_natCast, homothety_invOf_two, even_two_mul, NNReal.rpow_add_le_mul_rpow_add_rpow, Ordinal.toPGame_natCast, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, WeierstrassCurve.c₆_of_isCharNeTwoNF, Real.Convex.dimH_eq_finrank_vectorSpan, Nat.coe_ofDigits, Ring.choose_add_smul_choose, Rat.cast_def, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_paramSet_exp, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, SetTheory.PGame.birthday_half, Ordinal.lt_omega0_opow, PadicInt.isUnit_den, AddCommGroup.intCast_modEq_intCast', Diffeology.isPlot_iff_contDiff, pow_four_add_four_mul_pow_four, Nat.one_sub_one_div_cast_nonneg, Nat.cast_sum, add_sub_div_two_lt, RCLike.norm_natCast, Num.ofInt'_toZNum, PadicInt.norm_le_pow_iff_mem_span_pow, PMF.binomial_apply, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, MeasureTheory.condExpIndSMul_nonneg, CharP.natCast_eq_natCast, OrthonormalBasis.measurePreserving_repr_symm, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, lp.summable_inner, Int.floor_add_natCast, iteratedDerivWithin_pow, Finset.expect_boole_mul, Real.volume_eball, EuclideanSpace.piLpCongrLeft_single, WeierstrassCurve.coeff_preΨ₄, Ring.smeval_ascPochhammer_nat_cast, ZMod.χ₄_nat_three_mod_four, Finset.tendsto_Icc_neg, oneTangentSpaceIcc_def, descPochhammer_eval_eq_descFactorial, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, PadicInt.zmodRepr_natCast, WithTop.map_eq_ofNat_iff, WeierstrassCurve.Jacobian.polynomialZ_eq, ENNReal.tendsto_inv_nat_nhds_zero, ExpGrowth.frequently_le_exp, Int.fract_natCast_add, MeasureTheory.OuterMeasure.mkMetric'.mono_pre_nat, IccRightChart_extend_top_mem_frontier, Commute.add_sq, QuaternionAlgebra.natCast_imK, stdSimplex.barycenter_apply, WeierstrassCurve.Jacobian.dblU_eq, IsPrimitiveRoot.norm_pow_sub_one_two, PadicInt.norm_natCast_zmodRepr_eq, hasFDerivWithinAt_euclidean, FDRep.char_one, even_sub_two, SubringClass.coe_natCast, Polynomial.eval_one_cyclotomic_prime, QuaternionGroup.xa_mul_xa, PiLp.dist_sq_eq_of_L2, SymAlg.sym_mul_self, LinearGrowth.linearGrowthInf_eventually_monotone, Metric.coveringNumber_subset_le, WeierstrassCurve.Affine.degree_polynomial, DirichletCharacter.mul_convolution_distrib, NormedSpace.expSeries_div_summable_of_mem_ball, Matrix.IsHermitian.eigenvectorUnitary_coe, Asymptotics.IsBigO.natCast_atTop, ENNReal.ofNNReal_sub_natCast, MvPolynomial.pderiv_monomial_single, Polynomial.leadingCoeff_preHilbertPoly, PadicInt.ker_toZModPow, Cardinal.ord_nat, Finset.cast_subConst, Nat.cast_finsuppProd, IsPrimitiveRoot.toInteger_sub_one_dvd_prime, LinearRecurrence.charPoly_degree_eq_order, Ring.multichoose_eq, Ordinal.ofNat_lt_card, MeasureTheory.le_sub_of_le_upcrossingsBefore, parallelogram_law, Real.dimH_univ_pi, AnalyticAt.hasFPowerSeriesAt, RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_apply, fwdDiff_iter_eq_factorial, Matrix.ofNat_mulVec, ringKrullDim_le_ringKrullDim_add_card, midpoint_vsub_right, Matrix.toEuclideanLin_eq_toLin, Finset.nnratCast_dens, WeierstrassCurve.Δ_of_isCharNeTwoNF, WittVector.mul_polyOfInterest_aux1, Euclidean.closedBall_eq_preimage, Matrix.isHermitian_iff_isSymmetric, RootPairing.InvariantForm.apply_eq_or_aux, Nat.cast_mul, Lagrange.degree_interpolate_le, CategoryTheory.projectiveDimension_le_iff, Cubic.degree_of_a_ne_zero, Finset.subConst_le_card, tendsto_algebraMap_inverse_atTop_nhds_zero_nat, map_natCast, Nat.cast_eq_zero, ExpGrowth.frequently_exp_le, EuclideanSpace.basisFun_inner, ENNReal.natCast_lt_ofReal, Polynomial.eval_natCast_mul, ZMod.natCast_eq_zero_iff_even, Nat.Partition.powerSeriesMk_card_countRestricted_eq_tprod, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, Monotone.expGrowthInf_comp_le, NNReal.half_lt_self, LinearMap.IsReflective.dvd_two_mul, InnerProductSpace.toMatrix_rankOne, LinearMap.equivariantProjection_apply, WithTop.natCast_lt_top, contMDiffAt_vectorSpace_iff_contDiffAt, EuclideanSpace.ofLp_single, abs_pow_sub_pow_le, differentiableAt_euclidean, Nat.cast_multiset_prod, lp.inner_single_left, MvPolynomial.degree_finSuccEquiv, geom_series_mul_one_add, dist_pointReflection_right, Surreal.nat_toGame, Matrix.map_natCast, RootPairing.pairingIn_one_four_iff, MvPolynomial.pderiv_monomial, skewAdjointPart_apply_coe, WithLp.prod_norm_sq_eq_of_L2, ZMod.orderOf_one_add_prime, HahnSeries.ofPowerSeriesAlg_apply_coeff, ringChar.spec, tendsto_natCast_atTop_atTop, Finset.prod_range_natCast_sub, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.IsReflective.coroot_apply_self, Polynomial.derivative_pow, Finpartition.IsEquipartition.sum_nonUniforms_lt, one_half_pos, WeierstrassCurve.Projective.negDblY_eq', AnalyticAt.exists_eq_sum_add_pow_mul, odd_sub_two, SimpleGraph.le_card_nonuniformWitness, CategoryTheory.projectiveDimension_ge_iff, Field.primitive_element_iff_minpoly_degree_eq, selfAdjointPartL_apply_coe, Quaternion.natCast_im, Nat.cast_finsetInf', Even.two_dvd, nndist_midpoint_midpoint_le, ZMod.addOrderOf_coe', Matrix.ofNat_apply, mdifferentiable_addInvariantVectorField, ZeroLEOneClass.neZero.four, RootPairing.pairingIn_neg_one_neg_four_iff, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, LieAlgebra.IsKilling.root_apply_coroot, ZMod.LSeriesSummable_of_one_lt_re, CharP.sq_add_sq, DirichletCharacter.LSeries_eulerProduct_hasProd, AddSubgroup.nsmul_mem_zmultiples_iff_exists_sub_div, Polynomial.dickson_one_one_eq_chebyshev_T, SchwartzMap.inner_fourierTransformCLM_toL2_eq, tendsto_nat_ceil_div_atTop, mdifferentiableWithinAt_comp_projIcc_iff, RootPairing.GeckConstruction.f_lie_v_ne, MeasureTheory.Measure.count_apply_finset, Rat.cast_natCast, half_le_self, PiLp.norm_toLp_const, Diffeology.isOpen_iff_preimages_plots, AddCommGroup.ModEq.natCast, IsPrimitiveRoot.toInteger_sub_one_dvd_prime', differentiableOn_euclidean, Dvd.dvd.natCast, contDiffAt_infty, HasStrictFDerivAt.approximates_deriv_on_open_nhds, gaussSum_mul_gaussSum_pow_orderOf_sub_one, LSeries.one_convolution_eq_zeta_convolution, ZMod.χ₄_eq_neg_one_pow, VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symm, RCLike.natCast_im, tsum_prod_pow_eq_tsum_sigma, half_sub, WittVector.StandardOneDimIsocrystal.frobenius_apply, TangentBundle.symmL_model_space, MeasureTheory.integrable_condExpL2_indicator, Ordinal.ofNat_le_card, Diffeology.IsContDiffCompatible.isPlot_iff, NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral, ZMod.cast_descFactorial, LinearGrowth.linearGrowthInf_iInf, CategoryTheory.injectiveDimension_lt_iff, Finset.cast_mulConst, EuclideanSpace.ball_zero_eq, Real.fib_isSol_fibRec, Int.clog_zpow, range_mfderiv_coe_sphere, Diffeology.IsPlot.continuous, Polynomial.Chebyshev.iterate_derivative_U_eval_one, add_mul_self_eq, MeasureTheory.eLpNorm'_add_le_of_le_one, Polynomial.chebyshev_T_eq_dickson_one_one, Nat.cast_finsupp_sum, RootPairing.GeckConstruction.e_lie_v_ne, LinearGrowth.linearGrowthInf_monotone, Finset.subConst_mul_card, WithTop.ofNat_eq_map_iff, NumberField.linearDisjoint_of_isGalois_isCoprime_discr, ENNReal.le_tsum_condensed, Matrix.ofLp_toEuclideanLin_apply, tsum_dirichletSummand, ZMod.Ico_map_valMinAbs_natAbs_eq_Ico_map_id, Nat.cast_eq_one, Polynomial.ringKrullDim_le, Nat.cast_list_prod, RCLike.norm_two, Matrix.charpoly_sub_diagonal_degree_lt, toIcoMod_natCast_mul_add, descPochhammer_eval_coe_nat_of_lt, EuclideanSpace.volume_ball_fin_two, SimpleGraph.incMatrix_mul_transpose_diag, Matrix.isHermitian_natCast, Finset.card_mul_cast_mulConst, Complex.nnnorm_natCast, EuclideanSpace.inner_basisFun_real, DividedPowers.OfInvertibleFactorial.dpow_eq_of_mem, PartENat.ofENat_coe, Nat.one_div_cast_nonneg, iccLeftChart_extend_zero, jacobiSym.at_two, Algebra.normalizedTrace_minpoly, Complex.nndist_conj_self, MeasureTheory.eLpNorm_one_le_of_le, Polynomial.Chebyshev.C_eval_neg_two, Differential.logDeriv_pow, MvPolynomial.pderiv_pow, Euclidean.ball_eq_preimage, Ordinal.card_eq_nat, contDiff_nat_iff_continuous_differentiable, Ordinal.principal_mul_two, NNRat.ofNat_le_cast, ZMod.natCast_smul_units, LieAlgebra.Orthogonal.jd_transform, DirichletCharacter.LSeries_eulerProduct_exp_log, Cubic.equiv_symm_apply_c, legendreSym.eq_one_iff', IsCyclotomicExtension.Rat.inertiaDegIn_eq, EuclideanSpace.volume_ball, WithBot.map_eq_ofNat_iff, OrthonormalBasis.repr_symm_single, Order.not_isSuccLimit_natCast, Ordinal.opow_natCast, GenContFract.fib_le_of_contsAux_b, interior_range_modelWithCornersEuclideanHalfSpace, RootPairing.polarizationEquiv_symm_apply_coroot, Matrix.vecMul_natCast, ExpGrowth.eventually_exp_le, Real.dimH_ball_pi_fin, Polynomial.coeff_X_add_one_pow, Nat.one_sub_one_div_cast_le_one, LinearMap.BilinForm.IsSymm.polarization, ZMod.val_natCast, contDiffWithinAt_iff_forall_nat_le, Nat.abs_floor_sub_le, Int.fract_div_natCast_eq_div_natCast_mod, SetTheory.Game.birthday_ofNat, isUnit_iff_not_dvd_char_of_ringChar_ne_zero, LinearGrowth.linearGrowthSup_iSup, Nat.cast_div_le, ENNReal.half_pos, QuaternionAlgebra.natCast_imI, iter_deriv_inv, CFC.nnrpow_three, LinearGrowth.linearGrowthInf_comp_nonneg, WittVector.bind₁_verschiebungPoly_wittPolynomial, Finset.dens_singleton, Polynomial.iterate_derivative_X_pow_eq_C_mul, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, Path.trans_apply, WeierstrassCurve.b_relation, QuadraticMap.associated_linMulLin, Polynomial.derivative_X_pow, Real.natCastle_toNNReal', ENNReal.add_halves, OrthogonalFamily.range_linearIsometry, SeminormedAddCommGroup.lipschitzWith_sub, MvPolynomial.C_eq_coe_nat, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq, RCLike.nnnorm_two, zero_lt_two', NNReal.summable_one_div_rpow, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, HasDerivWithinAt.fun_pow, Nat.one_div_pos_of_nat, PreTilt.exists_smodEq_untiltAux, Ordinal.nadd_nat, ENNReal.iUnion_Ioo_coe_nat, add_pow_prime_pow_eq', ZMod.orderOf_one_add_mul_prime_pow, Fin.addRothNumber_le_rothNumberNat, WeierstrassCurve.Φ_two, Even.add_pow_le, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, iter_deriv_inv', toMatrix_innerSL_apply, FloorSemiring.eventually_mul_pow_lt_factorial_sub, Finset.box_succ_eq_sdiff, MeasureTheory.lpNorm_div_natCast, two_mul_le_add_of_sq_eq_mul, legendreSym.at_neg_one, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, Polynomial.card_roots, Polynomial.ofFn_degree_lt, ModP.preVal_zero, lp.infty_coeFn_natCast, Ordinal.isInitial_natCast, ProbabilityTheory.uniformOn_univ, 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, Diffeology.IsPlot.contDiff, tangentBundleModelSpaceHomeomorph_coe_symm, IntermediateField.adjoin_natCast, pow_pow_zmod_val_inv, PiLp.edist_eq_card, Ordinal.natCast_mod_omega0, sub_pow_two, lp.hasSum_inner, Polynomial.degree_eq_card_roots, deriv_pow_field, SchwartzMap.toLp_fourierTransform_eq, Nat.lt_of_ceil_lt, isAlgebraic_nat, MeasureTheory.setLIntegral_nnnorm_condExpIndSMul_le, PowerBasis.degree_minpolyGen, quadraticChar_odd_prime, meromorphicOrderAt_pow, SimpleGraph.degree_eq_sum_if_adj, ordinaryHypergeometricSeries_eq_zero_iff, pow_sum_le_card_mul_sum_pow, round_le_add_half, SimpleGraph.incMatrix_transpose_mul_diag, Quaternion.self_add_star, Nat.cast_ite, Nat.cast_finsetSup, WeierstrassCurve.Affine.evalEval_polynomialY, PreTilt.untiltAux_smodEq_untiltFun, lineMap_one_half, MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq, NNReal.bddAbove_natCast_image_iff, SkewMonoidAlgebra.natCast_def, QuaternionAlgebra.imI_natCast, Nat.coe_castRingHom, PadicInt.norm_p, UnitAddTorus.hasSum_prod_mFourierCoeff, isLittleO_coe_const_pow_of_one_lt, SimpleGraph.right_nonuniformWitnesses_card, Ordinal.IsNormal.apply_omega0, PadicInt.valuation_p_pow_mul, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_span, toIocDiv_sub_natCast_mul', Finset.natCast_card_mul_nnratCast_dens, Int.le_zpow_iff_clog_le, ZMod.mul_inv_eq_gcd, Prod.snd_natCast, Matrix.posDef_natCast_iff, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, TrivSqZeroExt.snd_natCast, WithBot.succ_natCast, IsStarProjection.two_mul_sub_one_mem_unitary, PowerSeries.invOneSubPow_val_eq_mk_sub_one_add_choose_of_pos, selfAdjointPart_apply_coe, Finset.expect_univ, MeasureTheory.aestronglyMeasurable_condExpIndSMul, MeasureTheory.Egorov.mem_notConvergentSeq_iff, skewAdjointPartL_apply_coe, Nat.floor_sub_natCast, PowerSeries.exp_pow_eq_rescale_exp, ringKrullDim_nat, Set.cast_ncard_sdiff, even_add_two, Polynomial.degree_lt_iff_coeff_zero, PartENat.ne_top_iff, ProbabilityTheory.iIndepFun_iff_charFun_pi, MeasureTheory.L2.mem_L1_inner, Finset.cast_addConst_mul_card, Nat.strictMono_cast, Matrix.det_vandermonde_id_eq_superFactorial, Matrix.trace_one, Nat.one_lt_cast, Nat.cast_withBot, PadicInt.zmodRepr_natCast_zmodRepr, PadicInt.pow_p_dvd_int_iff, ZMod.gauss_lemma_aux, map_ofNat', NNReal.tendsto_inverse_atTop_nhds_zero_nat, LinearGrowth.le_linearGrowthInf_iff, hasFTaylorSeriesUpToOn_succ_iff_left, LinearMap.IsProj.trace, ENat.map_natCast_nonneg, MeasureTheory.Lp.inner_fourier_eq, PairReduction.exists_radius_le, derivWithin_fun_pow, Commute.ofNat_right, RootPairing.coxeterWeight_eq_four_iff_not_linearIndependent, two_mul_le_add_pow_two, DividedPowers.RatAlgebra.dpow_eq_of_mem, WeierstrassCurve.c₄_of_isCharNeTwoNF, summable_indicator_mod_iff_summable, HilbertBasis.repr_self, nnnorm_commutator_sub_one_le, WittVector.polyOfInterest_vars_eq, Nat.cast_smul_eq_nsmul, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Real.contDiff_rpow_const_of_le, round_eq_half_ceil_two_mul, descPochhammer_eval_eq_ascPochhammer, Polynomial.derivative_monomial_succ, NormedSpace.expSeries_sum_eq_div, Zsqrtd.natCast_val, PreTilt.coeff_iterate_frobenius, add_pow, summable_pow_mul_geometric_of_norm_lt_one, toIocDiv_add_natCast_mul', descPochhammer_eval_eq_prod_range, ContDiffPointwiseHolderAt.contDiffAt, Even.natCast_zmod_two, Algebra.TensorProduct.natCast_def, NNReal.summable_rpow_inv, RootPairing.pairingIn_two_two_iff, Matrix.natCast_mulVec, Finset.cast_card_erase_of_mem, MeasureTheory.L2.integrable_inner, IsUltrametricDist.norm_natCast_le_one, AddCircle.addOrderOf_eq_pos_iff, PadicInt.p_nonunit, hasFTaylorSeriesUpTo_top_iff, Ordinal.omega0_opow_mul_nat_lt, Matrix.conjTranspose_ofNat_smul, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, NormedSpace.expSeries_div_hasSum_exp, DirichletCharacter.apply_eq_toArithmeticFunction_apply, Int.log_zpow, one_lt_two, Nat.norm_cast_le, ascPochhammer_nat_eq_natCast_ascFactorial, QuaternionAlgebra.natCast_imJ, Prod.card_box_succ, ExpGrowth.expGrowthInf_def, mdifferentiableAt_mulInvariantVectorField, Finset.centroid_pair, pos_invOf_of_invertible_cast, Affine.Simplex.point_vsub_centroid_eq_smul_vsub, Num.add_of_nat, gaussSum_pow_eq_prod_jacobiSum, Nat.choose_le_pow_div, Ordinal.nat_lt_omega0, Polynomial.degree_cyclotomic', ENNReal.nhdsGT_ofNat_neBot, Matrix.toEuclideanLin_apply_piLp_toLp, LinearGrowth.linearGrowthInf_le_of_eventually_le, add_pow_prime_eq', Even.natCast, LinearGrowth.linearGrowthInf_le_iff, Matrix.trace_permutation, WeierstrassCurve.Jacobian.polynomialX_eq, QuaternionGroup.xa_sq, Ordinal.toNatOrdinal_natCast, SimpleGraph.left_nonuniformWitnesses_card, Polynomial.coeff_mul_natCast, ascPochhammer_eval_succ, ENNReal.exists_inv_nat_lt, contMDiffWithinAt_infty, discrim_eq_sq_of_quadratic_eq_zero, ENat.floor_natCast_add, hasDerivAt_pow, SimpleGraph.adjMatrix_mulVec_const_apply_of_regular, Polynomial.le_degree_of_ne_zero, SkewMonoidAlgebra.single_nat, LieAlgebra.IsKilling.chainLength_smul, PadicInt.norm_sub_zmodRepr_lt_one, LinearGrowth.linearGrowthSup_comp_le, ENat.toENNReal_coe, Monotone.linearGrowthInf_comp_le, even_iff_two_dvd, EuclideanSpace.dist_eq, zero_lt_four, WeierstrassCurve.b₆_of_isCharNeTwoNF, DirichletCharacter.not_LSeriesSummable_at_one, Nat.cast_choose_two, Int.clog_natCast, MvPolynomial.psum_eq_mul_esymm_sub_sum, Cubic.equiv_apply_coe, Commute.natCast_mul_self, HasDerivWithinAt.pow, Finset.cast_divConst_mul_card, MeasureTheory.Measure.count_apply_finite', PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, CFC.sqrt_nnrpow_two, TrivSqZeroExt.fst_natCast, Rat.cast_le_natCast, Int.cast_subNatNat, Ordinal.card_nat, exists_add_pow_prime_eq, Monotone.linearGrowthInf_comp_mul, nsmul_eq_mul, one_le_two, Real.toNNReal_coe_nat, Int.nnnorm_natCast, contMDiffOn_comp_projIcc_iff, EReal.exp_nmul, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, Polynomial.fwdDiff_iter_degree_eq_factorial, AddConstMapClass.map_add_nat', Nat.floor_le, Finset.cast_card_sdiff, volume_euclideanSpace_eq_dirac, QuotientAddGroup.zmultiples_nsmul_eq_nsmul_iff, NNRat.cast_divNat_of_ne_zero, sub_sq', tendsto_nat_ceil_mul_div_atTop, Polynomial.le_degree_of_mem_supp, NumberField.house_nat_mul, PowerSeries.coeff_derivative, PartENat.some_eq_natCast, Int.cast_three, Polynomial.derivative_C_mul_X_pow, Matrix.frobenius_norm_diagonal, ZMod.valMinAbs_natCast_eq_self, GaussianInt.prime_of_nat_prime_of_mod_four_eq_three, AddCircle.nsmul_eq_zero_iff, CFC.sqrt_nnrpow, Zsqrtd.norm_natCast, Metric.lipschitz_infDist, nnnorm_commutator_units_sub_one_le, ZNum.of_nat_toZNum, QuadraticAlgebra.re_natCast, ZMod.natCast_mod, Polynomial.hasseDeriv_apply, height_le_ringKrullDim_quotient_add_spanFinrank, Polynomial.dickson_two_one_eq_chebyshev_U, zero_le_two, OrthonormalBasis.coe_toBasis_repr, IsManifold.instOfNatWithTopENat_2, SimpleGraph.lt_extremalNumber_iff_of_nonneg, inf_eq_half_smul_add_sub_abs_sub, ZMod.val_two_eq_two_mod, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, ENNReal.nhdsGT_nat_neBot, QuaternionAlgebra.coe_natCast, Mathlib.Tactic.Linarith.natCast_nonneg, WeierstrassCurve.twoTorsionPolynomial_disc, IsUltrametricDist.nnnorm_natCast_le_one, ZMod.toCircle_natCast, FDRep.char_orthonormal, ENNReal.tsum_geometric_two_encode_le_two, OrthonormalBasis.sum_repr, ZMod.orderOf_five, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, Int.zpow_lt_iff_lt_clog, Nat.lt_ceil, hasSum_sq_fourierCoeff, Real.nnnorm_natCast, ONote.repr_ofNat, Rat.cast_inv_nat, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, Polynomial.Chebyshev.iterate_derivative_T_eval_one, ascPochhammer_eval_cast, PowerSeries.isWeierstrassDivisionAt_iff, ZMod.coe_mul_inv_eq_one, Submodule.fstL_comp_coe_orthogonalDecomposition, NumberField.toNNReal_valued_eq_adicAbv, Finset.expect_dite_eq, iter_deriv_inv_linear_sub, PiLp.dist_eq_of_L2, midpoint_sub_left, Antivary.card_mul_sum_le_sum_mul_sum, odd_iff_exists_bit1, Asymptotics.IsLittleO.natCast_atTop, IsHilbertSum.linearIsometryEquiv_symm_apply_single, WittVector.exists_frobenius_solution_fractionRing_aux, Nat.sub_one_lt_floor, exists_embedding_euclidean_of_compact, UnitAddTorus.mFourierBasis_repr, MeasureTheory.condExpIndL1Fin_ae_eq_condExpIndSMul, zero_lt_four', midpoint_vsub, Mathlib.Tactic.RingNF.nat_rawCast_2, RingCon.coe_natCast, MeasureTheory.lpNorm_natCast_mul, Finset.cast_divConst, Subalgebra.natCast_mem, SetTheory.PGame.birthday_natCast, DoubleCentralizer.natCast_toProd, Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X, PMF.uniformOfFinset_apply, Matrix.sum_single_natCast, legendreSym.eq_neg_one_iff', Nat.le_ceil, fourierBasis_repr, ModP.v_p_lt_val, jacobiSum_mul_jacobiSum_inv, MeasureTheory.StronglyAdapted.isStoppingTime_lowerCrossingTime, PartENat.coe_le_iff, Polynomial.degree_update_le, MeasureTheory.BoundedContinuousFunction.inner_toLp, inf_eq_half_smul_add_sub_abs_sub', CharP.natCast_eq_natCast', Finset.tendsto_Ico_neg, NNReal.mk_natCast, SymAlg.unsym_mul_self, legendreSym.at_neg_two, IsPrimitiveRoot.self_sub_one_pow_dvd_order, RootPairing.InvariantForm.apply_eq_or, sum_Ioc_inv_sq_le_sub, toIcoDiv_sub_natCast_mul, MeasureTheory.OuterMeasure.mkMetric'.eq_iSup_nat, AddCircle.addOrderOf_period_div, ContDiff.dimH_range_le, RingCon.coe_intCast, Nat.smul_one_eq_cast, Quaternion.imI_natCast, Polynomial.Chebyshev.T_eq_half_mul_C_comp_two_mul_X, Matrix.disc_of_card_eq_two, sub_half, Nat.pow_le_choose, OrthonormalBasis.coe_toBasis_repr_apply, QuaternionAlgebra.imJ_natCast, MvPolynomial.counitNat_C, Polynomial.integralNormalization_coeff, Finset.centroid_pair_fin, Cubic.degree_of_b_ne_zero', NNReal.summable_schlomilch_iff, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, ENNReal.lintegral_Lp_add_le_of_le_one, LinearGrowth.linearGrowthInf_add_le, OrthonormalBasis.coe_equiv_euclideanSpace, ENNReal.iUnion_Ioc_coe_nat, Polynomial.degree_shiftedLegendre, PartENat.withTopEquiv_symm_coe, Nat.ceil_natCast, round_eq_iff, round_sub_natCast, Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, Finset.centroidWeights_eq_const, EuclideanSpace.dist_sq_eq, Polynomial.derivative_X_add_C_sq, Commute.add_pow_prime_eq, Order.krullDim_eq_length_of_finiteDimensionalOrder, Polynomial.span_le_degreeLE_of_finite, ZMod.coe_unitOfCoprime, Real.toNNReal_lt_natCast, descPochhammer_succ_eval, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, MvPolynomial.eval₂_natCast, ExpGrowth.expGrowthSup_le_iff, PartENat.lt_find, HahnSeries.ofPowerSeries_apply, WeierstrassCurve.Affine.evalEval_polynomialX, EuclideanSpace.inner_toLp_toLp, Mathlib.Tactic.Zify.Nat.cast_sub_of_lt, UnitAddTorus.hasSum_sq_mFourierCoeff, Finset.tendsto_Ioc_neg, Int.toNat_add_toNat_neg_eq_nnnorm, WithTop.map_natCast, ZMod.natCast_eq_natCast_iff, contDiff_infty, WeierstrassCurve.Jacobian.dblU_of_Z_eq_zero, contMDiffAt_addInvariantVectorField, ordinaryHypergeometric_radius_top_of_neg_nat₁, contMDiff_tangentBundleModelSpaceHomeomorph, Function.Periodic.sub_nat_mul_eq, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, Order.KrullDimLE.krullDim_le, EReal.natCast_div_le, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, NNReal.exists_nat_pos_inv_lt, RootPairing.pairingIn_neg_two_neg_two_iff, Finset.disjoint_box_succ_prod, IsCyclotomicExtension.norm_zeta_pow_sub_one_two, Int.floor_sub_natCast, Unitization.antilipschitzWith_addEquiv, ENNReal.natCast_lt_coe, FloorSemiring.gc_floor, NormedSpace.norm_expSeries_div_summable, SimpleGraph.adjMatrix_mul_self_apply_self, CoxeterSystem.lengthParity_eq_ofAdd_length, WeierstrassCurve.Δ_of_isCharThreeJNeZeroNF, WeierstrassCurve.c₄_of_isCharTwoJEqZeroNF, MeasureTheory.lintegral_nnnorm_condExpIndSMul_le, Zsqrtd.re_natCast, ringKrullDim_le_ringKrullDim_add_spanFinrank, PadicInt.norm_natCast_eq_one_iff, Polynomial.degree_cubic_le, AddCircle.addOrderOf_div_of_gcd_eq_one', Ordinal.lt_omega0, toIocMod_add_natCast_mul, CharP.isUnit_natCast_iff, Nat.cast_zero, MeasureTheory.integrable_condExpIndSMul, Function.mulSupport_natCast, deriv_fun_pow, Finset.prod_natCast, stereographic'_symm_apply, WeierstrassCurve.coeff_Ψ₃, DirichletCharacter.delta_mul, Cubic.equiv_symm_apply_d, Polynomial.Chebyshev.S_eval_two, sq_dvd_add_pow_sub_sub, ZMod.χ₄_nat_mod_four, Nat.cast_pow, Submodule.snd_orthogonalDecomposition_apply, ZMod.natAbs_mod_two, deriv_descPochhammer_eval_eq_sum_prod_range_erase, ENNReal.one_half_lt_one, Nat.cast_le, MvPolynomial.schwartz_zippel_sum_degreeOf, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, dist_midpoint_midpoint_le', ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, iteratedDeriv_fun_pow_zero, AbsoluteValue.apply_natAbs_eq, map_natCast', Polynomial.eval₂_one_cyclotomic_prime_pow, MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv, ZMod.cast_sub_one, IsPrimitiveRoot.zmodEquivZPowers_apply_coe_nat, Nat.cast_finprod_mem, MeasureTheory.Measure.exists_null_set_measure_lt_of_disjoint, Commute.natCast_mul_natCast_mul, EuclideanSpace.coe_measurableEquiv, Irreducible.degree_le_two, invOf_eq_of_coprime, Nat.Coprime.cast, iter_deriv_inv_linear, PairReduction.card_pairSet_le, ProbabilityTheory.IsGaussian.memLp_two_fun_id, NNRat.cast_le_natCast, DirichletCharacter.isMultiplicative_toArithmeticFunction, tendsto_inverse_atTop_nhds_zero_nat, Quaternion.natCast_imK, NumberField.mixedEmbedding.euclidean.finrank, PadicInt.ideal_eq_span_pow_p, contMDiffAt_infty, DirichletCharacter.convolution_mul_moebius, Polynomial.derivative_X_add_C_pow, Fintype.expect_ite_eq', BoxIntegral.unitPartition.volume_box, Finset.pluennecke_ruzsa_inequality_pow_mul, Matrix.map_ofNat, Mathlib.Meta.NormNum.IsNat.out, Polynomial.Chebyshev.leadingCoeff_T, SimpleGraph.degMatrix_mulVec_apply, Nat.neg_cast_eq_cast, nsmul_one, WittVector.mul_polyOfInterest_aux5, ArithmeticFunction.natCoe_apply, EuclideanSpace.nnnorm_eq, RCLike.nnnorm_natCast, ENNReal.tendsto_nhds_top_iff_nat, PiLp.inner_apply, Module.End.natCast_apply, CharP.cast_eq_zero_iff, contMDiff_tangentBundleModelSpaceHomeomorph_symm, IsCyclotomicExtension.Rat.inertiaDeg_of_not_dvd, Padic.valuation_natCast, Submodule.orthogonalDecomposition_apply, range_modelWithCornersEuclideanHalfSpace, Nonneg.coe_natCast, Monotone.linearGrowthSup_nonneg, CharP.cast_eq_iff_mod_eq, Polynomial.degree_eq_card_roots', NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, Nat.inv_pos_of_nat, Padic.norm_p, MeasureTheory.sub_eq_zero_of_upcrossingsBefore_lt, quadraticChar_neg_one, Num.of_natCast, Padic.norm_natCast_p_sub_one, Nat.lt_of_lt_floor, NNReal.agmSequences_succ', NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne, EuclideanSpace.inner_single_right, Monotone.linearGrowthSup_comp_mul, Finset.pluennecke_ruzsa_inequality_nsmul_sub, Nat.floor_eq_iff', IsCyclotomicExtension.neZero', right_sub_midpoint, PreTilt.pow_dvd_mul_untiltAux_sub_untiltAux_mul, Int.mul_natCast_floor_div_cancel, WeierstrassCurve.b₄_of_isCharNeTwoNF, Monotone.le_linearGrowthSup_comp, tsum_sq_fourierCoeff, Cubic.equiv_symm_apply_a, MeasureTheory.eLpNorm_condExpL2_le, Nat.cast_list_sum, MeasureTheory.Measure.count_apply_finite, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, AddGroupWithOne.intCast_ofNat, Ordinal.add_le_add_iff_right, four_mul_le_pow_two_add, ENNReal.inv_three_add_inv_three, exists_nat_gt, NNRat.floor_natCast_div_natCast, WeierstrassCurve.Projective.dblX_eq, zero_lt_two, Nat.cast_choose, Matrix.toEuclideanLin_eq_toLin_orthonormal, RootPairing.pairing_one_four_iff, Commute.self_natCast_mul_natCast_mul, Num.ofNat'_eq, WithTop.coe_natCast, ENNReal.iInter_Ioi_coe_nat, AntivaryOn.card_mul_sum_le_sum_mul_sum, summable_norm_pow_mul_geometric_of_norm_lt_one, Int.div_two_lt_floor, NNReal.summable_condensed_iff, star_natCast, birkhoffAverage_apply_sub_birkhoffAverage, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, Finset.sum_pow, NormedSpace.expSeries_hasSum_exp_of_mem_ball', Nat.cast_tsub, EuclideanSpace.measurableEquiv_toEquiv, SemiconjBy.natCast_mul_natCast_mul, Nat.cast_le_pow_div_sub, ZMod.χ₈_nat_eq_if_mod_eight, Matrix.natCast_kronecker_natCast, toIcoDiv_add_natCast_mul', Nat.cast_injective, Ordinal.card_lt_ofNat, ZMod.prod_Ico_one_prime, NNRat.cast_divNat, MvPolynomial.ringKrullDim_of_isNoetherianRing, Matrix.cstar_norm_def, ModP.preVal_eq_zero, ContMDiff.codRestrict_sphere, WittVector.mul_polyOfInterest_aux3, NNReal.sqrt_mul_le_half_add, jacobiSym.at_neg_one, Commute.add_pow_prime_eq', Surreal.double_powHalf_succ_eq_powHalf, homothety_inv_two, PartENat.natCast_inj, algebraMap.coe_natCast, ENNReal.add_rpow_le_two_rpow_mul_rpow_add_rpow, inner_matrix_row_row, MeasureTheory.condExpIndSMul_ae_eq_smul, Quaternion.linearIsometryEquivTuple_apply, Zsqrtd.im_natCast, odd_two_mul_add_one, isLittleO_pow_const_const_pow_of_one_lt, toIcoDiv_natCast_mul_add, Unitization.lipschitzWith_addEquiv, DirichletCharacter.modZero_eq_delta, Num.of_nat_inj, NNRat.cast_lt_natCast, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, NNRat.cast_natCast, Monotone.expGrowthSup_comp_mul, Order.IsPredLimit.lt_sub_natCast, bernsteinPolynomial.iterate_derivative_at_0, WeierstrassCurve.twoTorsionPolynomial_discr, PartENat.lt_coe_succ_iff_le, dist_midpoint_left, Ordinal.iSup_natCast, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, mfderiv_subtype_coe_Icc_one, NumberField.InfinitePlace.map_natCast, PowerSeries.binomialSeries_nat, Nat.cast_add_one, MeasureTheory.condExpIndSMul_smul', two_add_one_eq_three, ContDiffPointwiseHolderAt.zero_exponent_iff, VectorField.eventually_contMDiffWithinAt_mpullbackWithin_extChartAt_symm, Polynomial.degree_sum_fin_lt, midpoint_vsub_midpoint_same_left, Polynomial.degree_eq_iff_natDegree_eq, Int.absNorm_under_eq_sInf, Ordinal.lift_ofNat, Nat.cast_mul_floor_div_cancel, PiLp.norm_eq_of_L2, Nat.mul_cast_floor_div_cancel, eq_natCast', DividedPowers.prod_dpow, PreTilt.mk_untilt_eq_coeff_zero, PadicInt.unitCoeff_spec, ENNReal.natCast_sub, Nat.cast_lt, Mathlib.Meta.NormNum.NNRat.invOf_denom_swap, IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvd, WeierstrassCurve.j_of_isShortNF, Polynomial.degreeLE_eq_span_X_pow, right_vsub_midpoint, IsManifold.instLEInftyCastWithTopENat, PadicInt.norm_natCast_zmodRepr_eq_iff, Polynomial.aeval_natCast, WeierstrassCurve.Projective.dblX_eq', QuadraticAlgebra.im_natCast, Numbering.dens_prefixed, SetLike.GradeZero.coe_natCast, WittVector.mk_fontaineTheta, Polynomial.descPochhammer_smeval_eq_ascPochhammer, Quaternion.imJ_natCast, tendsto_algebraMap_inv_atTop_nhds_zero_nat, PowerSeries.coeff_one_pow, pow_sum_div_card_le_sum_pow, ordinaryHypergeometricSeries_norm_div_succ_norm, Nat.one_le_cast_iff_ne_zero, Quaternion.natCast_imJ, nndist_right_midpoint, MeasureTheory.ContinuousMap.inner_toLp, PiLp.nnnorm_toLp_const, two_add_two_eq_four, Polynomial.Chebyshev.S_eval_neg_two, Polynomial.natDegree_le_iff_degree_le, Polynomial.evalEval_natCast, Finset.expect_eq_sum_div_card, Ordinal.natCast_lt_epsilon, Ordinal.apply_omega0_of_isNormal, FDRep.scalar_product_char_eq_finrank_equivariant, CharP.charP_iff_prime_eq_zero, contMDiffOn_vectorSpace_iff_contDiffOn, PairReduction.iSup_edist_pairSet, EuclideanSpace.single_eq_zero_iff, NormedSpace.expSeries_summable_of_mem_ball', Matrix.IsHermitian.mulVec_eigenvectorBasis, Finset.sum_boole, Polynomial.degree_monomial, Matrix.l2_opNorm_def, Int.cast_negOfNat, OrthogonalFamily.linearIsometry_apply, Nat.cast_one, ZMod.natCast_toNat, Matrix.toEuclideanLin_toLp, ZMod.eq_unit_mul_divisor, WeierstrassCurve.b₄_of_isCharTwoJEqZeroNF, MeasureTheory.Lp.instContinuousFourier, Ordinal.preOmega_natCast, Polynomial.degree_mul_X_pow, add_div_two_lt_right, MeasureTheory.MemLp.eLpNorm_indicator_le', Nat.ceil_eq_iff, sub_self_div_two, DirichletCharacter.LSeries_eulerProduct, Rat.natCast_lt_cast, OrthonormalBasis.measurePreserving_measurableEquiv, ONote.nf_repr_split, ENNReal.coe_natCast, Finset.expect_ite_eq, PadicInt.unitCoeff_coe, ZMod.exists_sq_eq_neg_two_iff, ENNReal.ofReal_natCast, atTop_hasAntitoneBasis_of_archimedean, Ideal.span_singleton_absNorm_le, Cardinal.preBeth_nat, isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt, ArchimedeanClass.FiniteElement.mk_natCast, PMF.toOuterMeasure_uniformOfFintype_apply, LinearGrowth.linearGrowthSup_monotone, NeZero.charZero, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, PadicInt.coe_dpow_eq, LinearGrowth.linearGrowthInf_le_linearGrowthSup_of_frequently_le, two_mul_le_add_mul_sq, EuclideanSpace.nndist_single_same, Nat.infinite_setOf_prime_and_eq_mod, Nat.WithBot.coe_nonneg, inTangentCoordinates_model_space, Nat.add_one_le_ceil_iff, gaussSum_mul_gaussSum_eq_card, mul_two, LinearGrowth.le_linearGrowthInf_comp, RootPairing.InvariantForm.two_mul_apply_root_root, EuclideanSpace.edist_eq, EuclideanSpace.single_apply, Polynomial.degree_C_mul_X_pow, Pi.orthonormalBasis_repr, WithBot.coe_natCast, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, PadicInt.norm_natCast_p_sub_one, WeierstrassCurve.c₆_of_isShortNF, Set.natCast_mem_center, PadicInt.prime_p, even_iff_exists_two_mul, add_sq', pow_add_pow_le', Nat.cast_pos', MeasureTheory.charFun_eq_pi_iff, Polynomial.Chebyshev.degree_U_natCast, NNReal.tendsto_const_div_atTop_nhds_zero_nat, Matrix.sub_scalar_sq_eq_discr, toIocDiv_add_natCast_mul, Nat.cast_pow_eq_one, WithLp.prod_norm_eq_of_L2, Function.Periodic.neg_nat_mul, CharP.quotient_iff, ZMod.eisenstein_lemma_aux, Finset.cast_card, GaussianInt.prime_iff_mod_four_eq_three_of_nat_prime, Finset.box_succ_union_prod, NNRat.cast_le_ofNat, Nat.abs_ceil_sub_le, contMDiffWithinAt_iff_nat, Finset.nnratCast_dens_mul_natCast_card, logDeriv_pow, IccRightChart_extend_top, derivWithin_pow, LinearGrowth.le_linearGrowthSup_iff, ExpGrowth.le_expGrowthSup_iff, Int.fract_mul_natCast, Polynomial.degree_cyclotomic, eq_natCast, half_le_self_iff, NNRat.den_mul_eq_num, Complex.sum_div_factorial_le, ENNReal.ofNNReal_natCast_add, WeierstrassCurve.Projective.eval_polynomialY, MeasureTheory.Lp.fourier_toTemperedDistribution_eq, DihedralGroup.r_one_pow, boundary_Icc, Matrix.frobenius_norm_replicateRow, MeasureTheory.charFun_prod, Padic.norm_p_zpow, range_two_mul_add_one, ENat.natCast_lt_of_coe_top_le_withTop, SchwartzMap.toLp_fourier_eq, IsPrimitiveRoot.norm_sub_one_two, isUnit_two_iff_forall_even, Ordinal.natCast_lt_of_isSuccLimit, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, ArithmeticFunction.const_one_eq_zeta, EReal.natCast_le_iff, RootPairing.forall_pairing_eq_swap_or, ENNReal.ofReal_le_natCast, MonoidAlgebra.natCast_def, ZMod.coe_int_val_inv_mul, NNReal.dist_gm_am_le, wittPolynomial_eq_sum_C_mul_X_pow, Nonneg.mk_natCast, Ring.choose_eq_nat_choose, hasFTaylorSeriesUpToOn_top_iff_add, DiffeologicalSpace.CorePlotsOn.isPlotOn_univ, EuclideanSpace.volume_closedBall, Nat.cast_le_one, gaussSum_sq, Polynomial.card_roots_sub_C, finrank_euclideanSpace_fin, WeierstrassCurve.ofJ1728_Δ, Commute.add_pow_prime_pow_eq', Surreal.nsmul_pow_two_powHalf', Nat.cast_inv_le_one, CStarAlgebra.nnnorm_le_natCast_iff_of_nonneg, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, SetLike.natCast_mem_graded, boundary_product, Ordinal.natCast_add_omega0, MeasureTheory.norm_condExpL2_le_one, Nat.lt_floor_add_one, ProbabilityTheory.HasGaussianLaw.memLp_two, EqualCharZero.PNat.isUnit_natCast, Function.Antiperiodic.nat_odd_mul_antiperiodic, OrthonormalBasis.repr_reindex, NNRat.cast_lt_ofNat, Nat.one_div_lt_one_div, MeasureTheory.condExpL2_comp_continuousLinearMap, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, InnerProductSpace.symm_toEuclideanLin_rankOne, Polynomial.mem_degreeLT, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, inCoordinates_tangent_bundle_core_model_space, Polynomial.derivative_apply, tendsto_inv_atTop_nhds_zero_nat, EuclideanSpace.coe_measurableEquiv_symm, Zsqrtd.natCast_re, Finset.card_mul_cast_divConst, WeierstrassCurve.Jacobian.eval_polynomialZ, PadicInt.zmodRepr_natCast_of_lt, Finset.expect_ite_eq', Affine.Simplex.faceOppositeCentroid_eq_affineCombination, Finset.cast_addConst, NNReal.agmSequences_succ, Matrix.conjTranspose_ofNat, CauSeq.Completion.ofRat_natCast, jacobiSum_one_one, PowerBasis.dim_le_degree_of_root, PreTilt.coeff_def, Polynomial.coeff_preHilbertPoly_self, RCLike.wInner_cWeight_eq_smul_wInner_one, Matrix.transpose_eq_natCast, NNRat.ofNat_lt_cast, contMDiff_snd_tangentBundle_modelSpace, MeasureTheory.condExpL2_const_inner, PMF.toMeasure_uniformOfFinset_apply, one_dotProduct_one, PowerSeries.invOneSubPow_val_succ_eq_mk_add_choose, BoundedContinuousFunction.nndist_le_two_nnnorm, PadicInt.existsUnique_mem_range, lt_two_mul_self, left_lt_add_div_two, homothety_one_half, RootPairing.pairingIn_same, LinearGrowth.le_linearGrowthInf_add, RootPairing.EmbeddedG2.threeShortAddLongRoot_eq, PairReduction.logSizeRadius_le_card_smallBall, Nat.ceil_le, ENNReal.inv_two_add_inv_two, MeasureTheory.Lp.instFourierAdd, contDiff_euclidean, IccLeftChart_extend_bot_mem_frontier, PiLp.nndist_eq_of_L2, Affine.Simplex.centroid_vsub_point_eq_smul_vsub, WeierstrassCurve.leadingCoeff_Ψ₃, hasStrictDerivAt_pow, OrthonormalBasis.tensorProduct_repr_tmul_apply, Int.ceil_natCast_add, Quaternion.norm_toLp_equivTuple, Icc_isBoundaryPoint_top, MeasureTheory.Subgroup.index_mul_measure, Nat.cast_commute, WittVector.ghostComponentModPPow_map_mk, Polynomial.card_mahlerMeasure_le_prod, Real.natCast_le_toNNReal, RCLike.inner_eq_wInner_one, Ordinal.natCast_lt_gamma, MeasureTheory.measure_sigmaFiniteSetGE_ge, Nat.cast_descFactorial, Ordinal.toGame_natCast, Nat.ofNat_lt_cast, Ordinal.type_fin, MeasureTheory.Measure.toSphere_apply_univ', NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPart, Polynomial.coeff_X_add_C_pow, PerfectClosure.natCast, Int.fract_div_intCast_eq_div_intCast_mod, PadicInt.zmodRepr_eq_zero_iff_dvd, contMDiffOn_infty, Polynomial.degree_linear_lt, PreTilt.coeff_iterate_frobenius', left_sub_midpoint, Real.cast_natAbs_eq_nnabs_cast, Subring.coe_natCast, ENNReal.le_tsum_schlomilch, Int.ceil_natCast, Nat.preimage_Ico, PiLp.edist_eq_of_L2, midpoint_vsub_midpoint_same_right, Affine.Simplex.centroid_vsub_eq, toIcoMod_natCast_mul_add', HilbertBasis.hasSum_repr_symm, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', add_one_le_two_mul, Function.Antiperiodic.sub_nat_mul_eq, contDiff_succ_iff_hasFDerivAt, Polynomial.derivative_C_mul_X_sq, MeasureTheory.condExpL2_indicator_nonneg, Ring.choose_smul_choose, NNReal.bddAbove_range_natCast_iff, ModP.charP, instIsManifoldIcc, FDRep.simple_iff_char_is_norm_one, invOf_two_add_invOf_two, Ordinal.principal_mul_iff_le_two_or_omega0_opow_opow, EMetric.diam_closedBall, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, ZMod.χ₄_nat_eq_if_mod_four, inner_matrix_col_col, LieAlgebra.Orthogonal.pd_inv, NNRat.natCast_eq_divNat, AddCircle.gcd_mul_addOrderOf_div_eq, Quaternion.natCast_imI, Order.krullDimLE_iff, IsCyclotomicExtension.discr_prime_pow, contMDiffOn_projIcc, algebraMap_comp_natCast, DiffeologicalSpace.isOpen_iff_preimages_plots, PMF.ofMultiset_apply, left_vsub_midpoint, NNReal.summable_rpow, Commute.self_natCast_mul, Finset.max_abv_sum_one_le, dvd_geom_sum₂_iff_of_dvd_sub', NNRat.num_div_den, WittVector.peval_polyOfInterest, iter_deriv_pow, contMDiff_circleExp, Polynomial.exists_mul_add_mul_eq_C_resultant, Cubic.degree_of_b_ne_zero, CFC.nnrpow_two, Finset.cast_card_inter, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_pow_ne_two, Polynomial.roots_def, ENNReal.rpow_sum_le_const_mul_sum_rpow, Ordinal.natCast_div, Function.support_natCast, Real.natCast_lt_toNNReal, circleEquivGen_apply, nsmul_zmod_val_inv_nsmul, NNReal.tendsto_algebraMap_inverse_atTop_nhds_zero_nat, bernsteinPolynomial.iterate_derivative_at_1, LipschitzWith.dist, WithLp.prod_antilipschitzWith_ofLp, MeasureTheory.eLpNorm_nsmul, Nat.cast_eq_neg_cast, IsCyclotomicExtension.discr_prime_pow_ne_two', summable_indicator_mod_iff, Finpartition.IsEquipartition.card_interedges_sparsePairs_le', Subsemiring.coe_bot, WeierstrassCurve.ofJ1728_c₄, ArchimedeanClass.exists_nat_gt_of_mk_nonneg, Real.volume_emetric_ball, AddCircle.natCast_div_mul_eq_nsmul, add_self_div_two, factorial_mul_ascPochhammer, LinearGrowth.EReal.eventually_atTop_exists_nat_between, IsPrimitiveRoot.toInteger_sub_one_not_dvd_two, WeierstrassCurve.b₈_of_isCharTwoJNeZeroNF, PowerSeries.derivative_pow, WithBot.add_one_le_iff, natCast_memℓp_infty, Quaternion.natCast_re, Ordinal.card_eq_ofNat, Matrix.discr_fin_two, LinearGrowth.linearGrowthInf_neg, abs_two, Monotone.le_expGrowthSup_comp, ZMod.eq_one_iff_odd, hasStrictFDerivAt_euclidean, RootPairing.pairing_neg_two_neg_two_iff, tendsto_natCast_atTop_cobounded, PadicInt.norm_natCast_lt_one_iff, HasStrictDerivAt.fun_pow, Fintype.expect_eq_sum_div_card, WeierstrassCurve.variableChange_b₄, NormedSpace.exp_eq_ofScalarsSum
toOne 📖	CompOp	4803 math math: List.norm_prod_le, IsPrimitiveRoot.subOneIntegralPowerBasis_gen_prime, odd_add_one_self', ValuativeRel.ValueGroupWithZero.mk_one_one, IsCyclotomicExtension.Rat.Three.eta_sq_add_eta_add_one, MeasureTheory.L1.setToL1_eq_setToL1', MvPolynomial.eval_indicator_apply_eq_one, hasFDerivAt_iff_hasDerivAt, Quaternion.normSq_eq_zero, Finset.sum_Ico_add_eq_sum_Ico_add_one, HomotopyCategory.spectralObjectMappingCone_δ'_app, Order.coheight_add_one_le, ProbabilityTheory.lintegral_exponentialPDF_eq_one, odd_add_one_self, one_le_div_iff, ENNReal.one_rpow, Num.cast_to_int, GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_one, CategoryTheory.InjectiveResolution.Hom.hom'_f, Int.ceil_lt_iff, PiLp.lipschitzWith_toLp, DerivedCategory.instIsLocalizationCochainComplexIntQQuasiIsoUp, KaehlerDifferential.kerCotangentToTensor_toCotangent, Matrix.isTotallyUnimodular_iff, CategoryTheory.ShortComplex.ShortExact.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoX₃CochainComplexMapSingleFunctorOfNatX₁, Quaternion.star_mul_self, CoalgHom.ext_of_ring_iff, WeierstrassCurve.Jacobian.addXYZ_of_Z_ne_zero, WithLp.prod_edist_eq_card, ComplexShape.embeddingUpIntDownInt_f, MvPolynomial.dvd_monomial_one_iff_exists, Quaternion.coe_normSq_add, continuousOn_ceil, vsub_midpoint, Lagrange.interpolate_one, CauSeq.const_one, LSeries.convolution_one_eq_convolution_zeta, CochainComplex.triangleOfDegreewiseSplit_obj₁, Algebra.FormallyUnramified.one_tmul_mul_elem, CochainComplex.mappingConeCompTriangleh_comm₁_assoc, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, PiLp.norm_toLp_const', AffineMap.lineMap_apply_module, instContMDiffVectorBundleOfNatWithTopENatTangentSpaceOfIsManifold, Submodule.rTensorOne_symm_apply, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_symm_apply, Matrix.toLinAlgEquiv_one, PMF.tsum_coe, PEquiv.vecMul_toMatrix_toPEquiv, EReal.one_lt_exp_iff, Polynomial.MonicDegreeEq.monic, Quaternion.star_imJ, Topology.RelCWComplex.skeletonLT_union_iUnion_closedCell_eq_skeletonLT_succ, Module.Basis.equivFun_self, instLieAddGroupOfNatWithTopENat, MeasureTheory.condExpInd_of_measurable, Algebra.Generators.baseChange_val, TrivSqZeroExt.exp_inr, Matrix.list_prod_inv_reverse, RingHom.ker_evalRingHom, Matrix.swap_mul_self, RCLike.one_re, MeasureTheory.IsZeroOrProbabilityMeasure.measure_univ, even_sub_one, ofBoolRing_one, Quaternion.re_star, ENat.floor_pos, ENNReal.one_lt_two, MeasureTheory.condExpL1_smul, PrimeSpectrum.isClopen_iff_mul_add, DihedralGroup.r_one_zpow, Matrix.invOf_fromBlocks₂₂_eq, hasSum_geometric_of_norm_lt_one, CochainComplex.HomComplex.Cochain.fromSingleMk_neg, List.nnnorm_prod, Quaternion.add_imJ, CategoryTheory.DifferentialObject.shiftFunctor_obj_d, Matrix.transposeInvertibleEquivInvertible_symm_apply, CochainComplex.mappingCone.δ_inl, CochainComplex.mappingCone.inl_v_descCochain_v_assoc, SimpleGraph.vertexCoverNum_le_card_sub_one, Coalgebra.lTensor_counit_comul, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_neg, exists_nat_one_div_lt, MeasureTheory.aestronglyMeasurable_condExpInd, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim, Quaternion.instSMulCommClass, Module.Relations.Solution.ofπ'_var, Quaternion.add_imK, Algebra.Presentation.differentials.comm₁₂_single, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_apply, Nat.floor_add_one, uniq_inv_of_isField, IsStarNormal.one_sub, Polynomial.eval₂_one_cyclotomic_prime, ENNReal.HolderConjugate.instOneInfty, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add, AddChar.mulShift_one, DerivedCategory.right_fac, ZMod.pow_card_sub_one, selfZPow_of_nonpos, PMF.toMeasure_pure_apply, Even.one_add, Algebra.TensorProduct.intCast_def', ProbabilityTheory.measure_limsup_eq_one, QuaternionGroup.a_one_pow_n, Int.smul_one_eq_cast, NormedRing.inverse_one_sub_norm, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, Polynomial.coeff_derivative, ENat.lt_add_one_iff', TensorProduct.AlgebraTensorModule.rid_symm_apply, Quaternion.im_add, sq_eq_one_iff, Valuation.isEquiv_iff_val_sub_one_lt_one, MeasureTheory.L1.setToL1_indicatorConstLp, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left, Quaternion.snd_imJ_dualNumberEquiv_symm, ENNReal.coe_eq_one, ringKrullDim_succ_le_ringKrullDim_polynomial, sign_mul_self, ModularFormClass.hasFPowerSeries_cuspFunction, Polynomial.dickson_one_one_mul, Num.cast_lt, CompleteOrthogonalIdempotents.pair_iff, Matrix.Pivot.listTransvecCol_mul_mul_listTransvecRow_last_col, Quaternion.imI_zero, hasStrictFDerivAt_list_prod_finRange', Matrix.add_mul_mul_invOf_mul_eq_one, ModularFormClass.qExpansionFormalMultilinearSeries_radius, CFC.sqrt_eq_one_iff', CFC.posPart_one, InnerProductSpace.rankOne_one_left_eq_innerSL, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_symm_apply, instIsContMDiffRiemannianBundleOfNatWithTopENat_1, CochainComplex.mappingCone.inr_f_d_assoc, CliffordAlgebraQuaternion.j_quaternionBasis, IsPrimitiveRoot.zeta_sub_one_prime_of_two_pow, bernsteinPolynomial.eval_at_1, dotProductEquiv_symm_apply, Quaternion.imJ_im, Quaternion.coe_natCast, Quaternion.instNoZeroDivisors, sum_col_of_mem_doublyStochastic, PowerSeries.heval_C, modularCyclotomicCharacter.id, Quaternion.neg_re, IsIdempotentElem.coe_compl, MvPolynomial.one_def, tendsto_ceil_right', quadraticChar_card_card, PiTensorProduct.isEmptyEquiv_apply_tprod, CliffordAlgebra.foldl_prod_map_ι, EuclideanSpace.orthonormal_single, Affine.Simplex.smul_centroid_vsub_point_eq_smul_faceOppositeCentroid_vsub_point, CochainComplex.HomComplex.Cochain.δ_single, Finset.sum_boole_mul, Polynomial.resultant_X_add_C_right, Nat.cast_factorial, Nat.cast_descFactorial_two, Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty, abs_sub_round, Nat.cast_succ, Metric.unitSphere.coe_one, Valuation.map_one_add_of_lt, AffineMap.hasDerivAtFilter, Int.floor_one, CochainComplex.mappingConeCompTriangle_obj₂, ENat.toNat_one, Finset.prod_one_sub_ordered, Odd.intCast_zmod_two, QuaternionGroup.orderOf_a_one, Quaternion.star_smul, Matrix.one_div_pow, MeasureTheory.tendsto_condExpL1_of_dominated_convergence, Matrix.det_add_replicateCol_mul_replicateRow, Polynomial.Chebyshev.U_eval_one, BoundedContinuousFunction.algebraMap_apply, Rep.diagonalSuccIsoFree_inv_hom_single, spectrum.subset_closedBall_norm_mul, derivWithin_id', WeierstrassCurve.toCharNeTwoNF_t, algebraMap.coe_one, one_add_le_one_add_mul_one_sub, PEquiv.single_mul_single_of_ne, ENat.coe_one, SimpleGraph.adjMatrix_mulVec_apply, ZMod.val_eq_one, AlgebraicGeometry.StructureSheaf.const_mul_rev, CochainComplex.HomComplex.Cocycle.equivHom_symm_apply, Polynomial.coeff_one, WeierstrassCurve.Jacobian.add_of_Y_ne', IncidenceAlgebra.zeta_mul_kappa, MeasureTheory.Measure.hausdorffMeasure_zero_singleton, arithGeom_eq', CliffordAlgebra.foldr'_ι, selfZPow_zero, CochainComplex.isStrictlyGE_shift, ENNReal.toNNReal_eq_one_iff, right_lt_lineMap_iff_one_lt, CochainComplex.mappingCone.id, ProbabilityTheory.Kernel.borelMarkovFromReal_apply', Ring.multichoose_two, IsLprojection.Lnorm, PrimeSpectrum.isClopen_iff_mul_add_zeroLocus, hasSum_choose_mul_geometric_of_norm_lt_one, CochainComplex.shiftFunctorZero_eq, TwoSidedIdeal.one_mem_iff, Int.cast_one_le_of_pos, tsum_coe_mul_geometric_of_norm_lt_one', norm_natCast_eq_mul_norm_one, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, ContinuousLinearMap.continuous_integral_comp_L1, Algebra.algebraMap_eq_smul_one', spinGroup.coe_star_mul_self, one_le_pow_mul_abs_eval_div, CategoryTheory.InjectiveResolution.ι'_f_zero, Algebra.Generators.cotangentSpaceBasis_apply, CliffordAlgebra.involute_prod_map_ι, ContractingWith.edist_le_of_fixedPoint, Quaternion.imI_sub, NormedSpace.invOf_exp_of_mem_ball, Subring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallNeg, Quaternion.one_imI, Asymptotics.isLittleOTVS_one, TwoSidedIdeal.one_mem, one_div_add_one_div, Quaternion.rank_eq_four, CochainComplex.mappingCone.liftCochain_v_snd_v_assoc, ZMod.orderOf_one_add_mul_prime, ContinuousLinearMap.hasDerivAtFilter, FermatLastTheoremForThreeGen.Solution.lambda_sq_not_dvd_a_add_eta_sq_mul_b, ModuleCat.extendScalarsId_hom_app_one_tmul, Quaternion.star_eq_neg, MvPolynomial.X_pow_eq_monomial, Polynomial.MonicDegreeEq.degree, MeasureTheory.L1.norm_setToL1_le, thickenedIndicatorAux_tendsto_indicator_closure, CochainComplex.mappingCone.inr_f_fst_v, IsPrimitiveRoot.nthRoots_one_eq_biUnion_primitiveRoots, CochainComplex.isStrictlyLE_iff, Algebra.IsPushout.equiv_symm_algebraMap_left, PMF.toOuterMeasure_pure_apply, Int.fract_add_one, Quaternion.finrank_eq_four, inner_self_eq_one_of_norm_eq_one, pinGroup.coe_star_mul_self, FiniteField.isSquare_neg_one_iff, ArithmeticFunction.coe_moebius_mul_coe_zeta, ProbabilityTheory.lintegral_gaussianPDF_eq_one, CochainComplex.HomComplex.Cochain.leftShift_smul, WeierstrassCurve.Projective.nonsingularLift_some, Set.Icc.coe_zero, Polynomial.resultant_add_left_deg, IncidenceAlgebra.eulerChar_prod, KaehlerDifferential.mvPolynomialBasis_repr_D_X, Quaternion.intCast_imK, PiLp.norm_toLp_one, LinearMap.IsSymmetric.diagonalization_apply_self_apply, PartENat.ofENat_one, stdSimplexHomeomorphUnitInterval_symm_apply_coe, AlgebraicGeometry.StructureSheaf.const_self, Even.add_one, Algebra.PowerBasis.norm_gen_eq_coeff_zero_minpoly, CochainComplex.HomComplex.Cochain.fromSingleEquiv_fromSingleMk, AddConstMapClass.map_add_one, CancelDenoms.cancel_factors_le, FermatLastTheoremForThreeGen.Solution.lambda_dvd_a_add_eta_sq_mul_b, Algebra.Generators.toAlgHom_ofComp_localizationAway, IsIdempotentElem.one_sub, SimpleGraph.sum_incMatrix_apply, Polynomial.leadingCoeff_one, TensorProduct.piScalarRight_symm_algebraMap, continuousOn_floor, Matrix.Pivot.listTransvecCol_mul_last_col, QuaternionAlgebra.Basis.i_mul_i, FirstOrder.Field.realize_genericMonicPolyHasRoot, Polynomial.C_1, Matroid.eRk_singleton_le, Quaternion.star_imI, Nat.floor_eq_iff, AddChar.wInner_cWeight_self, MvPolynomial.divMonomial_add_modMonomial, IsNilpotent.isUnit_sub_one, CochainComplex.mappingCone.triangle_mor₁, AbsoluteValue.map_units_intCast, cfc_const_one, Quaternion.coe_inv, MeasureTheory.norm_setToFun_le_mul_norm', IsCyclic.val_mulAutMulEquiv_apply, seminormFromConst_seq_one, LinearMap.ext_ring_op_iff, ArithmeticFunction.intCoe_one, Algebra.TensorProduct.natCast_def', ENNReal.log_lt_zero_iff, HomologicalComplex₂.shiftFunctor₂XXIso_refl, ascPochhammer_eval_one, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, hasDerivAt_neg', Odd.exists_bit1, ringKrullDim_eq_one_iff_of_isLocalRing_isDomain, spectrum.units_smul_resolvent_self, Coalgebra.sum_map_tmul_counit_eq, Algebra.IsPushout.cancelBaseChange_tmul, Quaternion.normSq_natCast, CochainComplex.mappingCone.liftCochain_v_snd_v, SimplexCategory.toTopObj_one_coe_add_coe_eq_one, IsCyclotomicExtension.discr_odd_prime, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₂, fwdDiff_iter_pow_eq_zero_of_lt, frobenius_one, ComplexShape.instIsTruncLENatIntEmbeddingUpIntLE, WeierstrassCurve.Projective.equiv_some_of_Z_ne_zero, Module.exists_dual_forall_apply_eq_one, HahnSeries.SummableFamily.powers_zero, Matrix.mul_invOf_eq_iff_eq_mul_right, IsPrimitiveRoot.mem_nthRootsFinset, Cardinal.one_eq_ofENat, Quaternion.im_intCast, Quaternion.imJ_smul, Int.floor_add_one, Quaternion.imK_natCast, WithLp.prod_norm_eq_idemFst_of_L1, Polynomial.leadingCoeff_det_X_one_add_C, MeasureTheory.Measure.haarMeasure_closure_self, Coalgebra.sum_tmul_counit_eq, eventually_homothety_image_subset_of_finite_subset_interior, sbtw_iff_mem_image_Ioo_and_ne, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₃, LinearMap.toMatrix_one, CochainComplex.instIsStrictlyLEObjHomologicalComplexIntUpSingle, ModularGroup.bottom_row_coprime, Finsupp.weight_single_one_apply, MeasureTheory.L1.ofReal_norm_eq_lintegral, Algebra.FormallyUnramified.lmul_elem, List.nnnorm_prod_le', MeasureTheory.condExpIndL1Fin_smul, Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, SimpleGraph.dotProduct_mulVec_adjMatrix, MvPowerSeries.coeff_X_pow, CentroidHom.starCenterIsoCentroid_symm_apply_coe, CliffordAlgebraDualNumber.equiv_symm_eps, Algebra.Presentation.localizationAway_relation, Wbtw.right_mem_image_Ici_of_left_ne, MvPolynomial.monomial_finsupp_sum_index, Fin.sum_neg_one_pow, selfAdjoint.norm_sq_expUnitary_sub_one, WithLp.instCompleteSpace, SpecialLinearGroup.mem_center_iff_spec, Finset.affineCombinationLineMapWeights_apply_left, DerivedCategory.instCommShiftHomologicalComplexIntUpHomFunctorQuotientCompQhIso, Rep.diagonalHomEquiv_symm_apply, SetTheory.PGame.quot_one, FormalMultilinearSeries.derivSeries_coeff_one, MulAlgebraNorm.extends_norm', segment_eq_image₂, MeasureTheory.lintegral_indicator_one_le, Polynomial.derivative_pow_succ, 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, stdSimplex_fin_two, ZMod.cast_one, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, Int.cast_le_neg_one_of_neg, Hyperreal.epsilon_mul_omega, Order.pred_iterate, fact_one_le_two_ennreal, Polynomial.monomial_one_one_eq_X, MeasureTheory.L1.SimpleFunc.setToL1SCLM_const, cfc_apply_one, Polynomial.dickson_two_one_eq_chebyshev_S, CategoryTheory.DifferentialObject.d_squared_apply, hasSum_coe_mul_geometric_of_norm_lt_one', Subring.closure_singleton_one, UpperHalfPlane.specialLinearGroup_apply, AffineMap.hasDerivWithinAt, Order.height_add_one_le, Polynomial.isMonicOfDegree_iff, Matrix.detp_neg_one_one, IncidenceAlgebra.moebius_inversion_top, Quaternion.add_re, EuclideanSpace.basisFun_apply, ENat.one_lt_card_iff_nontrivial, invOf_pos, 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, MvPowerSeries.X_pow_eq, IsLocalRing.isUnit_or_isUnit_one_sub_self, ENat.map_one, NNRat.cast_one, tsum_geometric_lt_top, hasDerivAt_exp_zero_of_radius_pos, FractionalIdeal.one_mem_one, ZNum.of_natCast, SkewMonoidAlgebra.toFinsupp_eq_single_one_one_iff, Finset.one_le_mulConst_self, Int.floor_sub_one, mem_doublyStochastic_iff_sum, ZMod.exists_sq_eq_neg_one_iff, MeasureTheory.Integrable.toL1_zero, ValuativeRel.inv_srel_one, Matrix.le_one_of_mem_colStochastic, HahnSeries.ofPowerSeries_X_pow, LinearMap.BilinForm.toMatrix'_apply, PEquiv.toMatrix_toPEquiv_mulVec, ENNReal.HolderConjugate.one_sub_inv, PartENat.withTopEquiv_one, Polynomial.Chebyshev.S_eq_U_comp_half_mul_X, convexComboPair_one, Matrix.map_swap, LaurentSeries.valuation_single_zpow, Matrix.mulVec_single_one, ZMod.wilsons_lemma, CStarAlgebra.mem_Icc_iff_norm_le_one, Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_center, CochainComplex.instLinearIntFunctorSingleFunctors, NNRat.cast_listProd, TrivSqZeroExt.inv_one, tendsto_fract_left', round_sub_one, Module.Basis.mk_coord_apply_eq, Quaternion.imI_mul, ENat.coe_top_add_one, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂_assoc, SpecialLinearGroup.mem_center_iff, Finset.prod_Ico_mul_eq_prod_Ico_add_one, Order.krullDim_le_one_iff, Algebra.FormallyUnramified.finite_of_free_aux, WeierstrassCurve.isCharTwoJNeZeroNF_iff, Matrix.swap_mulVec_apply, IsNilpotent.exp_mul_exp_neg_self, Polynomial.eval₂_one, Matrix.permMatrix_mem_rowStochastic, ExpChar.pow_prime_pow_mul_eq_one_iff, Quaternion.snd_re_dualNumberEquiv_symm, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_C, MeasureTheory.withDensity_one, Quaternion.coe_ratCast, Quaternion.imJ_one, Algebra.TensorProduct.algebraMap_apply, ContFract.convs_eq_convs', minpoly_algHom_toLinearMap, Polynomial.chebyshev_U_eq_dickson_two_one, Ideal.ne_top_iff_one, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, MeasureTheory.condExpIndL1_add, Submodule.span_pow, CochainComplex.mappingCone.d_snd_v, Matrix.det_succ_row, MeasureTheory.L1.norm_setToL1_le_norm_setToL1SCLM, CochainComplex.HomComplex.Cochain.rightUnshift_neg, Algebra.PreSubmersivePresentation.baseChange_jacobian, Dynamics.coverMincard_univ, contDiff_one_iff_fderiv, CochainComplex.HomComplex.Cochain.δ_fromSingleMk, MeasureTheory.MemLp.norm_rpow, Set.Ioo.lt_one, FractionalIdeal.one_le, contMDiff_equivTangentBundleProd_symm, WeierstrassCurve.Affine.CoordinateRing.coe_basis, Polynomial.map_sub_roots_sprod_eq_prod_map_eval, PMF.binomial_apply_zero, ENNReal.lintegral_rpow_funMulInvSnorm_eq_one, ContinuousMultilinearMap.mkPiRing_apply_one_eq_self, GenContFract.of_partNum_eq_one_and_exists_int_partDen_eq, IsAlgebraic.invOf, IsPrimitiveRoot.zeta_sub_one_prime_of_ne_two, Matrix.adjugate_fin_succ_eq_det_submatrix, mulRightLinearMap_one, CochainComplex.HomComplex.Cochain.map_v, ModularGroup.bottom_row_surj, Module.Basis.repr_self_apply, Quaternion.coe_pow, MeasureTheory.L1.integral_smul, Matrix.exists_right_inverse_iff_isUnit, Quaternion.ratCast_re, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, KaehlerDifferential.kerToTensor_apply, Quaternion.imJ_fst_dualNumberEquiv, ENNReal.tendsto_pow_atTop_nhds_zero_iff, IsPrimitiveRoot.subOneIntegralPowerBasis_gen, IsFractionRing.mk'_eq_one_iff_eq, two_inv_lt_one, ProbabilityTheory.uniformOn_of_univ, Algebra.SubmersivePresentation.ofSubsingleton_algebra_algebraMap, ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, Algebra.Presentation.differentials.hom₁_single, Set.Icc.nonneg, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_hom_app, Subalgebra.coe_one, IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one', CochainComplex.ConnectData.map_comp_map, RingHom.SurjectiveOnStalks.exists_mul_eq_tmul, Quaternion.im_re, ConditionallyCompleteLinearOrderedField.toZeroLEOneClass, Module.Basis.det_isEmpty, TrivSqZeroExt.instNormOneClass, Matrix.SpecialLinearGroup.center_equiv_rootsOfUnity'_symm_apply_coe_coe, CochainComplex.HomComplex.leftHomologyData_K_coe, MeasureTheory.prob_compl_eq_one_iff₀, CochainComplex.mappingConeCompTriangle_mor₃, Algebra.TensorProduct.basis_apply, CochainComplex.HomComplex.Cochain.shift_add, geom_sum_two, MvPolynomial.pderiv_one, LinearMap.liftBaseChange_one_tmul, Matrix.toMvPolynomial_one, OrthonormalBasis.repr_self, Matrix.smul_one_eq_diagonal, Num.cast_le, WeierstrassCurve.Jacobian.addXYZ_of_X_eq, invOf_nonneg, Submodule.one_mem_div, CancelDenoms.cancel_factors_lt, NumberField.Embeddings.pow_eq_one_of_norm_le_one, CochainComplex.HomComplex.Cochain.comp_id, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, norm_sub_mul_le', CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_add, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_sub, Polynomial.resultant_comm, LinearMap.IsSymmetric.directSum_decompose_apply, CategoryTheory.ProjectiveResolution.cochainComplex_d, CochainComplex.HomComplex.Cochain.toSingleMk_neg, FermatLastTheoremForThreeGen.lambda_pow_four_dvd_c_cube, MeasureTheory.Measure.haarMeasure_self, CochainComplex.HomComplex.Cochain.ofHom_v_comp_d, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂_assoc, WeierstrassCurve.Projective.add_of_Z_eq_zero, Nat.one_div_le_one_div, IsPrimitiveRoot.prod_one_sub_pow_eq_order, ContractingWith.one_sub_K_pos', Polynomial.dickson_one_one_eq_chebyshev_C, conjneg_one, IsOrderedRing.toZeroLEOneClass, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁_assoc, MeasureTheory.condExpIndL1Fin_add, MeasureTheory.Measure.count_singleton', Matrix.rank_one, CochainComplex.shiftShortComplexFunctorIso_add'_hom_app, CochainComplex.HomComplex.Cochain.map_zero, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup_atTop, Quaternion.mul_imK, Polynomial.leadingCoeff_X_pow_add_C, CochainComplex.cm5b.fac, Convex.mapsTo_lineMap, Matrix.fromBlocks_eq_of_invertible₁₁, ContinuousLinearMap.toSpanSingleton_apply_one, ProbabilityTheory.Kernel.measure_eq_zero_or_one_of_indepSet_self', 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, QuaternionAlgebra.Basis.j_mul_j, Int.ceil_one_add, Quaternion.coe_commutes, ProbabilityTheory.Kernel.rnDeriv_eq_one_iff_eq, CochainComplex.HomComplex.Cochain.toSingleMk_v, CliffordAlgebra.toProd_ι_tmul_one, Matrix.isTotallyUnimodular_iff_fintype, ModularGroup.coe_apply_complex, CochainComplex.HomComplex.leftHomologyData'_i, stdSimplexHomeomorphUnitInterval_zero, tsum_geometric_of_norm_lt_one, finsuppTensorFinsupp'_symm_single_eq_tmul_single_one, List.norm_prod_le', Rep.finsuppToCoinvariantsTensorFree_single, ZMod.natCast_eq_one_iff_odd, Module.Relations.Solution.IsPresentation.linearEquiv_symm_var, MeasureTheory.condExpL1_measure_zero, CochainComplex.IsKInjective.rightOrthogonal, CStarAlgebra.mem_Icc_iff_nnnorm_le_one, pow_sub_one_mul_geom_sum_eq_pow_sub_one_mul_geom_sum, FirstOrder.Field.realize_eqZero, ENat.floor_add_one, CochainComplex.ConnectData.cochainComplex_X, Set.Ioc.coe_pow, Coalgebra.sum_counit_tmul_eq, selfAdjoint.val_one, CochainComplex.IsKInjective.Qh_map_bijective, Ordinal.toGame_one, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_vsub, IncidenceAlgebra.zeta_mul_zeta, MeasureTheory.AEEqFun.integrable_iff_mem_L1, instIsSemirealOfIsStrictOrderedRingOfExistsAddOfLE, edist_le_of_edist_le_geometric_of_tendsto, Set.Ioo.one_minus_pos, ComplexShape.Embedding.embeddingUpInt_areComplementary, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_apply, AddSubgroup.intCast_mem_zmultiples_one, CochainComplex.HomComplex.Cochain.shift_neg, HomotopyCategory.instIsHomologicalIntUpHomologyFunctor, UniformSpace.Completion.coe_eq_one_iff, Finset.prod_indicator_biUnion_finset_sub_indicator, Int.range_castAddHom, Height.logHeight₁_one, ExteriorAlgebra.algebraMap_eq_one_iff, ProbabilityTheory.cond_apply_self, formalMultilinearSeries_geometric_apply_norm_le, ProbabilityTheory.Kernel.bound_le_one, Quaternion.imJ_zero, Polynomial.X_pow_eq_monomial, ZNum.gcd_to_nat, IsIdempotentElem.one_sub_mul_self, IsCoprime.mulVecSL, LaurentSeries.ofPowerSeries_powerSeriesPart, wbtw_lineMap_iff, SeparatingDual.exists_eq_one, Quaternion.instFree, DerivedCategory.subsingleton_hom_of_isStrictlyLE_of_isStrictlyGE, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_snd, nndist_right_lineMap, MeasureTheory.L1.SimpleFunc.norm_setToL1S_le, LaurentSeries.single_order_mul_powerSeriesPart, Quaternion.sub_imJ, lt_one_div, neg_one_smul, IsNonarchimedean.apply_natCast_le_one_of_isNonarchimedean, Polynomial.resultant_X_sub_C_right, MvPolynomial.sum_antidiagonal_card_esymm_psum_eq_zero, PowerSeries.binomialSeries_coeff, Num.cast_bit0, sbtw_iff_left_ne_and_right_mem_image_Ioi, NormedRing.inverse_one_sub_nth_order, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, MeasureTheory.L1.SimpleFunc.setToL1S_neg, Quaternion.im_smul, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f_assoc, IsFoelner.mean_univ_eq_one, ordinaryHypergeometricSeries_radius_eq_one, Int.floor_eq_zero_iff, TensorProduct.flip_mk_surjective, complEDS_one, Finset.prod_sub, CochainComplex.homotopyUnop_hom_eq, Quaternion.imI_fst_dualNumberEquiv, CochainComplex.HomComplex.Cochain.toSingleMk_add, iteratedDerivWithin_eq_iteratedFDerivWithin, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.Measure.rnDeriv_eq_one_iff_eq, Nat.floor_sub_one, Matrix.permMatrixHom_apply, Quaternion.im_zero, MeasureTheory.Measure.addHaarMeasure_closure_self, MeasureTheory.continuous_condExpIndL1, LinearMap.toMatrixAlgEquiv'_id, AlgebraicGeometry.Proj.one_apply, FermatLastTheoremForThreeGen.Solution.hab, WithBot.lt_add_one_iff, mul_neg_one_pow_eq_zero_iff, Quaternion.algebraMap_def, Mathlib.Tactic.Linarith.zero_lt_one, CochainComplex.mappingCone.inr_f_d, Nat.eq_sq_add_sq_iff_eq_sq_mul, ENNReal.toReal_one, CauSeq.one_apply, Matrix.vandermonde_succ, le_one_div_of_neg, Quaternion.imJ_coe, Polynomial.eval₂_reflect_eq_zero_iff, FermatLastTheoremForThreeGen.Solution.a_add_eta_mul_b, PEquiv.map_toMatrix, Matrix.TransvectionStruct.det, mem_rootsOfUnity_iff_mem_nthRoots, MvPolynomial.coe_one, MeasureTheory.dominatedFinMeasAdditive_condExpInd, CochainComplex.HomComplex.δ_v, MeasureTheory.L1.SimpleFunc.integral_add, RatFunc.coe_X, MonoidAlgebra.lift_symm_apply, IsPrimitiveRoot.norm_toInteger_sub_one_of_eq_two, Positive.val_one, MeasureTheory.Integrable.edist_toL1_zero, CochainComplex.instIsStrictlyGEObjHomologicalComplexIntUpSingle, Algebra.Generators.cotangentSpaceBasis_repr_one_tmul, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim_of_mem_jacobson, CochainComplex.HomComplex.Cochain.comp_v, Polynomial.integralNormalization_coeff_natDegree, Polynomial.Splits.eval_derivative_eq_eval_mul_sum, ProbabilityTheory.Kernel.measure_eq_zero_or_one_of_indepSet_self, Matroid.IsNonloop.eRk_eq, EReal.tendsto_exp_nhds_zero_nhds_one, AffineBasis.coord_apply, Quaternion.normSq_smul, Matrix.op_smul_one_eq_diagonal, Quaternion.coe_re, QuadraticAlgebra.omega_mul_coe_mul_mk, CochainComplex.HomComplex.Cochain.comp_zero_cochain_v, HomologicalComplex.dgoToHomologicalComplex_obj_d, PadicInt.mul_inv, RCLike.I_mul_I, DualNumber.lift_apply_eps, selfZPow_neg_mul, ENNReal.one_le_inv, AlternatingMap.ext_ring_iff, OrthogonalIdempotents.prod_one_sub, MeasureTheory.L1.setToL1_smul_left, Algebra.TensorProduct.includeRight_apply, CochainComplex.mappingCone.inr_f_descShortComplex_f_assoc, MvPowerSeries.coeff_X, CochainComplex.HomComplex.Cochain.neg_v, Asymptotics.IsBigO.listProd, CochainComplex.HomComplex.Cocycle.equivHomShift'_symm_apply, MeasureTheory.L1.setToL1_zero_left, Finsupp.linearCombination_one_tmul, Matrix.updateRow_eq_transvection, CochainComplex.HomComplex.Cochain.sub_v, binomialSeries_radius_eq_one, ofNat_eq_one, WeierstrassCurve.Affine.polynomial_eq, WithLp.unitization_algebraMap, Matrix.mul_inv_of_invertible, WeierstrassCurve.Jacobian.Point.fromAffine_some, AffineBasis.toMatrix_mul_toMatrix, FormalMultilinearSeries.ofScalars_apply_zero, DualNumber.inv_eps, MeasureTheory.condExpInd_nonneg, 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, le_one_of_mem_doublyStochastic, ringKrullDim_succ_le_ringKrullDim_powerseries, HahnSeries.SummableFamily.powers_of_not_orderTop_pos, Polynomial.resultant_X_pow_right, AffineMap.homothety_one, Matrix.toLinearMapₛₗ₂'_single, CochainComplex.mappingCone.lift_f_fst_v, monotoneOn_descPochhammer_eval, CochainComplex.mappingCone.inl_v_triangle_mor₃_f, Polynomial.height_eq_height_add_one, CliffordAlgebra.foldl_one, MeasureTheory.condExpL1_of_aestronglyMeasurable', Matrix.SpecialLinearGroup.coe_one, spectrum.norm_le_norm_mul_of_mem, CochainComplex.XIsoOfEq_shift, Finset.mem_convexHull', HasStrictFDerivAt.list_prod', Quaternion.smul_imK, Dynamics.one_le_coverMincard_iff, Polynomial.isPrimitive_iff_content_eq_one, GradedTensorProduct.auxEquiv_one, LinearMap.BilinForm.apply_dualBasis_left, NormedField.exists_one_lt_enorm, ENNReal.top_rpow_def, segment_single_subset_stdSimplex, ENat.ceil_sub_one, Matrix.det_add_mul, geom_sum_pos_iff, ENat.ceil_lt_add_one, MvPolynomial.coeffs_one, MeasureTheory.L1.continuous_integral, div_le_one_iff, GenContFract.abs_sub_convergents_le', LieAlgebra.Orthogonal.jb_transform, HomogeneousLocalization.val_one, FreeRing.coe_one, PowerSeries.binomialSeries_add, ContinuousMultilinearMap.ext_ring_iff, Polynomial.dvd_comp_C_mul_X_add_C_iff, Polynomial.algEquivCMulXAddC_symm_eq, Matrix.PosSemidef.one, TensorProduct.toMatrix_assoc, CochainComplex.HomComplex.Cochain.rightUnshift_comp, CochainComplex.HomComplex.Cochain.rightUnshift_units_smul, Subalgebra.list_prod_mem, one_div_strictAntiOn, ComplexShape.eulerCharSignsUpInt_χ, MeasureTheory.L1.integrable_coeFn, MvPolynomial.coeffs_one_of_nontrivial, CochainComplex.mappingCone.inr_triangleδ, exteriorPower.ιMultiDual_apply_diag, AbsoluteValue.isEquiv_iff_lt_one_iff, multipliable_one_add_of_summable, CochainComplex.HomComplex.Cochain.ofHoms_comp, 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, uzpow_one, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_eq, Quaternion.normSq_le_zero, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_sub, ArithmeticFunction.moebius_mul_coe_zeta, MvPolynomial.monomial_mul_mem_coeffsIn, Matrix.det_one_add_smul, LinearMap.toMatrix_id, one_geom_sum, 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, contDiff_succ_iff_fderiv, RootPairing.pairing_one_four_iff', CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_sub, Matrix.mul_reindexLinearEquiv_one, WithLp.prod_nndist_eq_of_L1, ModularGroup.tendsto_abs_re_smul, tsum_geometric_le_of_norm_lt_one, CochainComplex.instIsStrictlyLEExtendNatIntEmbeddingDownNatOfNat, IsOfFinOrder.eq_neg_one, Finset.natCast_card_filter, spinGroup.coe_mul_star_self, Quaternion.inv_def, TrivSqZeroExt.fst_invOf, ProbabilityTheory.IsMarkovKernel.bound_eq_one, CongruenceSubgroup.Gamma1_mem', SkewMonoidAlgebra.one_def, Algebra.Generators.H1Cotangent.δAux_C, SimpleGraph.mul_adjMatrix_apply, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, LinearIndependent.repr_eq_single, IsContDiffImplicitAt.one_le, sub_half_lt_round, Finset.one_le_mulConst, MvPolynomial.monomial_one_dvd_iff_modMonomial_eq_zero, FirstOrder.Ring.realize_termOfFreeCommRing, CochainComplex.mappingCone.id_X, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom, Representation.leftRegular_norm_eq_zero_iff, LieAlgebra.Orthogonal.indefiniteDiagonal_assoc, Finsupp.supported_eq_span_single, ContinuousMultilinearMap.mkPiAlgebraFin_apply, seminormFromBounded_one_le, GradedTensorProduct.tmul_coe_mul_one_tmul, GenContFract.convs'_succ, Matrix.conjTranspose_permMatrix, ModuleCat.RestrictionCoextensionAdj.counit'_app, CochainComplex.HomComplex.Cochain.single_zero, CochainComplex.mappingCone.inr_descShortComplex_assoc, NeZero.charZero_one, Real.dimH_univ, MeasureTheory.exists_isSigmaFiniteSet_measure_ge, HopfAlgebra.sum_mul_antipode_eq_smul, hasDerivAt_id', MvPolynomial.coe_eq_one_iff, Pi.basis_repr_single, algebraMap_apply, SameRay.exists_eq_smul, Nat.binCast_eq, Matrix.IsHermitian.eigenvectorUnitary_mulVec, IsSimpleRing.one_mem_of_ne_zero_mem, QuadraticAlgebra.norm_eq_one_iff_mem_unitary, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left', FiniteMultiplicity.emultiplicity_self, LinearMap.isIdempotentElem_map_one_iff, Matrix.det_kroneckerMapBilinear, ContinuousLinearMap.deriv, Polynomial.eval₂_list_prod, Subsemiring.closure_insert_one, indicator_le_thickenedIndicatorAux, MvPowerSeries.coeff_index_single_X, Polynomial.aeval_one, Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap, IsIdempotentElem.spectrum_subset, Quaternion.zero_imJ, Module.Basis.sumQuot_repr_left, ringKrullDim_quotSMulTop_succ_eq_ringKrullDim, MeasureTheory.continuous_setToFun, IsOfFinOrder.eq_one, Matrix.toLinearMap₂'Aux_single, mulVec_one_of_mem_doublyStochastic, MeasureTheory.L1.dist_eq_integral_dist, ZNum.cmp_to_int, ProbabilityTheory.Kernel.bound_eq_one, EReal.one_le_exp_iff, MeasureTheory.L1.norm_def, Polynomial.prod_roots_eq_coeff_zero_of_monic_of_splits, PiLp.nnnorm_toLp_one, MvPolynomial.totalDegree_list_prod, Topology.RelCWComplex.iUnion_openCell_eq_skeleton, RingEquiv.moduleEndSelf_symm_apply, Dynamics.netMaxcard_zero, ZMod.inv_neg_one, LocalizedModule.equivTensorProduct_symm_apply_tmul_one, PadicInt.inv_mul, Nat.two_pow_sub_pow, 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, ZNum.of_intCast, LocalizedModule.equivTensorProduct_apply_mk, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_sub, Algebra.discr_powerBasis_eq_norm, jacobiSum_one_nontrivial, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id, PowerSeries.binomialSeries_zero, StdSimplex.ext_iff, PowerSeries.coeff_zero_one, QuadraticForm.polarBilin_tmul, openSegment_eq_image', SignType.map_cast, FirstOrder.Language.presburger.realize_sum, ContinuousLinearMap.hasDerivAt, CliffordAlgebra.foldr_prod_map_ι, mul_neg_geom_sum, Quaternion.smul_im, PosNum.cast_mul, IsPrimitiveRoot.norm_eq_neg_one_pow, isGroupLikeElem_iff, CochainComplex.HomComplex.leftHomologyData_i_hom_apply, PadicInt.fwdDiff_tendsto_zero, DividedPowers.OfInvertibleFactorial.dpow_zero, ENNReal.holderConjugate_iff, ContractingWith.apriori_edist_iterate_efixedPoint_le', Quaternion.normSq_nonneg, HomotopyCategory.instAdditiveIntUpShiftFunctor, WeierstrassCurve.b₂_of_isCharTwoJNeZeroNF, ENat.one_le_card_iff_nonempty, MeasureTheory.Integrable.tendsto_eLpNorm_condExp, StarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar, IsCyclotomicExtension.norm_zeta_pow_sub_one_of_prime_ne_two, Quaternion.instNontrivial, CochainComplex.HomComplex.Cochain.fromSingleMk_postcomp, contDiffAt_one_iff, IsAddFoelner.mean_univ_eq_zero, Algebra.TensorProduct.includeLeft_apply, Set.pairwise_disjoint_Ioo_add_intCast, WeierstrassCurve.Projective.addXYZ_of_X_eq, Order.coheight_eq_coe_add_one_iff, CochainComplex.mappingCone.d_snd_v'_assoc, IncidenceAlgebra.moebius_inversion_bot, instIsLocalizationHomologicalComplexIntUpHomotopyCategoryQuotientHomotopyEquivalences, ProbabilityTheory.measure_eq_zero_or_one_of_indepSet_self, PrimeSpectrum.basicOpen_eq_zeroLocus_of_isIdempotentElem, Matrix.mem_unitaryGroup_iff, Int.fract_one_add, Polynomial.coeff_X_pow, IsLprojection.coe_compl, DirichletCharacter.sum_characters_eq, Module.Relations.Solution.ofQuotient_var, MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub, ArithmeticFunction.one_smul', ModularGroup.denom_apply, MeasureTheory.Integrable.norm_toL1, CochainComplex.HomComplex.Cochain.shift_zero, ZNum.cast_succ, Complex.lift_apply, Finset.univ_of_card_le_three, Nat.preimage_floor_of_ne_zero, CategoryTheory.Functor.instCommShiftHomotopyCategoryIntUpDerivedCategoryHomMapDerivedCategoryFactorsh, Quaternion.coe_zpow, Polygon.edgeSet_eq_image_edgePath, ZNum.mod_to_int, single_mem_stdSimplex, MvPolynomial.expand_zero, WeierstrassCurve.Jacobian.negMap_of_Z_ne_zero, Quaternion.im_one, CochainComplex.shiftFunctorZero_inv_app_f, GradedTensorProduct.tmul_one_mul_one_tmul, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, ZMod.natCast_self', WeierstrassCurve.Jacobian.equiv_zero_of_Z_eq_zero, FirstOrder.Field.instModelACFOfCharPOfIsAlgClosed, AffineMap.homothety_neg_one_apply, hasDerivWithinAt_neg, Algebra.TensorProduct.right_algebraMap_apply, Quaternion.imJ_nnratCast, VitaliFamily.ae_tendsto_measure_inter_div_of_measurableSet, Unitary.norm_sub_one_lt_two_iff, Subfield.list_prod_mem, Ring.choose_neg, IsCoprime.vecMulSL, PresheafOfModules.unit_map_one, MeasureTheory.L1.setToL1_mono_left', CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_zero, ascPochhammer_eval_zero, Polynomial.sum_X_index, WeierstrassCurve.a₁_of_isCharTwoJNeZeroNF, Quaternion.re_zero, CochainComplex.HomComplex.Cochain.leftShift_comp, ENat.card_le_one_iff_subsingleton, Matrix.one_fromCols_isTotallyUnimodular_iff, IsLocalization.mk'_eq_mul_mk'_one, SemimoduleCat.MonoidalCategory.rightUnitor_inv_apply, 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, MeasureTheory.Integrable.toL1_eq_mk, Matrix.toLinearEquiv'_symm_apply, tendsto_one_div_add_atTop_nhds_zero_nat, stdSimplex.eq_one_of_unique, PowerSeries.constantCoeff_invUnitsSub, ValuativeRel.div_vle_one_iff, LinearMap.hasStrictDerivAt, summable_const_div_iff, CochainComplex.triangleOfDegreewiseSplit_obj₂, Matrix.SpecialLinearGroup.det_coe, LinearMap.toMatrixAlgEquiv_id, AddMonoidAlgebra.of_apply, WeierstrassCurve.toCharNeTwoNF_s, Metric.externalCoveringNumber_le_one_of_ediam_le, MvPowerSeries.trunc_one, Summable.tendsto_alternating_series_tsum, Subalgebra.LinearDisjoint.mulMapLeftOfSupEqTop_symm_apply, LinearMap.det_eq_one_of_not_module_finite, Matrix.SpecialLinearGroup.map_apply_coe, PEquiv.mul_toMatrix_apply, RingHom.isIntegralElem_one, one_lt_div, Matrix.permanent_one, Polynomial.nthRoots_two_one, CliffordAlgebraQuaternion.k_quaternionBasis, Quaternion.re_add_im, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen_prime, IsClosed.measure_eq_one_iff_eq_univ, Nat.cast_pred, List.nnnorm_prod_le, ENNReal.div_self_le_one, Subsemiring.coe_one, Nat.ofDigits_one_cons, CochainComplex.HomComplex.Cochain.zero_cochain_comp_v, CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id_assoc, MeasureTheory.prob_le_one, Polynomial.UniversalFactorizationRing.jacobian_resentation, SimpleGraph.eccent_le_one_iff, invOf_lt_zero, Ring.choose_zero_right, Rep.coindVEquiv_symm_apply_coe, ENat.lift_one, odd_add_self_one', RingEquiv.map_neg_one, CochainComplex.g_shortComplexTruncLEX₃ToTruncGE, Quaternion.fst_imK_dualNumberEquiv_symm, midpoint_eq_smul_add, abs_pow_eq_one, Int.ceil_eq_iff, MvPolynomial.coeff_X, Ideal.span_singleton_one, Matrix.mem_specialOrthogonalGroup_iff, CochainComplex.homologyFunctor_shift, abs_neg_one_pow, midpoint_sub_right, Mathlib.Tactic.Bound.Nat.one_le_cast_of_le, Matrix.vandermonde_eq_projVandermonde, contDiffOn_succ_of_fderivWithin, Nat.cast_add_one_pos, Quaternion.coe_zero, DerivedCategory.instIsTriangulatedHomotopyCategoryIntUpQh, AddCommGroupWithOne.ext_iff, ValuativeRel.one_rel_inv, PowerBasis.leftMulMatrix, ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_three, Algebra.SubmersivePresentation.ofSubsingleton_relation, IsPrincipalIdealRing.height_eq_one_of_isMaximal, DirectSum.toAddMonoidAlgebra_one, IsLocalization.mk'_self, MeasureTheory.setIntegral_condExpInd, IsCyclotomicExtension.Rat.p_mem_span_zeta_sub_one, CochainComplex.HomComplex.Cochain.toSingleMk_v_eq_zero, SimpleGraph.isUniform_one, mem_affineSpan_iff_eq_affineCombination, Int.cast_negOnePow, xInTermsOfW_eq, Order.krullDim_le_of_krullDim_preimage_le, Ideal.span_single_eq_top, Set.Icc.one_sub_le_one, ValuativeRel.zero_srel_one, DualNumber.fst_eq_zero_iff_eps_dvd, IsIdempotentElem.ker_toSpanSingleton_eq_span, deriv_id'', Function.mulSupport_intCast, MeasureTheory.eLpNorm_one_eq_lintegral_enorm, OrthonormalBasis.coe_ofRepr, TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf, convexHull_basis_eq_stdSimplex, Algebra.adjoin_insert_one, Module.Basis.trace_traceDual_mul, SimpleGraph.lapMatrix_mulVec_const_eq_zero, coevaluation_apply_one, CliffordAlgebraQuaternion.i_quaternionBasis, MonoidAlgebra.basis_apply, 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, Matrix.permMatrix_mul, CochainComplex.isStrictlyGE_iff, NNRat.one_le_cast, Function.FactorizedRational.mulSupport, LinearMap.toBilin'Aux_toMatrixAux, WithAbs.tendsto_one_div_one_add_pow_nhds_one, ModularGroup.c_eq_zero, ZMod.val_one'', Derivation.map_one_eq_zero, Matrix.Pivot.exists_isTwoBlockDiagonal_list_transvec_mul_mul_list_transvec, IsLocalRing.map_tensorProduct_mk_eq_top, AffineMap.lineMap_vsub_right, MeasureTheory.lpNorm_one_eq_integral_norm, MeasureTheory.L1.setToL1_eq_setToL1SCLM, ENat.add_one_le_iff, GradedTensorProduct.includeLeft_apply, ArchimedeanClass.orderHom_zero, Stream'.Seq.length'_cons, SimpleGraph.edist_top, PolynomialLaw.one_smul, Polynomial.Splits.coeff_zero_eq_prod_roots_of_monic, Polynomial.X_pow_sub_one_eq_prod, Int.floor_le_iff, MeasureTheory.prob_compl_eq_one_sub₀, Matrix.one_fromRows_isTotallyUnimodular_iff, Quaternion.one_im, MonomialOrder.span_leadingTerm_eq_span_monomial, MeasureTheory.Measure.addHaarMeasure_eq_iff, TensorPower.algebraMap₀_one, MvPowerSeries.one_le_order_iff_constCoeff_eq_zero, AddGroupWithOne.ext_iff, MonomialOrder.span_leadingTerm_eq_span_monomial₀, sign_mul_abs, SimpleGraph.vertexCoverNum_top, IsAbsoluteValue.abv_one, Quaternion.im_natCast, Polynomial.coeff_zero_eq_leadingCoeff_mul_prod_roots_of_splits, MeasureTheory.aestronglyMeasurable_condExpL1, PowerSeries.mk_one_pow_eq_mk_choose_add, AbsoluteValue.IsEquiv.le_one_iff, IsLocalization.tensorProduct_isLocalizedModule, MeasureTheory.prob_compl_eq_one_iff, Quaternion.star_add_self, PrimeSpectrum.isIdempotentElemEquivClopens_one_sub, Quaternion.sub_re_self, Matrix.TransvectionStruct.det_toMatrix_prod, KaehlerDifferential.kerTotal_mkQ_single_algebraMap_one, Int.fract_sub_one, Real.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, HahnSeries.embDomain_one, CochainComplex.HomComplex.Cochain.leftShift_rightShift_eq_negOnePow_rightShift_leftShift, Matroid.eRk_insert_le_add_one, iteratedDeriv_fun_id_zero, ENNReal.div_eq_one_iff, abs_one_div, unitary.norm_sub_eq, MatrixEquivTensor.invFun_algebraMap, SetTheory.Game.birthday_one, Algebra.TensorProduct.productMap_left_apply, LinearEquiv.det_symm_mul_det, PowerSeries.coeff_derivativeFun, CochainComplex.mappingCone.lift_f_fst_v_assoc, Subalgebra.lTensorBot_one_tmul, StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_span, Polynomial.MonicDegreeEq.freeMonic_coe, DualNumber.maximalIdeal_eq_span_singleton_eps, round_add_one, ENNReal.one_lt_top, MvPowerSeries.coeff_index_single_self_X, ext_iff, ENNReal.tsum_set_one, Nat.one_le_cast, ModuleCat.exteriorPower.iso₀_hom_apply, DerivedCategory.to_singleFunctor_obj_eq_zero_of_injective, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, IsPrimitiveRoot.sub_one_norm_isPrimePow, MeasureTheory.Measure.dirac_apply', MeasureTheory.L1.integral_def, GenContFract.IntFractPair.nth_stream_fr_lt_one, Odd.natCast_zmod_two, MvPolynomial.bind₂_monomial, DerivedCategory.right_fac_of_isStrictlyLE_of_isStrictlyGE, spectrum.spectralRadius_one, DualNumber.lift_inlAlgHom_eps, MvPolynomial.monomialOneHom_apply, norm_commutator_sub_one_le, ZMod.mul_inv_of_unit, MeasureTheory.L1.SimpleFunc.setToL1S_smul_real, ZMod.inv_one, one_le_two', CochainComplex.HomComplex.Cochain.leftShift_rightShift, Convex.mem_Ioo, Module.End.hasUnifEigenvalue_iff_mem_spectrum, ENNReal.inv_le_iff_le_mul, ComplexShape.embeddingUpNat_f, Hyperreal.coe_eq_one, CochainComplex.HomComplex.Cochain.ofHom_neg, CochainComplex.isSplitEpi_to_singleFunctor_obj_of_projective, lineMap_lt_right_iff_lt_one, GradedTensorProduct.auxEquiv_symm_one, Algebra.SubmersivePresentation.jacobianRelations_spec, SkewMonoidAlgebra.of_apply, toBilin'Aux_toMatrixAux, QuadraticAlgebra.lift_apply_apply, CharP.orderOf_eq_two_iff, Matrix.detp_one_one, Matrix.PosSemidef.sqrt_eq_one_iff, Ideal.height_le_height_add_one_of_mem, IntermediateField.AdjoinSimple.norm_gen_eq_one, ContinuousLinearMap.toSpanSingleton_apply_map_one, Quaternion.imK_coe, Finset.dens_le_one, Algebra.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, Int.ceil_eq_zero_iff, CochainComplex.HomComplex.Cochain.zero_v, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup, MeasureTheory.eLpNorm_one_le_of_le', egauge_le_one, DirectSum.decompose_symm_one, bernsteinPolynomial.iterate_derivative_at_1_eq_zero_of_lt, Matrix.toLpLin_one, Module.Basis.trace_mul_traceDual, PiLp.nnnorm_toLp_const', QuadraticAlgebra.norm_eq_one, hasDerivAtFilter_neg, Polynomial.eval_monomial_one_add_sub, ite_eq_mem_stdSimplex, MvPolynomial.IsSymmetric.one, DerivedCategory.instLinearCochainComplexIntQ, MeasureTheory.L1.SimpleFunc.setToL1S_eq_setToSimpleFunc, tsum_pow_div_one_sub_eq_tsum_sigma, ZMod.val_inv_mul, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_maximalIdeal, div_neg_self, IsIdempotentElem.mul_one_sub_self, Polynomial.fwdDiff_iter_degree_add_one_eq_zero, iUnion_Icc_intCast, Matroid.exists_eRk_insert_eq_add_one_of_lt, EuclideanDomain.mod_one, Module.End.Eigenvalues.mk_val, Module.Basis.reindexRange_repr_self, Sbtw.right_mem_image_Ioi, ENNReal.orderIsoIicOneBirational_apply_coe, GenContFract.zeroth_cont_eq_h_one, Rat.cast_list_prod, Nat.one_le_floor_iff, Matrix.invOf_eq_nonsing_inv, ComplexShape.instIsTruncGENatIntEmbeddingUpIntGE, LinearMap.toSpanSingleton_one_eq_algebraLinearMap, Matrix.inv_smul, CochainComplex.isZero_of_isStrictlyLE, MeasureTheory.Measure.haar.addHaarContent_self, Polynomial.UniversalCoprimeFactorizationRing.homEquiv_comp_fst, MeasureTheory.eLpNorm_one_smul_measure, Quaternion.add_imI, SkewMonoidAlgebra.lift_unique, MeasureTheory.L1.setToFun_eq_setToL1, Module.Basis.repr_eq_iff, Quaternion.smul_coe, MvPolynomial.coeff_X_pow, RingEquiv.map_one, TensorProduct.tmul_eq_smul_one_tmul, eq_affineCombination_of_mem_affineSpan_image, LinearMap.IsSymmetric.diagonalization_symm_apply, MvPolynomial.pow_idealOfVars_eq_span, DualNumber.isNilpotent_iff_eps_dvd, Quaternion.instIsDomain, div_lt_one_of_neg, neg_one_pow_char, PiTensorProduct.one_def, Matrix.equiv_compl_fromCols_mul_fromRows_eq_one_comm, Matrix.SpecialLinearGroup.isCoprime_col, DualNumber.isMaximal_span_singleton_eps, MeasureTheory.L1.integral_eq_setToL1, Polynomial.derivative_X_pow_succ, ValuativeRel.one_vle_div_iff, geom_sum_inv, ModularGroup.T_mul_apply_one, CauSeq.Completion.ofRat_one, iUnion_Ioc_add_intCast, IsPrimitiveRoot.norm_eq_one, CFC.sqrt_eq_one_iff, MeasureTheory.Integrable.toL1_smul, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, Nat.lt_one_of_floor_lt_one, Quaternion.neg_imJ, Order.succ_iterate, Matrix.det_eq_sum_column_mul_submatrix_succAbove_succAbove_det, CochainComplex.instAdditiveIntFunctorSingleFunctors, CochainComplex.shiftFunctor_obj_X, CochainComplex.mappingConeCompHomotopyEquiv_comm₁, PiLp.dist_eq_of_L1, ContinuousLinearMap.derivWithin, three_add_one_eq_four, Ideal.IsPrime.one_notMem, HahnSeries.SummableFamily.embDomain_succ_smul_powers, neg_div_self, Matrix.TransvectionStruct.inv_mul, PowerSeries.constantCoeff_one, Quaternion.coe_smul, one_div_mul_add_mul_one_div_eq_one_div_add_one_div, ENNReal.toNNReal_one, Int.lt_floor_add_one, MvPolynomial.bind₂_monomial_one, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_two, HomotopyCategory.mappingCone_triangleh_distinguished, Polynomial.IsPrimitive.content_eq_one, RingHom.map_one, invOf_sub_invOf, IncidenceAlgebra.mu_ofDual, PosNum.cast_succ, spectrum.one_eq, CliffordAlgebra.range_ι_le_evenOdd_one, ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf, Quaternion.imI_neg, LinearMap.liftBaseChangeEquiv_symm_apply, MeasureTheory.condExpL1CLM_indicatorConstLp, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₂, MeasureTheory.prob_compl_lt_one_sub_of_lt_prob, Field.DirectLimit.exists_inv, UnitAddCircle.measure_univ, Polynomial.eval₂_reflect_mul_pow, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂, meromorphicOrderAt_id, Matrix.TransvectionStruct.toMatrix_reindexEquiv_prod, CategoryTheory.DifferentialObject.d_squared, mul_gaussSum_inv_eq_gaussSum, Quaternion.mul_re, CFC.le_one_iff, ringKrullDim_succ_le_of_surjective, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup, Matrix.invOf_mul_eq_iff_eq_mul_left, MeasureTheory.L1.setToL1_add_left', 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, Besicovitch.exist_finset_disjoint_balls_large_measure, Set.Ico.coe_zero, ZNum.cast_lt, WeierstrassCurve.Jacobian.dblXYZ_of_Z_ne_zero, CategoryTheory.ProjectiveResolution.extMk_hom, Module.Basis.dualBasis_apply_self, SpecialLinearGroup.det_eq_one, Finpartition.isUniform_one, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_aux, Matrix.one_zpow, LaurentPolynomial.T_apply, CochainComplex.mappingCone.triangleRotateShortComplex_X₂, ENat.top_sub_one, CochainComplex.HomComplex.Cochain.fromSingleMk_v, Polynomial.isRoot_of_unity_of_root_cyclotomic, MvPolynomial.C_1, EuclideanDomain.xgcdAux_val, Quaternion.imK_fst_dualNumberEquiv, Quaternion.imK_nnratCast, RingEquiv.map_eq_one_iff, MvPolynomial.eval₂_one, MvPolynomial.rTensor_apply_X_tmul, FDRep.average_char_eq_finrank_invariants, MvPolynomial.pderiv_X, CochainComplex.HomComplex.Cochain.fromSingleMk_add, MeasureTheory.L1.SimpleFunc.coe_negPart, Nat.one_div_cast_pos, IsPrimitiveRoot.norm_pow_sub_one_of_prime_ne_two, IsPrimitiveRoot.prod_pow_sub_one_eq_order, Height.logHeight_one, Matrix.J_squared, IsNilpotent.isUnit_add_one, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_neg, MeasureTheory.L1.setToL1_mono_left, LinearMap.toSpanSingleton_apply_one, MeasureTheory.condExpInd_disjoint_union, WeierstrassCurve.Jacobian.negMap_of_Z_eq_zero, Matrix.nonsing_inv_mul, one_div_lt, ProbabilityTheory.Kernel.withDensity_one', Algebra.Generators.H1Cotangent.δAux_toAlgHom, Cardinal.one_le_ofENat, IsCyclic.val_inv_mulAutMulEquiv_apply, Int.sub_one_lt_floor, Polynomial.toFinsupp_X_pow, CochainComplex.HomComplex.Cochain.shift_smul, nnnorm_algebraMap, KaehlerDifferential.D_apply, Finset.prod_one_add_ordered, Nat.ceil_lt_add_one, Subsemiring.one_mem, natCast_eq_one, Matrix.eRank_one, instContMDiffInv₀OfNatWithTopENat, 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, Matrix.conjTranspose_swap, hasDerivAtFilter_id, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_apply, odd_neg_one, iUnion_Ico_add_intCast, CochainComplex.HomComplex.Cochain.ofHomotopy_refl, IsLocalization.Away.mvPolynomialQuotientEquiv_apply, Metric.coveringNumber_eq_one_of_ediam_le, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, CategoryTheory.ProjectiveResolution.Hom.hom'_f_assoc, hasDerivAt_update, quadraticCharFun_one, AffineMap.right_vsub_lineMap, Quaternion.re_fst_dualNumberEquiv, Int.ceil_add_one, Polynomial.leadingCoeff_pow_X_add_C, 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, RCLike.sqrt_one, EuclideanDomain.div_self, Quaternion.imK_zero, Wbtw.left_mem_image_Ici_of_right_ne, MvPowerSeries.rescaleAlgHom_one, MeasureTheory.norm_setToFun_le', one_le_cfc_iff, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₁, selfAdjoint.unitarySelfAddISMul_coe, Set.Icc.coe_mul, SimpleGraph.chromaticNumber_eq_iff_colorable_not_colorable, Topology.RelCWComplex.openCell_subset_skeletonLT, Matrix.det_permutation, neg_one_pow_expChar, FirstOrder.Language.presburger.realize_natCast, affineHomeomorph_image_I, DerivedCategory.instIsIsoMapCochainComplexIntQ, Matrix.toMatrix₂Aux_toLinearMap₂'Aux, Int.ModEq.listProd_map, AddSubmonoidWithOneClass.toOneMemClass, ValuativeRel.one_rel_div_iff, Topology.RelCWComplex.closedCell_subset_skeletonLT, Finset.sum_centroidWeights_eq_one_of_card_eq_add_one, ENNReal.tendsto_pow_atTop_nhds_top_iff, ModularGroup.coe_T_inv, Polynomial.leadingCoeff_X_pow_sub_C, ZNum.le_to_int, ENNReal.tsum_geometric_add_one, ModularGroup.T_inv_mul_apply_one, Algebra.adjoin_nonUnitalSubalgebra_eq_span, Set.pairwise_disjoint_Ico_add_intCast, CochainComplex.HomComplex.Cocycle.toSingleMk_zero, CochainComplex.HomComplex.Cochain.rightShiftAddEquiv_apply, hasSum_const_div_iff, Matrix.PosDef.one, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv, CategoryTheory.DifferentialObject.Hom.comm_assoc, MvPolynomial.isWeightedHomogeneous_one, KaehlerDifferential.one_smul_sub_smul_one_mem_ideal, Quaternion.norm_coe, Quaternion.sub_self_im, CochainComplex.HomComplex.Cochain.leftUnshift_v, ContractingWith.edist_efixedPoint_le', Matrix.UnitaryGroup.one_apply, Matrix.one_vecMul, IsNilpotent.isUnit_one_add, ENat.ceil_lt, SimplexCategory.toTopObj_one_add_eq_one, Matrix.mulVecLin_one, MonoidAlgebra.ofMagma_apply, Int.log_one_right, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, CochainComplex.mappingConeCompHomotopyEquiv_comm₁_assoc, IsPrimitiveRoot.subOneIntegralPowerBasis'_gen, mem_Icc_of_mem_stdSimplex, RootPairing.Base.eq_one_or_neg_one_of_mem_support_of_smul_mem, MeasureTheory.IsProbabilityMeasure.measure_univ, tendsto_natCast_div_add_atTop, div_le_one_of_neg, CochainComplex.ConnectData.map_f, GradedTensorProduct.tmul_one_mul_coe_tmul, MvPolynomial.tensorEquivSum_one_tmul_C, ZMod.val_one', ENNReal.zero_lt_log_iff, ZMod.coe_int_inv_mul_eq_one, OrthonormalBasis.volume_parallelepiped, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂, hasFDerivAt_list_prod', MeasureTheory.condExpL1_undef, CliffordAlgebra.invOf_ι_mul_ι_mul_ι, MeasureTheory.eLpNorm_smul_measure_of_ne_top, EuclideanDomain.gcdB_zero_left, Nat.cast_lt_one, arithGeom_same_eq_mul_div', EulerProduct.prod_filter_prime_geometric_eq_tsum_factoredNumbers, PadicInt.continuousAddCharEquiv_of_norm_mul_apply, MeasureTheory.OuterMeasure.dirac_apply, Finset.norm_prod_one_add_sub_one_le, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul, sbtw_iff_right_ne_and_left_mem_image_Ioi, contDiffOn_succ_iff_fderiv_of_isOpen, CochainComplex.mappingCone.triangleRotateShortComplex_X₃, one_half_lt_one, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, MeasureTheory.L1.SimpleFunc.setToL1S_sub, Char.card_pow_card, AddCircle.coe_fract, ENNReal.log_eq_one_iff, PadicInt.coe_one, ProbabilityTheory.lintegral_betaPDF_eq_one, LieSubmodule.mem_baseChange_iff, PowerSeries.coeff_invUnitsSub, SkewPolynomial.monomial_zero_one, hasProd_one_add_of_hasSum_prod, CochainComplex.HomComplex.Cochain.rightShift_leftShift, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, Set.Icc.coe_nonneg, pi_eq_sum_univ', Matrix.transvection_zero, ENNReal.HolderConjugate.div_conj_eq_sub_one, sup_eq_half_smul_add_add_abs_sub, RootPairing.pairing_neg_one_neg_four_iff, Summable.hasProdUniformlyOn_nat_one_add, geom_sum_Ico_mul, instQFactorsThroughHomotopyIntUp, WeierstrassCurve.Jacobian.nonsingularLift_some, WeierstrassCurve.Affine.CoordinateRing.norm_smul_basis, Matrix.IsTotallyUnimodular.apply, segment_eq_image, hasFDerivWithinAt_iff_hasDerivWithinAt, Subsemiring.closure_singleton_one, hasFTaylorSeriesUpToOn_succ_iff_right, CStarRing.instNormOneClassOfNontrivial, MonoidAlgebra.lift_unique, FermatLastTheoremForThreeGen.Solution'.ha, IsPrimitiveRoot.finite_quotient_span_sub_one', ordinaryHypergeometricSeries_apply_zero, IsPrimitiveRoot.minpoly_sub_one_eq_cyclotomic_comp, Quaternion.one_imK, Polynomial.MonicDegreeEq.coeff_of_ge, MulChar.val_neg_one_eq_one_of_odd_order, geom_sum_Ico_mul_neg, abs_sub_round_eq_min, Num.cast_bit1, CochainComplex.HomComplex.Cochain.ofHom_v, WithLp.prod_nnnorm_eq_of_L1, MeasureTheory.L2.inner_indicatorConstLp_one, hasStrictFDerivAt_iff_hasStrictDerivAt, CochainComplex.HomComplex.Cochain.ofHom_sub, geom_sum_eq, SkewMonoidAlgebra.coeff_one_one, LinearMap.toMatrixAlgEquiv'_apply, CochainComplex.instLinearHomologicalComplexIntUpShiftFunctor, IsDiscreteValuationRing.addVal_uniformizer, GroupLike.val_one, binomialSeries_apply, MeasureTheory.L1.setToL1_smul_left', WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, SubMulAction.algebraMap_mem, 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, MeasureTheory.L1.SimpleFunc.toLp_one_eq_toL1, Function.Antiperiodic.nat_mul_sub_eq, TensorProduct.lid_symm_apply, ValuativeRel.zero_vlt_one, NNRat.num_one, EulerProduct.eulerProduct_completely_multiplicative_tprod, CochainComplex.HomComplex.Cochain.leftUnshift_smul, Polynomial.trinomial_monic, instIsManifoldMinSmoothnessOfNatWithTopENat_1, fact_one_le_top_ennreal, Finset.nonneg_addConst, PiToModule.fromMatrix_apply_single_one, CochainComplex.mappingCone.inr_f_snd_v, exists_sum_eq_one_iff_pairwise_coprime', Quaternion.normSq_inv, IntermediateField.adjoin_one, toIcoDiv_zero_one, CochainComplex.instIsKInjectiveObjIntShiftFunctor, CochainComplex.mappingConeCompTriangle_mor₃_naturality, eventually_homothety_mem_of_mem_interior, CategoryTheory.Functor.instCommShiftCochainComplexIntDerivedCategoryHomMapDerivedCategoryFactors, MvPolynomial.pderiv_def, IsPrimitiveRoot.associated_sub_one_map_sub_one, AnalyticAt.analyticOrderAt_deriv_add_one, Quaternion.imI_im, one_div_le_one_div_of_neg, Nat.ceil_add_one, CochainComplex.HomComplex.Cochain.shiftLinearMap_apply, ZMod.algebraOfModule.proof, eq_pos_convex_span_of_mem_convexHull, IsPrimitiveRoot.finite_quotient_span_sub_one, Matrix.mem_range_scalar_iff_commute_single, Matrix.UnitaryGroup.one_val, neg_one_pow_eq_pow_mod_two, Matrix.TransvectionStruct.prod_mul_reverse_inv_prod, Module.ringKrullDim_quotient_add_one_of_mem_nonZeroDivisors, stdSimplex.vertex_coe, WeierstrassCurve.Projective.addXYZ_neg, mul_one_sub, FGModuleCat.FGModuleCatCoevaluation_apply_one, Order.krullDim_WithTop, Matrix.SpecialLinearGroup.isCoprime_row, CategoryTheory.ProjectiveResolution.π'_f_zero_assoc, SimpleGraph.IsSRGWith.matrix_eq, Int.fract_one, MvPolynomial.coeff_single_X, one_lt_div_of_neg, DerivedCategory.instIsLocalizationHomotopyCategoryIntUpQhQuasiIso, Int.fract_periodic, FermatLastTheoremForThreeGen.a_cube_b_cube_congr_one_or_neg_one, CancelDenoms.cancel_factors_ne, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left, Finset.dens_eq_one, HopfAlgebra.sum_antipode_mul_eq_smul, PEquiv.toMatrix_toPEquiv_mul, Ideal.mem_jacobson_iff, dvd_pow_sub_one_of_dvd, Matrix.permMatrix_l2_opNorm_le, MeasureTheory.norm_condExpIndL1_le, Summable.alternating, ZMod.isSquare_neg_one_iff, CompleteOrthogonalIdempotents.option, Set.Ico.nonneg, ZMod.val_one_eq_one_mod, Set.Icc.coe_pow, finsuppTensorFinsupp'_symm_single_eq_single_one_tmul, AffineMap.hasDerivAt, Dynamics.coverMincard_zero, MvPolynomial.modMonomial_add_divMonomial, TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf, MonomialOrder.span_leadingTerm_eq_span_monomial', Nat.floor_lt_one, HomologicalComplex₂.shiftFunctor₁XXIso_refl, star_lt_one_iff, ArithmeticFunction.coe_zeta_mul_coe_moebius, Polynomial.det_taylorLinearEquiv_toLinearMap, ProbabilityTheory.lintegral_exp_mul_sq_norm_le_of_map_rotation_eq_self, IsLocalization.mk'_self'', Coalgebra.sum_counit_tmul_map_eq, IncidenceAlgebra.sum_Icc_mu_left, Quaternion.im_coe, Finset.weightedVSubVSubWeights_apply_right, Quaternion.re_exp, ZMod.mul_val_inv, Polynomial.eval_list_prod, dist_lineMap_right, CochainComplex.mappingCone.triangleRotateShortComplex_X₁, MeasureTheory.condExpL1_add, Quaternion.algebraMap_injective, Field.DirectLimit.mul_inv_cancel, abs_mul_sign, CharP.addOrderOf_one, NormedDivisionRing.to_normOneClass, geom_sum_one, ENat.natCast_lt_succ, RCLike.sqrt_eq_real_add_ite, DerivedCategory.left_fac_of_isStrictlyLE_of_isStrictlyGE, WithBot.succ_one, CategoryTheory.Free.embedding_map, MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul, CochainComplex.shiftFunctor_map_f', IsPrimitiveRoot.associated_map_sub_one_map_sub_one, CochainComplex.mappingCone.ext_to_iff, MvPowerSeries.coeff_one, PowerSeries.one_le_order_iff_constCoeff_eq_zero, selfZPow_of_neg, MeasureTheory.norm_condExpInd_apply_le, ArchimedeanClass.stdPart_one, one_div_lt_of_neg, CochainComplex.ConnectData.restrictionLEIso_inv_f, IsLprojection.coe_top, ZMod.cast_one', PiLp.basisFun_apply, MvPolynomial.coeff_single_X_pow, WeierstrassCurve.coeff_Φ, IsCyclotomicExtension.zeta_pow, Polynomial.fwdDiff_iter_eq_zero_of_degree_lt, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, ExteriorAlgebra.liftAlternating_one, Ideal.height_le_ringKrullDim_quotient_add_one, SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet, Matrix.eval_charpolyRev, Polynomial.coeff_X_one, tsub_one_mul, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π', CochainComplex.HomComplex.Cochain.rightShift_zero, MvPolynomial.monomial_one_mul_cancel_left_iff, ENNReal.coe_one, Polynomial.integralNormalization_coeff_degree, tendsto_nat_floor_div_atTop, hasFDerivAtFilter_iff_hasDerivAtFilter, openSegment_eq_image, Rep.freeLiftLEquiv_apply, single_one_dotProduct, TrivSqZeroExt.mul_inv_cancel, AlgebraicGeometry.StructureSheaf.const_one, Matrix.adjugate_eq_one_of_card_eq_one, RingEquiv.map_list_prod, IsLocalization.away_snd, MvPolynomial.coe_basisMonomials, Unitization.val_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe, ZMod.pow_card_sub_one_eq_one, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃, sum_row_of_mem_doublyStochastic, MeasureTheory.dirac_eq_one_iff_mem, wbtw_zero_one_iff, IncidenceAlgebra.zeta_prod_apply, one_lt_div_iff, CategoryTheory.ProjectiveResolution.Hom.hom'_f, Quaternion.normSq_eq_norm_mul_self, Num.cast_succ, Summable.summable_log_norm_one_add, SimpleGraph.adjMatrix_pow_apply_eq_card_walk, CochainComplex.singleFunctor_obj_d, Matrix.adjugate_apply, SimpleGraph.dotProduct_adjMatrix, LinearMap.toMatrix'_apply, NNRat.cast_le_one, Matrix.det_transvection_of_ne, Set.Ico.coe_eq_zero, listProd_apply_eq_zero', IsIdempotentElem.ker_toSpanSingleton_one_sub_eq_span, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', TrivSqZeroExt.inv_mul_cancel, Ideal.ResidueField.exists_smul_eq_tmul_one, Profinite.NobelingProof.factors_prod_eq_basis_of_ne, ModularGroup.T_pow_mul_apply_one, instContMDiffVectorBundleOfNatWithTopENat, MeasureTheory.condExpL1_neg, LinearMap.ext_ring_iff, CoxeterSystem.lengthParity_comp_simple, smul_add_one_sub_smul, CochainComplex.quasiIso_shift_iff, RCLike.one_im, MeasureTheory.L1.nnnorm_integral_le, RCLike.toZeroLEOneClass, Num.cast_to_nat, Representation.asAlgebraHom_single_one, Unitization.val_inv_unitsFstOne_mulEquiv_quasiregular_symm_apply_coe, Finsupp.degree_eq_weight_one, ENNReal.HolderConjugate.one_le, CochainComplex.HomComplex.Cochain.rightUnshift_v, ProbabilityTheory.lintegral_paretoPDF_eq_one, HomotopyCategory.composableArrowsFunctor_obj, ModularGroup.exists_row_one_eq_and_min_re, MonoidAlgebra.ringHom_ext_iff, Int.ceil_sub_one, natCast_eq_zero_or_one_of_two_eq_zero, AddConstMapClass.map_one_add, AffineBasis.sum_coord_apply_eq_one, CliffordAlgebra.GradedAlgebra.ι_apply, HasFPowerSeriesAt.hasStrictDerivAt, Matrix.charpoly_one, ComplexShape.instIsRelIffNatIntEmbeddingDownNat, IsLocalization.isInteger_one, SymAlg.invOf_sym, Finsupp.isCompl_range_lmapDomain_span, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₂, hasFDerivAt_list_prod_finRange', ZMod.AddAutEquivUnits_apply, MeasureTheory.pdf.IsUniform.pdf_toReal_ae_eq, SimpleGraph.ediam_top, one_le_kstar, LinearMap.hasDerivWithinAt, Module.Relations.map_single, CochainComplex.shiftFunctorAdd'_inv_app_f', MeasureTheory.Measure.haar.haarContent_self, QuaternionAlgebra.Basis.lift_one, Finset.prod_one_add, Submodule.rTensorOne'_tmul_one, WeierstrassCurve.Jacobian.addMap_of_Z_ne_zero, ProbabilityTheory.Kernel.IsProper.restrict_eq_indicator_smul', ArithmeticFunction.natCoe_one, ContinuousMap.adjoin_id_eq_span_one_union, Matrix.TransvectionStruct.mul_sumInl_toMatrix_prod, CochainComplex.exactAt_of_isLE, baseChange_ext_iff, TrivSqZeroExt.invOf_eq_inv, DerivedCategory.instHasLeftCalculusOfFractionsHomotopyCategoryIntUpQuasiIso, geom_sum_mul, Order.coheight_coe_withTop, IsUltrametricDist.nnnorm_add_one_le_max_nnnorm_one, Quaternion.coe_imI, MeasureTheory.lintegral_indicator_one₀, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_inv_f_f, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, MeasureTheory.Measure.count_singleton, Finset.one_le_divConst, ModuleCat.free_ε_one, Int.ModEq.listProd_map_one, eq_affineCombination_of_mem_affineSpan_of_fintype, MeasureTheory.setIntegral_condExpL1, Int.le_ceil_iff, Asymptotics.continuousAt_iff_isLittleO, ENNReal.HolderConjugate.sub_one_mul_inv, Module.Basis.coe_singleton, Matrix.det_one_sub_mul_comm, Polynomial.UniversalFactorizationRing.monicDegreeEq_coe, WeierstrassCurve.Affine.addPolynomial_eq, iccHomeoI_apply_coe, Topology.RelCWComplex.skeleton_union_iUnion_closedCell_eq_skeleton_succ, KaehlerDifferential.derivationQuotKerTotal_apply, QuaternionAlgebra.Basis.k_self, one_le_sq_iff_one_le_abs, Orthonormal.linearIsometryEquiv_symm_apply_single_one, RingPreordering.one_notMem_support, CommRingCat.Colimits.quot_one, MvPolynomial.algebraTensorAlgEquiv_symm_X, Matrix.add_mul_mul_invOf_mul_eq_one', AddChar.tendsto_eval_one_sub_pow, Valuation.one_srel_iff, CStarAlgebra.inv_le_one, Num.cast_sub', EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, ENNReal.HolderConjugate.eq_top_iff_eq_one, dist_homothety_self, IsCyclotomicExtension.Rat.Three.eta_sq, MonomialOrder.monic_monomial, Quaternion.imJ_neg, 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, MeasureTheory.condExpIndL1_smul, Submodule.baseChange_eq_span, natCast_succ, WeierstrassCurve.Projective.addXYZ_of_Z_ne_zero, one_add_le_one_sub_mul_one_add, MeasureTheory.Measure.addHaarMeasure_self, Polynomial.leadingCoeff_X, CochainComplex.mappingCone.map_inr, cfc_predicate_one, Num.cast_ofZNum, CategoryTheory.Functor.mapCochainComplexShiftIso_inv_app_f, Fintype.expect_one, ENNReal.tsum_two_zpow_neg_add_one, CochainComplex.shiftFunctorAdd'_eq, Quaternion.sub_self_re, EulerProduct.prod_primesBelow_geometric_eq_tsum_smoothNumbers, CochainComplex.shiftFunctorAdd'_inv_app_f, Cardinal.ofENat_eq_one, DihedralGroup.orderOf_r_one, Coalgebra.rTensor_counit_comp_comul, ENat.one_le_iff_ne_zero_withTop, Subfield.coe_one, HomotopyCategory.instLinearIntUpShiftFunctor, CompleteOrthogonalIdempotents.single, IsSimpleRing.one_mem_of_ne_bot, CochainComplex.mappingCone.liftCochain_v_fst_v, tsum_choose_mul_geometric_of_norm_lt_one, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces', SkewMonoidAlgebra.liftNC_one, toMatrix_dualTensorHom, IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one, MeasureTheory.Integrable.enorm_toL1, Order.height_eq_iSup_lt_height, Order.height_eq_coe_add_one_iff, MeasureTheory.continuous_integral_integral, CochainComplex.mapBifunctorShift₂Iso_hom_naturality₂, Algebra.Generators.H1Cotangent.δAux_ofComp, SimpleGraph.eccent_eq_one_iff, exists_jacobiSum_eq_neg_one_add, SimpleGraph.incMatrix_mul_transpose, IsCoprime.exists_SL2_row, MeasureTheory.L1.SimpleFunc.setToL1S_indicatorConst, Matrix.SpecialLinearGroup.ext_iff, Module.Relations.Quotient.linearMap_ext_iff, Quaternion.intCast_imI, completeOrthogonalIdempotents_iff, AddChar.wInner_cWeight_eq_one_iff_eq, ENNReal.HolderConjugate.conj_eq, iteratedDerivWithin_one_div, LinearMap.pi_apply_eq_sum_univ, CochainComplex.HomComplex.Cochain.fromSingleMk_zero, ENNReal.coe_le_one_iff, Nat.abs_sub_ceil_le, 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, Bound.div_lt_one_of_pos_of_lt, Matrix.det_fromBlocks₁₁, AbsoluteValue.exists_one_lt_lt_one_pi_of_not_isEquiv, HomotopyCategory.Pretriangulated.distinguished_cocone_triangle, Quaternion.zero_imK, HahnSeries.ofPowerSeries_X, CochainComplex.mappingConeCompTriangle_mor₁, CochainComplex.mappingCone.inr_triangleδ_assoc, Matrix.vecMul_permMatrix, dist_self_homothety, MeasureTheory.Integrable.toL1_sub, PartENat.toWithTop_one, contDiffWithinAt_succ_iff_hasFDerivWithinAt', CochainComplex.cm5b.instIsStrictlyGEBiprodIntMappingConeIdIOfHAddOfNat, IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_two, ZMod.inv_mul_of_unit, Matrix.toLpLin_symm_id, CochainComplex.HomComplex.Cochain.leftShift_zero, contDiffOn_succ_iff_hasFDerivWithinAt, GenContFract.convs_succ, PosNum.cast_add, Order.height_eq_coe_iff, CochainComplex.mappingCone.inl_v_snd_v_assoc, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', Finset.sum_centroidWeights_eq_one_of_card_ne_zero, LinearAlgebra.FreeProduct.identify_one, iteratedDerivWithin_fun_id, CliffordAlgebra.reverse_prod_map_ι, Ideal.isMaximal_iff, LinearMap.BilinForm.dualBasis_eq_iff, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_zero, CategoryTheory.ProjectiveResolution.Hom.hom'_comp_π'_assoc, iUnion_Icc_add_intCast, SimpleGraph.ediam_eq_one, Polynomial.comp_neg_X_leadingCoeff_eq, MatrixModCat.mem_toModuleCatObj, Matrix.add_mul_mul_mul_invOf_eq_one, IsLocalization.mk'_mul_mk'_eq_one', Module.Basis.baseChange_apply, Differential.logDeriv_one, arithGeom_eq, AbsoluteValue.IsEquiv.lt_one_iff, NormedRing.inverse_add, CochainComplex.instLinearIntShiftFunctor, ENNReal.inv_mul_le_one, Matrix.toBilin'Aux_single, ENat.floor_one, sub_pow, AdjoinRoot.root_isInv, Polynomial.monomial_zero_one, Quaternion.imK_mul, ProbabilityTheory.Kernel.continuous_integral_integral, CStarAlgebra.nnnorm_le_one_iff_of_nonneg, Matrix.det_fromBlocks_one₁₁, CochainComplex.triangleOfDegreewiseSplit_mor₂, PiLp.norm_eq_of_L1, MonomialOrder.monic_monomial_one, nonunits.subset_compl_ball, RingHom.codomain_trivial_iff_map_one_eq_zero, Summable.multipliableLocallyUniformlyOn_one_add, Set.Icc.instIsCancelMulZero, Set.Icc.mul_le_left, Matrix.eRank_subsingleton, IsPrimitiveRoot.finite_quotient_toInteger_sub_one, Quaternion.coe_div, sub_one_lt, NormOneClass.induced, NormedSpace.expSeries_apply_zero, HomotopyCategory.instLinearIntUpSingleFunctor, PresheafOfModules.unitHomEquiv_apply_coe, 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, ProbabilityTheory.uniformOn_eq_one_of, IsLocalization.Away.quotient_of_isIdempotentElem, Height.fun_logHeight_one, DerivedCategory.isLE_Q_obj_iff, GradedTensorProduct.includeRight_apply, one_add_le_pow_of_two_add_nonneg, CochainComplex.cm5b.fac_assoc, ComplexShape.eulerCharSignsDownInt_χ, ENNReal.ofReal_le_one, ZNum.cast_inj, MeasureTheory.prob_compl_eq_zero_iff, IsLocalization.Away.mul_invSelf, Polynomial.natDegree_hilbertPoly_of_ne_zero, DualNumber.exp_eps, HomotopyCategory.instAdditiveIntUpSingleFunctor, round_eq, Set.equitableOn_singleton, 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, one_sub_invOf_two, Polynomial.cyclotomic_coeff_zero, Matrix.invOf_fromBlocks_zero₁₂_eq, EulerProduct.eulerProduct_completely_multiplicative_hasProd, Set.one_le_encard_insert, WeierstrassCurve.Jacobian.addXYZ_neg, IsManifold.instLEInftyOfNatWithTopENat_1, Algebra.Generators.ker_localizationAway, Polynomial.Chebyshev.derivative_U_eval_one, MeasureTheory.mem_ae_iff_prob_eq_one, CochainComplex.mapBifunctorHomologicalComplexShift₂Iso_hom_f_f, MeasureTheory.memL1_smul_of_L1_withDensity, amenable_of_maxFoelner_neBot, MeasureTheory.condExp_ae_eq_condExpL1, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv, GenContFract.of_s_head_aux, one_add_one_eq_two, midpoint_vsub_left, Summable.multipliableLocallyUniformlyOn_nat_one_add, CochainComplex.triangleOfDegreewiseSplit_obj₃, iteratedDeriv_comp_neg, Polynomial.monomial_one_eq_iff, Quaternion.im_imJ, AddMonoidAlgebra.lift_symm_apply, 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, NormedField.exists_enorm_lt_one, IsBaseChange.equiv_symm_apply, Matrix.transpose_invOf, NormedRing.inverse_one_sub, Quaternion.intCast_imJ, Polynomial.TrailingMonic.trailingCoeff, Ideal.add_eq_one_iff, Matrix.one_submatrix_mul, geom_sum₂_with_one, ENNReal.one_le_ofReal, MeasureTheory.condExpIndL1_smul', LinearMap.conjugate_apply, circleEquivGen_symm_apply, Polynomial.resultant_succ_left_deg, HomotopyCategory.Pretriangulated.contractible_distinguished, IsPrimitiveRoot.norm_toInteger_sub_one_eq_one, Nat.Prime.emultiplicity_self, Quaternion.mul_star_eq_coe, Polynomial.one_mem_nthRootsFinset, hasDerivAt_id, seminormFromBounded_one, SimpleGraph.adjMatrix_mulVec_const_apply, KaehlerDifferential.kerTotal_map, tprod_one_add, MvPolynomial.psumPart_zero, Ring.ascPochhammer_succ_succ, Algebra.TensorProduct.mul_one, Quaternion.fst_imI_dualNumberEquiv_symm, ComplexShape.instIsRelIffNatIntEmbeddingUpIntGE, Finset.mem_convexHull, ZNum.cast_le, deriv_update, invOf_two_smul_add_invOf_two_smul, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two', Module.length_eq_one, orthonormal_subtype_iff_ite, Summable.hasProdLocallyUniformlyOn_one_add, Metric.externalCoveringNumber_eq_one_of_ediam_le, ENat.epow_one, IsLocalization.mk'_self', nndist_lineMap_right, Finset.nonneg_addConst_self, TensorProduct.finsuppScalarRight_symm_apply_single, ProbabilityTheory.Kernel.isProper_iff_restrict_eq_indicator_smul, 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, Module.End.genEigenspace_one, AddSubmonoid.pow_eq_closure_pow_set, Summable.multipliableUniformlyOn_one_add, Algebra.TensorProduct.mk_one_injective_of_isScalarTower, ModuleCat.free_η_freeMk, CochainComplex.mappingCone.triangle_mor₂, ValuativeRel.inv_rel_one, OrthogonalIdempotents.surjective_pi, CliffordAlgebra.ofBaseChangeAux_ι, CochainComplex.HomComplex.Cocycle.leftUnshift_coe, enorm_one, Nat.ceil_one, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_of_eq, WithLp.prod_lipschitzWith_toLp, IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver', PolynomialLaw.one_tmul_ground, Matrix.sum_col_of_mem_colStochastic, IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one', Order.coheight_le_of_krullDim_preimage_le, Ideal.span_one, groupHomology.inhomogeneousChains.d_single, ENNReal.ofReal_one, ENNReal.one_eq_coe, alternating_series_error_bound, TwoSidedIdeal.listProd_mem, MeasureTheory.L1.SimpleFunc.setToL1S_const, IsDedekindDomain.HeightOneSpectrum.intValuation.map_one', CochainComplex.MappingConeCompHomotopyEquiv.hom_inv_id, Order.krullDim_le_one_iff_of_boundedOrder, Module.Basis.addHaar_eq_iff, SubMulAction.ENat_card_ofStabilizer_add_one_eq, LucasLehmer.X.one_fst, Algebra.adjoin_singleton_one, ENNReal.one_sub_inv_two, ZMod.val_neg_one, Quaternion.normSq_add, PrimeSpectrum.exists_mul_eq_zero_add_eq_one_basicOpen_eq_of_isClopen, CochainComplex.mappingCone.d_snd_v_assoc, contDiffOn_succ_iff_deriv_of_isOpen, VitaliFamily.ae_tendsto_measure_inter_div, WeierstrassCurve.Projective.Point.fromAffine_some, Algebra.FormallyUnramified.one_tmul_sub_tmul_one_mul_elem, Module.Basis.reindexFinsetRange_repr_self, Set.Icc.le_one, Algebra.Generators.comp_localizationAway_ker, CochainComplex.instAdditiveIntShiftFunctor, LieAlgebra.Orthogonal.s_as_blocks, Representation.coind'_apply_apply, MvPolynomial.mul_esymm_eq_sum, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, Polynomial.Chebyshev.iterate_derivative_U_eval_zero_recurrence, Quaternion.neg_im, CategoryTheory.HasExt.hasSmallLocalizedShiftedHom_of_isLE_of_isGE, ModularForm.slash_action_eq'_iff, CochainComplex.shiftFunctor_map_f, AlgebraicGeometry.Scheme.basicOpen_one, CochainComplex.quasiIsoAt_shift_iff, MeasureTheory.condExp_ae_eq_condExpL1CLM, TensorAlgebra.algebraMap_eq_one_iff, instContMDiffMulOfNatWithTopENat, 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, Ideal.isCoprime_tfae, Matrix.det_eq_one_of_card_eq_zero, CochainComplex.instIsKProjectiveObjIntShiftFunctor, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_vsub, Module.Basis.repr_symm_single_one, IntermediateField.list_prod_mem, GenContFract.first_contAux_eq_h_one, WithLp.prod_norm_eq_of_L1, Summable.one_sub_mul_tsum_pow, WeierstrassCurve.Projective.negMap_of_Z_ne_zero, MvPolynomial.universalFactorizationMapPresentation_relation, Polynomial.Chebyshev.derivative_U_eval_one_dvd, Polynomial.leadingCoeff_X_pow, MeasureTheory.Integrable.toL1_smul', inv_eq_self₀, CategoryTheory.HasExt.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoOfIsGEOfIsLEOfNat, one_div_le_one_div, Finset.sum_centroidWeightsIndicator_eq_one_of_card_ne_zero, QuadraticAlgebra.lift_symm_apply_coe, Matrix.mem_range_scalar_iff_commute_single', Int.floor_eq_iff, Algebra.PreSubmersivePresentation.aevalDifferential_single, Module.Flat.linearIndependent_one_tmul, Num.ofZNum_toNat, ProbabilityTheory.measure_eq_zero_or_one_or_top_of_indepSet_self, CancelDenoms.cancel_factors_eq, deriv_neg'', IsCyclotomicExtension.iff_singleton, Algebra.algebraMap_eq_smul_one, Cubic.monic_of_a_eq_one', CochainComplex.HomComplex.Cochain.rightShift_smul, NormedSpace.exp_zero, Valuation.map_one_sub_of_lt, ContractingWith.exists_fixedPoint, CochainComplex.HomComplex.Cochain.map_comp, WithLp.unitization_nnnorm_inr, PMF.coe_le_one, Quaternion.imI_star, MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le', Matrix.isUnit_fromBlocks_iff_of_invertible₂₂, Matrix.SpecialLinearGroup.toLin_equiv.symm_toLinearMap_eq, MeasureTheory.condExpL1CLM_indicatorConst, Polynomial.expand_zero, MvPolynomial.coeff_one, CliffordAlgebraQuaternion.ofQuaternion_mk, Matrix.SpecialLinearGroup.SL2_inv_expl, MeasureTheory.L1.nnnorm_Integral_le_one, MeasureTheory.L1.SimpleFunc.integrable, self_mul_sign, Manifold.riemannianEDist_def, Quaternion.imI_smul, spectralNorm_one, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, Module.Relations.solutionFinsupp_var, Matrix.BlockTriangular.toBlock_inverse_mul_toBlock_eq_one, Matrix.mem_specialUnitaryGroup_iff, RCLike.ofReal_alg, ProbabilityTheory.uniformOn_self, CochainComplex.homotopyOp_hom_eq, CochainComplex.mappingCone.inr_f_descCochain_v_assoc, MeasureTheory.L1.integral_eq_norm_posPart_sub, CochainComplex.HomComplex.Cochain.map_sub, ofBoolAlg_sdiff, add_one_pow_unbounded_of_pos, ProjectiveSpectrum.zeroLocus_singleton_one, IsLocalization.mem_invSubmonoid_iff_exists_mk', IsPrimitiveRoot.card_nthRootsFinset, Finset.convexHull_eq, CochainComplex.HomComplex.Cocycle.homOf_f, RingPreordering.neg_one_notMem', Subalgebra.rTensorBot_tmul_one, Matrix.mul_invOf_cancel_right, WeierstrassCurve.Projective.neg_of_Z_ne_zero, Quaternion.imK_star, Polynomial.eval_one_map, MvPolynomial.msymm_zero, Ideal.primeHeight_add_one_le_of_lt, RootPairing.Base.toCoweightBasis_repr_coroot, IsCyclotomicExtension.Rat.isPrime_span_zeta_sub_one', Nat.abs_sub_floor_le, Algebra.SubmersivePresentation.ofSubsingleton_val, Matrix.swap_mul_apply_right, arithGeom_same_eq_mul_div, CochainComplex.IsKProjective.Qh_map_bijective, Set.one_le_chainHeight_iff, CochainComplex.mappingCone.d_fst_v_assoc, geom_sum_eq_zero_iff_neg_one, LinearMap.isIdempotentElem_apply_one_iff, Quaternion.normSq_exp, HasFDerivWithinAt.hasDerivWithinAt, tangentBundleCore.isContMDiff, CochainComplex.homOfDegreewiseSplit_f, IsCyclotomicExtension.Rat.liesOver_span_zeta_sub_one, MonomialOrder.Monic.leadingCoeff_eq_one, TensorPower.toTensorAlgebra_gOne, Matrix.det_succ_column, Matrix.cRank_one, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, CStarAlgebra.one_le_inv_iff_le_one, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, PiTensorProduct.tprod_eq_tprodCoeff_one, Algebra.adjoin_inl_union_inr_eq_prod, MeasureTheory.laverage_one, Polynomial.resultant_C_left, CochainComplex.shiftFunctorAdd_inv_app_f, tsirelson_inequality, Algebra.PreSubmersivePresentation.ofBijectiveAlgebraMap_jacobian, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_nonZeroDivisors, ComplexShape.boundaryGE_embeddingUpIntGE_iff, DerivedCategory.isGE_Q_obj_iff, AffineMap.derivWithin, contDiff_succ_iff_fderiv_apply, ENat.add_one_eq_coe_top_iff, Set.Icc.mem_iff_one_sub_mem, Rep.standardComplex.d_of, MeasureTheory.setLIntegral_one, Quaternion.star_add_self', ENat.le_ceil, tendsto_floor_left', stdSimplexHomeomorphUnitInterval_apply_coe, IsLprojection.coe_one, QuadraticMap.half_moduleEnd_apply_eq_half_smul, CochainComplex.mappingCone.map_id, Besicovitch.ae_tendsto_measure_inter_div, Valuation.map_one, emultiplicity_geom_sum₂_eq_one, CochainComplex.shiftShortComplexFunctorIso_hom_app_τ₁, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₂, MvPolynomial.divMonomial_mul_monomial, Matrix.fromBlocks_eq_of_invertible₂₂, GenContFract.of_s_head, EReal.exp_le_one_iff, GenContFract.of_partNum_eq_one, AffineBasis.coord_apply_eq, PowerSeries.X_eq, TangentBundle.contMDiffVectorBundle, MeasureTheory.Measure.one_le_hausdorffMeasure_zero_of_nonempty, IsStarProjection.le_one, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_inv_app, segment_eq_image', Module.supportDim_quotSMulTop_succ_eq_supportDim, Matrix.SpecialLinearGroup.coe_inv, Matroid.IsCircuit.eRk_add_one_eq, IsCyclotomicExtension.norm_zeta_sub_one_of_prime_ne_two, Finset.sum_affineCombinationLineMapWeights, RCLike.sqrt_neg_one, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, Nat.not_ofNat_lt_one, ZMod.orderOf_one_add_four_mul, CliffordAlgebra.foldr_one, TrivSqZeroExt.snd_invOf, Set.pairwise_disjoint_Ioc_intCast, sbtw_mul_sub_add_iff, WithLp.unitization_norm_def, PosNum.cast_le, sq_lt_one_iff_abs_lt_one, one_lt_star_iff, MeasureTheory.pdf.IsUniform.pdf_eq, CochainComplex.mappingConeCompTriangle_obj₃, LinearMap.toMatrixRight'_id, IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomic, Subfield.one_mem, Matrix.mem_rowStochastic_iff_sum, DerivedCategory.instEssSurjHomotopyCategoryIntUpQh, CategoryTheory.ProjectiveResolution.π'_f_zero, MvPolynomial.prod_X_pow_eq_monomial, fderiv_apply_one_eq_deriv, IsCoprime.exists_SL2_col, PiToModule.fromEnd_apply_single_one, PartENat.withTopEquiv_symm_one, Quaternion.sub_im, matrixEquivTensor_apply_single, isStarProjection_one_sub_iff, stdSimplex.sum_eq_one, contDiffAt_succ_iff_hasFDerivAt, Finset.affineCombinationSingleWeights_apply_self, CochainComplex.mappingCone.inl_v_fst_v, MeasureTheory.L2.eLpNorm_inner_lt_top, SkewMonoidAlgebra.toFinsupp_one, AlgebraicGeometry.StructureSheaf.const_algebraMap, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left', meromorphicTrailingCoeffAt_id_sub_const, ENat.epow_eq_one_iff, Set.Subsingleton.equitableOn, Int.fract_neg, Nat.prime_iff_fac_equiv_neg_one, Algebra.TensorProduct.cancelBaseChange_symm_tmul, WeierstrassCurve.Jacobian.nonsingularLift_zero, MvPolynomial.universalFactorizationMapPresentation_algebra_algebraMap, Quaternion.im_exp, MvPolynomial.degrees_one, DivisibleHull.qsmul_def, PiLp.antilipschitzWith_ofLp, MeasureTheory.condExpL1CLM_lpMeas, ContinuousLinearEquiv.unitsEquivAut_symm_apply, MeasureTheory.L1.SimpleFunc.negPart_toSimpleFunc, Submodule.rTensorOne_tmul_one, PosNum.cast_to_nat, Quaternion.re_one, CochainComplex.isLE_iff, sign_one, CochainComplex.ConnectData.cochainComplex_d, Valuation.one_vlt_iff, Subring.exists_list_of_mem_closure, AbsoluteValue.trivial_apply, Matrix.le_one_of_mem_rowStochastic, openSegment_eq_image_lineMap, Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, ZMod.cast_neg_one, Matrix.invOf_add_mul_mul, MeasureTheory.setLAverage_one, logDeriv_id', ENNReal.zero_rpow_def, Cubic.monic_of_b_eq_one', Set.encard_singleton_inter, MeasureTheory.one_le_prob_iff, Set.Ioo.mem_iff_one_sub_mem, MvPolynomial.divMonomial_monomial, Matrix.Pivot.mul_listTransvecRow_last_row, Finset.sum_card_slice_div_choose_le_one, AlgebraicGeometry.Proj.basicOpen_one, MeasureTheory.L1.setToL1_apply_coeToLp, wbtw_iff_right_eq_or_left_mem_image_Ici, MeasureTheory.MemLp.enorm_rpow, Order.height_le_of_krullDim_preimage_le, conjneg_eq_one, HomotopyCategory.instIsTriangulatedIntUpSubcategoryAcyclic, ringKrullDim_quotient_succ_le_of_nonZeroDivisor, one_mem_inv_coe_ideal, PadicInt.fwdDiff_iter_le_of_forall_le, Module.DualBases.eval_same, Matrix.conjTranspose_one, MvPowerSeries.coeff_zero_one, IsStarProjection.mem_Icc, one_div_le_one_div_of_le, MatrixEquivTensor.invFun_smul, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, hasSum_geom_series_inverse, ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_jacobson, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, Quaternion.zero_re, LinearMap.det_id, Cubic.monic_of_c_eq_one', formalMultilinearSeries_geometric_eq_ofScalars, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_inv_app_f, PreTilt.pow_dvd_one_untiltAux_sub_one, eq_affineCombination_of_mem_affineSpan, IsNilpotent.exp_zero, Int.ceil_eq_add_one_sub_fract, LieAlgebra.LoopAlgebra.toFinsupp_single_tmul, SignType.intCast_cast, even_add_one, abs_unit_intCast, Matrix.det_fromBlocks_one₂₂, CochainComplex.exists_iso_single, Matrix.det_nonsing_inv_mul_det, hasSum_coe_mul_geometric_of_norm_lt_one, Module.length_eq_one_iff, WeierstrassCurve.Projective.dblXYZ_of_Z_ne_zero, Valuation.one_vle_iff, cfc_one, QuaternionGroup.a_one_pow, ENat.one_le_epow, IsLocalization.toInvSubmonoid_mul, Set.Ioc.coe_pos, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_symm_apply, ContinuousLinearMap.toSpanSingleton_one, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, wbtw_iff_left_eq_or_right_mem_image_Ici, Matrix.SpecialLinearGroup.coe_pow, CochainComplex.HomComplex.Cochain.shift_units_smul, tendsto_one_div_atTop_nhds_zero_nat, 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, MeasureTheory.L1.setToL1_congr_left', WeierstrassCurve.Projective.addMap_of_Y_eq, ENNReal.mul_inv_cancel, Polynomial.dickson_one_one_charP, LinearMap.IsSymmetric.direct_sum_isInternal, Submodule.det_reflection, LinearMap.toSpanSingleton_eq_algebra_linearMap, round_eq_zero_iff, CochainComplex.ConnectData.restrictionLEIso_hom_f, selfAdjoint.star_coe_unitarySelfAddISMul, deriv_neg', Finsupp.llift_symm_apply, WeakDual.CharacterSpace.eq_set_map_one_map_mul, Quaternion.smul_re, natCast_eq_one_of_odd_of_two_eq_zero, Quaternion.self_add_star', mul_geom_sum, Algebra.Generators.cMulXSubOneCotangent_eq, Polynomial.eval₂_at_one, MeasureTheory.Measure.dirac_apply_ne_zero_iff_eq_one, Polynomial.content_one, CochainComplex.exactAt_of_isGE, div_le_one, WithLp.prod_dist_eq_of_L1, CochainComplex.shiftFunctorAdd_eq, DerivedCategory.instFaithfulFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, CochainComplex.HomComplex.Cochain.leftShiftLinearEquiv_symm_apply, neg_npow_assoc, Quaternion.coe_mul_eq_smul, Matroid.eRk_eq_one_iff, hasSum_choose_mul_geometric_of_norm_lt_one', Set.Icc.coe_eq_zero, CochainComplex.mappingCone.inr_f_descCochain_v, CochainComplex.ι_mapBifunctorShift₂Iso_hom_f, dotProduct_single_one, IsPrimitiveRoot.norm_sub_one_of_prime_ne_two, Quaternion.instIsStarNormal, ContinuousAlgHom.ext_ring_iff, CochainComplex.cm5b.instQuasiIsoIntP, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃, Metric.externalCoveringNumber_singleton, SymplecticGroup.inv_left_mul_aux, IsPrincipalIdealRing.ringKrullDim_eq_one, Subalgebra.coe_eq_one, Polynomial.dickson_one_one_zmod_p, IsCyclotomicExtension.Rat.eq_span_zeta_sub_one_of_liesOver, normEDS_one, CategoryTheory.DifferentialObject.objEqToHom_d, ENNReal.inv_lt_one, Matrix.adjugate_def, ZMod.coe_int_mul_val_inv, IsPrimitiveRoot.subOnePowerBasis_dim, Matrix.isUnit_fromBlocks_iff_of_invertible₁₁, MonomialOrder.degree_one, Submodule.one_eq_span_one_set, MvPolynomial.isHomogeneous_one, Matrix.exists_left_inverse_iff_isUnit, IsPrimitiveRoot.subOnePowerBasis_gen, Ideal.eq_top_iff_one, CompleteOrthogonalIdempotents.unique_iff, instZeroLEOneClass, ModuleCat.MonoidalCategory.rightUnitor_inv_apply, Matrix.toLin'_one, MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral, Quaternion.summable_coe, summable_norm_pow_mul_geometric_div_one_sub, MeasureTheory.prob_compl_le_one_sub_of_le_prob, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₂_assoc, DualNumber.coe_lift_symm_apply, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁, Quaternion.zero_imI, CochainComplex.mappingCone.isZero_X_iff, QuaternionAlgebra.Basis.k_mul_k, Matrix.vecMul_surjective_iff_exists_left_inverse, Quaternion.sub_imI, WithBot.succ_zero, ENNReal.orderIsoUnitIntervalBirational_apply_coe, isIdempotentElem_iff_one_sub_mul_self, WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eq, inhomogeneousCochains.d_hom_apply, Algebra.Generators.toKaehler_tmul_D, Quaternion.imJ_snd_dualNumberEquiv, Quaternion.star_im, preNormEDS_one, ValuativeRel.not_vle_one_zero, TensorProduct.isBaseChange, Rep.coind'_ext_iff, doublyStochastic_eq_convexHull_permMatrix, neg_one_eq_invOf_mul_add_invOf_mul_iff, LinearEquiv.algEquivOfRing_symm_apply, MeasureTheory.L1.setToL1_congr_left, Quaternion.re_natCast, homothety_invOf_two, IsPrimitiveRoot.norm_eq_one_of_linearly_ordered, MeasureTheory.Measure.dirac_apply_eq_zero_or_one, Matrix.det_succ_column_zero, HilbertBasis.repr_symm_single, Ideal.isCoprime_iff_exists, DerivedCategory.instIsGEObjCochainComplexIntQOfIsGE, fderiv_deriv, WithLp.unitizationAlgEquiv_symm_apply_ofLp, MeasureTheory.L1.setToL1_smul, Ring.DirectLimit.quotientMk_of, WittVector.one_coeff_zero, Polynomial.MonicDegreeEq.map_coe, LinearMap.det_eq_sign_charpoly_coeff, QuadraticAlgebra.omega_mul_omega_eq_mk, Derivation.map_one_eq_zero', thickenedIndicatorAux_one, Representation.ker_leftRegular_norm_eq, Subalgebra.lTensorBot_symm_apply, AddMonoidAlgebra.of'_apply, IsNilpotent.exp_neg_mul_exp_self, MeasureTheory.L1.SimpleFunc.posPart_toSimpleFunc, EReal.coe_ennreal_eq_one, IsPrimitiveRoot.associated_pow_add_sub_sub_one, CochainComplex.mappingConeCompHomotopyEquiv_comm₂, NormedSpace.exp_def, ContractingWith.edist_inequality, norm_algebraMap, Nat.one_sub_one_div_cast_nonneg, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom_assoc, multipliable_one_add_of_summable_prod, ExteriorAlgebra.ιMulti_apply, ENNReal.mul_eq_left, Num.cast_succ', PMF.binomial_apply, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, Quaternion.snd_imK_dualNumberEquiv_symm, Polynomial.coe_basisMonomials, KaehlerDifferential.submodule_span_range_eq_ideal, exists_signed_sum', IsCyclotomicExtension.Rat.Three.lambda_dvd_or_dvd_sub_one_or_dvd_add_one, RingHom.one_notMem_ker, sectionOfRetractionKerToTensor_algebraMap, NumberField.RingOfIntegers.mk_one, ENNReal.div_self, OrthonormalBasis.enorm_eq_one, CochainComplex.HomComplex.δ_zero_cochain_v, CochainComplex.HomComplex.Cochain.units_smul_v, Algebra.SubmersivePresentation.sum_jacobianRelationsOfHasCoeffs_mul_relationOfHasCoeffs, Finset.weightedVSubVSubWeights_apply_left, AffineBasis.toMatrix_row_sum_one, wbtw_one_zero_iff, CochainComplex.HomComplex.Cochain.δ_toSingleMk, DividedPowers.dpow_zero, ModuleCat.MonoidalCategory.leftUnitor_inv_apply, PEquiv.single_mul_single_right, IsLocalization.smul_mk'_one, CauSeq.coe_one, Quaternion.sq_eq_neg_normSq, AffineMap.lineMap_apply_ring, CochainComplex.cm5b.instMonoFIntI, Lagrange.eval_basisDivisor_left_of_ne, Polynomial.eval_one_cyclotomic_not_prime_pow, mul_self_eq_one_iff, Matrix.mul_submatrix_one, CochainComplex.HomComplex.CohomologyClass.toHom_bijective, IsGroupLikeElem.antipode_mul_cancel, MvPolynomial.hsymmPart_zero, Quaternion.imK_neg, MeasureTheory.L1.dist_def, Finsupp.coe_basisSingleOne, Module.Basis.sumCoords_self_apply, AbsoluteValue.not_isNontrivial_iff, div_add_one, IsPrimitiveRoot.prime_norm_toInteger_sub_one_of_prime_ne_two, Num.cast_add, Order.one_le_krullDim_iff, Quaternion.coe_one, hasStrictFDerivAt_list_prod_attach', PadicInt.valuation_one, IsPrimitiveRoot.norm_pow_sub_one_two, deriv_single, ENNReal.log_le_zero_iff, Quaternion.imK_ratCast, MeasureTheory.mem_ae_iff_prob_eq_one₀, ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_coprime, HomogeneousLocalization.NumDenSameDeg.num_one, Set.pairwise_disjoint_Ioc_add_intCast, squarefree_iff_emultiplicity_le_one, NNRat.one_lt_cast, TensorProduct.piScalarRight_symm_single, Matrix.vandermonde_cons, geom_sum_neg_iff, CochainComplex.HomComplex.Cochain.fromSingleMk_precomp, MvPolynomial.ker_eval₂Hom_universalFactorizationMap, Set.encard_eq_one, Polynomial.eval_one_cyclotomic_prime, Algebra.TensorProduct.one_mul, MeasureTheory.tendsto_eLpNorm_condExp, FermatLastTheoremForThreeGen.Solution'.hcdvd, Matrix.Pivot.listTransvecCol_mul_last_row_drop, hasFPowerSeriesOnBall_inv_one_sub, WeierstrassCurve.b₂_of_isCharTwoJNeZeroNF_of_char_two, MeasureTheory.Measure.dirac_apply_of_mem, SymAlg.sym_mul_self, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, ENat.toENNReal_one, ENNReal.HolderConjugate.inv_add_inv_eq_one, MvPolynomial.monomial_sum_index, Matrix.add_mul_mul_mul_invOf_eq_one', CochainComplex.HomComplex.Cochain.leftUnshift_add, CochainComplex.isGE_iff, jacobiSum_nontrivial_inv, MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left', MeasureTheory.diracProba_toMeasure_apply', AbsoluteValue.exists_one_lt_lt_one_of_not_isEquiv, MeasureTheory.L1.norm_integral_le, exteriorPower.presentation_relation, AddMonoidAlgebra.ofMagma_apply, hasFPowerSeriesOnBall_inverse_one_sub, MvPolynomial.monic_monomial_eq, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, Polynomial.comp_one, ZMod.intCast_eq_one_iff_odd, CochainComplex.HomComplex.Cocycle.fromSingleMk_zero, Polynomial.coeffs_one, PowerSeries.coeff_X, CategoryTheory.DifferentialObject.shiftFunctor_map_f, Matrix.nonsing_inv_cancel_or_zero, Sbtw.left_mem_image_Ioi, ProbabilityTheory.Kernel.isProper_iff_inter_eq_indicator_mul, spectralAlgNorm_one, ordinaryHypergeometric_zero, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃_assoc, Polynomial.coeff_X_pow_self, iUnion_Ico_intCast, one_sub_le_one_add_mul_one_sub, HomotopyCategory.instIsCompatibleWithShiftHomologicalComplexIntUpHomotopic, IsPrimitiveRoot.toInteger_sub_one_dvd_prime, ProbabilityTheory.Kernel.continuous_integral_integral_comp, MultilinearMap.mkPiAlgebraFin_apply, Ring.multichoose_eq, one_le_norm_one, Quaternion.tsum_coe, MeasureTheory.isProbabilityMeasure_iff, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_hom, fwdDiff_iter_eq_factorial, CompleteOrthogonalIdempotents.iff_ortho_complete, Asymptotics.IsTheta.listProd, CFC.negPart_one, CoxeterSystem.lengthParity_simple, midpoint_vsub_right, CochainComplex.mappingCone.inr_f_fst_v_assoc, Num.cast_inj, Module.FaithfullyFlat.one_tmul_eq_zero_iff, CategoryTheory.ProjectiveResolution.instProjectiveXIntCochainComplex, Height.mulHeight₁_eq_mulHeight, analyticOrderAt_id, Cubic.prod_X_sub_C_eq, Set.encard_eq_add_one_iff, Polynomial.toFinsupp_X, Quaternion.continuous_im, CategoryTheory.InjectiveResolution.ι'_f_zero_assoc, Asymptotics.Filter.Tendsto.isBigOTVS_one, Quaternion.sq_eq_normSq, one_div_le, 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, SkewMonoidAlgebra.coeff_one, Matrix.det_neg, TannakaDuality.FiniteGroup.sumSMulInv_single_id, Quaternion.re_coe, IsRealClosed.toIsSemireal, MeasureTheory.L1.aemeasurable_coeFn, inner_eq_neg_one_iff_of_norm_eq_one, CochainComplex.HomComplex.Cochain.rightShift_units_smul, SimpleGraph.chromaticNumber_le_one_of_subsingleton, neg_one_pow_char_pow, Matrix.mul_swap_of_ne, CochainComplex.isZero_of_isStrictlyGE, CliffordAlgebra.invOf_ι, CategoryTheory.instHasSmallLocalizedShiftedHomHomologicalComplexIntUpQuasiIsoObjCochainComplexCompSingleFunctorOfNatOfHasExt, AffineMap.lineMap_eq_right_iff, HomologicalComplex.dgoToHomologicalComplex_map_f, Real.HolderConjugate.inv_add_inv_ennreal, neg_one_geom_sum, PadicInt.hasSum_mahler, DerivedCategory.exists_iso_Q_obj_of_isGE_of_isLE, pi_eq_sum_univ, IncidenceAlgebra.mu_eq_neg_sum_Ioc_of_ne, Int.ceil_lt_add_one, Quaternion.imJ_mul, SkewMonoidAlgebra.single_one_one, Module.Basis.toMatrix_mul_toMatrix_flip, HomotopyCategory.instIsTriangulatedIntUpMapHomotopyCategory, ProbabilityTheory.Kernel.IsProper.setLIntegral_eq_indicator_mul_lintegral, geom_series_mul_one_add, MeasureTheory.condExpIndL1Fin_disjoint_union, Int.image_fract, 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, MulSemiringActionHom.map_one, HomotopyCategory.composableArrowsFunctor_map, Complex.enorm_exp_I_mul_ofReal, Module.Basis.apply_eq_iff, inner_eq_one_iff_of_norm_eq_one, AddSubmonoid.one_eq_closure, skewAdjointPart_apply_coe, one_lt_sq_iff_one_lt_abs, Matrix.mul_right_eq_iff_eq_mul_invOf, Module.Basis.mk_coord_apply, HasFPowerSeriesAt.deriv, GradedTensorProduct.includeLeftRingHom_apply, ZMod.orderOf_one_add_prime, ENat.recTopCoe_one, MonoidAlgebra.GroupSMul.linearMap_apply, WittVector.coeff_p_pow, ArchimedeanClass.FiniteElement.val_one, QuadraticAlgebra.omega_mul_algebraMap_mul_mk, CochainComplex.HomComplex.Cocycle.equivHomShift'_apply, Set.encard_ne_add_one, LinearMap.mulRight_one, CochainComplex.instQuasiIsoIntMapHomologicalComplexUpShiftFunctor, DerivedCategory.instEssSurjArrowHomotopyCategoryIntUpMapArrowQh, Matrix.stdBasis_eq_single, WeierstrassCurve.Jacobian.add_of_X_ne, Quaternion.coe_sub, one_half_pos, LinearMap.det_eq_one_of_finrank_eq_zero, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom'_assoc, kstar_one, PiTensorProduct.one_mul, Module.supportDim_le_supportDim_quotSMulTop_succ, ValuativeRel.div_rel_one_iff, SymmetricAlgebra.algebraMap_eq_one_iff, IsPrimitiveRoot.nthRoots_one_nodup, ContinuousLinearMap.integral_comp_L1_comm, preNormEDS_mul_complEDS₂, PMF.apply_eq_one_iff, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃_assoc, LinearMap.toMatrix'_id, Module.Basis.det_self, WithLp.prod_edist_eq_of_L1, MvPolynomial.esymmAlgHomMonomial_single_one, LieModule.toEnd_baseChange, selfAdjointPartL_apply_coe, Quaternion.natCast_im, AffineMap.lineMap_apply_one, IncidenceAlgebra.one_prod_one, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_add, Complex.conjCLE_enorm, RootPairing.pairingIn_neg_one_neg_four_iff, Quaternion.self_mul_star, Polynomial.smeval_at_zero, WeierstrassCurve.leadingCoeff_Φ, Probability.lintegral_cauchyPDF_eq_one, MvPolynomial.dvd_monomial_mul_iff_exists, MeasureTheory.L1.measurable_coeFn, spectrum.differentiableOn_inverse_one_sub_smul, Ideal.exists_mul_add_sub_mem_of_mem_jacobson, MeasureTheory.aestronglyMeasurable_condExpL1CLM, ENat.lt_add_one_iff, Matrix.conjTranspose_eq_one, Module.supportDim_quotSMulTop_succ_eq_supportDim_mem_jacobson, Matrix.mul_swap_apply_left, 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, MeasureTheory.continuous_integral, LinearAlgebra.FreeProduct.rel_id, RootPairing.GeckConstruction.f_lie_v_ne, ProbabilityTheory.IsZeroOrMarkovKernel.bound_le_one, logDeriv_inv, Module.Basis.coe_ofRepr, MultilinearMap.mkPiRing_apply_one_eq_self, ZNum.cast_bitm1, CochainComplex.HomComplex.Cochain.smul_v, CochainComplex.isSplitMono_from_singleFunctor_obj_of_injective, Algebra.norm_eq_one_of_not_exists_basis, PiLp.norm_toLp_const, Valuation.srel_one_iff, DualNumber.range_inlAlgHom_sup_adjoin_eps, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_r, HomotopyCategory.quasiIso_eq_subcategoryAcyclic_W, IsPrimitiveRoot.toInteger_sub_one_dvd_prime', FiniteField.pow_dichotomy, floorDiv_one, Real.hasFPowerSeriesOnBall_linear_zero, ZNum.abs_to_nat, gaussSum_mul_gaussSum_pow_orderOf_sub_one, LSeries.one_convolution_eq_zeta_convolution, right_le_lineMap_iff_one_le, Quaternion.im_neg, Odd.one_add, PadicInt.instNormOneClass, UpperHalfPlane.coe_specialLinearGroup_apply, MultilinearMap.ext_ring_iff, preNormEDS'_two, CategoryTheory.InjectiveResolution.Hom.hom'_f_assoc, fact_one_le_one_ennreal, MonoidAlgebra.scalarTensorEquiv_symm_single, Quaternion.im_imK, Quaternion.neg_imK, IsPrimitiveRoot.ntRootsFinset_pairwise_associated_sub_one_sub_of_prime, MvPowerSeries.constantCoeff_one, one_le_star_iff, Quaternion.imK_intCast, Algebra.TensorProduct.tmul_one_eq_one_tmul, CochainComplex.HomComplex.Cochain.δ_shift, CategoryTheory.Functor.mapDifferentialObject_obj_d, CochainComplex.shiftShortComplexFunctor'_hom_app_τ₃, ZMod.cast_descFactorial, CochainComplex.HomComplex.Cochain.fromSingleMk_sub, FermatLastTheoremForThreeGen.Solution'.hb, GradedTensorProduct.algebraMap_def, HahnSeries.SummableFamily.one_sub_self_mul_hsum_powers, PowerSeries.coeff_one, CochainComplex.mappingCone.inl_v_descShortComplex_f_assoc, AddSubmonoid.one_eq_closure_one_set, Rat.smul_one_eq_cast, CochainComplex.IsKProjective.leftOrthogonal, LinearIsometry.enorm_toContinuousLinearMap, abs_neg_one_zpow, div_lt_one, SimpleGraph.adjMatrix_mul_apply, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, Polynomial.Chebyshev.iterate_derivative_U_eval_one, Hyperreal.coe_one, DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective, PosNum.cast_pos, Polynomial.chebyshev_T_eq_dickson_one_one, RootPairing.GeckConstruction.e_lie_v_ne, Module.FaithfullyFlat.tensorProduct_mk_injective, ProbabilityTheory.Fernique.measure_gt_normThreshold_le_rpow, AddSubmonoid.pow_subset_pow, orderOf_neg_one, IsPrimitiveRoot.primitiveRoots_one, IsCyclotomicExtension.union_left, PMF.toMeasure_apply_eq_one_iff, dividedPowersBot_dpow_eq, 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', PolyEquivTensor.invFun_monomial, SimpContFract.of_isContFract, Matrix.invOf_diagonal_eq, Nat.cast_eq_one, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_flip_inv_app, Matrix.mem_orthogonalGroup_iff, Quaternion.imI_add, GenContFract.zeroth_contAux_eq_one_zero, CochainComplex.cm5b.instInjectiveXIntI, Polynomial.ringKrullDim_le, Nat.cast_list_prod, Matrix.swap_mulVec, MeasureTheory.lpNorm_one, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, CochainComplex.cm5b.instMonoIntI, Matrix.inv_mul_of_invertible, SeparatingDual.exists_eq_one_ne_zero_of_ne_zero_pair, QuaternionAlgebra.Basis.i_self, CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass_apply, HasStrictFDerivAt.hasStrictDerivAt, Matrix.Pivot.isTwoBlockDiagonal_listTransvecCol_mul_mul_listTransvecRow, ValuationSubring.one_mem, SimpleGraph.incMatrix_mul_transpose_diag, GenContFract.of_one_le_get?_partDen, CompleteOrthogonalIdempotents.complete, QuadraticAlgebra.algHom_ext_iff, Valuation.vle_one_iff, Quaternion.ratCast_im, CongruenceSubgroup.Gamma1_mem, SkewMonoidAlgebra.ofFinsupp_eq_one, IsLocalization.toInvSubmonoid_eq_mk', one_vecMul_of_mem_doublyStochastic, PolynomialLaw.neg_def, Matrix.swap_mul_of_ne, Matrix.SpecialLinearGroup.coe_transpose, Valuation.IsEquiv.val_sub_one_lt_one_iff, Nat.one_div_cast_nonneg, fderivWithin_derivWithin, isIntegral_one, ComplexShape.instIsRelIffNatIntEmbeddingUpNat, AddSubmonoid.closure_pow, FiniteDimensional.exists_mul_eq_one, RCLike.sqrt_neg_I, PiTensorProduct.mul_one, HasFDerivAt.list_prod', IsPrimitiveRoot.card_quotient_toInteger_sub_one, MeasureTheory.eLpNorm_one_le_of_le, Polynomial.mirror_eval_one, MvPolynomial.coeff_X', Matrix.permMatrix_mulVec, Set.Ioc.coe_eq_one, ZMod.inv_mul_eq_one_of_isUnit, FirstOrder.Language.presburger.realize_nsmul, RingPreordering.one_notMem_supportAddSubgroup, PolyEquivTensor.toFunLinear_one_tmul_one, Matrix.SpecialLinearGroup.coe_GL_coe_matrix, Set.Ioc.coe_le_one, extremePoints_doublyStochastic, Matrix.det_fromBlocks₂₂, ENat.le_sub_one_of_lt, ContractingWith.exists_fixedPoint', lineMap_le_right_iff_le_one, ZNum.to_of_int, differentiableWithinAt_localInvariantProp, invOf_nonpos, ceilDiv_one, Quaternion.imK_smul, iteratedDeriv_comp_const_sub, FaithfulSMul.algebraMap_eq_one_iff, Finset.sum_centroidWeights_eq_one_of_nonempty, tendsto_fract_left, Subsemiring.mem_closure_iff_exists_list, Matrix.mul_left_eq_iff_eq_invOf_mul, OrthonormalBasis.repr_symm_single, MvPolynomial.vars_one, Quaternion.star_imK, Unitary.two_mul_one_sub_le_norm_sub_one_sq, CauSeq.one_not_equiv_zero, ofBoolAlg_top, WeakDual.CharacterSpace.norm_le_norm_one, DualNumber.commute_eps_left, MeasureTheory.L1.stronglyMeasurable_coeFn, FiniteField.isSquare_iff, EReal.exp_zero, Subring.one_mem_toNonUnitalSubring, IsMprojection.Mnorm, exteriorPower.zeroEquiv_ιMulti, Summable.tsum_pow_mul_one_sub, Nat.one_sub_one_div_cast_le_one, MeasureTheory.L1.norm_setToL1_le_mul_norm', Quaternion.im_star, Matrix.SpecialLinearGroup.eq_scalar_center_equiv_rootsOfUnity, Set.Icc.coe_one, ProbabilityTheory.lintegral_gaussianPDFReal_eq_one, odd_add_one, Matrix.fromCols_mul_fromRows_eq_one_comm, CochainComplex.isKProjective_iff_leftOrthogonal, Quaternion.coe_mul, Representation.FiniteCyclicGroup.coinvariantsKer_leftRegular_eq_ker, 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, Matrix.Pivot.exists_isTwoBlockDiagonal_of_ne_zero, MvPolynomial.degreeOf_one, Polynomial.content_X, mulLeftLinearMap_one, iter_deriv_inv, Module.Basis.toDual_apply, stdSimplexHomeomorphUnitInterval_one, Complex.lift_symm_apply_coe, formalMultilinearSeries_geometric_radius, Polynomial.discr_C, Int.floor_pos, CategoryTheory.InjectiveResolution.extMk_hom, ProbabilityTheory.condVar_of_sigmaFinite, ENNReal.zero_le_log_iff, IsLprojection.coe_sdiff, CategoryTheory.InjectiveResolution.cochainComplex_d_assoc, RCLike.sqrt_I, Matrix.GeneralLinearGroup.coe_map_mul_map_inv, DualNumber.algHom_ext_iff, ENat.add_one_pos, QuadraticMap.associated_linMulLin, isCoprime_one_right, Representation.coinvariantsTprodLeftRegularLEquiv_symm_apply, Subsemiring.list_prod_mem, ArchimedeanClass.mk_map_of_archimedean, Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype, hasFPowerSeriesOnBall_cuspFunction, Units.val_set_image_rootsOfUnity_two, ProbabilityTheory.Kernel.withDensity_one, ValuationSubring.mem_principalUnitGroup_iff, TensorAlgebra.tprod_apply, quadraticCharFun_eq_pow_of_char_ne_two, Units.add_eq_mul_one_add_div, WeierstrassCurve.Projective.add_of_Y_eq, Matrix.of_mem_specialOrthogonalGroup_fin_two_iff, Matrix.SpecialLinearGroup.toLin'_to_linearMap, MeasureTheory.L1.SimpleFunc.integral_smul, Quaternion.normSq_zpow, Quaternion.coe_nnratCast, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, Finset.centerMass_ite_eq, Nat.one_div_pos_of_nat, QuaternionAlgebra.Basis.j_self, ENNReal.rpow_zero, SimpleGraph.eq_top_iff_forall_eccent_eq_one, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, ZMod.orderOf_one_add_mul_prime_pow, Polynomial.leadingCoeff_X_sub_C, Matrix.mem_colStochastic, CochainComplex.shortComplexTruncLE_shortExact, Matrix.det_mul_add_one_comm, IsCyclotomicExtension.Rat.isPrime_span_zeta_sub_one, Module.Projective.exists_dual_eq_one, FirstOrder.Field.instModelField, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_zero, Cardinal.one_lt_ofENat, iteratedDeriv_eq_iteratedFDeriv, Height.fun_mulHeight_one, IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, Quaternion.coe_starAe, Topology.CWComplex.iUnion_openCell_eq_skeleton, iter_deriv_inv', MeasureTheory.L1.SimpleFunc.norm_setToL1SCLM_le, abs_sub_sq, isGroupLikeElem_self, ENat.ceil_one, CochainComplex.cm5b.i_f_comp, CochainComplex.HomComplex.Cochain.δ_rightUnshift, Finset.nonneg_subConst_self, MvPolynomial.esymmAlgHomMonomial_add, Matrix.linfty_opNormOneClass, CochainComplex.mappingCone.inr_snd, MvPolynomial.algebraTensorAlgEquiv_symm_map, TensorProduct.rid_symm_apply, Matrix.mem_colStochastic_iff_sum, Ideal.map_height_le_one_of_mem_minimalPrimes, Algebra.TensorProduct.productMap_right_apply, odd_one, 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, iccHomeoI_symm_apply_coe, Matrix.SpecialLinearGroup.SL2_inv_expl_det, Pi.basisFun_apply, Rep.leftRegularHomEquiv_symm_single, CochainComplex.HomComplex.leftHomologyData_H_coe, MvPolynomial.tensorEquivSum_C_tmul_one, CochainComplex.HomComplex.leftHomologyData'_K_coe, ModularGroup.tendsto_lcRow0, Nat.ceil_sub_one, Matrix.submatrixEquivInvertibleEquivInvertible_apply, Submodule.pow_eq_span_pow_set, CochainComplex.HomComplex.Cochain.leftUnshift_units_smul, MeasureTheory.L1.integral_of_fun_eq_integral, MeasureTheory.L1.integral_zero, Algebra.Extension.tensorCotangentInvFun_smul_mk, CochainComplex.mappingCone.inl_fst, PartENat.toWithTop_one', pow_eq_one_iff_of_ne_zero, PowerSeries.coe_X, Submodule.torsionBy_one, MvPolynomial.hsymm_zero, 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, Submodule.eq_span_singleton_of_surjective, CochainComplex.HomComplex.Cocycle.shift_coe, contDiff_one_iff_hasFDerivAt, AddMonoidAlgebra.algHom_ext_iff, Matrix.Pivot.listTransvecCol_mul_last_row, HasFPowerSeriesAt.hasDerivAt, pinGroup.star_mul_self_of_mem, Quaternion.im_imI, Algebra.TensorProduct.basis_repr_symm_apply, SimpleGraph.degree_eq_sum_if_adj, Int.two_pow_sub_pow, PiLp.nnnorm_eq_of_L1, ZMod.isSquare_neg_one_iff', round_le_add_half, MeasureTheory.condExpIndL1_of_not_measurableSet, Matrix.num_one, MeasureTheory.stoppedProcess_eq', MeasureTheory.L1.norm_setToL1_le', AbsoluteValue.map_units_int, MeasureTheory.withDensitySMulLI_apply, SimpleGraph.incMatrix_transpose_mul_diag, Quaternion.self_add_star, Quaternion.normSq_def, ComplexShape.embeddingUpIntLE_f, Quaternion.continuous_coe, Finsupp.single_mem_span_single, AbsoluteValue.IsEquiv.one_lt_iff, Quaternion.imK_one, CochainComplex.mappingCone.liftCochain_v_fst_v_assoc, Quaternion.ratCast_imK, IsLprojection.Lcomplement_iff, isCyclotomicExtension_iff, ProbabilityTheory.Kernel.deterministic_apply', polyEquivTensor_apply, lineMap_one_half, self_eq_inv₀, CliffordAlgebra.contractRight_one, Valuation.rel_one_iff, HomotopyCategory.mem_subcategoryAcyclic_iff, Quaternion.coe_commute, ENNReal.log_one, CochainComplex.isStrictlyLE_shift, Order.krullDim_le_one_iff_forall_isMax, ModularGroup.abs_c_le_one, Int.fract_eq_self, Quaternion.coe_injective, CliffordAlgebraDualNumber.equiv_ι, Algebra.Presentation.algebraTensorAlgEquiv_symm_relation, WeierstrassCurve.Projective.Point.zero_def, CochainComplex.ConnectData.restrictionGEIso_inv_f, Order.krullDim_withBot, cfc_unitary_iff, one_sub_le_one_sub_mul_one_add, IsLocalization.mk'_mul_mk'_eq_one, MvPolynomial.totalDegree_one, CochainComplex.instFullIntSingleFunctor, HasFDerivAt.hasDerivAt, Cardinal.ofENat_le_one, Matrix.diagonalInvertibleEquivInvertible_symm_apply, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₁, Metric.packingNumber_singleton, contMDiff_equivTangentBundleProd, FiniteField.sum_pow_units, geom_sum_mul_add, instIsManifoldOfNatWithTopENatOfMinSmoothness_1, Int.fract_lt_one, Quaternion.ratCast_imJ, LinearMap.transvection.det, Module.Invertible.rTensorEquiv_symm_apply_apply, Polynomial.disc_C, WeierstrassCurve.Projective.add_of_Y_ne', CochainComplex.HomComplex.Cochain.δ_rightShift, SubAddAction.ENat_card_ofStabilizer_add_zero_eq, DerivedCategory.right_fac_of_isStrictlyLE, Algebra.TensorProduct.algebraMap_apply', Polynomial.MonicDegreeEq.mk_coe, ContinuousMap.adjoin_id_eq_span_one_add, CochainComplex.ConnectData.map_id, Multiset.esymm_neg, WeierstrassCurve.Projective.neg_of_Z_eq_zero, Height.logHeight₁_eq_logHeight, NNRat.coe_one, Set.Ico.coe_mul, MeasureTheory.L1.norm_of_fun_eq_integral_norm, HahnSeries.inv_def, Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_top, WithBot.succ_natCast, IsStarProjection.two_mul_sub_one_mem_unitary, SL_reduction_mod_hom_val, CompleteOrthogonalIdempotents.of_isIdempotentElem, selfAdjointPart_apply_coe, MeasureTheory.L1.integral_add, Matrix.Represents.one, CliffordAlgebra.reverse.map_one, AddMonoidAlgebra.basis_apply, AlgEquiv.moduleEndSelfOp_symm_apply, PadicInt.fwdDiff_mahlerSeries, skewAdjointPartL_apply_coe, CochainComplex.HomComplex.Cochain.leftShift_v, CochainComplex.mappingCone.d_fst_v'_assoc, minpoly_algEquiv_toLinearMap, TensorProduct.AlgebraTensorModule.cancelBaseChange_symm_tmul, Finset.one_le_divConst_self, one_add_cpow_hasFPowerSeriesOnBall_zero, IsCoprime.exists, deriv_id, PowerSeries.X_pow_eq, RootPairing.pairing_neg_one_neg_four_iff', ContinuousAlternatingMap.ext_ring_iff, Quaternion.re_neg, CochainComplex.HomComplex.Cochain.rightUnshift_add, Quaternion.re_im, Quaternion.imI_intCast, MeasureTheory.L2.mem_L1_inner, 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, MvPolynomial.esymm_eq_sum_monomial, Subsemiring.one_mem_toNonUnitalSubsemiring, MeasureTheory.L1.integral_eq_integral, Matrix.trace_one, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_hom_f_f, Nat.one_lt_cast, ComplexShape.embeddingDownNat_f, Subalgebra.rTensorBot_symm_apply, div_add_same, IncidenceAlgebra.zeta_mul_mu, HomotopyCategory.homologyFunctor_shiftMap_assoc, openSegment_eq_image₂, CochainComplex.mappingCone.inl_v_d, CategoryTheory.DifferentialObject.Hom.comm, FirstOrder.realize_genericPolyMapSurjOnOfInjOn, Valuation.vlt_one_iff, WeierstrassCurve.Jacobian.dblXYZ_of_Z_eq_zero, minpoly.one, Int.ceil_sub_self_eq, Matrix.invOf_mul_cancel_right, DualNumber.commute_eps_right, PreErgodic.prob_eq_zero_or_one, IsNilpotent.isUnit_one_sub, MeasureTheory.Integrable.coeFn_toL1, Asymptotics.isEquivalent_iff_tendsto_one, IsGroupLikeElem.counit_eq_one, hasDerivAt_neg, LinearMap.derivWithin, CochainComplex.isZero_of_isGE, CochainComplex.shiftFunctor_obj_X', ENNReal.mul_eq_right, Module.End.mem_genEigenspace_one, RootPairing.EmbeddedG2.pairing_short_long, HomotopyCategory.distinguished_iff_iso_trianglehOfDegreewiseSplit, AbsoluteValue.IsEquiv.eq_one_iff, hasFTaylorSeriesUpToOn_succ_iff_left, KaehlerDifferential.derivationTensorProduct_algebraMap, CochainComplex.HomComplex.Cochain.shift_v, ComplexShape.σ_def, Matroid.eRk_insert_eq_add_one, PrimeSpectrum.isIdempotentElemEquivClopens_symm_top, CochainComplex.shiftFunctorZero_hom_app_f, one_div_lt_one_div, Unitary.norm_sub_eq, MeasureTheory.condExpIndL1_disjoint_union, Metric.unitClosedBall.coe_one, preNormEDS'_one, contDiffOn_succ_iff_fderivWithin, AddCommMonoidWithOne.ext_iff, Matrix.mul_invOf_cancel_left, one_div_lt_one_div_of_neg_of_lt, CochainComplex.mappingCone.inr_f_snd_v_assoc, Algebra.norm_one_add_smul, AffineMap.lineMap_lineMap_left, MeasureTheory.Integrable.norm_toL1_eq_lintegral_norm, AffineMap.hasStrictDerivAt, mem_doublyStochastic, MeasureTheory.Measure.le_count_apply, Polynomial.MonicDegreeEq.natDegree, MeasureTheory.L1.aestronglyMeasurable_coeFn, Convex.mem_Icc, Quaternion.normSq_neg, HilbertBasis.repr_self, Set.one_lt_encard_iff, nnnorm_commutator_sub_one_le, Coalgebra.rTensor_counit_comul, WeierstrassCurve.Affine.CoordinateRing.coe_norm_smul_basis, descPochhammer_eval_eq_ascPochhammer, Polynomial.derivative_monomial_succ, Polynomial.resultant_deriv, MeasureTheory.condExpInd_smul', Asymptotics.IsLittleO.listProd, EReal.exp_lt_one_iff, LaurentPolynomial.single_zero_one_eq_one, MeasureTheory.L1.setToL1_add_left, CochainComplex.triangleOfDegreewiseSplit_mor₃, CochainComplex.shift_f_comp_mappingConeHomOfDegreewiseSplitIso_inv_assoc, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk, lt_one_div_of_neg, StandardEtalePair.aeval_X_g_mul_mk_X, MvPolynomial.pderiv_inr_universalFactorizationMap_X, CochainComplex.HomComplex.Cochain.shiftAddHom_apply, ProbabilityTheory.Kernel.measure_zero_or_one_of_measurableSet_limsup_atBot, Algebra.TensorProduct.natCast_def, EulerProduct.one_sub_inv_eq_geometric_of_summable_norm, NNRat.smul_one_eq_cast, ZNum.of_to_int, GenContFract.zeroth_den_eq_one, Matrix.mem_unitaryGroup_iff', Finset.cast_card_erase_of_mem, PowerSeries.coeff_X_pow_self, ZNum.cast_bit1, Int.preimage_floor_singleton, Int.abs_one_sub_fract, CategoryTheory.InjectiveResolution.instQuasiIsoIntι', ValuativeRel.one_vle_inv, RatFunc.single_one_eq_pow, PadicInt.limNthHom_one, Polynomial.disc_of_degree_eq_one, PreTilt.valAux_one, Algebra.Presentation.tensorModelOfHasCoeffsEquiv_symm_tmul, IsAdjoinRootMonic.coeff_one, Quaternion.one_imJ, Polynomial.monomial_one_right_eq_X_pow, Affine.Simplex.smul_centroid_vsub_point_eq_sum_vsub, CochainComplex.mappingCone.trianglehMapOfHomotopy_hom₂, stdSimplex.add_eq_one, CongruenceSubgroup.Gamma1_to_Gamma0_mem, MonomialOrder.leadingCoeff_X, MulSemiringAction.smul_one, CochainComplex.HomComplex.Cochain.δ_leftUnshift, AdicCompletion.one_apply, Finsupp.lift_symm_apply, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, MeasureTheory.isZeroOrProbabilityMeasure_iff, HomotopyCategory.spectralObjectMappingCone_ω₁, Module.End.genEigenspace_div, ascPochhammer_zero_eval_zero, WeierstrassCurve.Projective.negMap_of_Z_eq_zero, Matrix.diagonalInvertibleEquivInvertible_apply, one_lt_two, LinearMap.ringLmapEquivSelf_apply, Nat.norm_cast_le, pow_one_sub_dvd_pow_mul_sub_one, Polynomial.Splits.coeff_zero_eq_leadingCoeff_mul_prod_roots, Submodule.lTensorOne_symm_apply, PresheafOfModules.Sheafify.one_smul, Units.val_oneSub, ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_add_of_squarefree, AddMonoidAlgebra.liftNC_one, MvPolynomial.mul_monomial_mem_coeffsIn, Nat.one_lt_ofNat, GenContFract.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero, CochainComplex.mappingCone.d_fst_v', MeasureTheory.condExp_of_sigmaFinite, AddMonoidAlgebra.scalarTensorEquiv_symm_single, MonoidAlgebra.one_def, sectionOfRetractionKerToTensorAux_algebraMap, DirectSum.liftRingHom_symm_apply_coe, WeierstrassCurve.Jacobian.nonsingular_some, PowerSeries.invOneSubPow_eq_inv_one_sub_pow, Polynomial.eval_one, CompleteOrthogonalIdempotents.pair_iff'ₛ, MeasureTheory.norm_setToFun_le_mul_norm, pos_invOf_of_invertible_cast, IsCyclotomicExtension.iff_adjoin_eq_top, contDiffOn_succ_iff_fderiv_apply, FormalMultilinearSeries.ofScalars_comp_neg_id, Unitization.instNormOneClass, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_pow_ne_two, same_add_div, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, CochainComplex.shiftFunctorAdd'_hom_app_f', mem_fintypeAffineCoords_iff_sum, gaussSum_pow_eq_prod_jacobiSum, SubringClass.toNormOneClass, MeasureTheory.L1.SimpleFunc.norm_eq_integral, IntermediateField.one_mem, Quaternion.coe_imK, MvPolynomial.esymmPart_zero, Algebra.baseChange_lmul, KaehlerDifferential.mvPolynomialBasis_repr_D, Polynomial.Monic.coeff_natDegree, MeasureTheory.condExpIndL1_of_measure_eq_top, CochainComplex.mappingCone.inl_v_descCochain_v, CochainComplex.HomComplex.Cochain.leftShift_add, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, edist_le_of_edist_le_geometric_of_tendsto₀, WeierstrassCurve.Affine.CoordinateRing.basis_zero, SemimoduleCat.MonoidalCategory.leftUnitor_inv_apply, 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, CochainComplex.HomComplex.Cochain.leftShift_comp_zero_cochain, Set.Ioo.pos, Matrix.trace_permutation, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃_assoc, ZNum.cast_mul, CochainComplex.shiftEval_hom_app, TensorProduct.toLinearMap_symm_lid, normEDS_ofNat, SimpleGraph.FarFromTriangleFree.lt_one, HahnSeries.orderTop_self_sub_one_pos_iff, RootPairing.Base.toWeightBasis_repr_root, ZNum.div_to_int, Matrix.invertibleEquivDetInvertible_apply, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, MeasureTheory.L1.SimpleFunc.norm_integral_le_norm, ascPochhammer_eval_succ, Module.supportDim_le_supportDim_quotSMulTop_succ_of_mem_jacobson, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, contDiff_succ_iff_deriv, SimpleGraph.adjMatrix_mulVec_const_apply_of_regular, Matrix.adjugate_subsingleton, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_comp_triangle_mor₃, IsManifold.instOfNatWithTopENat_1, Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal, Module.End.HasUnifEigenvalue.of_mem_spectrum, 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, AbsoluteValue.not_isNontrivial_apply, Dual.apply_one_mul_eq, Polynomial.TrailingMonic.def, 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, ProbabilityTheory.Kernel.measure_eq_zero_or_one_or_top_of_indepSet_self, toIcoMod_zero_one, MeasureTheory.L1.norm_setToL1_le_mul_norm, LinearEquiv.toSpanNonzeroSingleton_one, Submodule.lTensorOne'_one_tmul, Nat.cast_choose_two, contDiffOn_succ_iff_derivWithin, CochainComplex.cm5b.i_f_comp_assoc, CliffordAlgebra.EquivEven.e0_mul_e0, MvPolynomial.psum_eq_mul_esymm_sub_sum, Matrix.cramer_one, ProbabilityTheory.Kernel.IsProper.setLIntegral_inter_eq_indicator_mul_setLIntegral, CochainComplex.HomComplex_X, CochainComplex.instIsStrictlyGEExtendNatIntEmbeddingUpNatOfNat, CochainComplex.ConnectData.homologyMap_map_of_eq_succ, ENat.card_eq_one_iff_unique, UniqueFactorizationDomain.radical_neg_one, CFC.one_rpow, ZMod.exists_one_add_mul_pow_prime_eq, CochainComplex.HomComplex.leftHomologyData'_H_coe, seminormFromBounded_ge, ZMod.val_one, CochainComplex.mappingCone.triangleRotateShortComplex_g, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left', Matrix.det_one, CliffordAlgebra.toProd_one_tmul_ι, CochainComplex.shiftFunctor_obj_d', Matrix.GeneralLinearGroup.val_swap, MeasureTheory.Measure.dirac_apply, AlgEquiv.moduleEndSelf_symm_apply, geom_sum_Ico', stdSimplex.barycenter_eq_centerMass, KaehlerDifferential.tensorKaehlerEquivOfFormallyEtale_symm_D_algebraMap, QuadraticAlgebra.norm_one, Matrix.adjugate_one, Dynamics.netMaxcard_univ, Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eq, Quaternion.coe_imJ, CliffordAlgebra.even.lift.aux_apply, CochainComplex.instHasMapBifunctorObjIntShiftFunctor, one_le_two, EisensteinSeries.vecMulSL_gcd, Algebra.SubmersivePresentation.ofSubsingleton_algebra_smul, PowerSeries.rescale_neg_one_X, MeasureTheory.lintegral_indicator_one, Matrix.permMatrix_mem_colStochastic, Real.dimH_segment, KaehlerDifferential.mvPolynomialBasis_repr_comp_D, HahnSeries.C_one, PowerSeries.constantCoeff_exp, WittVector.bind₁_onePoly_wittPolynomial, PolynomialLaw.toFun_neg, Polynomial.fwdDiff_iter_degree_eq_factorial, MeasureTheory.diracProba_toMeasure_apply, norm_intCast_eq_abs_mul_norm_one, Bialgebra.comul_one, ZNum.lt_to_int, Int.clog_one_right, Module.End.Eigenvalues.val_mk, CochainComplex.HomComplex.Cocycle.equivHom_apply, RingCat.Colimits.quot_one, Matrix.det_isEmpty, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, jacobiSum_eq_sum_sdiff, ENNReal.HolderTriple.one_div_eq, Field.DirectLimit.inv_mul_cancel, Polynomial.content_primPart, Int.ModEq.listProd_one, CategoryTheory.Functor.mapHomologicalComplex_commShiftIso_hom_app_f, fderivWithin_list_prod', Matrix.SpecialLinearGroup.coe_GLPos_coe_GL_coe_matrix, OrthonormalBasis.inner_eq_one, Nat.preimage_floor_zero, Module.Basis.finTwoProd_zero, StarSubalgebra.one_mem_toNonUnitalStarSubalgebra, PowerSeries.coeff_derivative, instContMDiffAddOfNatWithTopENat, listProd_apply_eq_zero, iteratedDerivWithin_id, Finset.max_abv_sum_one_le_of_isNonarchimedean, Set.Icc.one_sub_nonneg, QuadraticAlgebra.mk_eq_add_smul_omega, Matrix.mem_specialOrthogonalGroup_fin_two_iff, MeasureTheory.norm_condExpInd_le, 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, Matrix.conjTranspose_list_prod, MeasureTheory.setToFun_mono_left, ProbabilityTheory.Kernel.eLpNorm_density_le, Matroid.eRk_singleton_eq, Int.abs_sub_lt_one_of_floor_eq_floor, CochainComplex.mappingCone.inr_descShortComplex, ModuleCat.extendScalarsComp_hom_app_one_tmul, IsPrimitiveRoot.subOneIntegralPowerBasisOfPrimePow_gen, PMF.hasSum_coe_one, Pi.linearIndependent_single_one, Module.Relations.Solution.ofπ_var, DerivedCategory.instAdditiveCochainComplexIntQ, ContinuousLinearMap.det_smulRight, Polynomial.dickson_two_one_eq_chebyshev_U, Nat.floor_eq_zero, Matrix.toLinAlgEquiv'_one, MeasureTheory.Measure.hausdorffMeasure_le_one_of_subsingleton, Algebra.mem_adjoin_of_map_mul, CochainComplex.ι_mapBifunctorShift₁Iso_hom_f_assoc, hasStrictFDerivAt_list_prod, Matrix.toLin_one, Order.coheight_eq_coe_iff, CategoryTheory.Mat.id_apply, CFC.sqrt_one, Rat.toNNRat_one, ENNReal.one_lt_coe_iff, Summable.hasProdLocallyUniformlyOn_nat_one_add, ArchimedeanClass.FiniteElement.mk_one, inf_eq_half_smul_add_sub_abs_sub, CochainComplex.cm5b.I_d, sub_one_div_inv_le_two, Quaternion.re_snd_dualNumberEquiv, FreeAlgebra.algebraMap_eq_one_iff, CochainComplex.triangleOfDegreewiseSplit_mor₁, PowerSeries.coeff_X_pow, Matrix.invOf_fromBlocks_zero₂₁_eq, CompleteOrthogonalIdempotents.prod_one_sub, Matrix.IsTotallyUnimodular.one_fromCols, geom_sum_succ, bernsteinPolynomial.eval_at_0, sq_le_one_iff_abs_le_one, Quaternion.re_add, KaehlerDifferential.span_range_eq_ideal, CochainComplex.mappingCone.mapHomologicalComplexXIso'_hom, MeasureTheory.Measure.rnDeriv_restrict_self, LaurentPolynomial.counit_T, AlgebraicGeometry.StructureSheaf.toOpenₗ_eq_const, Nat.one_le_ofNat, Subring.closure_insert_one, Representation.leftRegular_norm_apply, Odd.add_one, contDiffOn_succ_iff_hasFDerivWithinAt_of_uniqueDiffOn, FDRep.char_orthonormal, Matrix.invOf_submatrix_equiv_eq, ContinuousLinearMap.toSpanSingleton_one_eq_algebraMapCLM, one_div_lt_one_div_of_lt, Coalgebra.TensorProduct.rid_symm_apply, star_le_one_iff, CochainComplex.mapBifunctorHomologicalComplexShift₁Iso_inv_f_f, Algebra.TensorProduct.intCast_def, CochainComplex.HomComplex.Cochain.d_comp_ofHom_v, Polynomial.coeff_eq_esymm_roots_of_card, TensorProduct.mk_surjective, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, Polynomial.Chebyshev.iterate_derivative_U_eval_one_eq_div, SimpleGraph.adjMatrix_vecMul_apply, Matrix.det_one_add_replicateCol_mul_replicateRow, Matrix.zero_zpow_eq, MvPolynomial.support_esymm'', PositiveLinearMap.norm_apply_le_of_nonneg, CochainComplex.HomComplex.Cochain.leftShift_units_smul, Matrix.Pivot.exists_list_transvec_mul_diagonal_mul_list_transvec, stdSimplexEquivIcc_apply_coe, MeasureTheory.condExpInd_disjoint_union_apply, CochainComplex.HomComplex.Cochain.equivHomotopy_apply_coe, Polynomial.Chebyshev.iterate_derivative_T_eval_one, ENat.one_lt_top, MvPolynomial.divMonomial_monomial_mul, sbtw_lineMap_iff, ENat.floor_sub_one, ZMod.coe_mul_inv_eq_one, Matrix.mulVec_surjective_iff_exists_right_inverse, HomotopyCategory.homologyShiftIso_hom_app, Set.pairwise_disjoint_Ico_intCast, iter_deriv_inv_linear_sub, WeierstrassCurve.Jacobian.Point.zero_point, midpoint_sub_left, PrimeSpectrum.zeroLocus_singleton_one, odd_iff_exists_bit1, Quaternion.mul_coe_eq_smul, MeasureTheory.L1.setToL1_simpleFunc_indicatorConst, isQuasiregular_iff_isUnit', CochainComplex.shiftFunctorAdd_hom_app_f, ENat.lt_floor, RingPreordering.neg_one_notMem, Algebra.norm_eq_one_of_not_module_finite, MeasureTheory.L1.SimpleFunc.setToL1SCLM_zero_left, Nat.sub_one_lt_floor, lucas_primality_iff, ModularGroup.coe_T, Set.Icc.coe_eq_one, MeasureTheory.condExpIndL1Fin_ae_eq_condExpIndSMul, midpoint_vsub, Polynomial.Monic.def, pow_eq_one_iff_cases, WeierstrassCurve.Jacobian.Point.toAffine_zero, rootsOfUnityEquivNthRoots_apply, ComplexShape.instIsTruncLENatIntEmbeddingDownNat, Nat.not_ofNat_le_one, Int.fract_eq_zero_or_add_one_sub_ceil, IsStarProjection.one_sub, DerivedCategory.Qh_obj_singleFunctors_obj, Matrix.isHermitian_one, Polynomial.leadingCoeff_X_pow_sub_one, Matrix.J_det_mul_J_det, Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X, Quaternion.im_ratCast, Num.to_nat_to_int, Module.Basis.singleton_apply, MonomialOrder.Monic.coeff_degree, nnnorm_sub_mul_le, Algebra.Generators.compLocalizationAwayAlgHom_relation_eq_zero, RatFunc.single_zpow, ArchimedeanClass.mk_one, iteratedDeriv_id, Quaternion.imJ_add, Bialgebra.TensorProduct.rid_symm_apply, CochainComplex.HomComplex.δ_map, Ideal.Quotient.mk_eq_one_iff_sub_mem, NNRat.cast_lt_one, MeasureTheory.L1.setToL1_zero_left', exteriorPower.basis_repr, MvPolynomial.mem_ideal_span_monomial_image_iff_dvd, ConvexSpace.assoc, emultiplicity_pow_prime_sub_pow_prime, Num.ofZNum'_toNat, SymAlg.unsym_mul_self, CochainComplex.mapBifunctorShift₁Iso_trans_mapBifunctorShift₂Iso, Bialgebra.counit_one, amenable_of_maxAddFoelner_neBot, MeasureTheory.condExpL1_mono, Quaternion.im_sub, IsPrimitiveRoot.self_sub_one_pow_dvd_order, spinGroup.star_mul_self_of_mem, CochainComplex.mappingCone.inl_v_descShortComplex_f, hasStrictDerivAt_exp_zero_of_radius_pos, MeasureTheory.L1.norm_Integral_le_one, ContinuousLinearMap.toSpanSingletonLE_symm_apply, LinearMap.toMatrix_singleton, MvPolynomial.aeval_one_tmul, IsAlgebraic.invOf_iff, Algebra.SubmersivePresentation.ofSubsingleton_σ', one_add_div, derivWithin_neg, AffineMap.lineMap_symm, MeasureTheory.Integrable.uniformIntegrable_condExp_filtration, Nat.smul_one_eq_cast, Quaternion.imI_natCast, Algebra.discr_powerBasis_eq_prod'', Polynomial.algEquivCMulXAddC_symm_apply, Submodule.pow_subset_pow, Complex.imCLM_enorm, 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, MvPowerSeries.monomial_zero_one, MvPowerSeries.monomial_one_eq, Polynomial.UniversalFactorizationRing.factor₁_mul_factor₂, hasDerivAt_single, IsCyclotomicExtension.norm_zeta_eq_one, CochainComplex.HomComplex.Cochain.ofHom_add, Set.encard_insert_le, TensorProduct.lid'_symm_apply, SimpleGraph.radius_top, Polynomial.integralNormalization_coeff, preNormEDS_odd, Matrix.mul_one, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRing, CochainComplex.mappingCone.triangleRotateShortComplexSplitting_s, one_div_lt_one_div_of_neg, DistribMulActionHom.ext_ring_iff, PosNum.one_le_cast, CochainComplex.mappingCone.inr_f_descShortComplex_f, ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mul, orthonormal_iff_ite, DualNumber.exp_smul_eps, WeierstrassCurve.Jacobian.equation_zero, Basis.multilinearMap_apply, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atTop, Set.encard_le_one_iff, CochainComplex.HomComplex.Cochain.id_comp, Polynomial.coeff_eq_esymm_roots_of_splits, Cardinal.toENat_le_one, Rep.leftRegularHomEquiv_apply, Set.encard_diff_singleton_add_one, Quaternion.snd_imI_dualNumberEquiv_symm, ENNReal.mul_inv_le_one, neg_one_lt_zero, Polynomial.UniversalCoprimeFactorizationRing.factor₁_mul_factor₂, 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', inner_self_eq_one_of_norm_one, round_one, ZMod.isSquare_neg_one_of_eq_sq_add_sq_of_isCoprime, DirectSum.GAlgebra.map_one, DerivedCategory.exists_iso_Q_obj_of_isLE, ValuativeRel.inv_vle_one, EuclideanDomain.div_one, CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂, Complex.ofRealCLM_enorm, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₃, DihedralGroup.r_one_pow_n, norm_commutator_units_sub_one_le, CochainComplex.shiftFunctorAdd'_hom_app_f, Matrix.SpecialLinearGroup.coe_neg, DerivedCategory.instFullFunctorHomotopyCategoryIntUpObjWhiskeringLeftQh, MvPolynomial.monomial_one_dvd_monomial_one, CochainComplex.HomComplex.Cochain.ofHom_zero, Quaternion.add_im, MvPolynomial.mul_monomial_modMonomial, FormalMultilinearSeries.ofScalars_comp_neg, MvPolynomial.tensorEquivSum_one_tmul_X, CochainComplex.g_shortComplexTruncLEX₃ToTruncGE_assoc, Matrix.fromCols_one_isTotallyUnimodular_iff, 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, Set.encard_tsub_one_le_encard_diff_singleton, ProbabilityTheory.uniformOn_compl, div_sub_one, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add, WeierstrassCurve.Jacobian.Point.zero_def, Coalgebra.lTensor_counit_comp_comul, Int.preimage_ceil_singleton, quadraticChar_eq_pow_of_char_ne_two, IsCyclotomicExtension.Rat.associated_norm_zeta_sub_one, LinearMap.det_ring, GroupAlgebra.mul_average_left, EReal.coe_ennreal_one, ENat.ceil_add_one, Matrix.vecMul_swap_apply, convexHull_eq, geom_sum_mul_neg, MvPolynomial.one_coeffsIn, PosNum.cast_inj, AbsoluteValue.IsEquiv.one_le_iff, CliffordAlgebra.ofBaseChange_tmul_one, ZNum.cast_to_int, CategoryTheory.Mat.id_apply_self, HomogeneousLocalization.NumDenSameDeg.den_one, Set.one_lt_encard_iff_nontrivial, CanonicallyOrderedAdd.list_prod_pos, Bound.one_lt_div_of_pos_of_lt, ValuativeRel.not_rel_one_zero, MvPolynomial.universalFactorizationMapPresentation_val, IsCyclotomicExtension.norm_zeta_pow_sub_one_two, Algebra.norm_smul_one_eq_norm, ENNReal.inv_mul_cancel, PEquiv.toMatrix_mul_apply, IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_one, LocalizedModule.smul_eq_iff_of_mem, IsDiscreteValuationRing.addVal_one, CochainComplex.HomComplex.Cochain.map_ofHom, PowerSeries.coe_one, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, Quaternion.sub_re, IsIdempotentElem.one_sub_iff, SimpleGraph.adjMatrix_mul_self_apply_self, Set.Icc.coe_le_one, FractionalIdeal.spanSingleton_one, Quaternion.coe_intCast, GenContFract.get?_of_eq_some_of_succ_get?_intFractPair_stream, Ring.ord_one, ZMod.eq_one_or_isUnit_sub_one, Matrix.SpecialLinearGroup.coe_matrix_coe, Algebra.IsPushout.equiv_symm_algebraMap_right, ArithmeticFunction.coe_zeta_mul_moebius, FixedDetMatrices.smul_coe, RingEquiv.map_eq_neg_one_iff, Matrix.SpecialLinearGroup.mapGL_coe_matrix, ProbabilityTheory.measure_condCDF_univ, CStarAlgebra.norm_le_one_iff_of_nonneg, RingEquiv.unop_map_list_prod, CochainComplex.shiftFunctorComm_hom_app_f, Matrix.coe_det_isEmpty, ENat.succ_def, Profinite.NobelingProof.one_sub_e_mem_of_false, analyticAt_inverse_one_sub, AbsoluteValue.IsNontrivial.exists_abv_lt_one, Polynomial.leadingCoeff_X_pow_add_one, PowerSeries.order_X, ENNReal.ofReal_eq_one, IsLocalization.mul_toInvSubmonoid, Algebra.Norm.Transitivity.auxMat_toSquareBlock_ne, HahnSeries.coeff_toOrderTopSubOnePos_pow, Function.mulSupport_natCast, DirectSum.decompose_one, ContinuousLinearMap.smulRight_one_one, unitary.norm_sub_one_lt_two_iff, one_le_div_of_neg, Polynomial.evalEval_list_prod, Ring.multichoose_one, tendsto_add_one_pow_atTop_atTop_of_pos, Quaternion.re_smul, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, FermatLastTheoremForThreeGen.Solution.associated_of_dvd_a_add_eta_mul_b_of_dvd_a_add_eta_sq_mul_b, Mathlib.Tactic.RingNF.nat_rawCast_1, ValuativeRel.inv_vlt_one, PosNum.cast_sub', CochainComplex.mappingCone.inl_v_snd_v, MeasureTheory.Measure.le_dirac_apply, WeierstrassCurve.Jacobian.equation_some, LinearMap.toSpanSingleton_one, Finset.prod_indicator_biUnion_sub_indicator, Quaternion.eq_re_iff_mem_range_coe, Polynomial.Chebyshev.S_eval_two, SimpleGraph.one_add_adjMatrix_add_compl_adjMatrix_eq_allOnes, MvPolynomial.monomial_sum_one, Affine.Triangle.prod_div_one_sub_eq_one_of_mem_line_point_lineMap, SimpleGraph.adjMatrix_dotProduct, LinearMap.mulLeft_one, ENNReal.one_half_lt_one, CochainComplex.mappingConeHomOfDegreewiseSplitIso_inv_f, analyticAt_inv_one_sub, derivWithin_id, Num.cast_mul, CliffordAlgebra.ι_mem_evenOdd_one, IsStarProjection.one_sub_mul_self, IsStarNormal.one_add, CochainComplex.HomComplex.Cochain.leftShiftAddEquiv_symm_apply, fwdDiff_addChar_eq, MeasureTheory.eLpNorm'_measure_zero_of_exponent_zero, Polynomial.eval₂_one_cyclotomic_prime_pow, convexComboPair_zero, HomotopyCategory.Pretriangulated.rotate_distinguished_triangle, MeasureTheory.prob_compl_eq_one_sub, Quaternion.coe_add, CategoryTheory.DifferentialObject.d_squared_assoc, dist_algebraMap, ZMod.cast_sub_one, mul_self_tsub_one, CochainComplex.HomComplex.Cochain.rightShift_neg, Matrix.mem_orthogonalGroup_iff', ZMod.coe_int_mul_inv_eq_one, MeasureTheory.condExpL1_zero, zsmul_one, pow_eq_neg_one_iff, Polynomial.eval₂_reverse_mul_pow, Quaternion.normSq_intCast, CochainComplex.mappingConeCompTriangle_mor₃_naturality_assoc, invOf_eq_of_coprime, HomotopyCategory.quotient_obj_singleFunctors_obj, iter_deriv_inv_linear, IsNonarchimedean.apply_intCast_le_one_of_isNonarchimedean, List.norm_prod, SubMulAction.mem_one', ProbabilityTheory.uniformOn_singleton, IsCyclotomicExtension.adjoin_roots, Summable.hasProdUniformlyOn_one_add, Quaternion.natCast_imK, tendsto_floor_left, PadicInt.nthHomSeq_one, convexHull_rangle_single_eq_stdSimplex, Set.Icc.mul_le_right, CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃, Metric.unitClosedBall.coe_eq_one, Order.krullDim_eq_one_iff_of_boundedOrder, Set.encard_le_one_iff_eq, Matroid.eRk_le_one_iff, Orthonormal.enorm_eq_one, MeasureTheory.L1.SimpleFunc.setToL1S_add, BoxIntegral.unitPartition.volume_box, Basis.equivFun_symm_single, odd_sub_one, WithLp.unitization_mul, dist_right_lineMap, DerivedCategory.instEssSurjCochainComplexIntQ, IsIdempotentElem.quasispectrum_subset, MeasureTheory.L1.norm_sub_eq_lintegral, ENNReal.HolderConjugate.lt_top_iff_one_lt, CochainComplex.HomComplex.Cochain.fromSingleMk_v_eq_zero, nsmul_one, hasDerivWithinAt_id, MvPolynomial.scalarRTensor_symm_apply_single, IsLocalization.away_fst, Int.cast_le_neg_one_or_one_le_cast_of_ne_zero, Finset.sum_centroidWeights_eq_one_of_cast_card_ne_zero, ENNReal.one_lt_ofReal, ENat.floor_eq_zero, tendsto_ceil_right, ProbabilityTheory.lintegral_gammaPDF_eq_one, Matrix.permanent_eq_one_of_card_eq_zero, Subgroup.HasDetPlusMinusOne.abs_det, ModuleCat.FreeMonoidal.εIso_hom_one, selfZPow_neg_natCast, DerivedCategory.singleFunctorsPostcompQIso_hom_hom, Polynomial.Monic.leadingCoeff, Mathlib.Meta.NormNum.isNat_one, Ring.choose_succ_succ, cfc_le_one_iff, IsLocalization.invertible_mk'_one_invOf, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₂, CochainComplex.HomComplex.Cocycle.equivHomShift_symm_precomp, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, Quaternion.re_sub, Finsupp.range_lmapDomain, WeierstrassCurve.Projective.Point.toAffine_zero, stdSimplexEquivIcc_symm_apply_coe, MeasureTheory.Measure.pi_empty_univ, Matrix.det_fin_zero, CategoryTheory.Functor.mapCochainComplexShiftIso_hom_app_f, WeierstrassCurve.Jacobian.neg_of_Z_ne_zero, AffineBasis.coe_coord_of_subsingleton_eq_one, MeasureTheory.integrable_condExpL1, AddChar.wInner_cWeight_eq_boole, contDiffOn_succ_of_fderiv_apply, Matroid.eRk_singleton_eq_one_iff, Matrix.TransvectionStruct.reverse_inv_prod_mul_prod, LinearMap.toMatrix_basis_equiv, jacobiSym.list_prod_right, MeasureTheory.Integrable.toL1_add, Nat.inv_pos_of_nat, SimpleGraph.sum_incMatrix_apply_of_notMem_edgeSet, Nat.Prime.emultiplicity_factorial_mul_succ, Polynomial.Chebyshev.T_eval_neg_one, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, quadraticChar_neg_one, CochainComplex.shiftEval_inv_app, Num.of_natCast, AffineBasis.toMatrix_self, exists_sum_eq_one_iff_pairwise_coprime, Matrix.den_one, ZNum.dvd_to_int, Nat.floor_one, Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes, CochainComplex.mapBifunctorShift₁Iso_hom_naturality₁, EisensteinSeries.eisSummand_SL2_apply, IsPrimitiveRoot.zeta_sub_one_prime, MeasureTheory.L1.SimpleFunc.setToL1SCLM_mono_left, Set.Ioc.coe_one, MvPolynomial.mem_ideal_span_monomial_image, CFC.abs_one, unitary.norm_sub_one_sq_eq, Nat.floor_eq_iff', MeasureTheory.LpAddConst_zero, kstar_eq_self, CFC.log_one, Polynomial.resultant_one_left, MeasureTheory.setIntegral_condExpL1CLM, MeasureTheory.L1.hasFiniteIntegral_coeFn, PosNum.to_nat_to_int, NormedRing.inverse_one_sub_nth_order', abs_one, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, contDiff_norm_rpow, Matrix.single_one_vecMul, Quaternion.mul_imI, DualNumber.algHom_ext'_iff, Rep.diagonalHomEquiv_apply, hasStrictFDerivAt_list_prod', BooleanRing.mul_one_add_self, right_sub_midpoint, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_acyclic, ENNReal.HolderConjugate.top_one, DualNumber.ideal_trichotomy, ProjectiveSpectrum.basicOpen_one, ENNReal.one_le_coe_iff, Ring.multichoose_succ_succ, CategoryTheory.DifferentialObject.objEqToHom_d_assoc, Asymptotics.IsEquivalent.listProd, Quaternion.re_ratCast, selfZPow_mul_neg, BialgHom.ext_of_ring_iff, Quaternion.intCast_re, ContinuousLinearEquiv.coord_self, SkewMonoidAlgebra.ofFinsupp_one, Quaternion.coe_im, MonomialOrder.monic_one, ENNReal.inv_three_add_inv_three, Mathlib.Meta.NormNum.Rat.invOf_denom_swap, CochainComplex.HomComplex.Cocycle.rightShiftAddEquiv_apply, Submodule.one_le, ZNum.cast_sub, pinGroup.coe_mul_star_self, MeasureTheory.lpNorm_one', Quaternion.zero_im, KaehlerDifferential.DLinearMap_apply, CategoryTheory.DifferentialObject.d_squared_apply_assoc, CochainComplex.ConnectData.homologyMap_map_of_eq_neg_succ, MeasureTheory.L1.integral_eq', Order.krullDim_le_one_iff_forall_isMin, complEDS'_one, MvPolynomial.esymm_zero, Matrix.mem_rowStochastic, DualNumber.eps_mul_eps, RootPairing.pairing_one_four_iff, PadicInt.continuousAddCharEquiv_apply, CochainComplex.HomComplex.Cochain.equivHomotopy_symm_apply_hom, localization_unit_isIso', IsAdjoinRootMonic.coeff_root, zpow_eq_one_iff_cases₀, CliffordAlgebra.ofProd_ι_mk, MeasureTheory.eLpNorm_one_add_measure, Int.preimage_fract, DirectSum.liftRingHom_apply, WeierstrassCurve.Jacobian.nonsingular_zero, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, MeasureTheory.Measure.tprod_tprod, ComplexShape.ε_up_ℤ, AddMonoidAlgebra.lift_unique, Quaternion.instNormOneClassReal, Quaternion.instIsScalarTower, CFC.spectrum_one_eq, IncidenceAlgebra.mu_prod_mu, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, 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, ProbabilityTheory.Kernel.trajContent_eq_lmarginalPartialTraj, ContinuousLinearMap.hasDerivWithinAt, Polynomial.ringKrullDim_of_isNoetherianRing, CochainComplex.HomComplex.Cochain.rightShiftLinearEquiv_symm_apply, abs_le_one_iff_mul_self_le_one, Ring.descPochhammer_succ_succ_smeval, Order.height_coe_withBot, stdSimplex.le_one, Matrix.SpecialLinearGroup.toLin'_symm_apply, prod_vanishing_of_summable_norm, PMF.pure_apply_self, Matrix.swap_mul_apply_left, iUnion_Ioc_intCast, IsGroupLikeElem.one, descPochhammer_zero_eval_zero, ModularGroup.coe_T_zpow, CochainComplex.shiftShortComplexFunctor'_inv_app_τ₁, CochainComplex.mappingCone.lift_f_snd_v, Matrix.GeneralLinearGroup.val_inv_swap, CochainComplex.shiftShortComplexFunctorIso_zero_add_hom_app, Submodule.lTensorOne_one_tmul, hasDerivAt_exp_zero, GenContFract.sub_convs_eq, descPochhammer_eval_zero, IsPrimitiveRoot.associated_sub_one_pow_sub_one_of_coprime, CochainComplex.isKProjective_shift_iff, MvPowerSeries.rescale_one, ENNReal.tsum_geometric, ZMod.prod_Ico_one_prime, ComplexShape.embeddingDownIntUpInt_f, LinearMap.toMatrix'_one, mul_tsub_one, Matrix.one_kroneckerTMul_one, MeasureTheory.eLpNorm_smul_measure_of_ne_zero, AddValuation.map_one, PowerSeries.rescale_one, Submodule.baseChange_span, MvPolynomial.pderiv_X_self, LieAlgebra.Orthogonal.pb_inv, Quaternion.imJ_star, Set.one_le_encard_iff_nonempty, Set.Ioc.coe_mul, Matrix.invOf_eq, CochainComplex.instIsStrictlyLEObjIntSingleFunctor, MvPowerSeries.trunc'_one, ComplexShape.embeddingUpIntGE_f, one_le_div, CochainComplex.mappingCone.triangle_obj₂, sbtw_zero_one_iff, CochainComplex.instIsStrictlyGEObjIntSingleFunctor, Bialgebra.TensorProduct.lid_symm_apply, IncidenceAlgebra.eulerChar_orderDual, Set.Ico.coe_lt_one, Polynomial.shiftedLegendre_eval_symm, Matrix.TransvectionStruct.toMatrix_sumInl, Profinite.NobelingProof.list_prod_apply, OnePoint.equivProjectivization_apply_coe, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₃, Matrix.vec_mul_eq_vecMul, IsQuasiregular.isUnit_one_add, Matrix.IsTotallyUnimodular.fromRows_one, IsCyclotomicExtension.union_right, MonomialOrder.leadingCoeff_one, ValuativeRel.one_srel_inv, IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_nth_roots, MeasureTheory.withDensity_indicator_one, CochainComplex.mappingConeCompTriangle_mor₂, CFC.rpow_zero, DerivedCategory.instLinearHomotopyCategoryIntUpQh, LinearMap.toMatrixₛₗ₂'_apply, odd_two_mul_add_one, IsCyclotomicExtension.Rat.Three.cube_sub_one_eq_mul, LinearMap.transvection.baseChange, MvPolynomial.algebraTensorAlgEquiv_symm_monomial, geom_sum_Ico, MeasureTheory.Measure.rnDeriv_self, Module.Basis.coe_ofEquivFun, exists_signed_sum, PolynomialLaw.ground_apply, CochainComplex.cm5b.degreewiseEpiWithInjectiveKernel_p, Matrix.toLinearMapRight'_one, MvPolynomial.restrictSupport_eq_span, hasStrictDerivAt_id, CochainComplex.HomComplex.Cochain.rightShift_v, CochainComplex.HomComplex.Cochain.rightUnshift_zero, AffineMap.lineMap_apply_one_sub, MeasureTheory.prob_add_prob_compl, CochainComplex.mappingConeCompTriangleh_comm₁, Set.encard_insert_of_notMem, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_extMk, ValuativeRel.ValueGroupWithZero.lift_one, ENNReal.zero_zpow_def, CochainComplex.HomComplex.Cocycle.leftShift_coe, Affine.Simplex.interior_eq_image_Ioo, MeasureTheory.L1.setToL1'_eq_setToL1SCLM, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, one_sub_div, deriv_neg, Matrix.invertibleEquivDetInvertible_symm_apply, FermatLastTheoremForThreeGen.Solution.associated_of_dvd_a_add_b_of_dvd_a_add_eta_sq_mul_b, Metric.coveringNumber_singleton, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, PowerSeries.binomialSeries_nat, Module.supportDim_quotSMulTop_succ_eq_of_notMem_minimalPrimes_of_mem_jacobson, Nat.cast_add_one, WeierstrassCurve.Projective.add_of_Y_ne, permMatrix_mem_doublyStochastic, LinearMap.hasDerivAt, two_add_one_eq_three, kstar_zero, WithLp.unitizationAlgEquiv_apply, NNReal.HolderConjugate.inv_add_inv_ennreal, Polynomial.leadingCoeff_X_add_C, ENNReal.ofReal_lt_one, Matrix.submatrixEquivInvertibleEquivInvertible_symm_apply, TensorProduct.finsuppScalarLeft_symm_apply_single, neg_one_pow_mul_eq_zero_iff, midpoint_vsub_midpoint_same_left, QuadraticAlgebra.omega_mul_mk, LinearMap.hasDerivAtFilter, ProbabilityTheory.Kernel.rnDeriv_self, Ideal.IsLocal.mem_jacobson_or_exists_inv, MeasureTheory.condExpL1_sub, Quaternion.sub_imK, ENNReal.inv_le_one, Matroid.one_le_eRank, CochainComplex.HomComplex.Cochain.shift_v', Set.encard_diff_singleton_of_mem, PEquiv.mul_toMatrix_toPEquiv, Mathlib.Meta.NormNum.NNRat.invOf_denom_swap, norm_sub_mul_le, FermatLastTheoremForThreeGen.lambda_sq_dvd_c, right_vsub_midpoint, Lagrange.eval_basis_self, Subalgebra.one_mem, Matrix.det_succ_row_zero, WeierstrassCurve.Projective.equation_zero, WeierstrassCurve.IsCharTwoJNeZeroNF.a₁, IsAbsoluteValue.abv_one', Matrix.vec_mul_eq_mulVec, MvPolynomial.X_divMonomial, Complex.enorm_exp_ofReal_mul_I, Quaternion.im_sq, MeasureTheory.memLp_one_iff_integrable, CochainComplex.cm5b.instInjectiveXIntMappingConeIdI, reverse_lucas_primality, Ring.choose_zero_right', div_lt_one_iff, one_div_le_one_div_of_neg_of_le, FirstOrder.Field.model_fieldOfChar_of_charP, ModuleCat.extendScalarsId_inv_app_apply, Polynomial.descPochhammer_smeval_eq_ascPochhammer, Quaternion.imJ_natCast, Derivation.leibniz_invOf, PowerSeries.binomialSeries_constantCoeff, Pi.mem_span_range_single_inl_iff, Set.Ioc.le_one, ENNReal.le_inv_iff_mul_le, ordinaryHypergeometricSeries_norm_div_succ_norm, Int.cast_eq_one, MeasureTheory.L1.integral_sub, MeasureTheory.L1.ofReal_norm_sub_eq_lintegral, Polynomial.coeff_X, Nat.one_le_cast_iff_ne_zero, WeierstrassCurve.Jacobian.equiv_some_of_Z_ne_zero, Quaternion.natCast_imJ, TensorProduct.toLinearMap_symm_rid, Matrix.GeneralLinearGroup.coe_map_inv_mul_map, PiLp.nnnorm_toLp_const, Matrix.mul_nonsing_inv, Polynomial.Chebyshev.S_eval_neg_two, IsPrimitiveRoot.eq_neg_one_of_two_right, IsStrictOrderedRing.toZeroLEOneClass, preNormEDS_two, ModularGroup.coe_S, jacobiSym.list_prod_left, GradedTensorProduct.of_one, DerivedCategory.mem_distTriang_iff, MvPolynomial.tensorEquivSum_X_tmul_one, Quaternion.coe_neg, inner_eq_one_iff_of_norm_one, EisensteinSeries.eisensteinSeries_slash_apply, PMF.toOuterMeasure_apply_eq_one_iff, MonoidAlgebra.liftNC_one, exists_continuousLinearEquiv_fderiv_symm_eq, PrimeSpectrum.basicOpen_one, CochainComplex.HomComplex.Cochain.v_comp_XIsoOfEq_inv_assoc, IsPrimitiveRoot.norm_of_cyclotomic_irreducible, isIdempotentElem_iff_mul_one_sub_self, nnnorm_sub_mul_le', sbtw_one_zero_iff, CategoryTheory.Functor.instCommShiftCochainComplexIntMapMap₂CochainComplex, MeasureTheory.L1.SimpleFunc.integral_L1_eq_integral, FDRep.scalar_product_char_eq_finrank_equivariant, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_univ_le_one, 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, IsPrimitiveRoot.associated_pow_sub_one_pow_of_coprime, Finset.sum_boole, CochainComplex.HomComplex.Cochain.rightShift_add, CochainComplex.ShiftSequence.shiftIso_inv_app, mem_finsuppAffineCoords_iff_linearCombination, Quaternion.hasSum_coe, PEquiv.toMatrix_trans, Rep.free_ext_iff, RingHom.codomain_trivial_iff_range_trivial, Subsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMul, LinearMap.detAux_id, Nat.cast_one, matrixEquivTensor_apply, ZMod.euler_criterion, CochainComplex.HomComplex.Cochain.diff_v, LinearAlgebra.FreeProduct.lof_map_one, Module.Basis.repr_eq_iff', ENNReal.coe_lt_one_iff, stdSimplexEquivIcc_one, Set.Ico.coe_nonneg, isRoot_of_unity_iff, Quaternion.intCast_im, sub_one_dvd_pow_sub_one, Complex.reCLM_enorm, DerivedCategory.instIsLEObjCochainComplexIntQOfIsLE, Int.lt_floor_iff, Quaternion.imI_coe, MeasureTheory.condExpInd_empty, MeasureTheory.condExpL1CLM_smul, Manifold.exists_lt_of_riemannianEDist_lt, IsFoelner.amenable, CategoryTheory.Functor.instCommShiftCochainComplexIntMapFlipMap₂CochainComplex, PEquiv.toMatrix_swap, Module.Basis.toMatrix_self, Algebra.Norm.Transitivity.auxMat_toSquareBlock_eq, Quaternion.hom_ext_iff, PowerSeries.rescale_neg_one_invOneSubPow, MeasureTheory.L1.edist_def, CochainComplex.HomComplex.Cochain.toSingleEquiv_toSingleMk, CochainComplex.isGE_shift, MeasureTheory.continuous_setIntegral, Module.Presentation.tautologicalRelations_relation, RCLike.normSq_one, AffineMap.deriv, fwdDiff_iter_sum_mul_pow_eq_zero, Ideal.IsMaximal.exists_inv, 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, CategoryTheory.Functor.commShiftIso_map₂CochainComplex_hom_app, LinearMap.det_eq_one_of_subsingleton, ENat.one_lt_card, MeasureTheory.L1.SimpleFunc.integral_eq_integral, Order.coheight_eq_iSup_gt_coheight, tendsto_pow_atTop_nhds_zero_iff, Int.instNormOneClass, AnalyticAt.analyticOrderAt_sub_eq_one_of_deriv_ne_zero, ModularGroup.S_mul_S_eq, fderiv_list_prod', Polynomial.isMonicOfDegree_monomial_one, Quaternion.re_intCast, CochainComplex.mappingCone.triangleRotateShortComplex_f, HomogeneousLocalization.NumDenSameDeg.den_zero, QuadraticAlgebra.omega_mul_omega_eq_add, Finset.sum_mul_boole, HomotopyCategory.quotient_obj_mem_subcategoryAcyclic_iff_exactAt, Matrix.SpecialLinearGroup.coe_mul, CochainComplex.HomComplex.Cocycle.rightUnshift_coe, WeierstrassCurve.Jacobian.add_of_Z_eq_zero, Matrix.adjugate_mul, toBoolAlg_one, HahnSeries.mem_orderTopSubOnePos_iff, EuclideanDomain.gcd_one_left, rootsOfUnityEquivNthRoots_symm_apply, exists_continuousLinearEquiv_fderivWithin_symm_eq, spectrum.spectralRadius_le_pow_nnnorm_pow_one_div, Quaternion.re_mul, SimpleGraph.edist_top_of_ne, Quaternion.normSq_div, ENNReal.HolderConjugate.one_top, Matrix.UnitaryGroup.star_mul_self, Algebra.isEpi_iff_forall_one_tmul_eq, BoundedContinuousFunction.coe_npowRec, CFC.rpow_neg_mul_rpow, TensorProduct.toMatrix_comm, MonomialOrder.C_mul_leadingCoeff_monomial_degree, CochainComplex.mappingCone.rotateHomotopyEquiv_comm₃, Algebra.TensorProduct.lid_symm_apply, ComplexShape.instIsRelIffIntEmbeddingUpIntDownInt, ZNum.to_int_inj, ZSpan.mem_fundamentalDomain, MeasureTheory.Measure.rnDeriv_le_one_of_le, LinearMap.toMatrix₂'_apply, Submodule.toSubMulAction_one, Order.krullDim_of_isSimpleOrder, CliffordAlgebra.evenOdd_isCompl, CochainComplex.mappingCone.lift_f, PowerSeries.mk_one_mul_one_sub_eq_one, Order.lt_one_iff_nonpos, MeasureTheory.condExpIndL1Fin_smul', CochainComplex.HomComplex.Cochain.δ_leftShift, Ideal.one_notMem, GenContFract.of_isSimpContFract, DerivedCategory.isIso_Q_map_iff_quasiIso, Unitization.unitsFstOne_val_val_fst, Algebra.Generators.comp_σ, neg_one_pow_expChar_pow, ringKrullDim_le_ringKrullDim_quotSMulTop_succ, WithLp.unitization_norm_inr, ZNum.mul_to_int, Module.supportDim_quotSMulTop_succ_le_of_notMem_minimalPrimes, WithLp.unitization_nnnorm_def, DerivedCategory.isIso_Qh_map_iff, AbsoluteValue.IsNontrivial.exists_abv_gt_one, Nat.cast_pow_eq_one, Matrix.mul_adjp_add_detp, ContinuousLinearMap.hasStrictDerivAt, Quaternion.instFinite, Finset.cast_card, Mathlib.Tactic.ENatToNat.coe_one, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, ENNReal.tsum_one, Cardinal.ofENat_one, WeierstrassCurve.Projective.equation_some, PiTensorProduct.algebraMap_apply, CStarRing.norm_one, IsPrimitiveRoot.norm_toInteger_sub_one_of_prime_ne_two', CochainComplex.HomComplex.CohomologyClass.toHom_mk, Matrix.mulVec_one, ZMod.completedLFunction_modOne_eq, ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_sub_of_squarefree, Nat.abs_ceil_sub_le, Matrix.mul_swap_apply_right, ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup_atBot, MeasureTheory.L1.integral_eq, Polynomial.coeff_one_zero, Set.Finite.convexHull_eq, ContractingWith.apriori_edist_iterate_efixedPoint_le, CochainComplex.HomComplex.Cochain.add_v, MvPolynomial.coeff_zero_one, Sbtw.mem_image_Ioo, one_add_mul_le_pow, WeierstrassCurve.j_of_isCharTwoJNeZeroNF_of_char_two, CochainComplex.HomComplex.Cocycle.leftShiftAddEquiv_apply, IsGroupLikeElem.mul_antipode_cancel, CochainComplex.instIsMultiplicativeIntDegreewiseEpiWithInjectiveKernel, Complex.sum_div_factorial_le, Matrix.one_mulVec, DerivedCategory.left_fac_of_isStrictlyGE, CochainComplex.mappingConeHomOfDegreewiseSplitIso_hom_f, CliffordAlgebra.contractLeft_one, IsAddFoelner.amenable, CochainComplex.mappingCone.inl_v_fst_v_assoc, one_le_nnnorm_one, Quaternion.normSq_star, DihedralGroup.r_one_pow, PMF.pure_apply, Quaternion.imK_sub, NumberField.Embeddings.pow_eq_one_of_norm_eq_one, Matrix.invOf_fromBlocks₁₁_eq, nndist_self_homothety, ENat.ceil_le_floor_add_one, Algebra.FormallyUnramified.iff_exists_tensorProduct, FermatLastTheoremForThreeGen.Solution'.multiplicity_lambda_c_finite, WeierstrassCurve.Jacobian.addMap_of_Y_eq, ENNReal.one_lt_inv, MeasureTheory.L1.setToL1'_apply_coeToLp, KaehlerDifferential.kerTotal_map', RCLike.I_mul_I_of_nonzero, range_two_mul_add_one, PiLp.edist_eq_of_L1, CategoryTheory.ProjectiveResolution.cochainComplex_d_assoc, Polynomial.UniversalCoprimeFactorizationRing.isCoprime_factor₁_factor₂, IsPrimitiveRoot.norm_sub_one_two, Commute.one_div_add_one_div, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, zpow_eq_one_iff_of_ne_zero₀, FormalMultilinearSeries.radius_eq_liminf, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, ContractingWith.edist_efixedPoint_le, Module.Basis.addHaar_self, RingQuot.one_quot, isCoprime_one_left, ArithmeticFunction.const_one_eq_zeta, Matrix.charpoly.univ_coeff_card, Finset.univ_of_card_le_two, SimpleGraph.chromaticNumber_eq_one_iff, Polynomial.scaleRoots_one, MeasureTheory.L1.setToL1_const, IsStarProjection.mul_one_sub_self, Rep.barComplex.d_single, RCLike.span_one_I, Module.Presentation.tautological_relation, CFC.rpow_mul_rpow_neg, ENNReal.top_zpow_def, Matrix.one_mul, IsPrimitiveRoot.pow_sub_pow_eq_prod_sub_mul, PolynomialLaw.one_tmul_ground_apply', Dynamics.one_le_netMaxcard_iff, MeasureTheory.norm_condExpIndL1Fin_le, MeasureTheory.prob_compl_eq_zero_iff₀, Quaternion.normSq_ratCast, ZMod.coe_int_val_inv_mul, IncidenceAlgebra.zeta_prod_mk, Quaternion.imK_im, ModuleCat.ExtendScalars.hom_ext_iff, MeasureTheory.continuous_L1_toL1, Algebra.TensorProduct.rid_symm_apply, hasStrictDerivAt_exp_zero, HomotopyCategory.mappingConeCompTriangleh_distinguished, PerfectClosure.one_def, Coalgebra.TensorProduct.lid_symm_apply, Quaternion.imK_add, CochainComplex.HomComplex.Cochain.leftShift_neg, Finset.sum_affineCombinationSingleWeights, Matrix.det_eq_sign_charpoly_coeff, PrimeSpectrum.isIdempotentElemEquivClopens_symm_compl, CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom, Module.Basis.repr_self, exteriorPower.presentation.relations_relation, MvPolynomial.monomial_one_mul_cancel_right_iff, WeierstrassCurve.Projective.dblXYZ_of_Y_eq, Quaternion.fst_re_dualNumberEquiv_symm, Nat.cast_le_one, gaussSum_sq, MeasureTheory.Integrable.edist_toL1_toL1, Quaternion.continuous_normSq, Nat.cast_inv_le_one, FermatLastTheoremForThreeGen.ex_cube_add_cube_eq_and_isCoprime_and_not_dvd_and_dvd, WithLp.unitization_isometry_inr, Polynomial.Chebyshev.iterate_derivative_T_eval_one_eq_div, exists_eq_sum_perm_of_mem_doublyStochastic, hasFDerivAt_list_prod_attach', Quaternion.imI_snd_dualNumberEquiv, one_add_rpow_hasFPowerSeriesOnBall_zero, CFC.conjugate_rpow_neg_one_half, MeasureTheory.L1.setToL1_lipschitz, CategoryTheory.Functor.mapDerivedCategoryFactorsh_hom_app, CochainComplex.HomComplex.Cochain.toSingleMk_sub, MeasureTheory.Integrable.toL1_neg, Manifold.exists_lt_locally_constant_of_riemannianEDist_lt, geom_series_eq_inverse, Finsupp.lcomapDomain_eq_linearProjOfIsCompl, Nat.lt_floor_add_one, CStarAlgebra.inv_le_one_iff_one_le, ZMod.exists_one_add_mul_pow_prime_pow_eq, Ideal.Fiber.exists_smul_eq_one_tmul, SimpleGraph.edist_eq_one_iff_adj, Polynomial.IsMonicOfDegree.leadingCoeff_eq, MeasureTheory.setToFun_eq, CategoryTheory.Functor.mapDifferentialObject_map_f, Set.encard_le_one_iff_subsingleton, Polynomial.Chebyshev.derivative_T_eval_one, WeierstrassCurve.c₄_of_isCharTwoJNeZeroNF_of_char_two, Nat.one_div_lt_one_div, Int.cast_one, Set.encard_singleton, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, Polynomial.eval₂_list_prod_noncomm, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, HopfAlgebra.antipode_one, isAlgebraic_one, Surreal.one_toGame, IncidenceAlgebra.zeta_prod_zeta, CochainComplex.HomComplex.Cocycle.equivHomShift_apply, PosNum.cast_lt, Matrix.one_vecMul_of_mem_colStochastic, CochainComplex.shiftShortComplexFunctorIso_inv_app_τ₁, Int.cast_negOnePow_natCast, neg_one_eq_one_iff, ENat.lt_coe_add_one_iff, Finset.dens_univ, WeierstrassCurve.Projective.nonsingularLift_zero, Finset.prod_add_one, binomialSeries_radius_ge_one, CochainComplex.HomComplex.Cochain.leftUnshift_neg, ENat.card_le_one, Polynomial.le_trailingDegree_X, nndist_homothety_self, Subalgebra.one_mem_toNonUnitalSubalgebra, Set.Ioo.one_minus_lt_one, ENNReal.orderIsoIicOneBirational_symm_apply, CochainComplex.isLE_shift, CochainComplex.mappingCone.triangle_obj₁, Order.krullDim_le_of_krullDim_preimage_le', thickenedIndicatorAux_one_of_mem_closure, Quaternion.imJ_intCast, wbtw_mul_sub_add_iff, Order.one_le_iff_pos, le_one_div, FermatLastTheoremForThreeGen.Solution.lambda_dvd_a_add_eta_mul_b, AddMonoidAlgebra.toDirectSum_one, Quaternion.smul_imJ, Matrix.transposeInvertibleEquivInvertible_apply, IsCyclotomicExtension.Rat.ramificationIdx_span_zeta_sub_one, AddMonoidAlgebra.one_def, Height.mulHeight₁_one, Matrix.transpose_list_prod, CategoryTheory.Mat.id_def, HomotopyCategory.instIsClosedUnderIsomorphismsIntUpSubcategoryAcyclic, ascPochhammer_eval_neg_eq_descPochhammer, Set.pairwise_disjoint_Ioo_intCast, one_dotProduct_one, IsLocalRing.isUnit_one_sub_self_of_mem_nonunits, IsLocalization.mem_span_iff, Polynomial.evalEval_one, CochainComplex.mappingCone.lift_f_snd_v_assoc, Profinite.NobelingProof.factors_prod_eq_basis, ContinuousLinearMap.ext_ring_iff, CochainComplex.mappingCone.mapHomologicalComplexXIso'_inv, Matrix.vecMul_swap, Polynomial.content_X_pow, ComplexShape.boundaryLE_embeddingUpIntLE_iff, homothety_one_half, UniformSpace.Completion.coe_one, CochainComplex.cm5b, WithBot.one_le_iff_pos, Finsupp.linearIndependent_single_one, WithBot.succ_ofNat, Quaternion.one_re, ENNReal.inv_two_add_inv_two, Rep.FiniteCyclicGroup.resolution.π_f, ofBoolAlg_compl, WeierstrassCurve.Jacobian.neg_of_Z_eq_zero, Quaternion.exp_coe, AddChar.inv_mulShift, isUnit_one_sub_of_norm_lt_one, one_le_formalMultilinearSeries_geometric_radius, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, NNRat.den_one, Module.Relations.Solution.π_single, Module.Basis.finTwoProd_one, ProbabilityTheory.Kernel.swap_apply', instLieGroupOfNatWithTopENat, Quaternion.star_coe, ENNReal.nhdsGT_one_neBot, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, MeasureTheory.lintegral_one, CommSemiring.comul_apply, Quaternion.smul_imI, AddChar.expect_eq_ite, CategoryTheory.InjectiveResolution.Hom.ι'_comp_hom', convexHull_range_eq_exists_affineCombination, Quaternion.imI_one, IsLocalization.smul_toInvSubmonoid, Matrix.det_one_add_mul_comm, Order.one_lt_height_iff, stdSimplex_eq_inter, MeasureTheory.norm_setToFun_le, Profinite.NobelingProof.factors_prod_eq_basis_of_eq, Module.presentationFinsupp_var, Quaternion.exp_eq, IsPrimitiveRoot.pow_add_pow_eq_prod_add_mul, Unitization.mem_unitsFstOne, HasFDerivAtFilter.hasDerivAtFilter, ZNum.of_to_int', CategoryTheory.InjectiveResolution.extAddEquivCohomologyClass_symm_apply, Orientation.measure_orthonormalBasis, Algebra.TensorProduct.lift_includeLeft_includeRight, MeasureTheory.measure_sigmaFiniteSetGE_ge, Matrix.invOf_mul_cancel_left, Int.ceil_one, CategoryTheory.InjectiveResolution.instInjectiveXIntCochainComplex, Subring.one_mem, Polynomial.trailingDegree_X, pinGroup.mul_star_self_of_mem, Polynomial.emultiplicity_le_one_of_separable, CochainComplex.shiftFunctor_obj_d, CompleteOrthogonalIdempotents.pair_iffₛ, stdSimplex_unique, WittVector.coeff_p_one, Matrix.det_invOf, Quaternion.imJ_sub, Subring.coe_one, IsPrimitiveRoot.norm_toInteger_pow_sub_one_of_prime_ne_two, WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y, MeasureTheory.condExpL1_eq, Quaternion.normSq_coe, MonoidAlgebra.of_apply, MeasureTheory.L1.SimpleFunc.coe_posPart, SimplexCategory.toTopObj_zero_apply_zero, left_sub_midpoint, TensorProduct.lidIsometry_symm_apply, CochainComplex.HomComplex.Cochain.toSingleMk_precomp, Matrix.SpecialLinearGroup.toLin'_apply, Polynomial.coeff_list_prod_of_natDegree_le, DualNumber.isNilpotent_eps, Valuation.one_rel_iff, neg_add_eq_mul_invOf_mul_same_iff, CochainComplex.HomComplex.Cocycle.rightShift_coe, MvPolynomial.C_eq_smul_one, GenContFract.abs_sub_convs_le, midpoint_vsub_midpoint_same_right, CochainComplex.mappingCone.d_fst_v, MeasureTheory.Measure.haarMeasure_eq_iff, Affine.Simplex.centroid_vsub_eq, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', ENat.one_le_iff_ne_zero, FirstOrder.Field.charP_iff_model_fieldOfChar, Function.Antiperiodic.sub_nat_mul_eq, Algebra.TensorProduct.adjoin_one_tmul_image_eq_top, CochainComplex.mappingConeCompHomotopyEquiv_hom_inv_id_assoc, contDiff_succ_iff_hasFDerivAt, Module.End.hasUnifEigenvalue_iff_hasUnifEigenvalue_one, TrivSqZeroExt.eq_smul_exp_of_invertible, MeasureTheory.setToFun_toL1, exteriorPower.basis_repr_self, Unitization.unitsFstOne_val_inv_val_fst, AbsoluteValue.exists_lt_one_one_le_of_not_isEquiv, GradedTensorProduct.of_symm_one, Subgroup.hasDetPlusMinusOne_iff_abs_det, Convex.mem_Ioc, CochainComplex.HomComplex.Cochain.leftUnshift_zero, Quaternion.re_nnratCast, ENNReal.inv_eq_one, MvPolynomial.monomial_modMonomial, Algebra.Extension.cotangentComplex_mk, ENat.lt_one_iff_eq_zero, Polynomial.taylor_one, invOf_add_invOf, Matrix.SpecialLinearGroup.mem_center_iff, CompleteOrthogonalIdempotents.bijective_pi, FreeCommRing.isSupported_one, MeasureTheory.eLpNorm'_exponent_zero, invOf_two_add_invOf_two, zpow_eq_neg_one_iff₀, ENat.floor_le, MeasureTheory.L1.integral_neg, Matrix.permanent_isEmpty, DerivedCategory.left_fac, WeierstrassCurve.c₆_of_isCharTwoJNeZeroNF_of_char_two, IsPrimitiveRoot.toInteger_cube_eq_one, contDiff_one_iff_deriv, Algebra.TensorProduct.one_def, MeasureTheory.Integrable.uniformIntegrable_condExp, Height.mulHeight_one, GroupAlgebra.mul_average_right, LieAlgebra.Orthogonal.pd_inv, 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, Cardinal.toENat_eq_one, OrthonormalBasis.inner_eq_ite, MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left', zero_geom_sum, CochainComplex.isZero_of_isLE, Ideal.mem_jacobson_bot, left_vsub_midpoint, Finset.max_abv_sum_one_le, Set.Ioo.coe_mul, MeasureTheory.ae_iff_prob_eq_one, ENat.epow_zero, Matrix.sum_row_of_mem_rowStochastic, Matrix.TransvectionStruct.mul_inv, CochainComplex.HomComplex_d_hom_apply, Algebra.TensorProduct.includeLeftRingHom_apply, CochainComplex.instFaithfulIntSingleFunctor, Matrix.one_div_zpow, MeasureTheory.Measure.rnDeriv_le_one_iff_le, contDiffWithinAt_succ_iff_hasFDerivWithinAt, PEquiv.single_mul_single, Quaternion.nnnorm_coe, ENat.one_epow, Rat.cast_one, mul_self_sub_one, Matrix.conjTranspose_invOf, SimpleGraph.eccent_top, RingEquiv.moduleEndSelfOp_symm_apply, 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, 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, PiLp.nndist_eq_of_L1, ENNReal.toReal_eq_one_iff, CochainComplex.instAdditiveHomologicalComplexIntUpShiftFunctor, Matrix.mul_adjugate, Polynomial.eval₂_reverse_eq_zero_iff, MvPowerSeries.prod_smul_X_eq_smul_monomial_one, PowerSeries.coeff_one_X, Finset.nonneg_subConst, bernsteinPolynomial.iterate_derivative_at_1, SimpleGraph.chromaticNumber_bot, WithLp.prod_antilipschitzWith_ofLp, ProbabilityTheory.Kernel.IsProper.inter_eq_indicator_mul, AbsoluteValue.map_one, SimpleGraph.edist_le_one_iff_adj_or_eq, MvPolynomial.expand_zero_apply, LinearMap.toLinearMap₂'Aux_toMatrix₂Aux, ComplexShape.instIsTruncGENatIntEmbeddingUpNat, Quaternion.star_eq_self, MeasureTheory.diracProba_toMeasure_apply_of_mem, kstar_eq_one, Multiset.prod_X_sub_C_coeff, IsCyclotomicExtension.discr_prime_pow_ne_two', Polynomial.coeff_freeMonic, Matrix.toBilin'_single, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, thickenedIndicatorAux_le_one, PadicInt.addChar_of_value_at_one_def, Submodule.exists_sub_one_mem_and_smul_le_of_fg_of_le_sup, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Submodule.one_eq_span, IsPrimitiveRoot.pow_sub_one_mul_geom_sum_eq_pow_sub_one_mul_geom_sum, TensorProduct.includeRight_lid, IsField.mul_inv_cancel, HasFDerivWithinAt.list_prod', factorial_mul_ascPochhammer, 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, MvPolynomial.coe_mapEquivMonic_comp, 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, WithBot.add_one_le_iff, Quaternion.natCast_re, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, SimpleGraph.incMatrix_mul_transpose_apply_of_adj, Set.Icc.instZeroLEOneClass, MvPolynomial.monomial_mul_modMonomial, Quaternion.ext_iff, Int.fract_eq_iff, CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_neg, Metric.coveringNumber_le_one_of_ediam_le, MeasureTheory.L1.SimpleFunc.setToL1S_smul, AlgHom.norm_apply_le_self_mul_norm_one, MvPolynomial.pderiv_inl_universalFactorizationMap_X, LinearEquiv.piRing_apply, CochainComplex.HomComplex.Cochain.single_v_eq_zero, SkewMonoidAlgebra.lift_symm_apply, Matrix.one_vecMul_of_mem_rowStochastic, CategoryTheory.InjectiveResolution.cochainComplex_d, ENNReal.HolderTriple.one_div_add_one_div, ZMod.eq_one_iff_odd, LinearMap.IsSymmetric.eigenvectorBasis_def, Matrix.vecMul_one, 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, CochainComplex.ConnectData.restrictionGEIso_hom_f, MeasureTheory.L1.norm_eq_integral_norm, Algebra.Presentation.tensorModelOfHasCoeffsInv_aeval_val, Polynomial.toSubring_one, Nat.floor_pos, IntermediateField.coe_one, DerivedCategory.instHasRightCalculusOfFractionsHomotopyCategoryIntUpQuasiIso
unary 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
natCast_succ 📖	mathematical	—	toNatCast AddSemigroup.toAdd AddMonoid.toAddSemigroup toAddMonoid toOne	—	—
natCast_zero 📖	mathematical	—	toNatCast AddMonoid.toZero toAddMonoid	—	—

LibraryNote

Definitions

Name	Category	Theorems
«no_index_around_OfNat.ofNat» 📖	CompOp	—

Nat

Definitions

Name	Category	Theorems
binCast 📖	CompOp	1 math math: binCast_eq
unaryCast 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
binCast_eq 📖	mathematical	—	binCast AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddMonoidWithOne.toAddMonoid AddMonoidWithOne.toOne AddSemigroup.toAdd AddMonoid.toAddSemigroup AddMonoidWithOne.toNatCast	—	binCast.eq_1 cast_zero binCast.eq_2 cast_add cast_one
cast_add 📖	mathematical	—	AddMonoidWithOne.toNatCast AddSemigroup.toAdd AddMonoid.toAddSemigroup AddMonoidWithOne.toAddMonoid	—	cast_zero add_zero cast_succ add_assoc
cast_add_one 📖	mathematical	—	AddMonoidWithOne.toNatCast AddSemigroup.toAdd AddMonoid.toAddSemigroup AddMonoidWithOne.toAddMonoid AddMonoidWithOne.toOne	—	cast_succ
cast_four 📖	mathematical	—	instOfNatAtLeastTwo instAtLeastTwoHAddOfNat	—	—
cast_ite 📖	mathematical	—	AddMonoidWithOne.toNatCast	—	—
cast_ofNat 📖	—	—	—	—	—
cast_one 📖	mathematical	—	AddMonoidWithOne.toNatCast AddMonoidWithOne.toOne	—	cast_succ cast_zero zero_add
cast_succ 📖	mathematical	—	AddMonoidWithOne.toNatCast AddSemigroup.toAdd AddMonoid.toAddSemigroup AddMonoidWithOne.toAddMonoid AddMonoidWithOne.toOne	—	AddMonoidWithOne.natCast_succ
cast_three 📖	mathematical	—	instOfNatAtLeastTwo instAtLeastTwoHAddOfNat	—	—
cast_two 📖	mathematical	—	instOfNatAtLeastTwo instAtLeastTwoHAddOfNat	—	—
cast_zero 📖	mathematical	—	AddMonoidWithOne.toNatCast AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass AddMonoidWithOne.toAddMonoid	—	AddMonoidWithOne.natCast_zero

(root)

Definitions

Name	Category	Theorems
AddCommMonoidWithOne 📖	CompData	1 math math: AddCommMonoidWithOne.toAddMonoidWithOne_injective
AddMonoidWithOne 📖	CompData	1 math math: AddCommMonoidWithOne.toAddMonoidWithOne_injective
instOfNatAtLeastTwo 📖	CompOp	2414 math math: Unitary.openPartialHomeomorph_source, Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, Matrix.frobenius_norm_replicateCol, Behrend.roth_lower_bound, TangentBundle.continuousLinearMapAt_model_space, CuspFormClass.qExpansion_isBigO, HurwitzZeta.hasSum_int_hurwitzZetaOdd, Real.pi_div_four_le_arcsin, Real.hasDerivAt_fourier, DirectSum.IsInternal.isometryL2OfOrthogonalFamily_symm_apply, norm_sub_sq_real, vsub_midpoint, BoundedContinuousFunction.tietze_extension_step, Polynomial.Chebyshev.S_two_mul_complex_cos, WithLp.prod_inner_apply, RootPairing.pairing_two_two_iff, Circle.periodic_exp, half_lt_self, hasSum_mellin_pi_mul_sq', WeierstrassCurve.coeff_Ψ₂Sq, Real.le_log_one_add_of_nonneg, Real.abs_exp_sub_one_le, Real.tan_pi_div_four, EuclideanGeometry.dist_smul_vadd_sq, Real.cos_pi_div_five, Polynomial.mahlerMeasure_def_of_ne_zero, EulerSine.integral_cos_mul_cos_pow, Complex.ofNat_log, Real.sin_add_sin, Complex.log_I, Complex.norm_circleTransformBoundingFunction_le, ENNReal.one_lt_two, Real.Angle.sign_two_zsmul_eq_sign_iff, Polynomial.derivative_X_sq, ProbabilityTheory.isGaussian_iff_gaussian_charFun, RootPairing.pairing_smul_root_eq_of_not_linearIndependent, norm_torusIntegral_le_of_norm_le_const, EuclideanGeometry.Sphere.thales_theorem, Real.sinh_eq, MeasureTheory.eLpNorm_condExp_le, completedZeta_eq_tsum_of_one_lt_re, QuaternionAlgebra.self_add_star, LinearMap.IsSymmetric.inner_map_polarization, Real.sinh_log, mellin_eq_fourier, EuclideanGeometry.abs_oangle_right_toReal_lt_pi_div_two_of_dist_eq, LucasLehmer.X.two_mul_ω_pow, Real.pi_le_four, MeasureTheory.charFun_eq_fourierIntegral', Real.hasFDerivAt_fourierChar_neg_bilinear_left, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Complex.cos_three_mul, Real.arcsin_eq_pi_div_two_sub_arccos, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, EisensteinSeries.hasSum_e2Summand_symmetricIcc, IsHilbertSum.surjective_isometry, SimpleGraph.lapMatrix_toLinearMap₂', dist_midpoint_right, UnitAddTorus.coe_mFourierBasis, TsirelsonInequality.sqrt_two_inv_mul_self, Complex.Gammaℝ_def, Orientation.inner_rotation_pi_div_two_right_smul, Orientation.oangle_add_left_smul_rotation_pi_div_two, GaussianFourier.norm_cexp_neg_mul_sq_add_mul_I, RootPairing.coroot_eq_polarizationEquiv_apply_root, ProbabilityTheory.measure_sum_ge_le_of_HasCondSubgaussianMGF, Submodule.orthogonalDecomposition_symm_apply, ENNReal.exists_inv_two_pow_lt, OrthogonalFamily.linearIsometry_apply_single, Complex.sin_pi_div_two_sub, hasDerivAt_sqrt_mul_log, HurwitzZeta.hasSum_int_cosKernel₀, Complex.exp_eq_exp_iff_exists_int, HurwitzZeta.hasSum_int_hurwitzZetaEven, Complex.norm_sub_one_sq_eq_of_norm_eq_one, Real.sin_pi_div_two, SchwartzMap.inner_fourier_toL2_eq, Complex.re_eq_add_conj, SchwartzMap.toLp_fourierTransformInv_eq, EuclideanSpace.orthonormal_single, MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral, HurwitzZeta.LSeriesHasSum_cos, abs_sub_round, round_neg_two_inv, Real.fourierIntegralInv_eq', Real.Angle.two_zsmul_eq_pi_iff, Real.sqrt_one_add_le, Ordinal.card_le_ofNat, volume_iUnion_setOf_liouvilleWith, Cardinal.ofENat_lt_ofNat, Real.sin_add_two_pi, WeierstrassCurve.c_relation, EuclideanSpace.closedBall_zero_eq, integral_sin_mul_cos₂, Real.Angle.sin_add_pi_div_two, Stirling.factorial_isEquivalent_stirling, WithLp.prod_nndist_eq_of_L2, Filter.Germ.const_ofNat, Submodule.toLinearEquiv_orthogonalDecomposition_symm, OrthonormalBasis.repr_injective, norm_jacobiTheta₂_term_le, WeierstrassCurve.toCharNeTwoNF_t, RightDerivMeasurableAux.norm_sub_le_of_mem_A, contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt, Complex.norm_sub_mem_Icc_angle, Real.cos_eq_zero_iff, PeriodPair.derivWeierstrassPExcept_sub, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, Matrix.spectrum_toEuclideanLin, Ring.multichoose_two, MeasureTheory.norm_condExpL2_le, Real.dist_mulExpNegMulSq_le_two_mul_sqrt, HurwitzZeta.cosZeta_two_mul_nat', Real.log_div_le_sum_range_add, Matrix.cstar_nnnorm_def, parallelogram_law_with_nnnorm, summableLocallyUniformlyOn_iteratedDerivWithin_cexp, AddCircle.homeomorphCircle'_apply_mk, lp.inner_eq_tsum, Real.neg_pi_div_two_eq_arcsin, Real.log2_le_logb, Cardinal.ofENat_ofNat, three_pos, Cardinal.two_le_iff_one_lt, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, Complex.cos_eq_one_iff, PeriodPair.ω₁_div_two_notMem_lattice, Matrix.l2_opNorm_mulVec, Real.sin_periodic, Matrix.transpose_ofNat, Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_derivative_U_eq_poly_in_U, Quaternion.rank_eq_four, Real.log_sqrt, pow_four_add_four_mul_pow_four', ModularForm.eta_q_eq_pow, RootPairing.root_coroot_two, Surreal.nsmul_pow_two_powHalf, HurwitzZeta.sinZeta_neg_two_mul_nat_sub_one, circleIntegral_def_Icc, ZMod.LFunction_one_sub, MeasureTheory.inner_condExpL2_left_eq_right, Complex.arg_neg_I, Real.Gamma_nat_add_half, circleIntegrable_iff, Real.posLog_norm_add_le, Complex.tsum_exp_neg_mul_int_sq, Real.fderiv_fourierChar_neg_bilinear_right_apply, zero_le_three, Real.eulerMascheroniConstant_lt_two_thirds, Polynomial.degree_quadratic_lt, LinearMap.IsSymmetric.diagonalization_apply_self_apply, QuaternionAlgebra.star_eq_two_re_sub, Cardinal.ofENat_le_ofNat, Chebyshev.abs_psi_sub_theta_le_sqrt_mul_log, Submodule.toLinearEquiv_orthogonalDecomposition, Stirling.log_stirlingSeq_sub_log_stirlingSeq_succ, RCLike.sub_conj, bernoulliFun_eval_half_eq_zero, Real.cos_int_mul_two_pi, WeierstrassCurve.ofJNe0Or1728_Δ, SchwartzMap.lineDerivOp_fourier_eq, ProbabilityTheory.Fernique.lt_normThreshold_zero, Ordinal.succ_one, NumberField.dedekindZeta_residue_def, Real.Ioo_eq_ball, FiniteField.isSquare_two_iff, WeierstrassCurve.ψ₂_sq, EuclideanSpace.inner_single_left, EuclideanSpace.basisFun_toBasis, circleMap_neg_pi_div_two, Odd.exists_bit1, GaussianFourier.integral_cexp_neg_mul_sq_norm, Cardinal.ofNat_le_lift_iff, DiffeologicalSpace.CorePlotsOn.isOpen_iff_preimages_plots, dist_left_midpoint, contMDiff_addInvariantVectorField, EuclideanSpace.norm_sq_eq, Complex.angle_exp_one, RootPairing.Base.cartanMatrix_map_abs, circleIntegral.integral_sub_inv_of_mem_ball, Unitary.continuousOn_argSelfAdjoint, Real.norm_two, bernoulliFun_two, hasSum_one_div_nat_pow_mul_fourier, two_mul_riemannZeta_eq_tsum_int_inv_pow_of_even, Complex.nndist_self_conj, Complex.cos_eq_zero_iff, ContinuousMap.dist_le_two_norm, round_two_inv, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, Complex.cos_add_nat_mul_two_pi, LinearMap.IsReflective.apply_self_mul_coroot_apply, WeierstrassCurve.variableChange_a₁, TemperedDistribution.lineDerivOp_fourier_eq, selfAdjoint.norm_sq_expUnitary_sub_one, Behrend.roth_lower_bound_explicit, contMDiff_neg_sphere, PiCountable.min_dist_le_dist_pi, HurwitzZeta.cosZeta_two_mul_nat, two_mul_le_add_sq, Real.tendsto_cos_pi_div_two, Function.Antiperiodic.periodic_two_mul, fact_one_le_two_ennreal, NNReal.sqrt_mul_lt_half_add_of_ne, IsHilbertSum.linearIsometryEquiv_symm_apply, SmoothBumpCovering.exists_immersion_euclidean, Complex.sin_eq_neg_one_iff, Affine.Triangle.dist_point_faceOppositeCentroid, EuclideanHalfSpace.ext_iff, EuclideanSpace.basisFun_apply, riemannZeta_two, Real.isIntegral_two_mul_sin_rat_mul_pi, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable_aux, toLex_ofNat, WeierstrassCurve.Projective.polynomial_relation, HurwitzZeta.cosZeta_neg_two_mul_nat_add_one, ZeroLEOneClass.neZero.two, CFC.sqrt_rpow, fourierIntegral_gaussian_innerProductSpace', Set.encard_pair, Height.logHeight₁_add_le, Complex.sqrt_I, fourier_gaussian_pi', Real.hasSum_log_one_add_inv, Metric.ediam_closedEBall_le, Commute.ofNat_left, Polynomial.Chebyshev.S_eq_U_comp_half_mul_X, Differentiable.fderiv_norm_rpow, Behrend.sphere_subset_preimage_metric_sphere, integral_log_sin_zero_pi_div_two, Real.volume_closedEBall, iteratedDerivWithin_tsum_cexp_eq, contMDiff_mulInvariantVectorField, jacobiTheta₂_functional_equation, Real.sin_two_pi, ProbabilityTheory.sub_half_inf_sub_mem_Ioo, norm_add_pow_two_real, CFC.abs_nnrpow_two, WeierstrassCurve.ofJ_1728_of_two_ne_zero, sum_geometric_two_le, EuclideanGeometry.pi_div_three_le_angle_of_le_of_le, ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq, Hyperreal.coe_ofNat, WeierstrassCurve.Δ_of_isCharTwoJEqZeroNF, Complex.cosh_three_mul, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, Function.Antiperiodic.int_even_mul_periodic, ProbabilityTheory.cgf_gaussianReal, ProbabilityTheory.HasSubgaussianMGF.mgf_le, norm_sub_mul_self, NumberField.abs_discr_ge', Polynomial.chebyshev_U_eq_dickson_two_one, sub_sq, sum_cauchyPowerSeries_eq_integral, Complex.tan_pi_div_two_sub, Metric.diam_le_of_subset_closedBall, Real.vector_fourierIntegral_eq_integral_exp_smul, Matrix.IsHermitian.eigenvalues_eq, nndist_midpoint_right, Real.range_arctan, WeierstrassCurve.Jacobian.eval_polynomialY, IsLowerSet.exists_subset_ball, Nat.WithBot.add_eq_two_iff, Real.fourier_real_eq_integral_exp_smul, NumberField.abs_discr_ge, RootPairing.coxeterWeightIn_eq_four_iff_not_linearIndependent, setOf_liouvilleWith_subset_aux, EuclideanGeometry.Sphere.IsDiameter.dist_left_right, IsSl2Triple.lie_lie_smul_f, lineMap_inv_two, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, NNReal.agmSequences_zero, AddCircle.homeomorphCircle'_symm_apply, integral_sin_pow_three, quadraticChar_two, Height.logHeight₁_sub_le, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, two_inv_lt_one, MeasureTheory.Lp.instFourierInvSMul, round_eq_div, HurwitzZeta.jacobiTheta₂'_functional_equation', deriv_sqrt_mul_log, Real.volume_closedBall, Function.Periodic.norm_qParam_lt_iff, CharZero.NeZero.two, Real.Wallis.W_le, WeierstrassCurve.ofJNe0Or1728_c₄, Complex.cos_pi_div_two, Cardinal.ofNat_lt_lift_iff, ENNReal.ofReal_eq_ofNat, Circle.isAddQuotientCoveringMap_exp, Real.one_sub_sq_div_two_le_cos, hasSum_nat_jacobiTheta, OrthonormalBasis.repr_self, Real.fourier_deriv, DirichletCharacter.norm_LSeries_product_ge_one, Real.goldenRatio_lt_two, Surreal.zsmul_pow_two_powHalf, PeriodPair.hasSum_derivWeierstrassPExcept, MeasureTheory.L2.inner_def, div_two_sub_self, add_halves, Icc_isBoundaryPoint_bot, Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero, Complex.digamma_one_half, ZMod.stdAddChar_coe, Metric.ediam_thickening_le, ProbabilityTheory.evariance_lt_top_iff_memLp, DifferentiableOn.circleIntegral_sub_inv_smul, Function.Antiperiodic.int_odd_mul_antiperiodic, four_pos, summable_condensed_iff_of_eventually_nonneg, Real.Angle.abs_toReal_eq_pi_div_two_iff, EuclideanSpace.nndist_eq, WeierstrassCurve.leadingCoeff_preΨ₄, Stirling.log_stirlingSeq_formula, Complex.neg_pi_div_two_lt_arg_iff, WeierstrassCurve.b₂_of_isCharThreeJNeZeroNF, Real.cos_add_int_mul_two_pi, SimpleGraph.two_le_chromaticNumber_of_adj, Real.volume_pi_ball, stereographic'_source, ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zero, BoxIntegral.Box.upper_sub_lower_splitCenterBox, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, Polynomial.Chebyshev.iterate_derivative_T_eval_one_recurrence, jacobiSum_trivial_trivial, parallelogram_law_with_norm, NNReal.sqrt_eq_rpow, OrthonormalBasis.measurePreserving_repr, Real.sin_pi_div_three, Behrend.log_two_mul_two_le_sqrt_log_eight, Cardinal.toENat_eq_ofNat, Circle.exp_eq_exp, Complex.volume_sum_rpow_le, Cardinal.IsStrongLimit.two_power_lt, SimpleGraph.three_le_egirth, SchwartzMap.inner_toL2_toL2_eq, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, ModularForm.tsum_logDeriv_eta_q, Complex.norm_log_one_add_le, Complex.mul_angle_le_norm_sub, Cardinal.lift_lt_ofNat_iff, PiLp.nnnorm_eq_of_L2, Cardinal.ofENat_eq_ofNat, Complex.integral_circleTransform, half_pos, NNReal.half_le_self, Polynomial.toAddCircle_X_pow_eq_fourier, SimpleGraph.chromaticNumber_cycleGraph_of_even, Complex.arg_le_pi_div_two_iff, Matrix.IsHermitian.eigenvectorUnitary_col_eq, Metric.PiNatEmbed.edist_def, HasDerivAt.sqrt, Real.Angle.toReal_coe, zero_lt_three, HurwitzZeta.oddKernel_def', Complex.cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, Circle.exp_two_pi_mul_int, Real.arctan_mem_Ioo, Num.cast_bit0, fourier_gaussian_innerProductSpace, DirichletCharacter.IsPrimitive.completedLFunction_one_sub, Real.Angle.two_zsmul_coe_div_two, AddCircle.scaled_exp_map_periodic, SchwartzMap.toLp_fourierInv_eq, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, Complex.isPrimitiveRoot_exp_rat, Orientation.neg_rotation_neg_pi_div_two, Matrix.toEuclideanLin_apply, WeierstrassCurve.b₈_of_isCharNeTwoNF, even_two, VectorFourier.fourierPowSMulRight_eq_comp, Polynomial.Chebyshev.S_eq_X_mul_S_add_C, EisensteinSeries.E2_slash_action, IsHilbertSum.hasSum_linearIsometryEquiv_symm, WeierstrassCurve.Projective.dblU_eq, Complex.mem_rootsOfUnity, MeasureTheory.memLp_two_iff_integrable_sq_norm, mfderivWithin_projIcc_one, Real.Polynomial.isRoot_cos_pi_div_five, Complex.sin_int_mul_two_pi_sub, Polynomial.Chebyshev.S_comp_two_mul_X, image_circleMap_Ioc, Real.exp_one_lt_three, integral_cos_pow, Real.neg_pi_div_two_lt_arctan, Real.cos_nat_mul_two_pi_sub_pi, Complex.cos_nat_mul_two_pi_sub_pi, NumberField.mixedEmbedding.convexBodySumFun_apply', Chebyshev.psi_eq_sum_theta, Stirling.log_stirlingSeq_diff_hasSum, norm_sub_pow_two_real, EuclideanSpace.norm_single, Metric.coveringNumber_two_mul_le_externalCoveringNumber, Real.HolderConjugate.two_two, Real.Gamma_two, Real.artanh_eq_half_log, CHSH_inequality_of_comm, Euclidean.closedBall_eq_image, Complex.sin_bound, Real.sin_sub_pi_div_two, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable, Submodule.coe_orthogonalDecomposition_symm, Real.tan_int_mul_pi_div_two, Real.Wallis.tendsto_W_nhds_pi_div_two, Real.Angle.sign_two_nsmul_eq_neg_sign_iff, Real.cos_add_two_pi, MeasureTheory.aestronglyMeasurable_condExpL2, Real.isIntegral_two_mul_cos_rat_mul_pi, Ordinal.one_add_ofNat, Complex.two_sinh, HurwitzZeta.hasSum_nat_sinZeta, norm_sub_sq, Quaternion.linearIsometryEquivTuple_symm_apply, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, EuclideanGeometry.angle_orthogonalProjection_self, add_sq, Pi.counit_eq_adjoint, WithLp.prod_dist_eq_of_L2, Real.rpowIntegrand₀₁_le_rpow_sub_two_mul_self, stereoInvFunAux_apply, Icc_isInteriorPoint_interior, Cardinal.mk_eq_two_iff', fourierCoeff_bernoulli_eq, Complex.log_exp_eq_re_add_toIocMod, LDL.lowerInv_orthogonal, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, circleMap_eq_circleMap_iff, ENNReal.half_lt_self, Real.Gamma_mul_Gamma_add_half, Real.sin_gt_sub_cube, Real.two_mul_arctan_inv_2_sub_arctan_inv_7, EulerSine.integral_cos_mul_cos_pow_aux, SchwartzMap.fourier_lineDerivOp_eq, WeierstrassCurve.ofJ0_Δ, Real.Angle.toReal_neg_pi_div_two, tangentBundle_model_space_coe_chartAt, Real.cos_two_neg, LieAlgebra.Orthogonal.jb_transform, NeZero.charZero_ofNat, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, Real.log_two_near_10, Field.Emb.Cardinal.two_le_deg, InnerProductGeometry.norm_add_eq_norm_sub_iff_angle_eq_pi_div_two, TemperedDistribution.fourierInv_lineDerivOp_eq, MeasureTheory.condExpL2_indicator_ae_eq_smul, mfderivWithin_comp_projIcc_one, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, LucasLehmer.X.ofNat_fst, contDiffWithinAt_euclidean, Real.pi_div_two_le_two, NNReal.dist_agmSequences_fst_snd, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, Stirling.le_log_factorial_stirling, curveIntegralFun_trans_aeeq_right, even_neg_two, EuclideanGeometry.Sphere.IsTangentAt.angle_eq_pi_div_two, Complex.cos_eq_iff_quadratic, contMDiffAt_mulInvariantVectorField, LucasLehmer.X.one_add_α_sq, UpperHalfPlane.dist_eq_iff_eq_sinh, riemannZeta_one_sub, integral_sin_sq, PeriodPair.ω₂_div_two_notMem_lattice, Real.arcsin_eq_pi_div_two, sub_half_lt_round, Polynomial.Chebyshev.leadingCoeff_U_natCast, UnitAddTorus.mFourierCoeff_toLp, PiCountable.min_edist_le_edist_pi, EuclideanSpace.volume_closedBall_fin_three, IccLeftChart_extend_interior_pos, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, Polynomial.Chebyshev.T_two, PeriodPair.hasSum_derivWeierstrassP, PiCountable.edist_eq_tsum, Complex.sinh_three_mul, hasSum_zeta_four, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, Real.cos_pi_div_four, ProbabilityTheory.IsGaussian.memLp_two_id, Matrix.IsHermitian.eigenvectorUnitary_mulVec, Polynomial.Chebyshev.T_add_one, ZMod.exists_sq_eq_two_iff, Cubic.degree_of_a_eq_zero', FDerivMeasurableAux.norm_sub_le_of_mem_A, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, PeriodPair.hasSumLocallyUniformly_derivWeierstrassP, Complex.cos_nat_mul_two_pi, RootPairing.Base.cartanMatrixIn_apply_same, LucasLehmer.X.one_add_α_pow_q_succ, Metric.PiNatEmbed.dist_def, Real.deriv_sqrt_aux, OrthonormalBasis.prod_apply, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, ContinuousMap.HomotopyRel.trans_apply, cauchyPowerSeries_apply, Real.Angle.two_nsmul_toReal_eq_two_mul_sub_two_pi, MeasureTheory.integral_condExpL2_eq, Real.arccos_eq_pi_div_two_sub_arcsin, Real.cos_add_cos, mdifferentiableAt_addInvariantVectorField, QuadraticForm.polarBilin_tmul, Complex.sin_sub_nat_mul_two_pi, DiffContOnCl.circleIntegral_sub_inv_smul, SzemerediRegularity.hundred_lt_pow_initialBound_mul, HurwitzZeta.hurwitzZetaEven_apply_zero, Polynomial.Chebyshev.C_eq_S_sub_X_mul_S, WeierstrassCurve.b₂_of_isCharTwoJNeZeroNF, Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul, EuclideanSpace.dist_single_same, Real.arcsin_le_pi_div_two, Complex.sin_nat_mul_two_pi_sub, Module.Basis.coe_toOrthonormalBasis_repr, Real.cos_three_mul, Real.cos_two_pi, Complex.sin_two_mul, SimpleGraph.triangleRemovalBound_mul_cube_lt, orthonormal_fourier, Polynomial.Chebyshev.coeff_eq_iff_of_forall_abs_le_one, MeasureTheory.setIntegral_condExpL2_indicator, NumberField.IsCMField.regulator_div_regulator_eq_two_pow_mul_indexRealUnits_inv, contMDiff_coe_sphere, niven_sin, Real.tsum_exp_neg_mul_int_sq, HurwitzZeta.expZeta_one_sub, Polynomial.derivative_X_sub_C_sq, Real.tan_two_mul, HurwitzZeta.cosZeta_apply_zero, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, WeierstrassCurve.b₂_of_isCharNeTwoNF, Matrix.diagonal_ofNat', Polynomial.Chebyshev.U_two, WeierstrassCurve.Jacobian.polynomialY_eq, InnerProductGeometry.angle_zero_right, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, CFC.abs_nnrpow, Unitary.norm_sub_one_lt_two_iff, Real.cos_pi_div_sixteen, fourierIntegral_gaussian_pi, QuadraticMap.associated_apply, WeierstrassCurve.Jacobian.eval_polynomialX, Metric.diam_closedBall_eq, UniformConvexSpace.uniform_convex, Cubic.degree_of_a_ne_zero', Polynomial.Chebyshev.U_eq, Real.circleAverage_eq_circleIntegral, Complex.norm_exp_I_mul_ofReal_sub_one, WeierstrassCurve.c₆_of_isCharThreeJNeZeroNF, Real.Angle.cos_add_pi_div_two, Int.cast_two, Real.cos_two_pi_sub, Real.arctan_add_arctan_lt_pi_div_two, WeierstrassCurve.Projective.eval_polynomialX, CFC.sqrt_eq_rpow, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, Complex.arg_mul_cos_add_sin_mul_I_eq_toIocMod, CFC.nnrpow_sqrt_two, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, InnerProductGeometry.sin_eq_one_iff_angle_eq_pi_div_two, Complex.arg_cos_add_sin_mul_I_sub, Real.hasSum_log_one_add, WeierstrassCurve.toCharNeTwoNF_s, Real.Angle.cos_nonneg_iff_abs_toReal_le_pi_div_two, mellinInv_eq_fourierIntegralInv, HasDerivWithinAt.norm_sq, Real.Gamma_one_half_eq, WeierstrassCurve.variableChange_b₈, PiLp.volume_preserving_toLp, Real.pi_div_two_eq_arcsin, InnerProductGeometry.norm_toLp_symm_crossProduct, MeasureTheory.condExpIndSMul_empty, Real.two_le_pi, Chebyshev.integral_one_div_log_sq_isBigO, MeasureTheory.charFun_eq_prod_iff, Polynomial.degree_quadratic, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, midpoint_eq_smul_add, Complex.integral_exp_neg_rpow, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, midpoint_sub_right, le_ofDigits_cantorToTernary_sum, WeierstrassCurve.Affine.slope_of_Y_ne, Real.two_mul_arctan, CharTwo.two_eq_zero, Matrix.transpose_eq_ofNat, MeasureTheory.lintegral_abs_det_fderiv_le_addHaar_image_aux1, ENNReal.ofNat_le_ofReal, Real.pi_div_two_pos, Complex.hasDerivAt_Gammaℝ_one, Complex.dist_self_conj, WeierstrassCurve.c₄_of_isCharThreeJNeZeroNF, Real.arctan_eq_neg_pi_div_four, OrthonormalBasis.coe_ofRepr, Real.exists_isMinOn_Gamma_Ioi, EuclideanSpace.nnnorm_single, InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero, circleMap_pi_div_two, riemannZeta_four, Quaternion.star_eq_two_re_sub, Complex.cos_two_mul, Cardinal.beth_succ, Complex.orthonormalBasisOneI_repr_apply, Real.volume_emetric_closedBall, WeierstrassCurve.Affine.slope_of_Y_ne', MeasureTheory.norm_condExpL2_coe_le, WeierstrassCurve.b₆_of_isCharTwoJNeZeroNF, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, HurwitzZeta.hasSum_nat_completedCosZeta, Polynomial.toAddCircle.integrable, Real.toNNReal_ofNat, Complex.cos_sub_two_pi, Polynomial.degree_cubic_lt, ContinuousLinearMap.exists_approx_preimage_norm_le, Real.sqrt_two_lt_three_halves, Complex.sin_sub_two_pi, Real.cos_le_one_sub_mul_cos_sq, WeierstrassCurve.leadingCoeff_Ψ₂Sq, WeierstrassCurve.Δ_of_char_three, map_ofNat, Quaternion.star_add_self, mdifferentiable_mulInvariantVectorField, RootPairing.EmbeddedG2.twoShortAddLongRoot_eq, Complex.sin_sub_pi_div_two, SchwartzMap.norm_fourier_toL2_eq, norm_cauchyPowerSeries_le, WeierstrassCurve.Jacobian.polynomial_relation, hasFDerivAt_norm_rpow, Real.volume_ball, mellinInv_eq_fourierInv, Cardinal.toENat_le_ofNat, Polynomial.Chebyshev.U_sub_one, AkraBazziRecurrence.one_add_smoothingFn_le_two, Path.Homotopy.hcomp_half, Stirling.stirlingSeq_one, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, Path.Homotopy.hcomp_apply, MeasureTheory.Lp.instFourierPair, fourier_gaussian_innerProductSpace', HurwitzZeta.hasSum_nat_hurwitzZetaEven, HurwitzZeta.hasSum_int_cosKernel, quarters_mem_preCantorSet, MeasureTheory.volume_sum_rpow_lt, Real.cos_one_le, hasDerivAt_abs_rpow, Real.Angle.coe_eq_zero_iff, Matrix.toEuclideanCLM_toLp, hasSum_fourier_series_L2, norm_commutator_sub_one_le, one_le_two', Real.tendsto_integral_gaussian_smul', EuclideanGeometry.angle_le_pi_div_three_of_le_of_le, AddCircle.norm_half_period_eq, two_smul, Complex.norm_log_one_add_sub_self_le, Real.tendsto_cos_neg_pi_div_two, norm_jacobiTheta₂_term, dist_midpoint_midpoint_le, real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, Complex.exp_neg_pi_div_two_mul_I, two_mul, stereoInvFun_apply, ZetaAsymptotics.tendsto_Gamma_term_aux, Real.tan_pi_div_two, MeasureTheory.eLpNorm_one_le_of_le', Circle.exp_two_pi, WeierstrassCurve.Projective.polynomialZ_eq, Metric.packingNumber_two_mul_le_externalCoveringNumber, Complex.normSq_add, Polynomial.Chebyshev.S_two_mul_real_cos, two_pos, integrable_rpow_neg_one_add_norm_sq, inner_map_polarization', Real.arccos_le_pi_div_two, HilbertBasis.hasSum_repr, EisensteinSeries.D2_S, Polynomial.int_cyclotomic_rw, ZMod.LFunction_neg_two_mul_nat_sub_one, HasDerivWithinAt.sqrt, Complex.tan_int_mul_pi_div_two, WithLp.prod_edist_eq_of_L2, MeasureTheory.condExpIndSMul_smul, UpperHalfPlane.cosh_dist, MeasureTheory.lintegral_nnnorm_condExpL2_le, EisensteinSeries.G2_S_transform, Polynomial.Chebyshev.U_one, Chebyshev.sum_PrimePow_eq_sum_sum, Behrend.lower_bound_le_one, SchwartzMap.norm_fourierTransformCLM_toL2_eq, DiffContOnCl.deriv_eq_smul_circleIntegral, EuclideanSpace.volume_closedBall_fin_two, DifferentiableOn.deriv_eq_smul_circleIntegral, Real.sq_cos_pi_div_six, Pi.orthonormalBasis_apply, Matrix.piLp_ofLp_toEuclideanLin, LinearMap.IsSymmetric.diagonalization_symm_apply, Real.Angle.two_zsmul_toReal_eq_two_mul_sub_two_pi, stereographic'_target, RCLike.rank_le_two, MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux1, MeasureTheory.memLp_two_iff_integrable_sq, Commute.sub_sq, Complex.cos_int_mul_two_pi_sub, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, Behrend.norm_of_mem_sphere, UpperHalfPlane.dist_coe_center, OrthonormalBasis.tensorProduct_repr_tmul_apply', Subgroup.two_mul_withInfty_mem_strictPeriods, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, Real.tendsto_sin_neg_pi_div_two, SimpleGraph.chromaticNumber_eq_two_iff, three_add_one_eq_four, WeierstrassCurve.variableChange_b₂, Real.sqrtTwoAddSeries_two, Stirling.le_factorial_stirling, EuclideanGeometry.angle_self_right, ProbabilityTheory.exists_cgf_eq_iteratedDeriv_two_cgf_mul, dist_right_midpoint, Set.encard_eq_three, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Real.coe_fib_eq, Real.fourierIntegral_iteratedDeriv, ProbabilityTheory.IsGaussian.charFun_eq', Real.Gamma_strictMonoOn_Ici, HurwitzZeta.cosZeta_one_sub, contMDiff_vectorSpace_iff_contDiff, EulerSine.sin_pi_mul_eq, CircleDeg1Lift.transnumAuxSeq_dist_lt, integral_mul_cexp_neg_mul_sq, Matrix.l2_opNNNorm_mulVec, jacobiTheta_S_smul, EMetric.diam_ball, lp.inner_single_right, frontier_range_modelWithCornersEuclideanHalfSpace, HurwitzZeta.hasSum_nat_sinKernel, Complex.antilipschitz_equivRealProd, PartENat.withTopEquiv_ofNat, EuclideanSpace.instIsManifoldSphere, complEDS₂_zero, LucasLehmer.X.α_pow, Complex.isPrimitiveRoot_iff, MeasurableSpace.cardinal_generateMeasurableRec_le, Real.arcsin_neg_one, Complex.exp_periodic, WeierstrassCurve.variableChange_b₆, WeierstrassCurve.Δ_of_isShortNF, Height.mulHeight₁_add_le, Real.sin_nat_mul_two_pi_sub, TangentBundle.coordChange_model_space, Metric.diam_thickening_le, ENNReal.rpow_two, Complex.exp_nat_mul_two_pi_mul_I, Complex.log_exp_eq_sub_toIocDiv, RootPairing.EmbeddedG2.long_eq_three_mul_short, Polynomial.degree_quadratic_le, Function.Antiperiodic.nat_even_mul_periodic, dist_integral_mulExpNegMulSq_comp_le, MeasureTheory.setIntegral_condExpIndSMul, Affine.Triangle.acuteAngled_iff_angle_lt, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, WeierstrassCurve.b₆_of_isShortNF, Polynomial.intervalIntegrable_mahlerMeasure, Real.volume_real_closedBall, Real.sin_pi_div_two_sub, BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic, add_thirds, OrthonormalBasis.equiv_apply, Polynomial.Chebyshev.leadingCoeff_le_of_forall_abs_le_one, inner_eq_sum_norm_sq_div_four, Real.two_mul_le_exp, ProbabilityTheory.complexMGF_gaussianReal, Real.exp_one_near_20, add_pow_le, Real.arccos_eq_pi_div_two, HasStrictFDerivAt.sqrt, Matrix.diagonal_ofNat, Complex.isPrimitiveRoot_exp_of_isCoprime, div_two_lt_of_pos, Metric.ediam_cthickening_le, circleIntegral.norm_integral_le_of_norm_le_const, Real.arcsin_mem_Icc, Real.log_two_gt_d9, Complex.Gammaℝ_eq_zero_iff, MeasureTheory.volume_sum_rpow_le, DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul, MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_spec, HurwitzZeta.hurwitzZetaEven_neg_two_mul_nat_add_one, Real.cos_pi_div_two, Module.Basis.coe_toOrthonormalBasis_repr_symm, IsSl2Triple.lie_h_e_smul, Polynomial.Chebyshev.C_two_mul_complex_cosh, Convex.taylor_approx_two_segment, Matrix.frobenius_norm_def, integral_exp_mul_I_eq_sinc, contMDiff_subtype_coe_Icc, Orientation.inner_rotation_pi_div_two_right, gold_sub_goldConj, Complex.arg_one_add_mem_Ioo, Complex.normSq_sub, Function.Periodic.im_invQParam, HurwitzZeta.cosZeta_eq, ENNReal.ofReal_le_ofNat, sup_eq_half_smul_add_add_abs_sub', CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_left, RCLike.add_conj, Complex.sin_two_pi, UpperHalfPlane.norm_exp_two_pi_I_lt_one, RCLike.im_eq_conj_sub, HurwitzZeta.hasSum_int_cosZeta, integral_id, Complex.arg_exp_mul_I, Behrend.four_zero_nine_six_lt_exp_sixteen, AddCircle.volume_closedBall, MeasureTheory.charFun_pi, stereoToFun_apply, one_half_lt_one, Real.pow_mul_norm_iteratedFDeriv_fourier_le, Real.Angle.toReal_pi_div_two, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_Gammaℝ, ProbabilityTheory.evariance_eq_top_iff, Complex.tendsto_norm_tan_atTop, ProbabilityTheory.IsGaussian.charFunDual_eq_of_forall_strongDual_eq_zero, Real.arctan_inv_of_neg, OrthonormalBasis.repr_apply_apply, WithLp.prod_nnnorm_eq_of_L2, Orientation.inner_rotation_pi_div_two_left, Complex.hasDerivAt_Gammaℂ_one, sup_eq_half_smul_add_add_abs_sub, riemannZeta_neg_two_mul_nat_add_one, RootPairing.pairing_neg_one_neg_four_iff, QuadraticAlgebra.rank_eq_two, Complex.sub_conj, ProbabilityTheory.HasSubgaussianMGF.measure_sum_ge_le_of_iIndepFun, Complex.sin_add_two_pi, Affine.Simplex.excenterWeights_empty_lt_inv_two, Chebyshev.integrableOn_theta_div_id_mul_log_sq, Matrix.conjTranspose_inv_ofNat_smul, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, nndist_left_midpoint, EisensteinSeries.hasSum_e2Summand_symmetricIco, ModularForm.eta_q_eq_cexp, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, four_mul_le_sq_add, Real.arccos_le_pi_div_four, AffineIsometryEquiv.dist_pointReflection_self, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, AffineIsometryEquiv.dist_pointReflection_self_real, Num.cast_bit1, SlashInvariantForm.exists_one_half_le_im_and_norm_le, Complex.arg_lt_pi_div_two_iff, MeasureTheory.L2.inner_indicatorConstLp_one, NNReal.lipschitzWith_sub, BoxIntegral.Box.mem_splitCenterBox, ENNReal.sub_half, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, Real.sin_sq_eq_half_sub, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, Unitary.norm_sub_one_sq_eq, PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, EuclideanSpace.edist_single_same, InnerProductSpace.volume_ball, CFC.sqrt_eq_nnrpow, circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const, Submodule.coe_orthogonalDecomposition, EisensteinSeries.q_expansion_riemannZeta, HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat, Real.fourierIntegral_real_eq_integral_exp_smul, Real.deriv_mulExpNegMulSq, EuclideanHalfSpace.convex, fourier_coe_apply, Real.cos_pi_div_eight, Real.deriv_fourierIntegral, dist_right_pointReflection, integral_exp_mul_I_eq_sin, MeasureTheory.condExpIndSMul_add, norm_jacobiTheta_sub_one_le, QuadraticMap.associated_toQuadraticMap, QuaternionAlgebra.star_add_self, PiNat.mem_cylinder_iff_dist_le, quadratic_eq_zero_iff_discrim_eq_sq, MeasureTheory.Lp.norm_fourier_eq, SzemerediRegularity.coe_stepBound, jacobiTheta₂'_add_right, HurwitzZeta.hasSum_nat_cosZeta, FiniteField.isSquare_neg_two_iff, NumberField.mixedEmbedding.covolume_idealLattice, Real.injOn_tan, ValueDistribution.proximity_add_top_le, EuclideanSpace.sphere_zero_eq, Real.Angle.toReal_coe_eq_self_sub_two_mul_int_mul_pi_iff, hasSum_cauchyPowerSeries_integral, MeasureTheory.Lp.instFourierSMul, IsClosed.two_pow_mk_le_two_pow_mk_dense, Complex.sin_eq_sin_iff, Circle.exp_inj, Tactic.ComputeAsymptotics.Seq.dist_cons_cons, LinearMap.toMatrix_innerₛₗ_apply, Cardinal.power_self_eq, integral_sin_mul_cos₁, Real.Angle.two_zsmul_neg_pi_div_two, RCLike.wInner_one_eq_inner, ProbabilityTheory.isGaussian_iff_charFun_eq, Orientation.inner_rotation_pi_div_two_left_smul, EuclideanGeometry.Sphere.abs_oangle_center_left_toReal_lt_pi_div_two, Int.cast_four, InnerProductGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, fourierIntegral_eq_half_sub_half_period_translate, NNReal.HolderConjugate.two_two, InnerProductGeometry.angle_sub_le_pi_div_two_of_inner_eq_zero, CircleDeg1Lift.dist_map_zero_lt_of_semiconj, CFC.abs_nnrpow_two_mul, WeierstrassCurve.C_Ψ₂Sq, integral_comp_abs, MeasureTheory.hausdorffMeasure_prod_real, Circle.exp_add_two_pi, ContinuousMap.HomotopyWith.trans_apply, quadratic_eq_zero_iff_of_discrim_eq_zero, RCLike.sqrt_eq_real_add_ite, WithBot.succ_one, Nat.WithBot.add_eq_three_iff, ProbabilityTheory.mgf_fun_id_gaussianReal, Polynomial.Chebyshev.S_two_mul_real_cosh, Real.Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, has_antideriv_at_fourier_neg, PartENat.withTopEquiv_symm_ofNat, Metric.diam_ball, WeierstrassCurve.b₆_of_isCharThreeJNeZeroNF, SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet, tsum_geometric_two, ZFSet.card_pair_of_ne, Real.Angle.two_zsmul_toReal_eq_two_mul, ProbabilityTheory.sum_variance_truncation_le, contDiffAt_euclidean, HurwitzZeta.hasSum_expZeta_of_one_lt_re, Complex.sin_three_mul, PiCountable.dist_summable, Cardinal.lift_le_ofNat_iff, OrthogonalFamily.hasSum_linearIsometry, hasSum_one_div_nat_pow_mul_cos, finrank_euclideanSpace, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, Ordinal.card_ofNat, EuclideanGeometry.oangle_orthogonalProjection_self, EisensteinSeries.e2Summand_zero_eq_two_riemannZeta_two, ModularFormClass.exp_decay_sub_atImInfty, PartENat.ofENat_ofNat, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', Submodule.fst_orthogonalDecomposition_apply, NNReal.rpow_two, Real.sum_range_le_log_div, Real.two_pi_pos, nndist_midpoint_left, trivializationAt_model_space_apply, ProbabilityTheory.gaussianPDFReal_def, ENNReal.add_thirds, ENNReal.rpow_add_le_mul_rpow_add_rpow, Real.cos_eq_cos_iff, UpperHalfPlane.IsZeroAtImInfty.exp_decay_atImInfty, WeierstrassCurve.variableChange_def, mfderiv_coe_sphere_injective, SimpleGraph.chromaticNumber_le_two_iff_isBipartite, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, Cardinal.mk_perm_eq_two_power, Complex.two_pi_I_inv_smul_circleIntegral_sub_sq_inv_smul_of_differentiable, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, SymAlg.invOf_sym, Behrend.exp_neg_two_mul_le, InnerProductGeometry.angle_zero_left, SimpleGraph.CompleteBipartiteGraph.chromaticNumber, PeriodPair.derivWeierstrassP_sq, contDiffOn_euclidean, Complex.cos_sub_nat_mul_two_pi, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius, PiLp.volume_preserving_ofLp, EuclideanGeometry.sin_eq_one_iff_angle_eq_pi_div_two, integral_sin_pow_even_mul_cos_pow_even, Metric.diam_closedBall, Real.sin_two_pi_sub, Complex.cos_int_mul_two_pi_add_pi, SimpleGraph.two_le_chromaticNumber_iff_ne_bot, Cardinal.mk_equiv_of_eq, Real.sinOrderIso_apply, Tactic.ComputeAsymptotics.Seq.dist_eq_two_inv_pow, zero_le_four, hasDerivAt_fourier_neg, ValueDistribution.characteristic_add_top_eventuallyLE, Real.Angle.cos_eq_zero_iff, Real.Angle.angle_eq_iff_two_pi_dvd_sub, Real.sin_two_mul, WeierstrassCurve.Affine.addPolynomial_eq, InnerProductGeometry.norm_ofLp_crossProduct, Orthonormal.linearIsometryEquiv_symm_apply_single_one, nndist_midpoint_midpoint_le', InnerProductSpace.volume_ball_of_dim_odd, SchwartzMap.fourierInv_lineDerivOp_eq, Complex.cos_two_mul', WeierstrassCurve.variableChange_a₂, Real.cos_int_mul_two_pi_add_pi, MeasureTheory.integral_charFun_Icc, Finset.doubling_lt_golden_ratio, strongConcaveOn_iff_convex, sum_Ioo_inv_sq_le, Polynomial.Chebyshev.T_eq, ProbabilityTheory.Fernique.normThreshold_eq, WeierstrassCurve.variableChange_a₃, UnitAddTorus.orthonormal_mFourier, Matrix.ofLp_toEuclideanCLM, ENNReal.tsum_two_zpow_neg_add_one, Real.sin_eq_sin_iff, FiniteField.two_pow_card, Complex.arg_eq_pi_div_two_iff, add_pow_two, UpperHalfPlane.dist_eq, EulerSine.integral_sin_mul_sin_mul_cos_pow_eq, circleIntegral.norm_integral_lt_of_norm_le_const_of_lt, quadraticChar_neg_two, Metric.ediam_eball_le, AkraBazziRecurrence.bi_min_div_two_pos, fourierCoeff_toLp, CircleDeg1Lift.transnumAuxSeq_def, OrthogonalFamily.summable_of_lp, ProbabilityTheory.IsGaussian.charFunDual_eq, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, coe_fourierBasis, Complex.tsum_exp_neg_quadratic, Real.circleAverage_def, QuaternionAlgebra.rank_eq_four, Matrix.conjTranspose_eq_ofNat, NumberField.Ideal.tendsto_norm_le_div_atTop₀, riemannZeta_zero, Complex.isAddQuotientCoveringMap_exp, unitInterval.qRight_zero_right, WeierstrassCurve.ofJ1728_j, hasSum_geometric_two, Complex.cot_pi_eq_exp_ratio, WeierstrassCurve.c₆_of_isCharTwoJEqZeroNF, range_two_mul, Matrix.vecMul_ofNat, instIsContMDiffRiemannianBundleOfNatWithTopENat_2, Nat.div_two_lt_floor, differentiableWithinAt_euclidean, ProbabilityTheory.variance_le_sq_of_bounded, Complex.rank_real_complex', Matrix.isPositive_toEuclideanLin_iff, LieAlgebra.IsKilling.rootSpace_one_div_two_smul, Height.mulHeight₁_sub_le, Complex.integral_exp_neg_mul_rpow, QuaternionAlgebra.star_add_self', PiLp.norm_sq_eq_of_L2, RCLike.re_eq_add_conj, Complex.isIntegral_two_mul_sin_rat_mul_pi, Real.abs_sin_half, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, Real.two_mul_cos_mul_cos, Real.sqrtTwoAddSeries_succ, Cardinal.ofNat_lt_ofENat, HurwitzZeta.hurwitzZetaEven_one_sub, MeasureTheory.Egorov.notConvergentSeqLTIndex_spec, HasDerivAt.norm_sq, EuclideanGeometry.Sphere.abs_oangle_center_right_toReal_lt_pi_div_two, Polynomial.Chebyshev.C_eval_two, EuclideanQuadrant.convex, Matrix.discr_of_card_eq_two, ENNReal.coe_two, odd_add_two, MeasureTheory.L2.real_inner_indicatorConstLp_one_indicatorConstLp_one, Polynomial.hermite_eq_deriv_gaussian', ENNReal.HolderConjugate.instTwoTwo, Cardinal.ord_ofNat, HurwitzZeta.hasSum_int_sinKernel, tangentBundle_model_space_coe_chartAt_symm, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, Path.Homotopy.trans_apply, EuclideanSpace.toLp_single, HurwitzZeta.oddKernel_functional_equation, tangentBundleModelSpaceHomeomorph_coe, Real.tan_pi_div_two_sub, NNReal.agm_eq_agm_gm_am, ENNReal.half_le_self, round_eq, one_sub_invOf_two, WeierstrassCurve.Projective.eval_polynomialZ, Real.arcsin_of_le_neg_one, Polynomial.Chebyshev.derivative_U_eval_one, Cardinal.mk_powerset, one_add_one_eq_two, Real.sin_int_mul_two_pi_sub, midpoint_vsub_left, Complex.two_cosh, Real.tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, unitary.two_mul_one_sub_le_norm_sub_one_sq, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, Real.cos_pi_div_six, NNReal.le_gm_and_am_le, Real.range_arcsin, Real.nnnorm_two, range_euclideanHalfSpace, HurwitzZeta.LSeriesHasSum_exp, InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero, bernoulliFourierCoeff_eq, Real.coe_intFib_eq, CFC.nnrpow_sqrt, invOf_two_smul_add_invOf_two_smul, Real.circleAverage_eq_integral_add, Complex.sinh_two_mul, tangentBundleCore_coordChange_model_space, ENNReal.tsum_geometric_two, Complex.cosh_two_mul, Real.Gamma_nat_add_one_add_half, ContinuousMap.Homotopy.trans_apply, Complex.isPrimitiveRoot_exp_of_coprime, WithLp.prod_lipschitzWith_toLp, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, Real.pi_lt_four, Polynomial.Chebyshev.rootMultiplicity_T_real, periodic_circleMap, instIsManifoldMinSmoothnessOfNatWithTopENat, IccLeftChart_extend_bot, ModularForm.logDeriv_eta_eq_E2, TemperedDistribution.fourier_lineDerivOp_eq, Complex.sin_eq_one_iff, Matrix.l2_opNNNorm_def, Cardinal.nat_power_eq, Real.Angle.sign_two_nsmul_eq_sign_iff, PeriodPair.order_weierstrassP, Complex.add_conj, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, Complex.volume_sum_rpow_lt, ENNReal.one_sub_inv_two, Quaternion.normSq_add, Polynomial.quadratic_dvd_of_aeval_eq_zero_im_ne_zero, MeasureTheory.condExpL2_indicator_of_measurable, HurwitzZeta.hurwitzZetaEven_one_sub_two_mul_nat, Real.fourier_iteratedDeriv, Complex.cos_periodic, ProbabilityTheory.add_half_inf_sub_mem_Ioo, EuclideanSpace.basisFun_repr, tsum_geometric_two', Real.arcsin_le_neg_pi_div_two, ProbabilityTheory.indepFun_iff_charFun_prod, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, zero_lt_three', Real.inv_sqrt_two_sub_one, Polynomial.Chebyshev.derivative_U_eval_one_dvd, Complex.exp_pi_div_two_mul_I, Orientation.oangle_sub_right_smul_rotation_pi_div_two, Real.Angle.sin_pi_div_two_sub, Real.sin_add_pi_div_two, VectorFourier.fourierSMulRight_apply, SimpleGraph.unreduced_edges_subset, EMetric.pair_reduction, Submodule.sndL_comp_coe_orthogonalDecomposition, OrthonormalBasis.equiv_apply_euclideanSpace, integral_cexp_quadratic, Real.cos_sub_nat_mul_two_pi, RootPairing.pairing_same, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, Complex.circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, Complex.orthonormalBasisOneI_repr_symm_apply, HurwitzZeta.sinZeta_two_mul_nat_add_one', Manifold.riemannianEDist_def, NNReal.coe_two, WeierstrassCurve.b₄_of_isShortNF, WeierstrassCurve.Projective.polynomialX_eq, WeierstrassCurve.c₄_of_isShortNF, MeasureTheory.Lp.instContinuousFourierInv, uniformity_basis_edist_inv_two_pow, imaginaryPart_apply_coe, Cardinal.lift_eq_ofNat_iff, Complex.Gammaℂ_def, Complex.cos_bound, UnitAddTorus.hasSum_mFourier_series_L2, Complex.cpow_inv_two_im_eq_sqrt, Real.sinh_two_mul, WeierstrassCurve.c₆_of_isCharTwoJNeZeroNF, Complex.cpow_inv_two_re, Real.one_le_pi_div_two, modelWithCornersEuclideanHalfSpace_zero, Equiv.Perm.toList_formPerm_nontrivial, Real.pi_gt_sqrtTwoAddSeries, NumberField.mixedEmbedding.det_matrixToStdBasis, Real.cosh_le_exp_half_sq, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eval, tsirelson_inequality, Complex.abs_arg_le_pi_div_two_iff, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, hasDerivAt_fourier, Quaternion.star_add_self', LucasLehmer.X.mul_fst, QuadraticMap.half_moduleEnd_apply_eq_half_smul, RootPairing.coxeterWeightIn_le_four, rpow_mul_exp_neg_mul_sq_isLittleO_exp_neg, WeierstrassCurve.b₈_of_isCharThreeJNeZeroNF, RootPairing.EmbeddedG2.pairing_long_short, WeierstrassCurve.Projective.polynomialY_eq, half_lt_self_iff, SimpleGraph.ediam_le_two_mul_radius, Complex.isPrimitiveRoot_exp, ZMod.orderOf_one_add_four_mul, WeierstrassCurve.Projective.negDblY_eq, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, Real.Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, quadratic_eq_zero_iff, Matrix.sub_scalar_sq_eq_disc, ENNReal.coe_inv_two, Real.log_div_sqrt_antitoneOn, EuclideanSpace.norm_eq, mellin_eq_fourierIntegral, Matrix.IsHermitian.eigenvectorUnitary_apply, Matrix.disc_fin_two, HurwitzZeta.hasSum_nat_completedSinZeta, integral_cos_pow_three, Real.fourierIntegral_eq', RootPairing.coroot_root_two, AddCircle.norm_coe_eq_abs_iff, MeasureTheory.L2.eLpNorm_inner_lt_top, ModularGroup.exists_one_half_le_im_smul, hasFPowerSeriesOn_cauchy_integral, Metric.diam_ball_eq, Matrix.frobenius_nnnorm_replicateRow, Real.arctan_inv_2_add_arctan_inv_3, Real.arctan_one, Complex.circleIntegral_div_sub_of_differentiable_on_off_countable, contDiffOn_tsum_cexp, Complex.Gammaℂ_add_one, Complex.cos_add_pi_div_two, InnerProductSpaceable.parallelogram_identity, ValueDistribution.characteristic_add_top_le, EuclideanSpace.inner_eq_star_dotProduct, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, AddCircle.toCircle_apply_mk, OrthonormalBasis.sum_repr_symm, CFC.rpow_sqrt_nnreal, Real.Angle.two_nsmul_eq_pi_iff, QuaternionAlgebra.self_add_star', NumberField.mixedEmbedding.covolume_integerLattice, Polynomial.derivative_sq, Polynomial.hermite_eq_deriv_gaussian, Real.one_half_lt_eulerMascheroniSeq_six, Real.exp_half, Orientation.inner_smul_rotation_pi_div_two_right, Unitary.spectrum_subset_slitPlane_iff_norm_lt_two, Matrix.frobenius_nnnorm_replicateCol, Pi.orthonormalBasis.toBasis, SimpleGraph.chromaticNumber_cycleGraph_of_odd, contMDiffWithinAt_comp_projIcc_iff, fourierIntegral_gaussian_innerProductSpace, tangentBundle_model_space_chartAt, Real.sin_pi_over_two_pow_succ, trapezoidal_integral_one, Polynomial.Chebyshev.U_add_two, Polynomial.degree_cubic, IsClosed.two_pow_mk_lt_continuum, ProbabilityTheory.HasGaussianLaw.charFun_map_eq, Real.bijOn_sin, Real.toNNReal_lt_ofNat, Cubic.degree_of_a_eq_zero, EisensteinSeries.qExpansion_identity_pnat, ENNReal.tsum_condensed_le, Real.iteratedDeriv_fourier, SimpleGraph.FarFromTriangleFree.lt_half, Real.tan_pi_div_six, round_eq_zero_iff, Cardinal.lift_two, Quaternion.self_add_star', NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, MeasureTheory.Lp.instFourierPairInv, RootPairing.RootPositiveForm.two_mul_apply_root_root, Complex.angle_le_mul_norm_sub, Real.Angle.sign_two_zsmul_eq_neg_sign_iff, Cubic.equiv_symm_apply_b, EuclideanSpace.volume_ball_fin_three, Real.arctan_inv_sqrt_three, Complex.nnnorm_ofNat, PiCountable.edist_le_two, Cardinal.cantor, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius, add_sq_le, CHSH_id, integral_log_sin_zero_pi, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, InnerProductGeometry.angle_sub_lt_pi_div_two_of_inner_eq_zero, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, hasSum_geometric_two', Real.arcsin_of_one_le, Complex.norm_prime_cpow_le_one_half, Real.rpow_two, Complex.cos_add_cos, WeierstrassCurve.variableChange_a₄, Cardinal.ofNat_le_ofENat, ENNReal.ofNat_lt_ofReal, MeasureTheory.Lp.instFourierInvAdd, PiNat.dist_eq_of_ne, Matrix.frobenius_nnnorm_diagonal, ZeroLEOneClass.neZero.three, homothety_invOf_two, jacobiTheta₂'_add_left', Complex.norm_ofNat, even_two_mul, NNReal.rpow_add_le_mul_rpow_add_rpow, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, Polynomial.toAddCircle_monomial_eq_smul_fourier, WeierstrassCurve.c₆_of_isCharNeTwoNF, jacobiTheta₂'_functional_equation, preCantorSet_succ, riemannZeta_one, SetTheory.PGame.birthday_half, tsum_geometric_inv_two_ge, Real.tendsto_tan_pi_div_two, Diffeology.isPlot_iff_contDiff, pow_four_add_four_mul_pow_four, Orientation.neg_rotation_pi_div_two, add_sub_div_two_lt, Polynomial.Chebyshev.iterate_derivative_U_eval_one_recurrence, MeasureTheory.condExpIndSMul_nonneg, OrthonormalBasis.measurePreserving_repr_symm, lp.summable_inner, MeasureTheory.measureReal_abs_gt_le_integral_charFun, Real.volume_eball, EuclideanSpace.piLpCongrLeft_single, WeierstrassCurve.coeff_preΨ₄, Real.cos_pi_div_thirty_two, Complex.sin_pi_div_two, oneTangentSpaceIcc_def, ProbabilityTheory.HasSubgaussianMGF.measureReal_le_le_exp, WeierstrassCurve.j_of_isCharTwoJEqZeroNF, WeierstrassCurve.Jacobian.polynomialZ_eq, bernoulliFun_one, Complex.sin_periodic, Cardinal.preBeth_succ, Complex.differentiable_on_off_countable_deriv_eq_smul_circleIntegral, IccRightChart_extend_top_mem_frontier, Commute.add_sq, WeierstrassCurve.Jacobian.dblU_eq, Complex.cos_sub_pi_div_two, IsPrimitiveRoot.norm_pow_sub_one_two, hasFDerivWithinAt_euclidean, niven_angle_eq, Orientation.oangle_sub_left_smul_rotation_pi_div_two, Real.Angle.two_zsmul_toReal_eq_two_mul_add_two_pi, ProbabilityTheory.HasSubgaussianMGF.cgf_le, Real.binEntropy_eq_log_two, even_sub_two, pow_mul_le_of_le_of_pow_mul_le, PiLp.dist_sq_eq_of_L2, SymAlg.sym_mul_self, Metric.coveringNumber_subset_le, WeierstrassCurve.Affine.degree_polynomial, Cardinal.mk_bool, CuspFormClass.exists_bound, integral_sqrt_one_sub_sq, Matrix.IsHermitian.eigenvectorUnitary_coe, Nat.cast_three, Orientation.oangle_add_right_smul_rotation_pi_div_two, Ordinal.ofNat_lt_card, Real.sin_bound, Orientation.inner_smul_rotation_pi_div_two_left, Real.surjOn_sin, parallelogram_law, Real.sin_pi_div_thirty_two, Matrix.ofNat_mulVec, midpoint_vsub_right, Matrix.toEuclideanLin_eq_toLin, Cardinal.mk_eq_two_iff, Real.sqrtTwoAddSeries_one, WeierstrassCurve.Δ_of_isCharNeTwoNF, Real.neg_pi_div_two_lt_arcsin, trapezoidal_error_le, Euclidean.closedBall_eq_preimage, Matrix.isHermitian_iff_isSymmetric, RootPairing.InvariantForm.apply_eq_or_aux, Polynomial.Chebyshev.T_neg_two, Cardinal.mk_finset_of_fintype, Real.cos_eq_two_mul_tan_half_div_one_sub_tan_half_sq, Cubic.degree_of_a_ne_zero, DirichletCharacter.norm_LFunction_product_ge_one, Real.sin_pi_div_six, EulerSine.integral_cos_pow_eq, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, EuclideanSpace.basisFun_inner, Real.hasDerivAt_mulExpNegMulSq, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, NNReal.half_lt_self, LinearMap.IsReflective.dvd_two_mul, InnerProductSpace.toMatrix_rankOne, Real.image_tan_Ioo, contMDiffAt_vectorSpace_iff_contDiffAt, EuclideanSpace.ofLp_single, differentiableAt_euclidean, Mathlib.Tactic.ENatToNat.coe_ofNat, lp.inner_single_left, geom_series_mul_one_add, dist_pointReflection_right, RootPairing.pairingIn_one_four_iff, Complex.cos_int_mul_two_pi_sub_pi, HurwitzZeta.differentiableAt_update_of_residue, PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExcept, skewAdjointPart_apply_coe, WithLp.prod_norm_sq_eq_of_L2, Complex.cos_add_two_pi, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.IsReflective.coroot_apply_self, Finpartition.IsEquipartition.sum_nonUniforms_lt, one_half_pos, Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sq, ProbabilityTheory.measure_sum_ge_le_of_hasCondSubgaussianMGF, WeierstrassCurve.Projective.negDblY_eq', EuclideanGeometry.abs_oangle_left_toReal_lt_pi_div_two_of_dist_eq, odd_sub_two, inner_sum_smul_sum_smul_of_sum_eq_zero, Real.one_half_lt_eulerMascheroniConstant, Real.hasDerivAt_fourierChar, Real.le_integral_rpowIntegrand₀₁_one, MeasureTheory.norm_one_sub_charFun_le_two, ZMod.LFunction_neg_two_mul_nat_add_one, selfAdjointPartL_apply_coe, EuclideanGeometry.inner_weightedVSub, Even.two_dvd, nndist_midpoint_midpoint_le, mdifferentiable_addInvariantVectorField, ZeroLEOneClass.neZero.four, RootPairing.pairingIn_neg_one_neg_four_iff, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, LieAlgebra.IsKilling.root_apply_coroot, PeriodPair.deriv_derivWeierstrassPExcept_self, Polynomial.dickson_one_one_eq_chebyshev_T, SchwartzMap.inner_fourierTransformCLM_toL2_eq, mdifferentiableWithinAt_comp_projIcc_iff, Real.pi_lt_sqrtTwoAddSeries, Real.coe_fib_eq', half_le_self, Real.injOn_sin, Diffeology.isOpen_iff_preimages_plots, Complex.toIocMod_arg, differentiableOn_euclidean, norm_add_sq_real, EisensteinSeries.q_expansion_bernoulli, HasStrictFDerivAt.approximates_deriv_on_open_nhds, Real.Angle.coe_toIocMod, cotTerm_identity, Real.sin_sub_sin, VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symm, half_sub, BoxIntegral.norm_volume_sub_integral_face_upper_sub_lower_smul_le, EuclideanGeometry.cos_eq_zero_iff_angle_eq_pi_div_two, TangentBundle.symmL_model_space, MeasureTheory.integrable_condExpL2_indicator, Real.hasDerivAt_Gamma_one_half, quarter_mem_preCantorSet, EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, Ordinal.ofNat_le_card, Diffeology.IsContDiffCompatible.isPlot_iff, NumberField.mixedEmbedding.volume_eq_two_pow_mul_two_pi_pow_mul_integral, EuclideanSpace.ball_zero_eq, Real.Gamma_mul_Gamma_add_half_of_pos, Real.sigmoid_zero, range_mfderiv_coe_sphere, Diffeology.IsPlot.continuous, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist, add_mul_self_eq, MeasureTheory.eLpNorm'_add_le_of_le_one, Complex.norm_sub_one_sq_eqOn_sphere, Polynomial.chebyshev_T_eq_dickson_one_one, Complex.sqrt_neg_I, Complex.abs_arg_lt_pi_div_two_iff, HurwitzZeta.sinZeta_two_mul_nat_add_one, HasFDerivWithinAt.sqrt, ENNReal.le_tsum_condensed, MeasurableSpace.cardinal_measurableSet_le, Real.lt_sin_mul, Matrix.ofLp_toEuclideanLin_apply, NumberField.exists_ideal_in_class_of_norm_le, Complex.sqrt_eq_real_add_ite, Polynomial.ringKrullDim_le, Cardinal.lift_two_power, RCLike.norm_two, Polynomial.Chebyshev.S_two_mul_complex_cosh, EuclideanSpace.volume_ball_fin_two, Polynomial.fourierCoeff_toAddCircle_natCast, Cardinal.two_le_iff, norm_add_sq, MeasurableSpace.cardinal_generateMeasurable_le, fderivWithin_sqrt, Real.eulerMascheroniSeq'_six_lt_two_thirds, Real.cos_sub_cos, EuclideanSpace.inner_basisFun_real, summable_condensed_iff_of_nonneg, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, iccLeftChart_extend_zero, Real.cos_nat_mul_two_pi_sub, norm_jacobiTheta₂'_term_le, completedRiemannZeta₀_one, RCLike.sqrt_neg_I, fourierCoeffOn_of_hasDerivAt_Ioo, Complex.nndist_conj_self, MeasureTheory.eLpNorm_one_le_of_le, Cardinal.one_lt_two, Real.tendsto_tan_neg_pi_div_two, Polynomial.Chebyshev.C_eval_neg_two, tsum_geometric_inv_two, Euclidean.ball_eq_preimage, Real.cos_pi_over_two_pow, Real.binEntropy_two_inv_add, Ordinal.principal_mul_two, NNRat.ofNat_le_cast, NumberField.Ideal.tendsto_norm_le_div_atTop, HurwitzZeta.hurwitzZetaOdd_eq, Real.Angle.toIocMod_toReal, UpperHalfPlane.cosh_half_dist, norm_add_mul_self, Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable_of_tendsto, SchwartzMap.lineDerivOp_fourierInv_eq, ofLex_ofNat, LieAlgebra.Orthogonal.jd_transform, Cubic.equiv_symm_apply_c, EuclideanSpace.volume_ball, OrthonormalBasis.repr_symm_single, Real.fourierChar_apply, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, Unitary.two_mul_one_sub_le_norm_sub_one_sq, DirichletCharacter.Even.LFunction_neg_two_mul_nat, interior_range_modelWithCornersEuclideanHalfSpace, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, RootPairing.polarizationEquiv_symm_apply_coroot, Real.Angle.sign_coe_pi_div_two, Real.Angle.zsmul_eq_iff, LinearMap.BilinForm.IsSymm.polarization, SetTheory.Game.birthday_ofNat, ENNReal.half_pos, Circle.exp_int_mul_two_pi, Complex.Gammaℝ_residue_zero, CFC.nnrpow_three, GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_I, EulerSine.antideriv_cos_comp_const_mul, Real.cos_half, RCLike.sqrt_I, Path.trans_apply, WeierstrassCurve.b_relation, QuadraticMap.associated_linMulLin, Cardinal.mk_set, ENNReal.add_halves, OrthogonalFamily.range_linearIsometry, SeminormedAddCommGroup.lipschitzWith_sub, UpperHalfPlane.exp_half_dist, GaussianFourier.integral_cexp_neg_mul_sum_add, RootPairing.EmbeddedG2.threeShortAddTwoLongRoot_eq, HurwitzZeta.hurwitzZetaOdd_neg_two_mul_nat_sub_one, RCLike.nnnorm_two, zero_lt_two', Metric.diam_sphere_eq, Cardinal.two_le_iff', ModularFormClass.qExpansion_coeff_eq_circleIntegral, ProbabilityTheory.isGaussian_iff_charFunDual_eq, Real.tendsto_arctan_atTop, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, integral_sin_mul_cos_sq, Complex.sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, real_inner_sub_sub_self, fourierIntegral_gaussian, Complex.norm_exp_sub_one_le, LucasLehmer.X.α_sq, WeierstrassCurve.Φ_two, Even.add_pow_le, Algebra.trace_complex_apply, Real.quadratic_root_cos_pi_div_five, toMatrix_innerSL_apply, Real.cos_periodic, Polynomial.Chebyshev.C_comp_two_mul_X, two_mul_le_add_of_sq_eq_mul, Complex.sin_add_int_mul_two_pi, Real.sqrtTwoAddSeries_lt_two, HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, Complex.im_eq_sub_conj, Real.cosh_three_mul, EulerSine.antideriv_sin_comp_const_mul, Diffeology.IsPlot.contDiff, tangentBundleModelSpaceHomeomorph_coe_symm, HurwitzZeta.hurwitzZeta_one_sub, sub_pow_two, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, lp.hasSum_inner, Module.rank_eq_ofNat_iff_finrank_eq_ofNat, Set.encard_eq_four, Real.pi_gt_three, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eq_poly_in_T, Real.quadratic_le_exp_of_nonneg, Real.one_sub_sq_div_two_lt_cos, SchwartzMap.toLp_fourierTransform_eq, MeasureTheory.setLIntegral_nnnorm_condExpIndSMul_le, Polynomial.Chebyshev.U_add_one, DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smul, round_le_add_half, Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero, Chebyshev.theta_le_log4_mul_x, SimpleGraph.incMatrix_transpose_mul_diag, Quaternion.self_add_star, WeierstrassCurve.Affine.evalEval_polynomialY, lineMap_one_half, MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq, ProbabilityTheory.HasSubgaussianMGF.measure_ge_le, hasDerivAt_norm_rpow, UnitAddTorus.hasSum_prod_mFourierCoeff, Real.two_mul_arctan_sub_pi, GromovHausdorff.ghDist_le_of_approx_subsets, Real.tan_pi_div_three, Complex.isIntegral_two_mul_cos_rat_mul_pi, Real.pi_div_two_le_arcsin, Real.sin_three_mul, Real.arccos_lt_pi_div_two, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, Real.sin_add_nat_mul_two_pi, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, Complex.Gammaℝ_one_sub_mul_Gammaℝ_one_add, Real.tan_eq_zero_iff, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, IsStarProjection.two_mul_sub_one_mem_unitary, Real.volume_real_ball, Complex.circleTransformDeriv_periodic, selfAdjointPart_apply_coe, MeasureTheory.aestronglyMeasurable_condExpIndSMul, skewAdjointPartL_apply_coe, hasSum_one_div_nat_pow_mul_sin, Cardinal.mk_Prop, ringKrullDim_nat, Polynomial.Chebyshev.roots_T_real, even_add_two, Real.tendsto_arctan_atBot, SchwartzMap.fderivCLM_fourier_eq, Real.two_mul_arctan_add_pi, ProbabilityTheory.iIndepFun_iff_charFun_pi, MeasureTheory.L2.mem_L1_inner, Cardinal.lift_ofNat, Real.Angle.two_nsmul_coe_div_two, ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo, Real.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, Real.abs_sin_eq_one_iff, Complex.tan_eq_zero_iff, Complex.Gammaℝ_add_two, Real.Angle.cos_pos_iff_abs_toReal_lt_pi_div_two, Real.mapsTo_sin_Ioo, circleIntegral.norm_integral_le_of_norm_le_const', map_ofNat', BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter, SimpleGraph.triangleRemovalBound_le, Real.Wallis.W_eq_factorial_ratio, Chebyshev.psi_le, real_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, MeasureTheory.Lp.inner_fourier_eq, Commute.ofNat_right, RootPairing.coxeterWeight_eq_four_iff_not_linearIndependent, two_mul_le_add_pow_two, SeparationQuotient.mk_ofNat, WeierstrassCurve.c₄_of_isCharNeTwoNF, Real.Angle.coe_toIcoMod, Real.log_two_lt_d9, HilbertBasis.repr_self, nnnorm_commutator_sub_one_le, hasSum_zeta_two, Polynomial.Chebyshev.T_mul_T, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', norm_midpoint_lt_iff, round_eq_half_ceil_two_mul, Real.sin_eq_neg_one_iff, Polynomial.Chebyshev.T_sub_one, Real.sin_pi_div_sixteen, UpperHalfPlane.sinh_half_dist_add_dist, RootPairing.pairingIn_two_two_iff, Field.Emb.cardinal_eq_two_pow_sepDegree, ProbabilityTheory.HasSubgaussianMGF.measure_sum_range_ge_le_of_iIndepFun, MeasureTheory.L2.integrable_inner, Real.two_mul_arctan_inv_3_add_arctan_inv_7, Complex.sin_add_sin, Matrix.conjTranspose_ofNat_smul, Real.circleAverage_eq_intervalAverage, NumberField.abs_discr_ge_of_isTotallyComplex, Real.Angle.cos_neg_iff_pi_div_two_lt_abs_toReal, Real.cos_add_pi_div_two, Real.arctan_inv_of_pos, Real.lt_log_one_add_of_pos, one_lt_two, Real.tendsto_sum_pi_div_four, rpow_neg_one_add_norm_sq_le, ZMod.LFunction_apply_zero_of_even, derivWithin_sqrt, Real.fourierChar_apply', Real.cos_sub_two_pi, Real.Angle.cos_pi_div_two_sub, mdifferentiableAt_mulInvariantVectorField, Finset.centroid_pair, ProbabilityTheory.complexMGF_id_gaussianReal, EuclideanGeometry.oangle_self_orthogonalProjection, Real.cos_two_mul, ENNReal.nhdsGT_ofNat_neBot, Matrix.toEuclideanLin_apply_piLp_toLp, Real.cos_int_mul_two_pi_sub_pi, rank_real_of_complex, circleIntegrable_def, VectorFourier.fourierPowSMulRight_apply, Set.encard_eq_two, WeierstrassCurve.Jacobian.polynomialX_eq, Polynomial.Chebyshev.C_two_mul_complex_cos, discrim_eq_sq_of_quadratic_eq_zero, SzemerediRegularity.pow_mul_m_le_card_part, ModularGroup.exists_one_half_le_im_smul_and_norm_denom_le, even_iff_two_dvd, EuclideanSpace.dist_eq, zero_lt_four, WeierstrassCurve.b₆_of_isCharNeTwoNF, Chebyshev.integral_theta_div_log_sq_isBigO, exists_forall_sphere_dist_add_le_two_sub, Nat.cast_choose_two, Cubic.equiv_apply_coe, EisensteinSeries.G2_eq_tsum_cexp, IsUpperSet.exists_subset_ball, Polynomial.Chebyshev.C_zero, AddCircle.norm_le_half_period, Real.hasStrictDerivAt_sqrt, CFC.sqrt_nnrpow_two, one_le_two, Real.arcsin_lt_pi_div_two, contMDiffOn_comp_projIcc_iff, Function.Periodic.norm_qParam, HurwitzZeta.hurwitzOddFEPair_k, Complex.circleIntegral_one_div_sub_center_pow_smul_of_differentiable_on_off_countable, Real.cosh_log, PartENat.toWithTop_ofNat, Real.arctan_lt_pi_div_two, EisensteinSeries.qExpansion_identity, fderiv_sqrt, GaussianFourier.integral_cexp_neg_sum_mul_add, volume_euclideanSpace_eq_dirac, sub_sq', integral_sin_sq_mul_cos, Real.arctan_sqrt_three, Complex.cos_pi_div_two_sub, EuclideanGeometry.pi_div_three_lt_angle_of_le_of_le_of_ne, Int.cast_three, tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow, Polynomial.dickson_zero, Real.cos_eq_one_iff, gold_lt_two, Matrix.frobenius_norm_diagonal, curveIntegralFun_trans_aeeq_left, CFC.sqrt_nnrpow, Metric.lipschitz_infDist, nnnorm_commutator_units_sub_one_le, rootsOfUnityCircleEquiv_comp_rootsOfUnityAddChar_val, Chebyshev.integral_theta_div_log_sq_isLittleO, Polynomial.dickson_two_one_eq_chebyshev_U, zero_le_two, Real.binEntropy_lt_log_two, OrthonormalBasis.coe_toBasis_repr, IsManifold.instOfNatWithTopENat_2, InnerProductSpace.Core.cauchy_schwarz_aux', EulerSine.integral_cos_pow_pos, HurwitzZeta.hasSum_int_sinZeta, inf_eq_half_smul_add_sub_abs_sub, ZMod.val_two_eq_two_mod, Real.sin_sq_pi_over_two_pow, Real.sq_sin_pi_div_three, ZMod.toCircle_intCast, WeierstrassCurve.twoTorsionPolynomial_disc, stereographic_apply, Complex.cos_sub_cos, ModularGroup.three_le_four_mul_im_sq_of_mem_fd, integral_pow_mul_le_of_le_of_pow_mul_le, ZMod.toCircle_natCast, inner_map_polarization, ENNReal.tsum_geometric_two_encode_le_two, Real.deriv_fourierChar, OrthonormalBasis.sum_repr, ZMod.orderOf_five, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, jacobiTheta_eq_tsum_nat, Stirling.log_stirlingSeq_diff_le_geo_sum, hasSum_sq_fourierCoeff, Complex.neg_pi_div_two_le_arg_iff, ENNReal.ofReal_lt_ofNat, Behrend.le_sqrt_log, EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two, Submodule.fstL_comp_coe_orthogonalDecomposition, Behrend.two_div_one_sub_two_div_e_le_eight, ProbabilityTheory.mgf_gaussianReal, PiLp.dist_eq_of_L2, midpoint_sub_left, odd_iff_exists_bit1, IsHilbertSum.linearIsometryEquiv_symm_apply_single, Real.monotoneOn_sin, exists_embedding_euclidean_of_compact, UnitAddTorus.mFourierBasis_repr, MeasureTheory.condExpIndL1Fin_ae_eq_condExpIndSMul, zero_lt_four', Real.cos_nat_mul_two_pi_add_pi, midpoint_vsub, Mathlib.Tactic.RingNF.nat_rawCast_2, Complex.hasDerivAt_Gamma_one_half, Polynomial.Chebyshev.U_sub_two, Real.Angle.coe_two_pi, Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X, ProbabilityTheory.Kernel.HasSubgaussianMGF.measure_ge_le, fourierBasis_repr, Complex.norm_log_one_sub_inv_sub_self_le, ProbabilityTheory.mgf_id_gaussianReal, MeasureTheory.BoundedContinuousFunction.inner_toLp, inf_eq_half_smul_add_sub_abs_sub', Real.tendsto_integral_gaussian_smul, SymAlg.unsym_mul_self, Complex.sin_sub_int_mul_two_pi, RootPairing.InvariantForm.apply_eq_or, bernoulliFourierCoeff_recurrence, DirichletCharacter.Even.LFunction_neg_two_mul_nat_add_one, Real.arcsin_image_Icc, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, Polynomial.Chebyshev.T_eq_half_mul_C_comp_two_mul_X, Matrix.disc_of_card_eq_two, CFC.sqrt_rpow_nnreal, Complex.Gamma_mul_Gamma_add_half, sub_half, OrthonormalBasis.coe_toBasis_repr_apply, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, Finset.centroid_pair_fin, Complex.cpow_inv_two_im_eq_neg_sqrt, Cubic.degree_of_b_ne_zero', Real.tendsto_abs_tan_atTop, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, ENNReal.lintegral_Lp_add_le_of_le_one, Complex.sin_two_pi_sub, Real.cos_sub_int_mul_two_pi, OrthonormalBasis.coe_equiv_euclideanSpace, VectorFourier.norm_fourierSMulRight_le, round_eq_iff, EuclideanGeometry.angle_lt_pi_div_three_of_le_of_le_of_ne, Polynomial.dickson_two, EuclideanSpace.dist_sq_eq, summable_geometric_two', Polynomial.derivative_X_add_C_sq, norm_commutator_units_sub_one_le, HurwitzZeta.sinKernel_def, EuclideanGeometry.law_cos, Complex.cot_eq_exp_ratio, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, Real.Gamma_integrand_isLittleO, Real.goldenRatio_sub_goldenConj, Real.neg_pi_div_two_le_arcsin, EuclideanGeometry.angle_self_orthogonalProjection, fourier_coe_apply', NumberField.abs_discr_rpow_ge_of_isTotallyComplex, Behrend.lower_bound_le_one', WeierstrassCurve.Affine.evalEval_polynomialX, EuclideanSpace.inner_toLp_toLp, UnitAddTorus.hasSum_sq_mFourierCoeff, TemperedDistribution.lineDerivOp_fourierInv_eq, Complex.cos_sq, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, Orientation.abs_oangle_sub_left_toReal_lt_pi_div_two, WeierstrassCurve.Jacobian.dblU_of_Z_eq_zero, contMDiffAt_addInvariantVectorField, integral_sin_pow_odd, EuclideanGeometry.dist_affineCombination, ProbabilityTheory.Fernique.sq_normThreshold_add_one_le, contMDiff_tangentBundleModelSpaceHomeomorph, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, RootPairing.pairingIn_neg_two_neg_two_iff, realPart_apply_coe, IsCyclotomicExtension.norm_zeta_pow_sub_one_two, Unitization.antilipschitzWith_addEquiv, Cardinal.two_power_aleph0, ProbabilityTheory.IsGaussian.charFun_eq, Real.exp_one_near_10, Real.rpow_div_two_eq_sqrt, VectorFourier.norm_fourierPowSMulRight_le, EuclideanGeometry.dist_smul_vadd_eq_dist, integral_gaussian_complex, summable_pow_mul_jacobiTheta₂_term_bound, WeierstrassCurve.Δ_of_isCharThreeJNeZeroNF, WeierstrassCurve.c₄_of_isCharTwoJEqZeroNF, Real.hasFDerivAt_fourierChar_neg_bilinear_right, MeasureTheory.lintegral_nnnorm_condExpIndSMul_le, summable_bernoulli_fourier, Real.cos_sq, AffineSubspace.mem_perpBisector_iff_inner_eq, Polynomial.degree_cubic_le, Orientation.rotation_pi_div_two, Cardinal.ofNat_eq_lift_iff, ZFSet.card_powerset, VectorFourier.norm_fourierSMulRight, ZMod.toCircle_apply, MeasureTheory.integrable_condExpIndSMul, InnerProductSpace.volume_closedBall, Real.cos_int_mul_two_pi_sub, Tactic.ComputeAsymptotics.Seq.dist_eq_half_of_head, unitary.norm_sub_one_lt_two_iff, cantorSequence_eq_self_sub_sum_cantorToTernary, stereographic'_symm_apply, WeierstrassCurve.coeff_Ψ₃, Matrix.frobenius_nnnorm_def, Cubic.equiv_symm_apply_d, Polynomial.Chebyshev.S_eval_two, circleIntegral.integral_sub_center_inv, Real.binEntropy_le_log_two, Submodule.snd_orthogonalDecomposition_apply, summable_geometric_two, MeasureTheory.Egorov.exists_notConvergentSeq_lt, HurwitzZeta.evenKernel_functional_equation, strongConvexOn_iff_convex, ENNReal.one_half_lt_one, norm_add_sub_norm_sub_le_two_mul_min, completedRiemannZeta_one, EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, dist_midpoint_midpoint_le', ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc_of_integral_eq_zero, SchwartzMap.fourier_fderivCLM_eq, Real.sum_range_sub_log_div_le, DirichletCharacter.Odd.LFunction_neg_two_mul_nat_sub_one, MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv, Complex.Gammaℝ_div_Gammaℝ_one_sub, UpperHalfPlane.sinh_half_dist, Real.iteratedDeriv_fourierIntegral, MeasureTheory.Measure.exists_null_set_measure_lt_of_disjoint, EuclideanSpace.coe_measurableEquiv, InnerProductSpace.volume_closedBall_of_dim_odd, norm_add_mul_self_real, UpperHalfPlane.dist_le_iff_le_sinh, Irreducible.degree_le_two, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, Real.sin_pi_div_eight, ProbabilityTheory.IsGaussian.memLp_two_fun_id, Real.binEntropy_strictAntiOn, Complex.cos_eq_neg_one_iff, NumberField.mixedEmbedding.euclidean.finrank, Real.arctan_eq_pi_div_four, integral_Ioi_inv_one_add_sq, Complex.log_neg_I, Matrix.map_ofNat, Complex.volume_sum_rpow_lt_one, Polynomial.Chebyshev.leadingCoeff_T, Complex.betaIntegral_convergent_left, jacobiTheta₂_add_left', hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, Polynomial.Chebyshev.T_sub_two, EuclideanSpace.nnnorm_eq, PiLp.inner_apply, contMDiff_tangentBundleModelSpaceHomeomorph_symm, Submodule.orthogonalDecomposition_apply, schnirelmannDensity_setOf_Odd, range_modelWithCornersEuclideanHalfSpace, UpperHalfPlane.dist_coe_center_sq, Real.Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal, InnerProductGeometry.norm_sub_sq_eq_norm_sq_add_norm_sq_sub_two_mul_norm_mul_norm_mul_cos_angle, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, DiffContOnCl.ball_subset_image_closedBall, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, Real.binEntropy_two_inv, norm_add_pow_two, HasFDerivAt.sqrt, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, Real.half_mul_log_add_log_abs, ruzsaSzemerediNumberNat_lower_bound, NNReal.agmSequences_succ', NumberField.mixedEmbedding.fundamentalCone.volume_normLeOne, Complex.exp_two_pi_mul_I, Filter.Germ.coe_ofNat, EuclideanSpace.inner_single_right, real_inner_add_add_self, unitary.norm_sub_one_sq_eq, Complex.arg_exp, hofer, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_of_isDiameter, unitInterval.eq_closedBall, IsPrimitiveRoot.arg, right_sub_midpoint, Real.tendsto_sin_pi_div_two, WeierstrassCurve.b₄_of_isCharNeTwoNF, Real.Angle.cos_sub_pi_div_two, tsum_sq_fourierCoeff, Cubic.equiv_symm_apply_a, RCLike.normSq_add, MeasureTheory.eLpNorm_condExpL2_le, Real.arccos_zero, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Orientation.inner_smul_rotation_pi_div_two_smul_left, integral_sin_pow, Polynomial.instTwoPiPos, four_mul_le_pow_two_add, integral_mul_cpow_one_add_sq, integral_gaussian_Ioi, ENNReal.inv_three_add_inv_three, Polynomial.Chebyshev.coeff_le_of_forall_abs_le_one, Circle.exp_eq_one, Real.cosh_eq, WeierstrassCurve.Projective.dblX_eq, PiCountable.dist_eq_tsum, zero_lt_two, Real.strictMonoOn_sin, fderiv_norm_rpow, unitInterval.half_le_symm_iff, UpperHalfPlane.cosh_dist', Matrix.toEuclideanLin_eq_toLin_orthonormal, Polynomial.toAddCircle_X_eq_fourier_one, RootPairing.pairing_one_four_iff, Orientation.inner_smul_rotation_pi_div_two_smul_right, GaussianFourier.verticalIntegral_norm_le, Int.div_two_lt_floor, NNReal.summable_condensed_iff, CircleIntegrable.out, Complex.borelCaratheodory, Polynomial.Chebyshev.T_add_two, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, Real.hasDerivAt_fourierIntegral, Complex.cos_nat_mul_two_pi_sub, EuclideanSpace.measurableEquiv_toEquiv, fourier_add_half_inv_index, Real.cos_add_nat_mul_two_pi, Affine.Simplex.Equilateral.angle_eq_pi_div_three, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, fourierCoeffOn_of_hasDerivAt, Real.Angle.two_nsmul_neg_pi_div_two, CuspFormClass.exp_decay_atImInfty, integral_sin_sq_mul_cos_sq, integral_mul_rpow_one_add_sq, Ordinal.card_lt_ofNat, IsClosed.mk_lt_two_pow_mk_dense, Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable, Matrix.cstar_norm_def, norm_sub_pow_two, UpperHalfPlane.tanh_half_dist, ContMDiff.codRestrict_sphere, jacobiTheta₂_add_right, NNReal.sqrt_mul_le_half_add, Real.Angle.toReal_coe_eq_self_add_two_pi_iff, Surreal.double_powHalf_succ_eq_powHalf, Complex.exp_eq_one_iff, homothety_inv_two, Complex.cos_nat_mul_two_pi_add_pi, Complex.inv_Gammaℝ_one_sub, ENNReal.add_rpow_le_two_rpow_mul_rpow_add_rpow, inner_matrix_row_row, MeasureTheory.condExpIndSMul_ae_eq_smul, Complex.norm_two, Quaternion.linearIsometryEquivTuple_apply, DifferentiableOn.circleIntegral_one_div_sub_center_pow_smul, Stirling.stirlingSeq_pow_four_div_stirlingSeq_pow_two_eq, Real.strictMonoOn_tan, integral_Iic_inv_one_add_sq, isIntegral_two_mul_cos_rat_mul_pi, rothNumberNat_le_ruzsaSzemerediNumberNat', odd_two_mul_add_one, cantorSet_eq_union_halves, Real.cos_eq_neg_one_iff, Unitization.lipschitzWith_addEquiv, SimpleGraph.chromaticNumber_pathGraph, Real.sin_sub_two_pi, HurwitzZeta.hasSum_int_completedCosZeta, Real.Wallis.W_succ, integral_cos_sq, TorusIntegrable.function_integrable, NumberField.mixedEmbedding.volume_eq_two_pi_pow_mul_integral, WeierstrassCurve.twoTorsionPolynomial_discr, dist_midpoint_left, Polynomial.Chebyshev.derivative_U_eval_one_eq_div, mfderiv_subtype_coe_Icc_one, HurwitzZeta.LSeriesHasSum_sin, ruzsaSzemerediNumberNat_asymptotic_lower_bound, ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo, MeasureTheory.condExpIndSMul_smul', two_add_one_eq_three, Complex.arg_mul_cos_add_sin_mul_I_sub, VectorField.eventually_contMDiffWithinAt_mpullbackWithin_extChartAt_symm, midpoint_vsub_midpoint_same_left, Ordinal.lift_ofNat, PiLp.norm_eq_of_L2, Real.sinh_three_mul, Real.exp_one_gt_two, Real.cos_pi_div_three, WeierstrassCurve.j_of_isShortNF, HurwitzZeta.sinZeta_eq, Real.Icc_eq_closedBall, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, Complex.cos_two_pi_sub, right_vsub_midpoint, Real.le_sin_mul, ProbabilityTheory.IsGaussian.charFunDual_eq', WeierstrassCurve.Projective.dblX_eq', riemannZeta_two_mul_nat, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_U_eq_poly_in_U, Real.Angle.toReal_eq_pi_div_two_iff, Complex.abs_cpow_inv_two_im, nndist_right_midpoint, MeasureTheory.ContinuousMap.inner_toLp, two_add_two_eq_four, Polynomial.Chebyshev.S_eval_neg_two, ModularForm.logDeriv_qParam, Complex.norm_le_sqrt_two_mul_max, unitInterval.two_mul_sub_one_mem_iff, hasSum_zeta_nat, ProbabilityTheory.charFun_gaussianReal, Polynomial.Chebyshev.C_two, ZLattice.sum_piFinset_Icc_rpow_le, Real.Angle.toReal_coe_eq_self_sub_two_pi_iff, AddChar.zmod_intCast, norm_mul_sub_norm_div_le_two_mul_min, Complex.sin_sub_sin, Real.surjOn_tan, Real.arcsin_eq_neg_pi_div_two, contMDiffOn_vectorSpace_iff_contDiffOn, HurwitzZeta.hurwitzZetaOdd_one_sub, PairReduction.iSup_edist_pairSet, EuclideanGeometry.Sphere.secondInter_eq_lineMap, Real.sin_sub_int_mul_two_pi, EuclideanSpace.single_eq_zero_iff, HurwitzZeta.hasSum_int_completedSinZeta, Matrix.IsHermitian.mulVec_eigenvectorBasis, Matrix.l2_opNorm_def, Real.fourierInv_eq', OrthogonalFamily.linearIsometry_apply, Matrix.toEuclideanLin_toLp, WeierstrassCurve.b₄_of_isCharTwoJEqZeroNF, HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc, Real.fourierIntegral_deriv, MeasureTheory.Lp.instContinuousFourier, norm_sub_mul_self_real, Polynomial.toAddCircle_C_eq_smul_fourier_zero, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_ofDiameter, add_div_two_lt_right, MeasureTheory.MemLp.eLpNorm_indicator_le', sub_self_div_two, OrthonormalBasis.measurePreserving_measurableEquiv, Complex.sin_add_nat_mul_two_pi, Real.cos_sub_pi_div_two, strictConcaveOn_cos_Icc, Real.ofNat_le_toNNReal, CStarAlgebra.exists_sum_four_unitary, Real.exp_neg_one_lt_half, ZMod.exists_sq_eq_neg_two_iff, norm_mul_sub_norm_div_le_two_mul, AddCircle.homeomorphCircle'_apply, Real.volume_pi_closedBall, EuclideanGeometry.angle_self_left, Complex.exp_mul_I_periodic, Complex.borelCaratheodory_zero, Real.sin_eq_one_iff, ValueDistribution.abs_characteristic_sub_characteristic_shift_le, HurwitzZeta.hasSum_nat_cosKernel₀, Nat.cast_four, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, two_mul_le_add_mul_sq, EuclideanSpace.nndist_single_same, SimpleGraph.Walk.three_le_chromaticNumber_of_odd_loop, inTangentCoordinates_model_space, ProbabilityTheory.Fernique.normThreshold_add_one, Real.Angle.sin_sub_pi_div_two, Real.cos_nat_mul_two_pi, BoundedContinuousFunction.dist_le_two_norm, Real.one_lt_sqrt_two, mul_two, Cardinal.mk_equiv_of_lift_eq, RootPairing.InvariantForm.two_mul_apply_root_root, Circle.exp_sub_two_pi, EuclideanSpace.edist_eq, EuclideanSpace.single_apply, Pi.orthonormalBasis_repr, Complex.cos_eq_cos_iff, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, WeierstrassCurve.c₆_of_isShortNF, Complex.norm_sub_one_sq_eq_of_norm_one, FirstOrder.Ring.card_ring, even_iff_exists_two_mul, add_sq', pow_add_pow_le', MeasureTheory.charFun_eq_pi_iff, Matrix.sub_scalar_sq_eq_discr, WithLp.prod_norm_eq_of_L2, Polynomial.fourierCoeff_toAddCircle, NNRat.cast_le_ofNat, Real.rpowIntegrand₀₁_one_ge_rpow_sub_two, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_right, summable_pow_mul_cexp, Real.sin_add_int_mul_two_pi, HurwitzZeta.sinZeta_one_sub, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, Real.tendsto_prod_pi_div_two, one_half_le_sum_primes_ge_one_div, Real.hasDerivAt_sqrt, IccRightChart_extend_top, SchwartzMap.one_add_le_sup_seminorm_apply, Cardinal.ofNat_eq_ofENat, padicNorm_two_harmonic, half_le_self_iff, Polynomial.Chebyshev.C_neg_two, WeierstrassCurve.Projective.eval_polynomialY, Real.cosh_two_mul, Complex.cpow_two, MeasureTheory.Lp.fourier_toTemperedDistribution_eq, Chebyshev.eventually_primeCounting_le, Field.Emb.cardinal_eq_two_pow_rank, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, boundary_Icc, Real.Gamma_three_div_two_lt_one, Matrix.frobenius_norm_replicateRow, MeasureTheory.charFun_prod, deriv_sqrt_mul_log', summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp, range_two_mul_add_one, Complex.inv_Gammaℝ_two_sub, SchwartzMap.toLp_fourier_eq, IsPrimitiveRoot.norm_sub_one_two, Polynomial.Chebyshev.leadingCoeff_eq_iff_of_forall_abs_le_one, isUnit_two_iff_forall_even, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Chebyshev.psi_le_const_mul_self, Polynomial.Chebyshev.one_sub_X_sq_mul_iterate_derivative_T_eval, Real.fderiv_fourierChar_neg_bilinear_left_apply, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, Complex.Gamma_one_half_eq, WeierstrassCurve.Ψ_odd, Polynomial.Chebyshev.roots_T_real_nodup, RootPairing.forall_pairing_eq_swap_or, Real.cos_pi_div_two_sub, exists_forall_closed_ball_dist_add_le_two_mul_sub, NNReal.dist_gm_am_le, Real.fourier_eq', Stirling.second_wallis_limit, Complex.cos_int_mul_two_pi, Nat.cast_two, DiffeologicalSpace.CorePlotsOn.isPlotOn_univ, Complex.sq_cpow_two_inv, Complex.cos_two_pi, EuclideanSpace.volume_closedBall, Real.sqrt_eq_rpow, Complex.cos_add_int_mul_two_pi, Real.Angle.toReal_eq_neg_pi_div_two_iff, exists_forall_closed_ball_dist_add_le_two_sub, finrank_euclideanSpace_fin, WeierstrassCurve.ofJ1728_Δ, Surreal.nsmul_pow_two_powHalf', fourierCoeffOn_of_hasDeriv_right, Real.two_mul_sin_mul_sin, Real.toNNReal_eq_ofNat, AkraBazziRecurrence.bi_min_div_two_lt_one, CFC.conjugate_rpow_neg_one_half, boundary_product, MeasureTheory.norm_condExpL2_le_one, Complex.arg_I, ProbabilityTheory.HasGaussianLaw.memLp_two, Metric.diam_cthickening_le, Function.Antiperiodic.nat_odd_mul_antiperiodic, OrthonormalBasis.repr_reindex, NNRat.cast_lt_ofNat, MeasureTheory.condExpL2_comp_continuousLinearMap, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, InnerProductSpace.symm_toEuclideanLin_rankOne, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, inCoordinates_tangent_bundle_core_model_space, PeriodPair.derivWeierstrassPExcept_def, Complex.exp_int_mul_two_pi_mul_I, Complex.arg_cos_add_sin_mul_I_eq_toIocMod, EuclideanSpace.coe_measurableEquiv_symm, WeierstrassCurve.Jacobian.eval_polynomialZ, Real.cos_two_mul', irrational_sqrt_two, NNReal.agmSequences_succ, Matrix.conjTranspose_ofNat, RCLike.normSq_sub, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, jacobiSum_one_one, Complex.log_exp_exists, Real.four_mul_arctan_inv_5_sub_arctan_inv_239, Real.sin_eq_two_mul_tan_half_div_one_add_tan_half_sq, fourier_gaussian_pi, le_iff_norm_sqrt_mul_rpow, NNRat.ofNat_lt_cast, MeasureTheory.volume_sum_rpow_lt_one, contMDiff_snd_tangentBundle_modelSpace, MeasureTheory.condExpL2_const_inner, Polynomial.Chebyshev.C_two_mul_real_cos, Complex.dist_conj_self, cantorSequence_get_succ, ZMod.toCircle_eq_circleExp, BoundedContinuousFunction.nndist_le_two_nnnorm, lt_two_mul_self, left_lt_add_div_two, BoundedContinuousFunction.dist_le_two_norm', homothety_one_half, RootPairing.pairingIn_same, Real.deriv_fourier, RootPairing.EmbeddedG2.threeShortAddLongRoot_eq, CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux, ENNReal.inv_two_add_inv_two, MeasureTheory.Lp.instFourierAdd, Real.hasSum_log_sub_log_of_abs_lt_one, contDiff_euclidean, IccLeftChart_extend_bot_mem_frontier, PiLp.nndist_eq_of_L2, WeierstrassCurve.leadingCoeff_Ψ₃, OrthonormalBasis.tensorProduct_repr_tmul_apply, Complex.arg_eq_neg_pi_div_two_iff, EulerSine.integral_cos_mul_cos_pow_even, Quaternion.norm_toLp_equivTuple, Icc_isBoundaryPoint_top, integral_sin_pow_even, bernoulliFun_eval_half, Real.Angle.two_nsmul_toReal_eq_two_mul, RCLike.inner_eq_wInner_one, Real.cos_bound, Real.Angle.sign_coe_neg_pi_div_two, HasStrictDerivAt.sqrt, NumberField.mixedEmbedding.volume_eq_two_pow_mul_volume_plusPart, Behrend.exp_four_lt, niven, hasSum_L_function_mod_four_eval_three, Polynomial.degree_linear_lt, Orientation.abs_oangle_sub_right_toReal_lt_pi_div_two, Cardinal.toNat_eq_ofNat, left_sub_midpoint, fourierIntegral_gaussian_pi', Function.Periodic.exp_decay_sub_of_bounded_at_inf, PiLp.edist_eq_of_L2, midpoint_vsub_midpoint_same_right, quarter_mem_cantorSet, Complex.rank_real_complex, NumberField.IsCMField.regOfFamily_realFunSystem, HilbertBasis.hasSum_repr_symm, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', add_one_le_two_mul, EuclideanGeometry.Sphere.IsDiameter.dist_left_right_div_two, Complex.tan_two_mul, Affine.Triangle.dist_point_centroid, Polynomial.derivative_C_mul_X_sq, HurwitzZeta.hurwitzZetaEven_eq, integral_gaussian_complex_Ioi, summable_geometric_two_encode, Real.log_doublingGamma_eq, MeasureTheory.condExpL2_indicator_nonneg, instIsManifoldIcc, Real.two_mul_sin_mul_cos, invOf_two_add_invOf_two, Ordinal.principal_mul_iff_le_two_or_omega0_opow_opow, deriv_sqrt, EMetric.diam_closedBall, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, hasSum_mellin_pi_mul_sq, Real.arcsin_one, inner_matrix_col_col, Function.Periodic.exp_decay_of_zero_at_inf, deriv2_sqrt_mul_log, LieAlgebra.Orthogonal.pd_inv, ConvexOn.lipschitzOnWith_of_abs_le, jacobiTheta_two_add, contMDiffOn_projIcc, DiffeologicalSpace.isOpen_iff_preimages_plots, left_vsub_midpoint, Real.coe_sinOrderIso_apply, Complex.two_sin, differentiableAt_iteratedDerivWithin_cexp, contMDiff_circleExp, pi_mul_cot_pi_q_exp, Cubic.degree_of_b_ne_zero, CFC.nnrpow_two, Stirling.tendsto_self_div_two_mul_self_add_one, Real.Wallis.le_W, Real.Angle.nsmul_eq_iff, Real.sin_pi_div_four, Complex.cos_sub_int_mul_two_pi, norm_jacobiTheta₂_term_fderiv_le, Complex.tan_eq_one_sub_tan_half_sq_div_one_add_tan_half_sq, Complex.sin_add_pi_div_two, circleEquivGen_apply, Real.posLog_add, GaussianFourier.integral_rexp_neg_mul_sq_norm, Real.sin_sq_pi_over_two_pow_succ, LipschitzWith.dist, WithLp.prod_antilipschitzWith_ofLp, Real.binEntropy_strictMonoOn, Complex.angle_exp_exp, WeierstrassCurve.ofJ1728_c₄, Complex.two_cos, Polynomial.Chebyshev.C_two_mul_real_cosh, Real.volume_emetric_ball, Real.continuousOn_tan_Ioo, add_self_div_two, norm_add_sub_norm_sub_le_two_mul, IsPrimitiveRoot.toInteger_sub_one_not_dvd_two, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, WeierstrassCurve.b₈_of_isCharTwoJNeZeroNF, unitary.continuousOn_argSelfAdjoint, Real.exists_cos_eq_zero, unitary.spectrum_subset_slitPlane_iff_norm_lt_two, CFC.rpow_sqrt, Ordinal.card_eq_ofNat, rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg, ConcaveOn.lipschitzOnWith_of_abs_le, Matrix.discr_fin_two, abs_two, Real.sin_sub_nat_mul_two_pi, one_add_norm_le_sqrt_two_mul_sqrt, hasStrictFDerivAt_euclidean, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq, RootPairing.pairing_neg_two_neg_two_iff, WeierstrassCurve.variableChange_b₄, ModularGroup.coe_truncatedFundamentalDomain

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
nsmul_one 📖	mathematical	—	AddMonoid.toNatSMul AddMonoidWithOne.toAddMonoid AddMonoidWithOne.toOne AddMonoidWithOne.toNatCast	—	zero_nsmul Nat.cast_zero succ_nsmul Nat.cast_add Nat.cast_one
one_add_one_eq_two 📖	mathematical	—	AddSemigroup.toAdd AddMonoid.toAddSemigroup AddMonoidWithOne.toAddMonoid AddMonoidWithOne.toOne instOfNatAtLeastTwo AddMonoidWithOne.toNatCast Nat.instAtLeastTwoHAddOfNat	—	Nat.instAtLeastTwoHAddOfNat Nat.cast_one Nat.cast_add
three_add_one_eq_four 📖	mathematical	—	AddSemigroup.toAdd AddMonoid.toAddSemigroup AddMonoidWithOne.toAddMonoid instOfNatAtLeastTwo AddMonoidWithOne.toNatCast Nat.instAtLeastTwoHAddOfNat AddMonoidWithOne.toOne	—	Nat.instAtLeastTwoHAddOfNat two_add_one_eq_three one_add_one_eq_two Nat.cast_one Nat.cast_add
two_add_one_eq_three 📖	mathematical	—	AddSemigroup.toAdd AddMonoid.toAddSemigroup AddMonoidWithOne.toAddMonoid instOfNatAtLeastTwo AddMonoidWithOne.toNatCast Nat.instAtLeastTwoHAddOfNat AddMonoidWithOne.toOne	—	Nat.instAtLeastTwoHAddOfNat one_add_one_eq_two Nat.cast_one Nat.cast_add
two_add_two_eq_four 📖	mathematical	—	AddSemigroup.toAdd AddMonoid.toAddSemigroup AddMonoidWithOne.toAddMonoid instOfNatAtLeastTwo AddMonoidWithOne.toNatCast Nat.instAtLeastTwoHAddOfNat	—	Nat.instAtLeastTwoHAddOfNat add_assoc

---

← Back to Index