name: leandojo-eval num_files: 729 language: LEAN4 few_shot_data_path_for_retrieval: null few_shot_metadata_filename_for_retrieval: null dfs_data_path_for_retrieval: null dfs_metadata_filename_for_retrieval: local.meta.json theorem_cnt: 1035 datasets: - project: /mathlib4 files: - path: Mathlib/Data/Set/Pointwise/Basic.lean theorems: - Set.div_subset_range - Set.pow_mem_pow - path: Mathlib/Analysis/SpecialFunctions/Pow/Real.lean theorems: - Complex.abs_cpow_eq_rpow_re_of_nonneg - Real.rpow_div_two_eq_sqrt - path: Mathlib/Order/Filter/AtTopBot.lean theorems: - Filter.exists_eventually_atTop - Filter.tendsto_const_mul_atTop_of_pos - path: Mathlib/Algebra/Homology/ShortComplex/RightHomology.lean theorems: - CategoryTheory.ShortComplex.HasRightHomology.hasKernel - path: Mathlib/RingTheory/WittVector/Verschiebung.lean theorems: - WittVector.verschiebungFun_coeff - path: Mathlib/Order/WellFounded.lean theorems: - WellFounded.eq_strictMono_iff_eq_range_aux - path: Mathlib/Algebra/Order/Group/MinMax.lean theorems: - max_one_div_max_inv_one_eq_self - path: Mathlib/Data/List/Intervals.lean theorems: - List.Ico.filter_lt_of_succ_bot - List.Ico.length - path: Mathlib/Data/Seq/Computation.lean theorems: - Computation.results_of_terminates' - path: Mathlib/Probability/ProbabilityMassFunction/Basic.lean theorems: - PMF.toMeasure_injective - path: Mathlib/Analysis/SpecialFunctions/SmoothTransition.lean theorems: - expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul - expNegInvGlue.pos_of_pos - path: Mathlib/SetTheory/Game/PGame.lean theorems: - SetTheory.PGame.add_le_add_right' - SetTheory.PGame.isOption_neg - SetTheory.PGame.moveLeft_neg_symm - SetTheory.PGame.bddAbove_range_of_small - path: Mathlib/Data/List/Range.lean theorems: - List.unzip_enum_eq_prod - List.pairwise_lt_finRange - List.chain'_range_succ - path: Mathlib/LinearAlgebra/CliffordAlgebra/Conjugation.lean theorems: - "CliffordAlgebra.\u03B9_range_map_reverse" - CliffordAlgebra.submodule_comap_pow_reverse - path: Mathlib/Data/Nat/Order/Basic.lean theorems: - Nat.div_eq_self - Nat.add_sub_one_le_mul - path: Mathlib/Topology/Compactness/Compact.lean theorems: - IsCompact.nhdsSet_prod_eq_biSup - IsCompact.union - IsCompact.inter_right - path: .lake/packages/std/Std/Data/List/Lemmas.lean theorems: - List.diff_cons_right - List.length_insert_of_not_mem - List.forall_mem_append - List.map_subset - List.take_take - List.exists_of_replaceF - List.drop_sizeOf_le - List.suffix_of_suffix_length_le - List.append_ne_nil_of_left_ne_nil - List.findIdx?_eq_some_iff - List.erase_of_not_mem - List.drop_eq_nil_iff_le - List.take_eq_take - path: Mathlib/NumberTheory/ADEInequality.lean theorems: - ADEInequality.admissible_of_one_lt_sumInv_aux' - path: Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean theorems: - InnerProductGeometry.norm_div_sin_angle_add_of_inner_eq_zero - EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two - InnerProductGeometry.angle_sub_eq_arccos_of_inner_eq_zero - InnerProductGeometry.norm_div_sin_angle_sub_of_inner_eq_zero - path: Mathlib/FieldTheory/SeparableDegree.lean theorems: - IntermediateField.finSepDegree_bot - path: Mathlib/NumberTheory/FLT/Four.lean theorems: - Fermat42.exists_pos_odd_minimal - path: Mathlib/Data/Matrix/Basis.lean theorems: - Matrix.StdBasisMatrix.mul_of_ne - path: Mathlib/Data/Matrix/Block.lean theorems: - Matrix.toBlock_diagonal_disjoint - path: Mathlib/Data/Polynomial/AlgebraMap.lean theorems: - Polynomial.aeval_apply_smul_mem_of_le_comap' - path: Mathlib/Algebra/Order/Sub/Canonical.lean theorems: - tsub_tsub_eq_add_tsub_of_le - path: Mathlib/Data/Nat/Parity.lean theorems: - Nat.even_add - Odd.ne_two_of_dvd_nat - pow_eq_neg_one_iff - path: Mathlib/ModelTheory/Basic.lean theorems: - FirstOrder.Language.Embedding.coe_injective - path: Mathlib/Topology/Covering.lean theorems: - isCoveringMap_iff_isCoveringMapOn_univ - path: Mathlib/Data/Int/Cast/Lemmas.lean theorems: - Int.cast_nonneg - Int.cast_le_neg_one_of_neg - path: Mathlib/Algebra/Algebra/Subalgebra/Unitization.lean theorems: - NonUnitalSubalgebra.toSubalgebra_toNonUnitalSubalgebra - path: Mathlib/Data/Polynomial/FieldDivision.lean theorems: - Polynomial.mod_eq_self_iff - Polynomial.rootSet_prod - Polynomial.monic_normalize - Polynomial.one_lt_rootMultiplicity_iff_isRoot_iterate_derivative - path: Mathlib/MeasureTheory/Measure/WithDensity.lean theorems: - MeasureTheory.withDensity_eq_zero - MeasureTheory.withDensity_add_measure - MeasureTheory.restrict_withDensity - path: Mathlib/Topology/Algebra/InfiniteSum/Constructions.lean theorems: - HasSum.sigma - path: Mathlib/Data/Set/Lattice.lean theorems: - Set.biUnion_iUnion - Set.iUnion_of_singleton_coe - path: Mathlib/GroupTheory/Perm/Fin.lean theorems: - Fin.cycleRange_apply - path: Mathlib/Data/Set/Basic.lean theorems: - Set.ite_right - Set.ite_compl - path: Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean theorems: - CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_hom - CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_inv - "CategoryTheory.Limits.image.\u03B9_zero'" - "CategoryTheory.Limits.image_\u03B9_comp_eq_zero" - CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_inv - path: Mathlib/Analysis/Seminorm.lean theorems: - Seminorm.smul_inf - Seminorm.bddBelow_range_add - Seminorm.comp_smul - absorbent_ball_zero - path: Mathlib/Analysis/Calculus/FDeriv/Basic.lean theorems: - DifferentiableWithinAt.hasFDerivWithinAt - fderivWithin_zero_of_isolated - HasFDerivWithinAt.lim - path: Mathlib/Data/Complex/ExponentialBounds.lean theorems: - Real.exp_neg_one_gt_d9 - path: Mathlib/SetTheory/Cardinal/Ordinal.lean theorems: - Cardinal.ciSup_mul_ciSup - Cardinal.mk_cardinal - path: Mathlib/Geometry/Euclidean/Circumcenter.lean theorems: - Affine.Simplex.dist_circumcenter_sq_eq_sq_sub_circumradius - path: Mathlib/Order/Filter/Archimedean.lean theorems: - Filter.Tendsto.atBot_zsmul_const - Filter.Tendsto.atTop_mul_const' - Filter.Eventually.int_cast_atBot - path: Mathlib/Data/Polynomial/Eval.lean theorems: - "Polynomial.eval\u2082_monomial" - Polynomial.coeff_comp_degree_mul_degree - Polynomial.eval_ofNat - path: Mathlib/Data/PNat/Factors.lean theorems: - PNat.factorMultiset_gcd - path: Mathlib/MeasureTheory/MeasurableSpace/Defs.lean theorems: - MeasurableSpace.generateFrom_insert_univ - MeasurableSet.univ - path: Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean theorems: - CategoryTheory.Limits.KernelFork.app_one - "CategoryTheory.Limits.CokernelCofork.IsColimit.isIso_\u03C0" - CategoryTheory.Limits.cokernel.map_desc - path: Mathlib/SetTheory/Surreal/Dyadic.lean theorems: - Surreal.dyadicMap_apply_pow' - path: Mathlib/Order/LocallyFinite.lean theorems: - Multiset.mem_Ioo - path: Mathlib/Condensed/Equivalence.lean theorems: - Condensed.StoneanProfinite.coverDense.inducedTopology_Sieve_iff_EffectiveEpiFamily - path: Mathlib/Analysis/NormedSpace/lpSpace.lean theorems: - lp.norm_le_of_tendsto - "Mem\u2113p.infty_mul" - path: Mathlib/GroupTheory/Subgroup/Pointwise.lean theorems: - Subgroup.sup_eq_closure_mul - Subgroup.conj_smul_le_of_le - path: Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean theorems: - SimpleGraph.ComponentCompl.exists_adj_boundary_pair - path: Mathlib/Algebra/Module/Zlattice.lean theorems: - Zspan.repr_floor_apply - path: Mathlib/Analysis/InnerProductSpace/Symmetric.lean theorems: - LinearMap.IsSymmetric.conj_inner_sym - path: Mathlib/Tactic/Abel.lean theorems: - Mathlib.Tactic.Abel.term_add_termg - path: Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean theorems: - PartialHomeomorph.contDiffOn_extend_coord_change - path: Mathlib/Data/Fintype/Basic.lean theorems: - Set.toFinset_image - path: Mathlib/Order/Filter/Basic.lean theorems: - Filter.frequently_and_distrib_left - Filter.iInf_principal_finite - Filter.iSup_join - Filter.sup_join - path: Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean theorems: - Orientation.two_zsmul_oangle_smul_right_of_ne_zero - Orientation.oangle_self - path: Mathlib/Algebra/BigOperators/Intervals.lean theorems: - Finset.prod_Ioc_mul_eq_prod_Icc - path: Mathlib/Topology/Compactification/OnePoint.lean theorems: - OnePoint.ne_infty_iff_exists - OnePoint.continuousAt_infty - OnePoint.inseparable_iff - path: Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean theorems: - UniformOnFun.topologicalSpace_eq - UniformOnFun.tendsto_iff_tendstoUniformlyOn - path: Mathlib/LinearAlgebra/Matrix/Determinant.lean theorems: - Matrix.det_eq_of_forall_col_eq_smul_add_pred - path: Mathlib/Topology/Algebra/Group/Basic.lean theorems: - QuotientGroup.isOpenMap_coe - topologicalGroup_iInf - tendsto_inv_nhdsWithin_Iic - path: Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean theorems: - CategoryTheory.Limits.biprod.mapBiprod_hom_desc - path: Mathlib/Data/Set/Pairwise/Basic.lean theorems: - Set.pairwise_insert - path: Mathlib/Topology/MetricSpace/Perfect.lean theorems: - Perfect.small_diam_aux - path: Mathlib/Topology/PartialHomeomorph.lean theorems: - PartialHomeomorph.subtypeRestr_symm_eqOn - PartialHomeomorph.ofSet_trans' - PartialHomeomorph.IsImage.interior - path: Mathlib/Analysis/InnerProductSpace/Basic.lean theorems: - inner_add_right - Orthonormal.sum_inner_products_le - path: Mathlib/Order/SuccPred/Limit.lean theorems: - Order.mem_range_pred_of_not_isPredLimit - path: Mathlib/Data/Polynomial/Module/Basic.lean theorems: - PolynomialModule.comp_smul - path: Mathlib/Data/Int/Bitwise.lean theorems: - Int.bit_val - Int.testBit_bit_zero - path: Mathlib/Probability/Kernel/Disintegration.lean theorems: - ProbabilityTheory.set_integral_condKernel_univ_right - path: Mathlib/FieldTheory/RatFunc.lean theorems: - RatFunc.num_mul_eq_mul_denom_iff - RatFunc.induction_on - RatFunc.ofFractionRing_sub - path: Mathlib/Data/Finset/Card.lean theorems: - Finset.le_card_of_inj_on_range - path: Mathlib/Topology/Order/LowerUpperTopology.lean theorems: - Topology.IsLower.isClosed_upperClosure - path: Mathlib/Analysis/Calculus/SmoothSeries.lean theorems: - differentiable_tsum - path: Mathlib/GroupTheory/Index.lean theorems: - Subgroup.relindex_self - Subgroup.relindex_bot_right - path: Mathlib/Analysis/Complex/UpperHalfPlane/Metric.lean theorems: - UpperHalfPlane.isometry_pos_mul - path: Mathlib/Data/Polynomial/EraseLead.lean theorems: - Polynomial.eraseLead_C_mul_X_pow - path: Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean theorems: - Asymptotics.isLittleO_pow_pow_atTop_of_lt - path: Mathlib/Data/Finsupp/Basic.lean theorems: - Finsupp.equivMapDomain_trans - path: Mathlib/Order/SupIndep.lean theorems: - Finset.supIndep_univ_bool - CompleteLattice.independent_iff_supIndep_univ - path: Mathlib/RingTheory/PowerBasis.lean theorems: - PowerBasis.natDegree_minpoly - path: Mathlib/CategoryTheory/Subobject/Basic.lean theorems: - CategoryTheory.Subobject.ofMkLEMk_refl - path: Mathlib/Order/SupClosed.lean theorems: - infClosed_empty - path: Mathlib/Algebra/Ring/Hom/Defs.lean theorems: - RingHom.map_ite_one_zero - path: Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean theorems: - InnerProductGeometry.cos_angle_mul_norm_mul_norm - path: Mathlib/MeasureTheory/PiSystem.lean theorems: - generateFrom_piiUnionInter_le - MeasurableSpace.DynkinSystem.ext - path: Mathlib/RingTheory/Localization/InvSubmonoid.lean theorems: - IsLocalization.finiteType_of_monoid_fg - path: Mathlib/Analysis/Calculus/ContDiff/Bounds.lean theorems: - norm_iteratedFDeriv_clm_apply - norm_iteratedFDeriv_clm_apply_const - path: Mathlib/LinearAlgebra/Matrix/Adjugate.lean theorems: - Matrix.adjugate_diagonal - Matrix.adjugate_transpose - path: Mathlib/RingTheory/WittVector/Teichmuller.lean theorems: - WittVector.map_teichmullerFun - path: Mathlib/Geometry/Manifold/Instances/Sphere.lean theorems: - contMDiff_coe_sphere - stereographic_apply_neg - path: Mathlib/CategoryTheory/Abelian/RightDerived.lean theorems: - CategoryTheory.InjectiveResolution.toRightDerivedZero'_comp_iCycles - path: Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean theorems: - MvQPF.wrepr_equiv - path: Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean theorems: - CategoryTheory.Limits.biprod.braid_natural - path: Mathlib/RingTheory/DedekindDomain/Ideal.lean theorems: - FractionalIdeal.coe_ideal_span_singleton_inv_mul - multiplicity_normalizedFactorsEquivSpanNormalizedFactors_eq_multiplicity - Ideal.prime_span_singleton_iff - path: Mathlib/Analysis/Convex/StrictConvexSpace.lean theorems: - combo_mem_ball_of_ne - path: Mathlib/Deprecated/Subgroup.lean theorems: - IsGroupHom.injective_of_trivial_ker - Group.normalClosure_subset - path: Mathlib/LinearAlgebra/Lagrange.lean theorems: - Lagrange.eval_basis_self - Lagrange.eval_nodal_at_node - path: Mathlib/Algebra/Algebra/NonUnitalSubalgebra.lean theorems: - NonUnitalAlgHom.coe_range - path: Mathlib/Data/Fintype/Perm.lean theorems: - mem_perms_of_finset_iff - path: Mathlib/GroupTheory/Subgroup/Basic.lean theorems: - Subgroup.eq_bot_of_subsingleton - Subgroup.Normal.mem_comm - CommGroup.center_eq_top - path: Mathlib/Algebra/Module/LocalizedModule.lean theorems: - IsLocalizedModule.iso_symm_apply_aux - IsLocalizedModule.mk'_sub - path: Mathlib/GroupTheory/Coset.lean theorems: - Subgroup.card_comap_dvd_of_injective - path: Mathlib/Data/Real/NNReal.lean theorems: - NNReal.mul_eq_mul_left - Real.toNNReal_pos - NNReal.sSup_of_not_bddAbove - path: Mathlib/Algebra/Homology/HomotopyCategory/HomComplexShift.lean theorems: - CochainComplex.HomComplex.Cochain.leftUnshift_smul - CochainComplex.HomComplex.Cochain.shift_v' - path: Mathlib/Algebra/EuclideanDomain/Defs.lean theorems: - EuclideanDomain.lt_one - path: Mathlib/Combinatorics/Hall/Basic.lean theorems: - Fintype.all_card_le_filter_rel_iff_exists_injective - path: Mathlib/Analysis/InnerProductSpace/Rayleigh.lean theorems: - IsSelfAdjoint.hasEigenvector_of_isMaxOn - path: Mathlib/Order/Bounds/Basic.lean theorems: - IsGreatest.insert - path: Mathlib/Tactic/Ring/RingNF.lean theorems: - Mathlib.Tactic.RingNF.mul_neg - path: Mathlib/Data/Matrix/Basic.lean theorems: - Matrix.dotProduct_pUnit - Matrix.mulVec_zero - Matrix.mul_neg - path: Mathlib/GroupTheory/Sylow.lean theorems: - IsPGroup.sylow_mem_fixedPoints_iff - path: Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean theorems: - gramSchmidt_orthonormal' - gramSchmidt_triangular - path: Mathlib/Analysis/NormedSpace/OperatorNorm/Basic.lean theorems: - ContinuousLinearMap.le_of_opNorm_le_of_le - path: Mathlib/Algebra/GroupWithZero/Basic.lean theorems: - "mul_eq_right\u2080" - path: Mathlib/Data/Finsupp/Multiset.lean theorems: - Finsupp.toMultiset_sup - path: Mathlib/Data/Polynomial/RingDivision.lean theorems: - Polynomial.roots_C - Polynomial.root_mul - Polynomial.not_dvd_of_natDegree_lt - Polynomial.zero_of_eval_zero - Polynomial.roots_pow - path: Mathlib/CategoryTheory/Limits/Shapes/Images.lean theorems: - CategoryTheory.Limits.image.factorThruImage_preComp - path: Mathlib/MeasureTheory/Integral/IntegrableOn.lean theorems: - MeasureTheory.hasFiniteIntegral_restrict_of_bounded - integrableOn_Ico_iff_integrableOn_Ioo - path: Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean theorems: - Gamma_is_cong_sub - Gamma1_in_Gamma0 - path: Mathlib/Order/Monotone/Odd.lean theorems: - monotone_of_odd_of_monotoneOn_nonneg - path: Mathlib/Data/Nat/Log.lean theorems: - Nat.log_le_clog - path: Mathlib/Data/Set/Sigma.lean theorems: - Set.range_sigmaMk - path: Mathlib/Algebra/Order/Ring/Abs.lean theorems: - abs_lt_of_sq_lt_sq - path: Mathlib/Algebra/Order/Field/Basic.lean theorems: - one_le_one_div - inv_le_one - inv_le_inv - path: Mathlib/MeasureTheory/OuterMeasure/Basic.lean theorems: - MeasureTheory.OuterMeasure.restrict_mono - MeasureTheory.OuterMeasure.sUnion_null_iff - MeasureTheory.OuterMeasure.isCaratheodory_iUnion_lt - MeasureTheory.OuterMeasure.ext_nonempty - MeasureTheory.OuterMeasure.iSup_apply - MeasureTheory.OuterMeasure.union_null - path: Mathlib/Combinatorics/SimpleGraph/Prod.lean theorems: - SimpleGraph.Connected.boxProd - path: Mathlib/Logic/Equiv/PartialEquiv.lean theorems: - PartialEquiv.symm_symm - PartialEquiv.prod_symm - PartialEquiv.IsImage.leftInvOn_piecewise - path: Mathlib/Topology/MetricSpace/IsometricSMul.lean theorems: - nndist_div_left - path: Mathlib/Topology/Category/Profinite/Nobeling.lean theorems: - Profinite.NobelingProof.contained_eq_proj - path: .lake/packages/std/Std/Data/AssocList.lean theorems: - Std.AssocList.length_toList - path: Mathlib/Analysis/Calculus/ContDiff/Basic.lean theorems: - ContinuousLinearEquiv.iteratedFDerivWithin_comp_right - ContDiff.pow - contDiffOn_top_iff_derivWithin - path: Mathlib/InformationTheory/Hamming.lean theorems: - hammingDist_lt_one - path: Mathlib/Data/Nat/Count.lean theorems: - Nat.count_lt_count_succ_iff - path: Mathlib/Analysis/BoundedVariation.lean theorems: - LocallyBoundedVariationOn.ae_differentiableWithinAt - variationOnFromTo.eq_left_iff - path: Mathlib/Data/List/NodupEquivFin.lean theorems: - List.sublist_iff_exists_fin_orderEmbedding_get_eq - path: Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean theorems: - Real.Angle.neg_coe_abs_toReal_of_sign_nonpos - path: Mathlib/Probability/Kernel/MeasurableIntegral.lean theorems: - MeasureTheory.StronglyMeasurable.integral_kernel_prod_left'' - Measurable.lintegral_kernel_prod_right' - path: Mathlib/NumberTheory/Padics/PadicVal.lean theorems: - one_le_padicValNat_of_dvd - path: Mathlib/Topology/Connected/PathConnected.lean theorems: - PathConnectedSpace.exists_path_through_family' - path: Mathlib/Algebra/BigOperators/Finprod.lean theorems: - finprod_mem_insert' - finprod_mem_eq_one_of_infinite - finprod_eq_dif - path: Mathlib/MeasureTheory/Measure/Restrict.lean theorems: - MeasureTheory.Measure.restrict_toMeasurable - MeasureTheory.Measure.restrict_sUnion_congr - path: Mathlib/Topology/LocallyConstant/Basic.lean theorems: - LocallyConstant.piecewise_apply_right - path: Mathlib/CategoryTheory/MorphismProperty.lean theorems: - CategoryTheory.MorphismProperty.RespectsIso.isoClosure_eq - path: Mathlib/Logic/Function/Basic.lean theorems: - Function.surjective_of_right_cancellable_Prop - path: Mathlib/SetTheory/Ordinal/NaturalOps.lean theorems: - Ordinal.nadd_nat - path: Mathlib/MeasureTheory/Integral/Bochner.lean theorems: - MeasureTheory.SimpleFunc.integral_eq_sum_filter - MeasureTheory.integral_undef - MeasureTheory.ae_le_trim_of_stronglyMeasurable - path: Mathlib/MeasureTheory/Function/LpSeminorm/TriangleInequality.lean theorems: - MeasureTheory.LpAddConst_of_one_le - path: Mathlib/NumberTheory/Padics/PadicNumbers.lean theorems: - padicNormE.eq_of_norm_add_lt_right - Padic.valuation_one - PadicSeq.norm_nonarchimedean_aux - Padic.padicNormE_lim_le - path: Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean theorems: - CategoryTheory.tensorLeftHomEquiv_whiskerLeft_comp_evaluation - path: Mathlib/Data/Fin/Basic.lean theorems: - Fin.val_bit1 - Fin.le_pred_iff - Fin.rev_castPred - path: Mathlib/RingTheory/Polynomial/Bernstein.lean theorems: - bernsteinPolynomial.sum_mul_smul - path: Mathlib/Analysis/Convex/Body.lean theorems: - ConvexBody.hausdorffEdist_ne_top - path: Mathlib/Analysis/Matrix.lean theorems: - Matrix.linfty_opNorm_def - path: Mathlib/Algebra/Homology/Single.lean theorems: - "ChainComplex.toSingle\u2080Equiv_symm_apply_f_zero" - path: Mathlib/Data/MvPolynomial/Basic.lean theorems: - MvPolynomial.prod_X_pow_eq_monomial - MvPolynomial.induction_on_monomial - "MvPolynomial.eval_eval\u2082" - path: Mathlib/Analysis/Asymptotics/Asymptotics.lean theorems: - Asymptotics.isLittleO_pow_sub_sub - Asymptotics.isLittleO_insert - path: Mathlib/Analysis/NormedSpace/Pointwise.lean theorems: - cthickening_cthickening - path: Mathlib/LinearAlgebra/BilinearForm/Basic.lean theorems: - BilinForm.flip_flip_aux - path: Mathlib/Topology/MetricSpace/Contracting.lean theorems: - ContractingWith.isFixedPt_fixedPoint_iterate - path: Mathlib/Data/Int/CharZero.lean theorems: - Int.cast_eq_one - path: Mathlib/Topology/IndicatorConstPointwise.lean theorems: - tendsto_indicator_const_apply_iff_eventually - path: Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean theorems: - Polynomial.IsWeaklyEisensteinAt.map - path: Mathlib/Topology/Algebra/Constructions.lean theorems: - Units.topology_eq_inf - path: Mathlib/RingTheory/TensorProduct/Basic.lean theorems: - Algebra.TensorProduct.map_comp_includeLeft - path: Mathlib/Data/QPF/Univariate/Basic.lean theorems: - QPF.Cofix.dest_corec - QPF.Fix.rec_eq - QPF.Fix.ind - path: Mathlib/Algebra/Group/Hom/Defs.lean theorems: - map_comp_div' - path: Mathlib/Topology/Instances/NNReal.lean theorems: - NNReal.summable_nat_add_iff - NNReal.tendsto_tsum_compl_atTop_zero - path: Mathlib/Algebra/GroupPower/Ring.lean theorems: - add_sq - path: Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean theorems: - Measurable.ennreal_tsum - path: Mathlib/Analysis/Convex/Side.lean theorems: - AffineSubspace.sSameSide_vadd_right_iff - AffineSubspace.wOppSide_iff_exists_right - path: Mathlib/Data/NNRat/Lemmas.lean theorems: - Rat.toNNRat_div - Rat.toNNRat_inv - path: Mathlib/Analysis/Normed/Group/Basic.lean theorems: - dist_prod_prod_le_of_le - path: Mathlib/Algebra/Homology/Exact.lean theorems: - CategoryTheory.exact_of_image_eq_kernel - path: Mathlib/CategoryTheory/Preadditive/Generator.lean theorems: - CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda - path: Mathlib/Data/List/Sigma.lean theorems: - List.mem_keys_kinsert - path: Mathlib/Analysis/BoxIntegral/Partition/Split.lean theorems: - BoxIntegral.Box.coe_splitUpper - BoxIntegral.Prepartition.IsPartition.exists_splitMany_le - BoxIntegral.Box.splitLower_eq_self - path: Mathlib/Geometry/Euclidean/Angle/Oriented/RightAngle.lean theorems: - Orientation.tan_oangle_add_right_smul_rotation_pi_div_two - Orientation.oangle_add_right_eq_arccos_of_oangle_eq_pi_div_two - path: Mathlib/MeasureTheory/Integral/Lebesgue.lean theorems: - MeasureTheory.lintegral_iSup - ENNReal.count_const_le_le_of_tsum_le - MeasureTheory.lintegral_lintegral_mul - path: Mathlib/GroupTheory/PushoutI.lean theorems: - Monoid.PushoutI.NormalWord.eq_one_of_smul_normalized - path: Mathlib/Order/LiminfLimsup.lean theorems: - Filter.blimsup_mono - Filter.isCobounded_principal - Filter.limsup_congr - path: Mathlib/Data/Fin/OrderHom.lean theorems: - Fin.predAbove_rev_left - path: Mathlib/Algebra/Algebra/Spectrum.lean theorems: - spectrum.add_mem_add_iff - spectrum.unit_smul_eq_smul - spectrum.map_star - path: Mathlib/Data/Polynomial/Derivative.lean theorems: - Polynomial.derivative_C_mul_X_sq - path: Mathlib/CategoryTheory/Subobject/Comma.lean theorems: - CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unop - path: Mathlib/MeasureTheory/Measure/Dirac.lean theorems: - MeasureTheory.Measure.tsum_indicator_apply_singleton - path: Mathlib/Order/CompactlyGenerated/Basic.lean theorems: - DirectedOn.disjoint_sSup_left - path: Mathlib/Data/Polynomial/Inductions.lean theorems: - Polynomial.divX_X_pow - path: Mathlib/Data/Real/Basic.lean theorems: - Real.cauchy_sub - path: .lake/packages/std/Std/Data/Nat/Gcd.lean theorems: - Nat.Coprime.gcd_mul_left_cancel_right - path: Mathlib/Topology/NoetherianSpace.lean theorems: - TopologicalSpace.NoetherianSpace.exists_finset_irreducible - path: Mathlib/NumberTheory/Dioph.lean theorems: - Dioph.ext - path: Mathlib/LinearAlgebra/Matrix/ToLin.lean theorems: - Matrix.toLin'_mul_apply - path: .lake/packages/std/Std/Data/Nat/Lemmas.lean theorems: - Nat.compare_eq_eq - path: Mathlib/Analysis/Convex/Gauge.lean theorems: - gauge_neg - continuousAt_gauge - path: Mathlib/Data/Multiset/Sum.lean theorems: - Multiset.mem_disjSum - path: Mathlib/Order/ConditionallyCompleteLattice/Basic.lean theorems: - WithTop.iInf_empty - ciSup_unique - path: Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean theorems: - CochainComplex.mappingCone.inr_snd - CochainComplex.mappingCone.inl_v_descCochain_v - path: Mathlib/Data/Set/Intervals/OrdConnected.lean theorems: - OrderEmbedding.image_Ioo - path: Mathlib/Data/Set/Card.lean theorems: - Set.encard_union_le - Set.Nat.encard_range - Set.one_lt_ncard_iff - Set.eq_of_subset_of_ncard_le - path: Mathlib/Data/Part.lean theorems: - Part.bind_some_eq_map - Part.mem_restrict - Part.sdiff_get_eq - Part.bind_none - path: Mathlib/ModelTheory/Types.lean theorems: - FirstOrder.Language.Theory.CompleteType.setOf_subset_eq_univ_iff - path: Mathlib/Data/List/Rotate.lean theorems: - List.rotate'_cons_succ - List.rotate'_length_mul - List.rotate_rotate - path: Mathlib/Analysis/Convex/StoneSeparation.lean theorems: - exists_convex_convex_compl_subset - path: Mathlib/LinearAlgebra/Orientation.lean theorems: - Basis.orientation_unitsSMul - path: Mathlib/GroupTheory/CoprodI.lean theorems: - Monoid.CoprodI.lift_word_prod_nontrivial_of_not_empty - path: Mathlib/Algebra/GCDMonoid/Basic.lean theorems: - gcd_mul_dvd_mul_gcd - path: Mathlib/Data/Nat/Bitwise.lean theorems: - Nat.xor_self - path: Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean theorems: - MeasureTheory.StronglyMeasurable.norm_approxBounded_le - MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae - MeasureTheory.StronglyMeasurable.piecewise - List.aestronglyMeasurable_prod' - path: Mathlib/Algebra/Order/Monoid/Lemmas.lean theorems: - lt_one_of_mul_lt_right - path: Mathlib/Algebra/Order/Monovary.lean theorems: - monovaryOn_iff_mul_rearrangement - path: Mathlib/Order/UpperLower/Basic.lean theorems: - isLowerSet_iff_Iic_subset - UpperSet.codisjoint_coe - path: Mathlib/LinearAlgebra/Vandermonde.lean theorems: - Matrix.det_vandermonde - path: Mathlib/Combinatorics/SimpleGraph/Subgraph.lean theorems: - SimpleGraph.Subgraph.deleteVerts_le - SimpleGraph.Subgraph.coe_degree - path: Mathlib/Algebra/Group/Basic.lean theorems: - div_mul_mul_cancel - path: Mathlib/Analysis/NormedSpace/OperatorNorm/NormedSpace.lean theorems: - LinearIsometry.norm_toContinuousLinearMap_comp - path: Mathlib/Data/Set/Intervals/Group.lean theorems: - Set.pairwise_disjoint_Ioo_add_int_cast - path: .lake/packages/std/Std/Data/RBMap/WF.lean theorems: - Std.RBNode.RedRed.balance2 - path: Mathlib/CategoryTheory/Comma/Presheaf.lean theorems: - "CategoryTheory.OverPresheafAux.MakesOverArrow.map\u2081" - CategoryTheory.OverPresheafAux.counitForward_val_snd - path: Mathlib/Topology/VectorBundle/Basic.lean theorems: - VectorBundleCore.coordChange_linear_comp - path: Mathlib/Topology/NhdsSet.lean theorems: - nhdsSet_diagonal - path: Mathlib/Data/Nat/Pairing.lean theorems: - Nat.unpair_left_le - path: Mathlib/RingTheory/MvPolynomial/Homogeneous.lean theorems: - MvPolynomial.homogeneousComponent_zero - path: Mathlib/Geometry/Manifold/Sheaf/LocallyRingedSpace.lean theorems: - smoothSheafCommRing.isUnit_stalk_iff - path: Mathlib/Topology/Algebra/UniformGroup.lean theorems: - UniformGroup.uniformContinuous_iff_open_ker - path: Mathlib/Algebra/Lie/Killing.lean theorems: - LieAlgebra.IsKilling.ker_restrictBilinear_eq_bot_of_isCartanSubalgebra - path: Mathlib/Geometry/Euclidean/Sphere/Power.lean theorems: - EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi - path: Mathlib/Geometry/Manifold/ChartedSpace.lean theorems: - TopologicalSpace.Opens.chartAt_inclusion_symm_eventuallyEq - path: Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean theorems: - MeasureTheory.integrable_of_intervalIntegral_norm_bounded - path: Mathlib/GroupTheory/Complement.lean theorems: - Subgroup.IsComplement.equiv_snd_eq_iff_rightCosetEquivalence - path: Mathlib/RingTheory/Localization/Basic.lean theorems: - IsLocalization.map_eq_zero_iff - IsLocalization.algebraMap_eq_map_map_submonoid - path: Mathlib/Data/MvPolynomial/Degrees.lean theorems: - MvPolynomial.degrees_rename - MvPolynomial.totalDegree_zero - MvPolynomial.degrees_monomial_eq - path: Mathlib/LinearAlgebra/CliffordAlgebra/Fold.lean theorems: - "CliffordAlgebra.foldl_prod_map_\u03B9" - path: Mathlib/Topology/MetricSpace/Bounded.lean theorems: - Metric.dist_le_diam_of_mem' - path: Mathlib/Analysis/NormedSpace/Banach.lean theorems: - LinearMap.continuous_of_seq_closed_graph - ContinuousLinearMap.range_eq_map_coprodSubtypeLEquivOfIsCompl - path: Mathlib/Data/List/Basic.lean theorems: - List.head_mem - List.getLastI_eq_getLast? - List.get_set_of_ne - List.map_bijective_iff - List.disjoint_map - List.zipWith_flip - path: Mathlib/GroupTheory/FiniteAbelian.lean theorems: - AddCommGroup.equiv_directSum_zmod_of_finite - path: Mathlib/Data/Bool/Count.lean theorems: - List.Chain'.length_div_two_le_count_bool - path: Mathlib/Analysis/SpecialFunctions/Gaussian.lean theorems: - GaussianFourier.integrable_cexp_neg_mul_sq_norm_add - norm_cexp_neg_mul_sq - integrable_mul_cexp_neg_mul_sq - path: Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean theorems: - SimpleGraph.incMatrix_apply_eq_zero_iff - SimpleGraph.incMatrix_apply' - path: Mathlib/NumberTheory/Cyclotomic/CyclotomicCharacter.lean theorems: - ModularCyclotomicCharacter.id - path: Mathlib/Data/Polynomial/Degree/Definitions.lean theorems: - Polynomial.eq_X_add_C_of_degree_eq_one - Polynomial.ne_zero_of_natDegree_gt - Polynomial.degree_linear - path: Mathlib/Analysis/InnerProductSpace/Adjoint.lean theorems: - LinearIsometryEquiv.adjoint_eq_symm - path: Mathlib/Topology/ContinuousFunction/Bounded.lean theorems: - BoundedContinuousFunction.add_norm_nonneg - BoundedContinuousFunction.abs_diff_coe_le_dist - path: Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean theorems: - CategoryTheory.Limits.pullback_symmetry_hom_of_epi_eq - path: Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean theorems: - CircleDeg1Lift.translationNumber_one - CircleDeg1Lift.translationNumber_mul_of_commute - path: Mathlib/Combinatorics/SimpleGraph/Basic.lean theorems: - SimpleGraph.not_mem_neighborSet_self - SimpleGraph.mem_incidence_iff_neighbor - SimpleGraph.disjoint_edgeSet - path: Mathlib/Analysis/Convex/Combination.lean theorems: - Set.Finite.convexHull_eq_image - path: Mathlib/LinearAlgebra/Matrix/Circulant.lean theorems: - Matrix.circulant_mul_comm - path: Mathlib/NumberTheory/Divisors.lean theorems: - Nat.image_div_divisors_eq_divisors - Nat.swap_mem_divisorsAntidiagonal - path: Mathlib/Topology/MetricSpace/Basic.lean theorems: - dist_pos - MetricSpace.replaceUniformity_eq - path: Mathlib/CategoryTheory/Adjunction/AdjointFunctorTheorems.lean theorems: - CategoryTheory.solutionSetCondition_of_isRightAdjoint - path: Mathlib/Topology/UniformSpace/Completion.lean theorems: - CauchyFilter.uniformInducing_pureCauchy - path: Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean theorems: - Set.self_mem_ordConnectedComponent - path: Mathlib/Data/Nat/ModEq.lean theorems: - Nat.add_mod_add_of_le_add_mod - Nat.odd_mod_four_iff - path: Mathlib/Topology/UniformSpace/Equicontinuity.lean theorems: - Filter.HasBasis.uniformEquicontinuousOn_iff_left - path: Mathlib/Algebra/GroupWithZero/NeZero.lean theorems: - inv_mul_cancel - path: Mathlib/Data/Fin/Tuple/Curry.lean theorems: - Function.FromTypes.curry_uncurry - path: Mathlib/Order/JordanHolder.lean theorems: - JordanHolderLattice.second_iso_of_eq - path: Mathlib/Data/Vector/Snoc.lean theorems: - Vector.map_snoc - path: Mathlib/Topology/ContinuousOn.lean theorems: - continuous_mulIndicator - nhdsWithin_pi_eq' - path: Mathlib/NumberTheory/SumPrimeReciprocals.lean theorems: - one_half_le_sum_primes_ge_one_div - path: Mathlib/Data/Polynomial/Basic.lean theorems: - Polynomial.coeff_update_apply - Polynomial.support_monomial - Polynomial.toFinsupp_add - path: Mathlib/Analysis/Calculus/LineDeriv/Basic.lean theorems: - hasLineDerivAt_iff_tendsto_slope_zero - HasLineDerivAt.of_comp - path: Mathlib/Topology/Baire/Lemmas.lean theorems: - "IsG\u03B4.dense_biUnion_interior_of_closed" - "dense_biInter_of_G\u03B4" - path: Mathlib/LinearAlgebra/Span.lean theorems: - Submodule.iSup_eq_span - Submodule.mem_sSup - Submodule.sup_span - path: Mathlib/Algebra/BigOperators/Fin.lean theorems: - Fin.partialProd_succ' - path: Mathlib/CategoryTheory/Abelian/ProjectiveResolution.lean theorems: - CategoryTheory.ProjectiveResolution.iso_inv_naturality - path: Mathlib/Algebra/Order/Ring/Defs.lean theorems: - le_mul_of_le_one_right - one_le_bit1 - path: Mathlib/RingTheory/Valuation/Basic.lean theorems: - Valuation.one_lt_val_iff - Valuation.map_sub_le - path: Mathlib/Order/GaloisConnection.lean theorems: - "GaloisConnection.l_iSup\u2082" - path: Mathlib/GroupTheory/Transfer.lean theorems: - MonoidHom.transferSylow_eq_pow_aux - path: Mathlib/LinearAlgebra/Basis.lean theorems: - Basis.constr_apply - path: Mathlib/Computability/Primrec.lean theorems: - Nat.Primrec.sub - Primrec.bind_decode_iff - Primrec.const - path: Mathlib/Analysis/Subadditive.lean theorems: - Subadditive.apply_mul_add_le - path: Mathlib/RingTheory/UniqueFactorizationDomain.lean theorems: - Associates.map_subtype_coe_factors' - UniqueFactorizationMonoid.multiplicity_eq_count_normalizedFactors - Associates.FactorSet.prod_eq_zero_iff - UniqueFactorizationMonoid.dvdNotUnit_iff_normalizedFactors_lt_normalizedFactors - path: Mathlib/Data/Seq/WSeq.lean theorems: - Stream'.WSeq.LiftRel.refl - path: Mathlib/Combinatorics/Composition.lean theorems: - List.map_length_splitWrtCompositionAux - CompositionAsSet.mem_boundaries_iff_exists_blocks_sum_take_eq - path: Mathlib/Order/WellFoundedSet.lean theorems: - Set.PartiallyWellOrderedOn.wellFoundedOn - path: Mathlib/Analysis/Calculus/FDeriv/Analytic.lean theorems: - ContinuousMultilinearMap.cPolynomialAt - path: Mathlib/LinearAlgebra/BilinearForm/Properties.lean theorems: - BilinForm.dualBasis_dualBasis - path: Mathlib/Data/Set/Defs.lean theorems: - Set.mem_univ_pi - path: Mathlib/Data/Rat/Defs.lean theorems: - Rat.coe_nat_eq_divInt - Rat.zero_add - path: .lake/packages/std/Std/Data/Array/Lemmas.lean theorems: - Array.get?_push_lt - Array.contains_def - path: Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean theorems: - FreeAbelianGroup.support_nsmul - path: Mathlib/LinearAlgebra/CliffordAlgebra/Contraction.lean theorems: - CliffordAlgebra.changeForm_changeForm - CliffordAlgebra.changeForm.associated_neg_proof - path: Mathlib/Data/List/OfFn.lean theorems: - List.last_ofFn - path: Mathlib/Algebra/Ring/Defs.lean theorems: - ite_sub_ite - path: Mathlib/Analysis/Convex/Between.lean theorems: - wbtw_iff_right_eq_or_left_mem_image_Ici - path: Mathlib/Analysis/Convex/Star.lean theorems: - StarConvex.preimage_add_left - path: Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean theorems: - IsCoercive.antilipschitz - IsCoercive.bounded_below - path: Mathlib/Logic/Basic.lean theorems: - xor_false - path: Mathlib/Analysis/Calculus/LHopital.lean theorems: - HasDerivAt.lhopital_zero_atTop_on_Ioi - deriv.lhopital_zero_nhds - path: Mathlib/Data/Polynomial/Reverse.lean theorems: - Polynomial.reverse_neg - Polynomial.reverse_mul - path: Mathlib/Algebra/Homology/HomotopyCofiber.lean theorems: - "HomologicalComplex.cylinder.map_\u03B9\u2080_eq_map_\u03B9\u2081" - path: Mathlib/Probability/Independence/Kernel.lean theorems: - ProbabilityTheory.kernel.iIndep_comap_mem_iff - path: Mathlib/Data/Real/Pointwise.lean theorems: - Real.sSup_smul_of_nonpos - path: Mathlib/Geometry/Euclidean/Angle/Oriented/Rotation.lean theorems: - Orientation.det_rotation - path: Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean theorems: - affineSpan_le_toAffineSubspace_span - vectorSpan_eq_span_vsub_set_left - AffineSubspace.spanPoints_subset_coe_of_subset_coe - path: Mathlib/MeasureTheory/Group/Convolution.lean theorems: - MeasureTheory.Measure.mconv_add - path: Mathlib/Algebra/BigOperators/Basic.lean theorems: - Multiset.prod_sum - path: Mathlib/LinearAlgebra/LinearIndependent.lean theorems: - LinearIndependent.maximal_iff - LinearIndependent.disjoint_span_image - path: Mathlib/RingTheory/Polynomial/GaussLemma.lean theorems: - Polynomial.Monic.irreducible_iff_irreducible_map_fraction_map - path: Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean theorems: - CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd - CategoryTheory.Limits.diagonalObjPullbackFstIso_hom_snd - path: Mathlib/Data/Polynomial/Expand.lean theorems: - Polynomial.contract_expand - Polynomial.natDegree_expand - path: Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean theorems: - TopCat.pullback_fst_image_snd_preimage - path: Mathlib/Data/PFunctor/Univariate/Basic.lean theorems: - PFunctor.liftp_iff' - PFunctor.liftr_iff - path: .lake/packages/std/Std/Data/Int/DivMod.lean theorems: - Int.fdiv_self - path: Mathlib/Data/String/Lemmas.lean theorems: - String.leftpad_suffix - String.leftpad_length - path: Mathlib/RingTheory/MvPowerSeries/Basic.lean theorems: - MvPowerSeries.monomial_mul_monomial - MvPowerSeries.algebraMap_apply - MvPowerSeries.commute_monomial - path: Mathlib/Data/Nat/Size.lean theorems: - Nat.size_pow - path: Mathlib/AlgebraicTopology/DoldKan/Decomposition.lean theorems: - "AlgebraicTopology.DoldKan.MorphComponents.preComp_\u03C6" - path: Mathlib/Data/Finset/Fold.lean theorems: - Finset.fold_image - path: Mathlib/Combinatorics/Partition.lean theorems: - Nat.Partition.partition_one_parts - path: Mathlib/Combinatorics/Derangements/Basic.lean theorems: - derangements.Equiv.RemoveNone.fiber_none - path: Mathlib/Computability/TuringMachine.lean theorems: - Turing.TM2to1.addBottom_modifyNth - "Turing.eval_maximal\u2081" - path: Mathlib/Logic/Equiv/Basic.lean theorems: - Equiv.sumCongr_refl - path: Mathlib/CategoryTheory/Category/Basic.lean theorems: - CategoryTheory.eq_whisker - path: Mathlib/CategoryTheory/EqToHom.lean theorems: - CategoryTheory.eqToIso_map_trans - path: Mathlib/Data/Real/GoldenRatio.lean theorems: - geom_gold_isSol_fibRec - goldConj_neg - path: Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean theorems: - Complex.cos_pi_div_two - Real.sin_lt_sin_of_lt_of_le_pi_div_two - path: Mathlib/MeasureTheory/Measure/EverywherePos.lean theorems: - MeasureTheory.Measure.measure_eq_zero_of_subset_diff_everywherePosSubset - path: Mathlib/GroupTheory/OrderOfElement.lean theorems: - Commute.orderOf_mul_dvd_lcm - isOfFinOrder_iff_zpow_eq_one - orderOf_eq_prime - path: Mathlib/Algebra/Order/Monoid/WithTop.lean theorems: - WithTop.map_add - path: Mathlib/Combinatorics/Additive/SalemSpencer.lean theorems: - MulSalemSpencer.mul_right - path: Mathlib/Probability/ProbabilityMassFunction/Constructions.lean theorems: - PMF.map_comp - path: Mathlib/Data/Polynomial/Coeff.lean theorems: - Polynomial.coeff_mul_C - path: Mathlib/Data/Complex/Exponential.lean theorems: - Real.exp_approx_start - Real.quadratic_le_exp_of_nonneg - Complex.sin_zero - Complex.cos_two_mul - path: Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean theorems: - Path.Homotopy.continuous_transReflReparamAux - path: Mathlib/RingTheory/WittVector/Truncated.lean theorems: - TruncatedWittVector.card - path: Mathlib/Analysis/ODE/Gronwall.lean theorems: - ODE_solution_unique_of_eventually - path: Mathlib/Topology/Connected/Basic.lean theorems: - "PreconnectedSpace.induction\u2082'" - IsPreconnected.prod - IsPreconnected.union' - connectedComponentIn_eq - path: Mathlib/Data/Option/NAry.lean theorems: - "Option.map\u2082_assoc" - "Option.map\u2082_map_left_anticomm" - path: Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean theorems: - Real.surjOn_tan - path: Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean theorems: - NNReal.rpow_neg_one - ENNReal.top_rpow_of_neg - path: Mathlib/Probability/Kernel/Basic.lean theorems: - ProbabilityTheory.kernel.sum_add - ProbabilityTheory.kernel.integral_piecewise - ProbabilityTheory.kernel.integral_deterministic - ProbabilityTheory.kernel.restrict_apply' - path: Mathlib/RingTheory/Ideal/Operations.lean theorems: - Submodule.mem_smul_span - Ideal.IsPrime.multiset_prod_le - path: Mathlib/RingTheory/Etale.lean theorems: - Algebra.FormallyUnramified.localization_map - path: Mathlib/RingTheory/Ideal/QuotientOperations.lean theorems: - Ideal.mem_quotient_iff_mem - Ideal.fst_comp_quotientInfEquivQuotientProd - path: Mathlib/CategoryTheory/EffectiveEpi/Preserves.lean theorems: - CategoryTheory.effectiveEpiFamilyStructOfEquivalence_aux - path: Mathlib/Logic/Relation.lean theorems: - Relation.TransGen.head_induction_on - Relation.map_map - Relation.reflTransGen_eq_reflGen - Relation.ReflTransGen.trans_induction_on - path: Mathlib/RingTheory/Polynomial/Vieta.lean theorems: - MvPolynomial.prod_C_add_X_eq_sum_esymm - path: Mathlib/Algebra/Periodic.lean theorems: - Function.Periodic.const_inv_smul - path: Mathlib/Algebra/Lie/Solvable.lean theorems: - LieAlgebra.derivedSeriesOfIdeal_le - path: Mathlib/Algebra/BigOperators/Module.lean theorems: - Finset.sum_range_by_parts - path: Mathlib/CategoryTheory/Sites/Sheaf.lean theorems: - CategoryTheory.Presheaf.isSheaf_iff_multiequalizer - path: Mathlib/SetTheory/Cardinal/Basic.lean theorems: - Cardinal.one_lt_iff_nontrivial - Cardinal.self_le_power - Cardinal.mk_subset_ge_of_subset_image_lift - path: Mathlib/Topology/Basic.lean theorems: - closure_diff_frontier - interior_eq_empty_iff_dense_compl - path: Mathlib/Data/Finsupp/ToDFinsupp.lean theorems: - finsuppLequivDFinsupp_apply_apply - path: Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean theorems: - one_lt_mul_iff - path: Mathlib/NumberTheory/RamificationInertia.lean theorems: - Ideal.ramificationIdx_lt - path: Mathlib/Analysis/Analytic/Meromorphic.lean theorems: - MeromorphicAt.order_eq_top_iff - path: Mathlib/Algebra/Order/ToIntervalMod.lean theorems: - toIcoMod_sub_zsmul - toIocMod_eq_iff - path: Mathlib/Computability/Language.lean theorems: - Language.mul_self_kstar_comm - path: Mathlib/MeasureTheory/MeasurableSpace/Basic.lean theorems: - MeasurableSpace.comap_compl - MeasurableEmbedding.iff_comap_eq - measurableSet_tendsto - path: Mathlib/Analysis/Convex/GaugeRescale.lean theorems: - image_gaugeRescaleHomeomorph_interior - path: Mathlib/LinearAlgebra/Basis/VectorSpace.lean theorems: - LinearMap.exists_rightInverse_of_surjective - Submodule.exists_le_ker_of_lt_top - path: Mathlib/AlgebraicTopology/DoldKan/PInfty.lean theorems: - AlgebraicTopology.DoldKan.PInfty_comp_QInfty - AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f - AlgebraicTopology.DoldKan.QInfty_idem - path: Mathlib/MeasureTheory/Function/ConditionalExpectation/Basic.lean theorems: - MeasureTheory.condexp_condexp_of_le - path: Mathlib/MeasureTheory/Integral/FundThmCalculus.lean theorems: - intervalIntegral.integral_comp_smul_deriv'' - path: Mathlib/Algebra/ModEq.lean theorems: - AddCommGroup.intCast_modEq_intCast' - path: Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean theorems: - CategoryTheory.Limits.Multiequalizer.hom_ext - path: Mathlib/Analysis/SpecialFunctions/Log/Basic.lean theorems: - Mathlib.Meta.Positivity.log_pos_of_isRat_neg - Real.tendsto_log_atTop - path: Mathlib/Data/QPF/Multivariate/Basic.lean theorems: - MvQPF.liftR_iff - path: Mathlib/Algebra/Homology/HomotopyCategory/DegreewiseSplit.lean theorems: - HomotopyCategory.distinguished_iff_iso_trianglehOfDegreewiseSplit - path: Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean theorems: - midpoint_sub_add - path: Mathlib/LinearAlgebra/Eigenspace/Minpoly.lean theorems: - Module.End.isRoot_of_hasEigenvalue - path: Mathlib/Data/Finmap.lean theorems: - Finmap.mem_singleton - path: Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean theorems: - Real.Gamma_one - Complex.Gamma_ofReal - path: Mathlib/Data/Rat/Floor.lean theorems: - Rat.floor_def' - path: Mathlib/Algebra/Homology/Homotopy.lean theorems: - Homotopy.comp_nullHomotopicMap - path: Mathlib/LinearAlgebra/Matrix/Symmetric.lean theorems: - Matrix.IsSymm.fromBlocks - path: Mathlib/NumberTheory/ModularForms/JacobiTheta/TwoVariable.lean theorems: - "jacobiTheta\u2082_add_left" - path: Mathlib/Data/PFunctor/Univariate/M.lean theorems: - PFunctor.M.cases_mk - path: Mathlib/Geometry/RingedSpace/PresheafedSpace.lean theorems: - AlgebraicGeometry.PresheafedSpace.Hom.ext - path: Mathlib/Topology/Algebra/Order/Compact.lean theorems: - IsCompact.exists_isLeast - path: Mathlib/Topology/UniformSpace/UniformConvergence.lean theorems: - TendstoUniformly.prod_map - path: Mathlib/Data/Set/Pointwise/ListOfFn.lean theorems: - Set.mem_pow - path: Mathlib/RingTheory/Derivation/Basic.lean theorems: - Derivation.eqOn_adjoin - path: Mathlib/RingTheory/FractionalIdeal/Basic.lean theorems: - FractionalIdeal.coeIdeal_mul - path: Mathlib/CategoryTheory/Abelian/LeftDerived.lean theorems: - CategoryTheory.ProjectiveResolution.isoLeftDerivedObj_hom_naturality - path: Mathlib/Combinatorics/Young/YoungDiagram.lean theorems: - YoungDiagram.exists_not_mem_row - path: Mathlib/CategoryTheory/Monoidal/Preadditive.lean theorems: - CategoryTheory.leftDistributor_assoc - path: Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean theorems: - AkraBazziRecurrence.GrowsPolynomially.neg_iff - path: Mathlib/LinearAlgebra/Finsupp.lean theorems: - Finsupp.totalOn_range - path: Mathlib/Data/IsROrC/Basic.lean theorems: - IsROrC.exists_norm_eq_mul_self - IsROrC.div_re - IsROrC.nonneg_iff - IsROrC.conj_smul - IsROrC.one_re - path: Mathlib/Data/Nat/Defs.lean theorems: - Nat.mul_div_cancel_left' - Nat.div_le_div_right - Nat.div_lt_one_iff - path: Mathlib/Order/CompleteBooleanAlgebra.lean theorems: - "disjoint_iSup\u2082_iff" - path: Mathlib/Algebra/CharP/MixedCharZero.lean theorems: - MixedCharZero.reduce_to_maximal_ideal - path: Mathlib/Data/Set/Pointwise/BigOperators.lean theorems: - Set.multiset_prod_subset_multiset_prod - path: Mathlib/Probability/StrongLaw.lean theorems: - ProbabilityTheory.abs_truncation_le_abs_self - path: Mathlib/Combinatorics/SetFamily/LYM.lean theorems: - Finset.mem_falling - path: Mathlib/NumberTheory/Rayleigh.lean theorems: - compl_beattySeq - path: Mathlib/Init/Data/Int/CompLemmas.lean theorems: - Int.natAbs_bit0_step - path: Mathlib/Algebra/Star/StarAlgHom.lean theorems: - NonUnitalStarAlgHom.mk_coe - path: Mathlib/FieldTheory/IsAlgClosed/AlgebraicClosure.lean theorems: - AlgebraicClosure.Step.isIntegral - path: Mathlib/NumberTheory/NumberField/Embeddings.lean theorems: - NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConj - NumberField.InfinitePlace.card_eq_card_isUnramifiedIn - NumberField.InfinitePlace.isReal_of_mk_isReal - NumberField.InfinitePlace.ComplexEmbedding.exists_comp_symm_eq_of_comp_eq - path: Mathlib/Topology/Maps.lean theorems: - OpenEmbedding.open_iff_image_open - path: Mathlib/Topology/Order/Basic.lean theorems: - eventually_abs_sub_lt - path: Mathlib/Data/Finset/Image.lean theorems: - Finset.image_biUnion - path: Mathlib/Topology/Constructions.lean theorems: - continuous_sigma_iff - path: Mathlib/RingTheory/Adjoin/Basic.lean theorems: - Algebra.adjoin_adjoin_coe_preimage - path: Mathlib/CategoryTheory/Groupoid/Subgroupoid.lean theorems: - CategoryTheory.Subgroupoid.generated_le_generatedNormal - path: Mathlib/Combinatorics/SetFamily/AhlswedeZhang.lean theorems: - Finset.sups_aux - Finset.truncatedInf_union - path: Mathlib/Topology/MetricSpace/Thickening.lean theorems: - Metric.ediam_cthickening_le - path: Mathlib/LinearAlgebra/Eigenspace/Basic.lean theorems: - Module.End.iSup_generalizedEigenspace_inf_le_add - Module.End.hasGeneralizedEigenvalue_of_hasEigenvalue - path: Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean theorems: - AlgebraicTopology.alternatingFaceMapComplex_obj_d - path: Mathlib/Topology/Order/MonotoneConvergence.lean theorems: - tendsto_atBot_isLUB - path: Mathlib/Analysis/NormedSpace/Multilinear/Basic.lean theorems: - MultilinearMap.bound_of_shell - path: Mathlib/MeasureTheory/Integral/SetToL1.lean theorems: - MeasureTheory.tendsto_setToFun_of_L1 - path: Mathlib/Data/Matrix/Notation.lean theorems: - Matrix.tail_transpose - path: Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean theorems: - Basis.addHaar_eq_iff - path: Mathlib/Data/Finset/LocallyFinite/Basic.lean theorems: - Finset.Ioc_subset_Ioo_right - Finset.map_add_left_Ioc - Finset.Ioc_insert_left - path: Mathlib/Data/Sign.lean theorems: - SignType.pos_iff - SignType.mul_assoc - abs_mul_sign - SignType.le_trans - path: Mathlib/Data/Real/Sqrt.lean theorems: - Real.sqrt_one_add_le - path: Mathlib/GroupTheory/FixedPointFree.lean theorems: - MonoidHom.FixedPointFree.prod_pow_eq_one - path: Mathlib/CategoryTheory/Whiskering.lean theorems: - CategoryTheory.Functor.pentagon - path: Mathlib/NumberTheory/NumberField/CanonicalEmbedding.lean theorems: - NumberField.canonicalEmbedding.nnnorm_eq - NumberField.mixedEmbedding.finrank - path: Mathlib/Data/Nat/Sqrt.lean theorems: - Nat.sqrt_le_add - Nat.le_three_of_sqrt_eq_one - path: Mathlib/Topology/MetricSpace/Isometry.lean theorems: - IsometryEquiv.ediam_preimage - path: Mathlib/Topology/Homotopy/Contractible.lean theorems: - ContinuousMap.nullhomotopic_of_constant - path: Mathlib/AlgebraicTopology/DoldKan/SplitSimplicialObject.lean theorems: - "SimplicialObject.Splitting.cofan_inj_\u03C0Summand_eq_id" - path: Mathlib/GroupTheory/GroupAction/Hom.lean theorems: - DistribMulActionHom.ext_ring - path: Mathlib/Algebra/MonoidAlgebra/Support.lean theorems: - MonoidAlgebra.mem_span_support - path: Mathlib/SetTheory/Lists.lean theorems: - Lists'.to_ofList - Lists'.ofList_subset - path: Mathlib/Data/Nat/Prime.lean theorems: - Nat.prime_mul_iff - Nat.minFac_le_div - path: Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean theorems: - Euclidean.closure_ball - path: Mathlib/Topology/MetricSpace/PseudoMetric.lean theorems: - edist_le_ofReal - nndist_dist - dist_dist_dist_le_right - Metric.eventually_isCompact_closedBall - path: Mathlib/Tactic/NormNum/OfScientific.lean theorems: - Mathlib.Meta.NormNum.isRat_ofScientific_of_true - path: Mathlib/SetTheory/Ordinal/Arithmetic.lean theorems: - Ordinal.bsup_eq_blsub_iff_succ - Ordinal.IsNormal.blsub_eq - Ordinal.enum_succ_eq_top - Ordinal.sup_typein_succ - path: Mathlib/RingTheory/RootsOfUnity/Complex.lean theorems: - Complex.isPrimitiveRoot_exp - path: Mathlib/Analysis/InnerProductSpace/Projection.lean theorems: - smul_orthogonalProjection_singleton - path: Mathlib/Analysis/ConstantSpeed.lean theorems: - hasConstantSpeedOnWith_of_subsingleton - path: Mathlib/CategoryTheory/Monoidal/Category.lean theorems: - CategoryTheory.MonoidalCategory.comp_tensor_id - CategoryTheory.MonoidalCategory.associator_naturality_right - path: Mathlib/Tactic/NormNum/LegendreSymbol.lean theorems: - "Mathlib.Meta.NormNum.jacobiSymNat.qr\u2083" - path: Mathlib/LinearAlgebra/RootSystem/Basic.lean theorems: - RootPairing.isReduced_iff - path: Mathlib/NumberTheory/ZetaFunction.lean theorems: - riemannZeta_one_sub - path: Mathlib/Analysis/Convex/Normed.lean theorems: - Convex.thickening - path: Mathlib/Algebra/Free.lean theorems: - FreeMagma.length_toFreeSemigroup - path: Mathlib/Algebra/Ring/CentroidHom.lean theorems: - CentroidHom.centroid_eq_centralizer_mulLeftRight - path: Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean theorems: - AffineMap.image_vsub_image - path: Mathlib/Topology/Partial.lean theorems: - pcontinuous_iff' - path: Mathlib/MeasureTheory/Constructions/Cylinders.lean theorems: - MeasureTheory.disjoint_cylinder_iff - path: Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian.lean theorems: - WeierstrassCurve.Jacobian.equation_zero' - WeierstrassCurve.Jacobian.equation_some - path: Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean theorems: - GeneralizedContinuedFraction.IntFractPair.succ_nth_stream_eq_none_iff - path: Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean theorems: - MeasureTheory.ProbabilityMeasure.continuous_map - MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasure - path: Mathlib/LinearAlgebra/Matrix/SchurComplement.lean theorems: - Matrix.det_one_sub_mul_comm - path: Mathlib/Order/Directed.lean theorems: - directedOn_image - path: .lake/packages/std/Std/Data/List/Pairwise.lean theorems: - List.Pairwise.imp_of_mem - path: Mathlib/LinearAlgebra/Matrix/ZPow.lean theorems: - Matrix.pow_inv_comm' - path: Mathlib/Geometry/Manifold/MFDeriv/SpecificFunctions.lean theorems: - mfderiv_sub - path: Mathlib/Data/Multiset/Basic.lean theorems: - Multiset.filter_attach' - Multiset.union_le - Multiset.one_le_count_iff_mem - Multiset.pairwise_coe_iff - Multiset.lt_replicate_succ - path: Mathlib/LinearAlgebra/Matrix/Transvection.lean theorems: - Matrix.transvection_mul_apply_of_ne - path: Mathlib/Geometry/Manifold/ContMDiff/Basic.lean theorems: - contMDiff_inclusion - path: Mathlib/Algebra/GeomSum.lean theorems: - geom_sum_pos' - path: Mathlib/Data/Vector/Basic.lean theorems: - Vector.reverse_get_zero - path: Mathlib/LinearAlgebra/Matrix/PosDef.lean theorems: - Matrix.PosSemidef.one - path: Mathlib/MeasureTheory/Measure/MeasureSpace.lean theorems: - "MeasureTheory.measure_sUnion\u2080" - MeasureTheory.Measure.measure_le_sInf - MeasureTheory.sum_measure_preimage_singleton - path: Mathlib/MeasureTheory/Measure/Hausdorff.lean theorems: - MeasureTheory.Measure.mkMetric_le_liminf_sum - path: Mathlib/MeasureTheory/Measure/GiryMonad.lean theorems: - MeasureTheory.Measure.join_map_join - MeasureTheory.Measure.measurable_of_measurable_coe - path: Mathlib/Data/Nat/Factorial/Cast.lean theorems: - Nat.cast_descFactorial_two - path: Mathlib/MeasureTheory/Measure/Typeclasses.lean theorems: - "MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion\u2080" - path: Mathlib/Data/Nat/Factorial/DoubleFactorial.lean theorems: - Nat.doubleFactorial_two_mul - path: Mathlib/Data/Finset/Basic.lean theorems: - Finset.singleton_inter_of_not_mem - Finset.filter_inter - Finset.erase_insert - path: Mathlib/Geometry/RingedSpace/LocallyRingedSpace/HasColimits.lean theorems: - AlgebraicGeometry.LocallyRingedSpace.HasCoequalizer.imageBasicOpen_image_preimage - path: .lake/packages/std/Std/Data/Rat/Lemmas.lean theorems: - Rat.mkRat_mul_mkRat - Rat.maybeNormalize_eq - path: Mathlib/LinearAlgebra/Determinant.lean theorems: - Basis.det_unitsSMul - path: Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean theorems: - "AlgebraicTopology.DoldKan.h\u03C3'_eq" - path: Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean theorems: - Complex.cpow_neg - path: Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean theorems: - Real.arccos_neg_one - path: Mathlib/GroupTheory/Submonoid/Operations.lean theorems: - Submonoid.mrange_inl_sup_mrange_inr - Submonoid.equivMapOfInjective_coe_mulEquiv - path: Mathlib/Analysis/InnerProductSpace/LinearPMap.lean theorems: - LinearPMap.adjoint_apply_of_not_dense - path: Mathlib/Algebra/Group/Units.lean theorems: - Units.isUnit_units_mul - path: Mathlib/RingTheory/Polynomial/IntegralNormalization.lean theorems: - Polynomial.integralNormalization_support - path: Mathlib/MeasureTheory/Function/LocallyIntegrable.lean theorems: - MeasureTheory.IntegrableOn.continuousOn_mul_of_subset - path: Mathlib/Data/Finset/NAry.lean theorems: - "Finset.image\u2082_left_comm" - path: Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean theorems: - hasFDerivAt_of_restrictScalars - path: Mathlib/Algebra/Order/Chebyshev.lean theorems: - sum_div_card_sq_le_sum_sq_div_card - path: Mathlib/NumberTheory/Padics/RingHoms.lean theorems: - PadicInt.denseRange_int_cast - path: Mathlib/Analysis/Calculus/Deriv/Add.lean theorems: - deriv_sub_const - path: Mathlib/LinearAlgebra/Dual.lean theorems: - TensorProduct.dualDistribInvOfBasis_apply - Subspace.finrank_add_finrank_dualCoannihilator_eq - LinearMap.range_dualMap_le_dualAnnihilator_ker - Submodule.iSup_dualAnnihilator_le_iInf - path: Mathlib/Analysis/NormedSpace/MStructure.lean theorems: - IsLprojection.compl_mul - path: .lake/packages/std/Std/Data/PairingHeap.lean theorems: - Std.PairingHeapImp.Heap.noSibling_merge - path: Mathlib/RingTheory/RootsOfUnity/Basic.lean theorems: - IsPrimitiveRoot.of_map_of_injective - path: Mathlib/Data/Finset/Pointwise.lean theorems: - Finset.preimage_mul_right_one - Finset.op_smul_finset_smul_eq_smul_smul_finset - Finset.inv_smul_mem_iff - path: Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean theorems: - Matrix.Represents.one - path: Mathlib/RingTheory/Noetherian.lean theorems: - isNoetherian_of_fg_of_noetherian - path: Mathlib/Probability/Independence/ZeroOne.lean theorems: - ProbabilityTheory.measure_eq_zero_or_one_of_indepSet_self - ProbabilityTheory.kernel.measure_eq_zero_or_one_of_indepSet_self - path: Mathlib/AlgebraicGeometry/ProjectiveSpectrum/StructureSheaf.lean theorems: - AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf.SectionSubring.addMem' - path: Mathlib/Topology/Homeomorph.lean theorems: - Homeomorph.symm_map_nhds_eq - path: Mathlib/ModelTheory/Substructures.lean theorems: - FirstOrder.Language.Substructure.comap_id - path: Mathlib/Topology/AlexandrovDiscrete.lean theorems: - isOpen_iff_forall_specializes - path: Mathlib/CategoryTheory/Products/Bifunctor.lean theorems: - CategoryTheory.Bifunctor.diagonal' - path: Mathlib/Data/Nat/Digits.lean theorems: - Nat.toDigitsCore_lens_eq - path: Mathlib/Combinatorics/SimpleGraph/Connectivity.lean theorems: - SimpleGraph.Walk.edges_copy - SimpleGraph.Walk.support_concat - path: Mathlib/RingTheory/Polynomial/Dickson.lean theorems: - Polynomial.map_dickson - path: Mathlib/ModelTheory/Semantics.lean theorems: - FirstOrder.Language.BoundedFormula.realize_toPrenex - path: Mathlib/Analysis/SpecificLimits/Normed.lean theorems: - isLittleO_pow_const_mul_const_pow_const_pow_of_norm_lt - path: Mathlib/Analysis/Normed/Group/Pointwise.lean theorems: - singleton_div_closedBall - path: Mathlib/Analysis/MeanInequalitiesPow.lean theorems: - ENNReal.rpow_add_rpow_le_add - path: Mathlib/Computability/TMToPartrec.lean theorems: - Turing.PartrecToTM2.codeSupp_case - Turing.PartrecToTM2.trNormal_supports - Turing.PartrecToTM2.K'.elim_update_main - Turing.PartrecToTM2.trNormal_respects - path: Mathlib/RingTheory/Coprime/Basic.lean theorems: - IsCoprime.of_mul_right_right - path: Mathlib/Data/Sym/Basic.lean theorems: - Sym.map_id' - path: Mathlib/Geometry/Manifold/LocalDiffeomorph.lean theorems: - IsLocalDiffeomorphAt.contMDiffAt - path: Mathlib/MeasureTheory/Function/LpSeminorm/CompareExp.lean theorems: - MeasureTheory.snorm_le_snorm_mul_snorm_of_nnnorm - path: Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean theorems: - MeasureTheory.Measure.inv_rnDeriv_aux - path: Mathlib/Order/CompleteLattice.lean theorems: - iSup_split_single - path: Mathlib/Topology/UniformSpace/Basic.lean theorems: - uniformity_lift_le_swap - UniformSpace.toTopologicalSpace_iInf - Disjoint.exists_uniform_thickening - path: Mathlib/Data/Nat/Interval.lean theorems: - Nat.Ico_insert_succ_left - path: Mathlib/Algebra/Order/Rearrangement.lean theorems: - Monovary.sum_smul_comp_perm_eq_sum_smul_iff - path: Mathlib/Data/List/AList.lean theorems: - AList.lookup_insert - path: Mathlib/LinearAlgebra/SesquilinearForm.lean theorems: - LinearMap.IsRefl.nondegenerate_of_separatingRight - path: Mathlib/NumberTheory/DiophantineApproximation.lean theorems: - Real.exists_rat_eq_convergent - path: Mathlib/RingTheory/Jacobson.lean theorems: - Ideal.Polynomial.jacobson_bot_of_integral_localization - path: Mathlib/Data/Vector3.lean theorems: - Vector3.append_left - path: Mathlib/Topology/Homotopy/Product.lean theorems: - Path.Homotopic.comp_pi_eq_pi_comp - path: Mathlib/AlgebraicGeometry/Gluing.lean theorems: - "AlgebraicGeometry.Scheme.GlueData.\u03B9_isoCarrier_inv" - path: Mathlib/Algebra/Homology/ShortComplex/ConcreteCategory.lean theorems: - CategoryTheory.Preadditive.epi_iff_surjective' - path: Mathlib/Data/Polynomial/Splits.lean theorems: - Polynomial.splits_of_splits_mul' - path: Mathlib/Data/ENNReal/Real.lean theorems: - ENNReal.ofReal_sub - ENNReal.mul_iInf - path: Mathlib/Order/BooleanAlgebra.lean theorems: - inf_sdiff_eq_bot_iff - path: Mathlib/Data/List/Zip.lean theorems: - List.revzip_map_fst - List.map_prod_right_eq_zip - path: Mathlib/Analysis/Normed/Group/Hom.lean theorems: - NormedAddGroupHom.mem_ker - path: Mathlib/RingTheory/NonUnitalSubring/Basic.lean theorems: - "NonUnitalSubring.closure_induction\u2082" - path: Mathlib/MeasureTheory/Group/Measure.lean theorems: - MeasureTheory.Measure.isHaarMeasure_map - path: Mathlib/CategoryTheory/Pi/Basic.lean theorems: - CategoryTheory.isIso_pi_iff - path: Mathlib/Logic/Equiv/List.lean theorems: - Denumerable.list_ofNat_succ - path: Mathlib/AlgebraicGeometry/Morphisms/FiniteType.lean theorems: - AlgebraicGeometry.locallyOfFiniteType_eq - path: Mathlib/MeasureTheory/Covering/Vitali.lean theorems: - Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall - path: Mathlib/CategoryTheory/Abelian/FunctorCategory.lean theorems: - CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app' - path: Mathlib/CategoryTheory/Preadditive/OfBiproducts.lean theorems: - CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_leftAdd - path: Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean theorems: - Complex.abs_mul_cos_add_sin_mul_I - path: Mathlib/RingTheory/Localization/Module.lean theorems: - LinearIndependent.of_isLocalizedModule - path: Mathlib/Data/Real/EReal.lean theorems: - EReal.exists_between_coe_real - EReal.sub_lt_sub_of_lt_of_le - path: Mathlib/Topology/Gluing.lean theorems: - "TopCat.GlueData.eqvGen_of_\u03C0_eq" - path: Mathlib/MeasureTheory/Measure/Sub.lean theorems: - MeasureTheory.Measure.sub_apply - path: Mathlib/MeasureTheory/Covering/VitaliFamily.lean theorems: - VitaliFamily.mem_filterAt_iff - path: Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean theorems: - Matrix.nondegenerate_of_det_ne_zero - path: Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean theorems: - MulChar.pow_apply' - path: Mathlib/Order/ModularLattice.lean theorems: - wellFounded_lt_exact_sequence - path: Mathlib/Data/Sym/Sym2.lean theorems: - Sym2.other_spec - path: Mathlib/RingTheory/DedekindDomain/Different.lean theorems: - Submodule.le_traceDual - aeval_derivative_mem_differentIdeal - path: Mathlib/Analysis/NormedSpace/CompactOperator.lean theorems: - IsCompactOperator.continuous - path: Mathlib/Algebra/Order/CompleteField.lean theorems: - LinearOrderedField.cutMap_bddAbove - path: Mathlib/Analysis/Convolution.lean theorems: - BddAbove.continuous_convolution_left_of_integrable - HasCompactSupport.convolution_integrand_bound_left - path: Mathlib/MeasureTheory/Measure/Stieltjes.lean theorems: - StieltjesFunction.measure_Ioo - path: Mathlib/Topology/Algebra/InfiniteSum/Basic.lean theorems: - Set.Finite.summable - path: Mathlib/Order/Filter/Cofinite.lean theorems: - "Filter.coprod\u1D62_cofinite" - path: Mathlib/CategoryTheory/Monoidal/End.lean theorems: - "CategoryTheory.\u03BC_inv_naturality\u2097" - path: Mathlib/Probability/Kernel/MeasureCompProd.lean theorems: - MeasureTheory.Measure.dirac_compProd_apply - path: Mathlib/Data/List/Sublists.lean theorems: - List.sublists'_eq_sublists - path: Mathlib/Algebra/Divisibility/Units.lean theorems: - isRelPrime_mul_unit_right_right - path: Mathlib/Data/Int/Units.lean theorems: - Int.isUnit_iff - path: Mathlib/Data/Num/Lemmas.lean theorems: - PosNum.to_nat_inj - path: Mathlib/RingTheory/PrincipalIdealDomain.lean theorems: - gcd_isUnit_iff - path: Mathlib/GroupTheory/Perm/Cycle/Type.lean theorems: - Equiv.Perm.cycleType_eq - path: Mathlib/Data/Int/Parity.lean theorems: - Int.add_one_ediv_two_mul_two_of_odd - Int.ne_of_odd_add - path: Mathlib/Combinatorics/Additive/Behrend.lean theorems: - Behrend.map_succ - path: Mathlib/Data/Set/Intervals/Monoid.lean theorems: - Set.image_const_add_Ioi - path: Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL2.lean theorems: - MeasureTheory.snorm_condexpL2_le - path: Mathlib/LinearAlgebra/AffineSpace/Combination.lean theorems: - Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one - path: Mathlib/Data/Nat/Choose/Basic.lean theorems: - Nat.choose_one_right - path: Mathlib/Order/Disjoint.lean theorems: - Disjoint.left_le_of_le_sup_left - path: Mathlib/Algebra/Category/Ring/Constructions.lean theorems: - CommRingCat.pushoutCocone_inl - path: Mathlib/Data/List/Indexes.lean theorems: - List.foldlIdx_eq_foldlIdxSpec - path: Mathlib/Analysis/InnerProductSpace/Orientation.lean theorems: - Orientation.abs_volumeForm_apply_of_pairwise_orthogonal - path: Mathlib/GroupTheory/GroupAction/Basic.lean theorems: - MulAction.disjoint_image_image_iff - path: Mathlib/Analysis/LocallyConvex/WithSeminorms.lean theorems: - WithSeminorms.partial_sups - path: Mathlib/Algebra/GroupPower/Order.lean theorems: - zero_pow_le_one - path: Mathlib/Data/Ordmap/Ordset.lean theorems: - Ordnode.balanceL_eq_balance - Ordnode.Raised.add_left - path: Mathlib/Data/List/Nodup.lean theorems: - List.Nodup.erase_get - path: Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean theorems: - integrableOn_exp_Iic - path: Mathlib/Analysis/Calculus/InverseFunctionTheorem/ApproximatesLinearOn.lean theorems: - ApproximatesLinearOn.open_image - path: Mathlib/RingTheory/Polynomial/Basic.lean theorems: - MvPolynomial.prime_rename_iff - path: Mathlib/Topology/Order/NhdsSet.lean theorems: - nhdsSet_Ici - path: Mathlib/NumberTheory/Multiplicity.lean theorems: - padicValNat.pow_add_pow - path: Mathlib/Analysis/Calculus/Deriv/Basic.lean theorems: - DifferentiableAt.derivWithin - path: Mathlib/RingTheory/RootsOfUnity/Minpoly.lean theorems: - IsPrimitiveRoot.minpoly_eq_pow_coprime - path: Mathlib/Data/List/MinMax.lean theorems: - List.getElem_le_maximum_of_length_pos - path: Mathlib/Analysis/Calculus/ContDiff/Defs.lean theorems: - iteratedFDerivWithin_succ_apply_right - contDiffWithinAt_succ_iff_hasFDerivWithinAt' - path: Mathlib/SetTheory/Cardinal/Cofinality.lean theorems: - Cardinal.nfpBFamily_lt_ord_of_isRegular - path: Mathlib/Geometry/Manifold/MFDeriv/Basic.lean theorems: - mfderiv_comp_of_eq - path: Mathlib/Algebra/Quaternion.lean theorems: - Quaternion.self_mul_star - path: Mathlib/Logic/Denumerable.lean theorems: - Nat.Subtype.ofNat_surjective_aux - path: Mathlib/LinearAlgebra/QuadraticForm/TensorProduct.lean theorems: - QuadraticForm.associated_baseChange - path: Mathlib/Init/Data/Nat/Bitwise.lean theorems: - Nat.bodd_add - path: Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean theorems: - hasDerivAt_sqrt_mul_log - path: Mathlib/RingTheory/PowerSeries/Order.lean theorems: - PowerSeries.coeff_of_lt_order - path: Mathlib/MeasureTheory/Function/LpSpace.lean theorems: - MeasureTheory.Lp.dist_def - path: Mathlib/Geometry/Manifold/VectorBundle/Basic.lean theorems: - Bundle.contMDiffAt_totalSpace - path: Mathlib/RepresentationTheory/Rep.lean theorems: - Rep.ihom_ev_app_hom - path: Mathlib/Data/Int/GCD.lean theorems: - Int.ne_zero_of_gcd - path: Mathlib/CategoryTheory/Yoneda.lean theorems: - CategoryTheory.isIso_of_yoneda_map_bijective - path: Mathlib/CategoryTheory/Shift/Pullback.lean theorems: - CategoryTheory.pullbackShiftFunctorZero_hom_app - path: Mathlib/Computability/PartrecCode.lean theorems: - Nat.Partrec.Code.eval_prec_zero - path: Mathlib/Algebra/Homology/ShortComplex/LeftHomology.lean theorems: - CategoryTheory.ShortComplex.LeftHomologyMapData.cyclesMap_eq - CategoryTheory.ShortComplex.f'_cyclesMap' - path: Mathlib/RingTheory/WittVector/Identities.lean theorems: - WittVector.coeff_p_pow_eq_zero - path: Mathlib/Topology/Instances/ENNReal.lean theorems: - ENNReal.tendsto_nhds_top_iff_nnreal - path: Mathlib/Computability/Halting.lean theorems: - ComputablePred.computable_iff_re_compl_re - path: Mathlib/Data/Fin/Tuple/Basic.lean theorems: - Fin.snoc_init_self - Fin.snoc_zero - path: Mathlib/AlgebraicGeometry/GammaSpecAdjunction.lean theorems: - "AlgebraicGeometry.\u0393Spec.right_triangle" - path: Mathlib/GroupTheory/Perm/Cycle/Basic.lean theorems: - Equiv.Perm.isCycleOn_singleton - path: Mathlib/RingTheory/Ideal/LocalRing.lean theorems: - LocalRing.isLocalRingHom_residue - path: Mathlib/Data/PFunctor/Multivariate/Basic.lean theorems: - MvPFunctor.comp.get_mk - path: .lake/packages/std/Std/Data/Array/Monadic.lean theorems: - Array.SatisfiesM_anyM - path: Mathlib/CategoryTheory/SmallObject/Construction.lean theorems: - "CategoryTheory.SmallObject.\u03B9FunctorObj_\u03C0FunctorObj" - path: Mathlib/GroupTheory/Subsemigroup/Center.lean theorems: - Set.neg_mem_center - path: Mathlib/Topology/Category/TopCat/Opens.lean theorems: - TopologicalSpace.Opens.map_eq - path: Mathlib/Data/Set/Prod.lean theorems: - Set.univ_prod_univ - path: Mathlib/LinearAlgebra/Semisimple.lean theorems: - Module.End.isSemisimple_neg - path: Mathlib/SetTheory/Ordinal/Exponential.lean theorems: - Ordinal.log_opow_mul_add - path: Mathlib/Topology/MetricSpace/Lipschitz.lean theorems: - LipschitzWith.dist - path: Mathlib/RingTheory/FractionalIdeal/Operations.lean theorems: - FractionalIdeal.spanSingleton_eq_spanSingleton - path: Mathlib/LinearAlgebra/PiTensorProduct.lean theorems: - PiTensorProduct.induction_on' - path: Mathlib/Data/DFinsupp/Basic.lean theorems: - DFinsupp.extendWith_zero - path: Mathlib/Deprecated/Submonoid.lean theorems: - Submonoid.isSubmonoid - path: Mathlib/LinearAlgebra/LinearPMap.lean theorems: - LinearPMap.mem_graph_snd_inj - path: Mathlib/Topology/Algebra/GroupCompletion.lean theorems: - AddMonoidHom.completion_add - path: Mathlib/Topology/Compactness/LocallyCompact.lean theorems: - exists_mem_nhdsSet_isCompact_mapsTo - path: Mathlib/Algebra/Lie/IdealOperations.lean theorems: - LieSubmodule.lie_sup - path: Mathlib/CategoryTheory/Limits/MonoCoprod.lean theorems: - CategoryTheory.Limits.MonoCoprod.monoCoprod_of_preservesCoprod_of_reflectsMono - path: Mathlib/Topology/Algebra/Ring/Ideal.lean theorems: - QuotientRing.quotientMap_coe_coe - path: Mathlib/LinearAlgebra/AffineSpace/Ordered.lean theorems: - left_lt_lineMap_iff_lt - path: Mathlib/Analysis/MellinInversion.lean theorems: - rexp_neg_image_aux - path: Mathlib/Algebra/Lie/Nilpotent.lean theorems: - LieSubmodule.lowerCentralSeries_eq_lcs_comap - LieModule.isTrivial_of_nilpotencyLength_le_one - path: Mathlib/LinearAlgebra/Prod.lean theorems: - Submodule.prod_comap_inl - LinearMap.tailing_sup_tunnel_succ_le_tunnel - path: Mathlib/FieldTheory/Adjoin.lean theorems: - IntermediateField.adjoin_simple_toSubalgebra_of_integral - path: Mathlib/Analysis/Convex/Strict.lean theorems: - DirectedOn.strictConvex_sUnion - path: Mathlib/Data/List/BigOperators/Basic.lean theorems: - List.prod_drop_succ - path: Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean theorems: - ProjectiveSpectrum.vanishingIdeal_iUnion - path: Mathlib/Data/Multiset/Powerset.lean theorems: - Multiset.powersetCard_zero_left - path: Mathlib/Algebra/Ring/BooleanRing.lean theorems: - ofBoolAlg_symmDiff - path: Mathlib/MeasureTheory/Measure/VectorMeasure.lean theorems: - MeasureTheory.VectorMeasure.nonpos_of_restrict_le_zero - path: Mathlib/Analysis/Convex/Segment.lean theorems: - openSegment_eq_Ioo' - path: Mathlib/Control/Fold.lean theorems: - Traversable.toList_spec - path: Mathlib/Analysis/SpecialFunctions/Log/Base.lean theorems: - Real.logb_inv - path: Mathlib/FieldTheory/Finite/Basic.lean theorems: - ZMod.pow_card_sub_one_eq_one - path: Mathlib/Probability/Martingale/Upcrossing.lean theorems: - MeasureTheory.upperCrossingTime_le - path: Mathlib/Topology/Separation.lean theorems: - Filter.coclosedCompact_eq_cocompact - path: Mathlib/AlgebraicTopology/FundamentalGroupoid/InducedMaps.lean theorems: - ContinuousMap.Homotopy.apply_zero_path - path: Mathlib/Order/OmegaCompletePartialOrder.lean theorems: - OmegaCompletePartialOrder.ContinuousHom.map_continuous' - path: Mathlib/LinearAlgebra/TensorProduct/RightExactness.lean theorems: - Algebra.TensorProduct.rTensor_ker - path: Mathlib/Init/Data/Bool/Lemmas.lean theorems: - Bool.and_eq_false_eq_eq_false_or_eq_false - path: Mathlib/Order/Filter/NAry.lean theorems: - "Filter.map_map\u2082" - path: Mathlib/LinearAlgebra/Matrix/BilinearForm.lean theorems: - Matrix.toBilin_comp - path: Mathlib/Order/InitialSeg.lean theorems: - InitialSeg.acc - path: Mathlib/Analysis/Calculus/TangentCone.lean theorems: - uniqueDiffWithinAt_of_mem_nhds - path: Mathlib/Algebra/Star/Subalgebra.lean theorems: - StarSubalgebra.sInf_toSubalgebra - path: Mathlib/MeasureTheory/Decomposition/Lebesgue.lean theorems: - MeasureTheory.Measure.rnDeriv_smul_left' - path: Mathlib/Data/Finsupp/Defs.lean theorems: - Finsupp.support_single_disjoint - Finsupp.erase_single_ne - path: Mathlib/LinearAlgebra/AffineSpace/Basis.lean theorems: - AffineBasis.affineCombination_coord_eq_self - path: Mathlib/Order/CompleteLatticeIntervals.lean theorems: - Set.Iic.coe_iInf - path: Mathlib/Algebra/Order/Group/PosPart.lean theorems: - leOnePart_one - path: Mathlib/Algebra/Homology/ShortComplex/HomologicalComplex.lean theorems: - HomologicalComplex.d_pOpcycles - path: Mathlib/RingTheory/ClassGroup.lean theorems: - ClassGroup.mk_eq_one_of_coe_ideal - path: Mathlib/Analysis/InnerProductSpace/PiL2.lean theorems: - OrthonormalBasis.sum_repr_symm - path: Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean theorems: - "Wbtw.oangle\u2083\u2081\u2082_eq_zero" - path: Mathlib/Order/Heyting/Basic.lean theorems: - Disjoint.sup_sdiff_cancel_left - sup_sdiff_distrib - path: Mathlib/Algebra/Lie/Matrix.lean theorems: - Matrix.lieConj_symm_apply - path: Mathlib/RingTheory/Discriminant.lean theorems: - Algebra.discr_of_matrix_mulVec - path: Mathlib/Probability/Kernel/Condexp.lean theorems: - MeasureTheory.AEStronglyMeasurable.comp_snd_map_prod_id - path: Mathlib/Data/ENNReal/Inv.lean theorems: - ENNReal.mul_lt_of_lt_div - path: Mathlib/Algebra/Homology/HomotopyCategory/HomComplex.lean theorems: - CochainComplex.HomComplex.Cochain.ofHom_injective - path: Mathlib/RingTheory/Localization/Away/Basic.lean theorems: - selfZPow_pow_sub - path: Mathlib/Order/Hom/Lattice.lean theorems: - LatticeHom.withTopWithBot_id - path: Mathlib/RingTheory/JacobsonIdeal.lean theorems: - Ideal.exists_mul_sub_mem_of_sub_one_mem_jacobson - path: Mathlib/Data/Nat/GCD/Basic.lean theorems: - Nat.gcd_add_self_right - path: .lake/packages/std/Std/Data/String/Lemmas.lean theorems: - String.Iterator.forward_eq_nextn - path: Mathlib/Algebra/Order/Ring/Lemmas.lean theorems: - mul_eq_mul_iff_eq_and_eq_of_pos' - path: Mathlib/Data/List/Perm.lean theorems: - List.length_permutations'Aux - path: Mathlib/RingTheory/FreeCommRing.lean theorems: - FreeCommRing.isSupported_of - path: Mathlib/Data/ZMod/Basic.lean theorems: - ZMod.nontrivial_iff - ZMod.nat_cast_self' - path: Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean theorems: - ModuleCat.MonoidalCategory.associator_naturality - path: Mathlib/Data/Set/Intervals/WithBotTop.lean theorems: - WithTop.preimage_coe_Ioc - WithTop.preimage_coe_Iio_top - path: Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean theorems: - CliffordAlgebra.induction - path: Mathlib/Order/Filter/Lift.lean theorems: - Filter.lift_iInf_of_map_univ - path: Mathlib/Topology/UrysohnsBounded.lean theorems: - exists_bounded_mem_Icc_of_closed_of_le - path: Mathlib/NumberTheory/Zsqrtd/GaussianInt.lean theorems: - GaussianInt.toComplex_re - path: Mathlib/Algebra/GroupPower/Basic.lean theorems: - pow_bit0' - path: Mathlib/Algebra/Lie/Submodule.lean theorems: - LieSubmodule.iInf_coe - path: Mathlib/RingTheory/ChainOfDivisors.lean theorems: - coe_factor_orderIso_map_eq_one_iff - path: Mathlib/MeasureTheory/Decomposition/Jordan.lean theorems: - MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iff - path: Mathlib/Analysis/Complex/Liouville.lean theorems: - Complex.liouville_theorem_aux - path: Mathlib/Analysis/InnerProductSpace/Positive.lean theorems: - ContinuousLinearMap.isPositive_zero - path: Mathlib/Data/Set/Image.lean theorems: - Set.range_subtype_map - path: Mathlib/Combinatorics/Additive/ETransform.lean theorems: - Finset.MulETransform.card - path: Mathlib/Algebra/GroupWithZero/Units/Basic.lean theorems: - Units.mk0_one - path: Mathlib/AlgebraicTopology/DoldKan/Degeneracies.lean theorems: - "AlgebraicTopology.DoldKan.\u03C3_comp_PInfty" - path: Mathlib/Algebra/Order/Sub/Defs.lean theorems: - AddLECancellable.lt_add_of_tsub_lt_right - path: Mathlib/Topology/Category/TopCat/Limits/Products.lean theorems: - TopCat.prodIsoProd_hom_apply - path: Mathlib/RingTheory/IntegralDomain.lean theorems: - sum_hom_units_eq_zero - path: Mathlib/Algebra/Order/Group/Defs.lean theorems: - div_le_div_iff_right - path: Mathlib/Computability/Partrec.lean theorems: - Nat.rfindOpt_mono - path: Mathlib/RingTheory/Subsemiring/Basic.lean theorems: - Subsemiring.mem_sSup_of_directedOn - path: Mathlib/NumberTheory/LegendreSymbol/QuadraticChar/Basic.lean theorems: - quadraticChar_eq_pow_of_char_ne_two' - path: Mathlib/Probability/IdentDistrib.lean theorems: - ProbabilityTheory.IdentDistrib.ae_snd - path: Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus.lean theorems: - elementalStarAlgebra.isUnit_of_isUnit_of_isStarNormal - path: Mathlib/Topology/MetricSpace/Infsep.lean theorems: - Set.infsep_pair_le_toReal_inf - path: Mathlib/RingTheory/WittVector/Basic.lean theorems: - WittVector.ghostFun_sub - path: Mathlib/Data/Nat/Choose/Multinomial.lean theorems: - Nat.multinomial_nil - path: Mathlib/RingTheory/Filtration.lean theorems: - Ideal.isIdempotentElem_iff_eq_bot_or_top_of_localRing - path: Mathlib/FieldTheory/Laurent.lean theorems: - RatFunc.laurentAux_algebraMap - path: Mathlib/Probability/Kernel/CondDistrib.lean theorems: - MeasureTheory.Integrable.integral_norm_condDistrib_map - path: Mathlib/MeasureTheory/Constructions/Prod/Integral.lean theorems: - measurableSet_integrable - path: Mathlib/Data/Finset/Sigma.lean theorems: - Finset.sigma_nonempty - path: Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean theorems: - "CategoryTheory.Limits.\u03B9_colimitConstInitial_hom" - path: Mathlib/Topology/MetricSpace/HausdorffDistance.lean theorems: - Metric.infDist_image - path: Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean theorems: - "CategoryTheory.Pretriangulated.Triangle.mor\u2083_eq_zero_iff_mono\u2081" - path: Mathlib/LinearAlgebra/Contraction.lean theorems: - comp_dualTensorHom - path: Mathlib/Order/Filter/ModEq.lean theorems: - Nat.frequently_modEq - path: Mathlib/Data/Set/Pointwise/Interval.lean theorems: - Set.preimage_neg_Ioc - path: Mathlib/Data/PNat/Basic.lean theorems: - PNat.sub_coe - path: Mathlib/MeasureTheory/Measure/Haar/Basic.lean theorems: - MeasureTheory.Measure.haar.index_elim - path: Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean theorems: - Matrix.det_smul_inv_vecMul_eq_cramer_transpose - path: Mathlib/NumberTheory/LucasLehmer.lean theorems: - "LucasLehmer.X.\u03C9_mul_\u03C9b" - path: Mathlib/Analysis/BoxIntegral/Partition/Basic.lean theorems: - BoxIntegral.Prepartition.ofWithBot_le - path: Mathlib/RepresentationTheory/Basic.lean theorems: - Representation.asAlgebraHom_single - path: Mathlib/LinearAlgebra/Dimension/DivisionRing.lean theorems: - rank_dual_eq_card_dual_of_aleph0_le_rank' - path: Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean theorems: - CategoryTheory.Limits.parallelPair_functor_obj - path: Mathlib/AlgebraicGeometry/EllipticCurve/Group.lean theorems: - WeierstrassCurve.Affine.CoordinateRing.mk_XYIdeal'_mul_mk_XYIdeal' - path: Mathlib/RingTheory/PowerSeries/Trunc.lean theorems: - PowerSeries.trunc_coe_eq_self - path: Mathlib/Analysis/SpecialFunctions/Log/NegMulLog.lean theorems: - Real.negMulLog_one - path: Mathlib/Data/Polynomial/Degree/TrailingDegree.lean theorems: - Polynomial.nextCoeffUp_C_eq_zero - path: Mathlib/MeasureTheory/Function/ConditionalExpectation/Real.lean theorems: - MeasureTheory.snorm_one_condexp_le_snorm - path: Mathlib/Topology/Sheaves/SheafCondition/EqualizerProducts.lean theorems: - "TopCat.Presheaf.SheafConditionEqualizerProducts.res_\u03C0"