| name: leandojo-eval | |
| num_files: 709 | |
| 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: 991 | |
| datasets: | |
| - project: <path-to-repo>/mathlib4 | |
| files: | |
| - path: Mathlib/Analysis/SpecificLimits/Normed.lean | |
| theorems: | |
| - tendsto_pow_const_mul_const_pow_of_abs_lt_one | |
| - dist_partial_sum_le_of_le_geometric | |
| - path: Mathlib/SetTheory/Cardinal/Cofinality.lean | |
| theorems: | |
| - Ordinal.cof_eq_one_iff_is_succ | |
| - Ordinal.aleph0_le_cof | |
| - path: Mathlib/GroupTheory/GroupAction/Quotient.lean | |
| theorems: | |
| - MulAction.Quotient.mk_smul_out' | |
| - Subgroup.normalCore_eq_ker | |
| - path: Mathlib/Data/Complex/Abs.lean | |
| theorems: | |
| - Complex.lim_im | |
| - Complex.abs_le_abs_re_add_abs_im | |
| - path: Mathlib/Tactic/ComputeDegree.lean | |
| theorems: | |
| - Mathlib.Tactic.ComputeDegree.coeff_int_cast_ite | |
| - path: Mathlib/RingTheory/ChainOfDivisors.lean | |
| theorems: | |
| - DivisorChain.second_of_chain_is_irreducible | |
| - path: Mathlib/Algebra/GroupWithZero/NonZeroDivisors.lean | |
| theorems: | |
| - mul_right_mem_nonZeroDivisors_eq_zero_iff | |
| - path: Mathlib/Algebra/Algebra/NonUnitalSubalgebra.lean | |
| theorems: | |
| - Set.smul_mem_centralizer | |
| - path: Mathlib/Dynamics/PeriodicPts.lean | |
| theorems: | |
| - MulAction.pow_add_period_smul | |
| - path: Mathlib/Algebra/Order/ToIntervalMod.lean | |
| theorems: | |
| - toIcoMod_eq_iff | |
| - toIcoMod_add_zsmul | |
| - toIcoMod_apply_left | |
| - toIcoMod_le_toIocMod | |
| - iUnion_Ioc_int_cast | |
| - toIcoMod_zsmul_add' | |
| - path: Mathlib/Analysis/InnerProductSpace/Projection.lean | |
| theorems: | |
| - sub_orthogonalProjection_mem_orthogonal | |
| - exists_norm_eq_iInf_of_complete_convex | |
| - path: Mathlib/Data/Real/Sign.lean | |
| theorems: | |
| - Real.sign_zero | |
| - path: Mathlib/LinearAlgebra/Reflection.lean | |
| theorems: | |
| - Module.preReflection_preReflection | |
| - path: .lake/packages/std/Std/Data/String/Lemmas.lean | |
| theorems: | |
| - Substring.ValidFor.all | |
| - String.data_take | |
| - String.Iterator.ValidFor.nextn | |
| - path: Mathlib/Order/Iterate.lean | |
| theorems: | |
| - Monotone.seq_pos_lt_seq_of_lt_of_le | |
| - path: Mathlib/Data/Polynomial/Eval.lean | |
| theorems: | |
| - "Polynomial.eval\u2082_at_zero" | |
| - "Polynomial.eval\u2082_mul'" | |
| - path: Mathlib/Algebra/Group/Commute/Defs.lean | |
| theorems: | |
| - mul_pow_sub_one | |
| - path: Mathlib/Data/Complex/Cardinality.lean | |
| theorems: | |
| - mk_complex | |
| - mk_univ_complex | |
| - path: Mathlib/FieldTheory/AbelRuffini.lean | |
| theorems: | |
| - gal_isSolvable_tower | |
| - path: Mathlib/Computability/TuringMachine.lean | |
| theorems: | |
| - Turing.TM1to1.tr_supports | |
| - Turing.TM0.univ_supports | |
| - Turing.BlankExtends.below_of_le | |
| - path: Mathlib/Data/Ordmap/Ordset.lean | |
| theorems: | |
| - Ordnode.pos_size_of_mem | |
| - Ordnode.node4L_size | |
| - Ordnode.size_dual | |
| - path: Mathlib/SetTheory/Ordinal/FixedPoint.lean | |
| theorems: | |
| - Ordinal.apply_lt_nfpBFamily | |
| - path: Mathlib/RingTheory/WittVector/Identities.lean | |
| theorems: | |
| - WittVector.coeff_p_pow | |
| - path: Mathlib/Data/Real/EReal.lean | |
| theorems: | |
| - EReal.add_lt_add_left_coe | |
| - path: Mathlib/Data/List/Basic.lean | |
| theorems: | |
| - List.map_bind | |
| - "List.map\u2082Left_eq_map\u2082Left'" | |
| - List.nthLe_cons | |
| - Function.LeftInverse.list_map | |
| - path: Mathlib/RingTheory/Algebraic.lean | |
| theorems: | |
| - IsAlgebraic.algHom | |
| - path: Mathlib/Algebra/Group/Defs.lean | |
| theorems: | |
| - inv_mul_cancel_comm_assoc | |
| - path: Mathlib/RingTheory/HahnSeries/Multiplication.lean | |
| theorems: | |
| - HahnSeries.single_mul_coeff_add | |
| - path: Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | |
| theorems: | |
| - EulerSine.tendsto_integral_cos_pow_mul_div | |
| - path: Mathlib/Topology/Algebra/Group/Basic.lean | |
| theorems: | |
| - nhds_translation_mul_inv | |
| - Subgroup.coe_topologicalClosure_bot | |
| - path: Mathlib/RepresentationTheory/GroupCohomology/LowDegree.lean | |
| theorems: | |
| - groupCohomology.map_one_snd_of_isTwoCocycle | |
| - path: Mathlib/Analysis/Normed/Group/Basic.lean | |
| theorems: | |
| - MonoidHomClass.lipschitz_of_bound | |
| - NormedCommGroup.uniformity_basis_dist | |
| - path: Mathlib/Order/GaloisConnection.lean | |
| theorems: | |
| - OrderIso.bddBelow_preimage | |
| - path: Mathlib/Data/Num/Lemmas.lean | |
| theorems: | |
| - Num.add_toZNum | |
| - path: Mathlib/MeasureTheory/Function/SimpleFuncDense.lean | |
| theorems: | |
| - MeasureTheory.SimpleFunc.nearestPtInd_succ | |
| - MeasureTheory.SimpleFunc.tendsto_nearestPt | |
| - path: Mathlib/Probability/Kernel/IntegralCompProd.lean | |
| theorems: | |
| - ProbabilityTheory.set_integral_compProd_univ_left | |
| - path: Mathlib/FieldTheory/RatFunc.lean | |
| theorems: | |
| - RatFunc.ofFractionRing_mk' | |
| - RatFunc.num_eq_zero_iff | |
| - path: Mathlib/Algebra/AddConstMap/Basic.lean | |
| theorems: | |
| - AddConstMapClass.map_add_zsmul | |
| - path: Mathlib/MeasureTheory/Measure/AEDisjoint.lean | |
| theorems: | |
| - Disjoint.aedisjoint | |
| - path: Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | |
| theorems: | |
| - "TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_\u03B9_eq_\u03B9" | |
| - path: Mathlib/Analysis/Convex/Between.lean | |
| theorems: | |
| - Wbtw.left_ne_right_of_ne_right | |
| - Wbtw.left_ne_right_of_ne_left | |
| - path: Mathlib/Data/Finset/Sups.lean | |
| theorems: | |
| - Finset.sized_compls | |
| - Finset.powerset_infs_powerset_self | |
| - Finset.forall_disjSups_iff | |
| - path: Mathlib/Algebra/Module/PID.lean | |
| theorems: | |
| - Submodule.isSemisimple_torsionBy_of_irreducible | |
| - path: Mathlib/RingTheory/Polynomial/Dickson.lean | |
| theorems: | |
| - Polynomial.dickson_add_two | |
| - path: Mathlib/MeasureTheory/Function/LpSpace.lean | |
| theorems: | |
| - ContinuousLinearMap.add_compLpL | |
| - MeasureTheory.indicatorConstLp_empty | |
| - MeasureTheory.dist_indicatorConstLp_eq_norm | |
| - "MeasureTheory.Lp.cauchy_complete_\u2112p" | |
| - ContinuousLinearMap.smul_compLp | |
| - path: .lake/packages/std/Std/Data/List/Perm.lean | |
| theorems: | |
| - List.nil_subperm | |
| - List.Perm.pmap | |
| - List.Perm.symm | |
| - path: Mathlib/Data/Real/NNReal.lean | |
| theorems: | |
| - NNReal.iSup_div | |
| - Real.toNNReal_sum_of_nonneg | |
| - path: Mathlib/Topology/UniformSpace/UniformEmbedding.lean | |
| theorems: | |
| - uniformEmbedding_iff' | |
| - path: Mathlib/LinearAlgebra/Matrix/Charpoly/Basic.lean | |
| theorems: | |
| - Matrix.charmatrix_apply_ne | |
| - path: Mathlib/Data/PFunctor/Multivariate/M.lean | |
| theorems: | |
| - MvPFunctor.M.dest'_eq_dest' | |
| - path: Mathlib/Analysis/Calculus/ContDiff/Defs.lean | |
| theorems: | |
| - hasFTaylorSeriesUpToOn_top_iff | |
| - HasFTaylorSeriesUpTo.continuous | |
| - ftaylorSeriesWithin_univ | |
| - ContDiffWithinAt.continuousWithinAt | |
| - path: Mathlib/FieldTheory/Adjoin.lean | |
| theorems: | |
| - IntermediateField.adjoin_eq_top_of_adjoin_eq_top | |
| - IntermediateField.exists_finset_of_mem_supr'' | |
| - path: Mathlib/Analysis/SpecialFunctions/Stirling.lean | |
| theorems: | |
| - Stirling.log_stirlingSeq_bounded_by_constant | |
| - Stirling.stirlingSeq_zero | |
| - path: Mathlib/Algebra/Homology/Exact.lean | |
| theorems: | |
| - CategoryTheory.kernel_comp_cokernel | |
| - CategoryTheory.exact_zero_left_of_mono | |
| - path: Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | |
| theorems: | |
| - Matrix.coeff_det_one_add_X_smul_one | |
| - path: Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | |
| theorems: | |
| - Real.borel_eq_generateFrom_Ioi_rat | |
| - borel_eq_generateFrom_Ico | |
| - borel_eq_generateFrom_Ioc | |
| - path: Mathlib/Order/Filter/Bases.lean | |
| theorems: | |
| - Filter.generate_eq_generate_inter | |
| - Filter.IsBasis.mem_filter_iff | |
| - path: Mathlib/Data/Real/Hyperreal.lean | |
| theorems: | |
| - Hyperreal.infinitesimal_pos_iff_infinitePos_inv | |
| - path: Mathlib/Probability/CondCount.lean | |
| theorems: | |
| - ProbabilityTheory.condCount_singleton | |
| - path: Mathlib/Analysis/InnerProductSpace/Basic.lean | |
| theorems: | |
| - norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero | |
| - inner_eq_norm_mul_iff_div | |
| - InnerProductSpace.Core.inner_self_ofReal_re | |
| - OrthogonalFamily.summable_iff_norm_sq_summable | |
| - DFinsupp.inner_sum | |
| - path: Mathlib/Analysis/InnerProductSpace/Calculus.lean | |
| theorems: | |
| - HasDerivWithinAt.norm_sq | |
| - path: Mathlib/Algebra/BigOperators/Basic.lean | |
| theorems: | |
| - Finset.mulIndicator_biUnion | |
| - Multiset.add_eq_union_left_of_le | |
| - path: Mathlib/Analysis/Complex/AbelLimit.lean | |
| theorems: | |
| - Real.tendsto_tsum_powerSeries_nhdsWithin_lt | |
| - Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzSet | |
| - path: Mathlib/Order/JordanHolder.lean | |
| theorems: | |
| - CompositionSeries.Equivalent.symm | |
| - CompositionSeries.mem_eraseTop | |
| - path: Mathlib/Geometry/Euclidean/Angle/Oriented/Affine.lean | |
| theorems: | |
| - Collinear.two_zsmul_oangle_eq_right | |
| - "EuclideanGeometry.oangle_swap\u2081\u2082_sign" | |
| - path: Mathlib/Data/MvPolynomial/Degrees.lean | |
| theorems: | |
| - MvPolynomial.degreeOf_lt_iff | |
| - path: Mathlib/Data/Set/Pointwise/Interval.lean | |
| theorems: | |
| - Set.image_sub_const_Ici | |
| - Set.image_neg_Ioo | |
| - Set.image_mul_right_Icc | |
| - path: Mathlib/Algebra/IsPrimePow.lean | |
| theorems: | |
| - isPrimePow_nat_iff | |
| - path: Mathlib/Data/Nat/Factorial/Cast.lean | |
| theorems: | |
| - Nat.cast_descFactorial | |
| - path: Mathlib/Data/List/BigOperators/Lemmas.lean | |
| theorems: | |
| - unop_map_list_prod | |
| - path: Mathlib/NumberTheory/VonMangoldt.lean | |
| theorems: | |
| - ArithmeticFunction.vonMangoldt_ne_zero_iff | |
| - path: Mathlib/Topology/Sober.lean | |
| theorems: | |
| - genericPoint_specializes | |
| - path: .lake/packages/std/Std/Data/Rat/Lemmas.lean | |
| theorems: | |
| - Rat.neg_divInt | |
| - Rat.neg_mkRat | |
| - path: Mathlib/RingTheory/Polynomial/Pochhammer.lean | |
| theorems: | |
| - descPochhammer_zero_eval_zero | |
| - path: Mathlib/Topology/ContinuousOn.lean | |
| theorems: | |
| - continuousWithinAt_update_same | |
| - nhdsWithin_pi_univ_eq | |
| - path: Mathlib/MeasureTheory/Measure/Portmanteau.lean | |
| theorems: | |
| - MeasureTheory.le_liminf_measure_open_of_forall_tendsto_measure | |
| - path: Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | |
| theorems: | |
| - EuclideanGeometry.angle_eq_zero_of_angle_eq_pi_left | |
| - path: Mathlib/Data/Matrix/Basis.lean | |
| theorems: | |
| - Matrix.StdBasisMatrix.mul_right_apply_of_ne | |
| - Matrix.mem_range_scalar_iff_commute_stdBasisMatrix | |
| - path: Mathlib/LinearAlgebra/SesquilinearForm.lean | |
| theorems: | |
| - LinearMap.IsRefl.domRestrict | |
| - LinearMap.IsAdjointPair.sub | |
| - path: Mathlib/Topology/MetricSpace/Antilipschitz.lean | |
| theorems: | |
| - antilipschitzWith_iff_le_mul_nndist | |
| - AntilipschitzWith.comp | |
| - path: Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | |
| theorems: | |
| - pow_div_pow_eventuallyEq_atTop | |
| - path: Mathlib/Algebra/FreeAlgebra.lean | |
| theorems: | |
| - FreeAlgebra.induction | |
| - path: Mathlib/Probability/Martingale/Upcrossing.lean | |
| theorems: | |
| - MeasureTheory.upcrossingsBefore_bot | |
| - path: Mathlib/Data/Set/UnionLift.lean | |
| theorems: | |
| - Set.iUnionLift_const | |
| - path: Mathlib/NumberTheory/Divisors.lean | |
| theorems: | |
| - Nat.properDivisors_eq_empty | |
| - Nat.sup_divisors_id | |
| - path: Mathlib/ModelTheory/Substructures.lean | |
| theorems: | |
| - FirstOrder.Language.Substructure.range_subtype | |
| - FirstOrder.Language.Substructure.closure_withConstants_eq | |
| - path: Mathlib/RingTheory/UniqueFactorizationDomain.lean | |
| theorems: | |
| - Associates.le_of_count_ne_zero | |
| - UniqueFactorizationMonoid.prime_of_normalized_factor | |
| - path: Mathlib/Probability/Distributions/Geometric.lean | |
| theorems: | |
| - ProbabilityTheory.geometricPMFRealSum | |
| - path: Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | |
| theorems: | |
| - SeminormFamily.basisSets_add | |
| - WithSeminorms.hasBasis | |
| - path: Mathlib/Analysis/Normed/Group/SemiNormedGroupCat/Kernels.lean | |
| theorems: | |
| - SemiNormedGroupCat.ExplicitCoker.map_desc | |
| - SemiNormedGroupCat.explicitCokernelDesc_normNoninc | |
| - SemiNormedGroupCat.explicitCokernelIso_hom_desc | |
| - "SemiNormedGroupCat.explicitCokernel\u03C0_apply_dom_eq_zero" | |
| - path: Mathlib/Data/Seq/Computation.lean | |
| theorems: | |
| - Computation.LiftRel.equiv | |
| - path: Mathlib/MeasureTheory/Covering/Besicovitch.lean | |
| theorems: | |
| - Besicovitch.ae_tendsto_measure_inter_div | |
| - path: Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | |
| theorems: | |
| - Real.cos_pi | |
| - Real.cos_pi_div_four | |
| - Real.sin_pi_div_two_sub | |
| - Real.sin_eq_sqrt_one_sub_cos_sq | |
| - path: Mathlib/Computability/AkraBazzi/AkraBazzi.lean | |
| theorems: | |
| - AkraBazziRecurrence.eventually_r_lt_n | |
| - AkraBazziRecurrence.base_nonempty | |
| - path: Mathlib/Topology/MetricSpace/Thickening.lean | |
| theorems: | |
| - Metric.cthickening_eq_biUnion_closedBall | |
| - Metric.mem_thickening_iff | |
| - path: Mathlib/Analysis/Calculus/Gradient/Basic.lean | |
| theorems: | |
| - HasGradientWithinAt.congr | |
| - path: Mathlib/Analysis/InnerProductSpace/PiL2.lean | |
| theorems: | |
| - OrthonormalBasis.orthogonalProjection_eq_sum | |
| - path: Mathlib/Topology/Instances/NNReal.lean | |
| theorems: | |
| - NNReal.tendsto_atTop_zero_of_summable | |
| - path: Mathlib/Data/Finsupp/Basic.lean | |
| theorems: | |
| - Finsupp.embDomain_eq_mapDomain | |
| - Finsupp.comapDomain_zero | |
| - path: Mathlib/Logic/Relation.lean | |
| theorems: | |
| - Relation.comp_assoc | |
| - path: Mathlib/Order/Filter/AtTopBot.lean | |
| theorems: | |
| - Filter.HasAntitoneBasis.subbasis_with_rel | |
| - Filter.tendsto_const_mul_atBot_of_neg | |
| - path: Mathlib/Topology/UniformSpace/Compact.lean | |
| theorems: | |
| - nhdsSet_diagonal_eq_uniformity | |
| - path: Mathlib/Algebra/Lie/Semisimple.lean | |
| theorems: | |
| - LieAlgebra.subsingleton_of_semisimple_lie_abelian | |
| - path: Mathlib/Analysis/Convex/Segment.lean | |
| theorems: | |
| - mem_segment_translate | |
| - mem_segment_sub_add | |
| - path: Mathlib/Algebra/Order/Group/Defs.lean | |
| theorems: | |
| - inv_mul_lt_one_iff | |
| - path: Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | |
| theorems: | |
| - BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion | |
| - path: Mathlib/GroupTheory/Submonoid/Membership.lean | |
| theorems: | |
| - MulMemClass.mul_mem_add_closure | |
| - Submonoid.mem_closure_singleton | |
| - path: Mathlib/CategoryTheory/Subobject/Limits.lean | |
| theorems: | |
| - CategoryTheory.Limits.factorThruKernelSubobject_comp_kernelSubobjectIso | |
| - CategoryTheory.Limits.le_kernelSubobject | |
| - path: Mathlib/Topology/Gluing.lean | |
| theorems: | |
| - TopCat.GlueData.rel_equiv | |
| - path: Mathlib/CategoryTheory/Abelian/Generator.lean | |
| theorems: | |
| - CategoryTheory.Abelian.has_injective_coseparator | |
| - path: Mathlib/Analysis/Calculus/Deriv/Inv.lean | |
| theorems: | |
| - HasDerivWithinAt.div | |
| - path: Mathlib/Topology/CompactOpen.lean | |
| theorems: | |
| - ContinuousMap.compactOpen_eq_iInf_induced | |
| - path: Mathlib/Algebra/Homology/HomotopyCategory/HomComplexShift.lean | |
| theorems: | |
| - CochainComplex.HomComplex.Cochain.shift_zero | |
| - path: Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | |
| theorems: | |
| - MeasureTheory.ProbabilityMeasure.apply_mono | |
| - path: Mathlib/LinearAlgebra/DFinsupp.lean | |
| theorems: | |
| - Submodule.mem_iSup_finset_iff_exists_sum | |
| - Submodule.biSup_eq_range_dfinsupp_lsum | |
| - path: Mathlib/MeasureTheory/Measure/Restrict.lean | |
| theorems: | |
| - mem_map_indicator_ae_iff_mem_map_restrict_ae_of_zero_mem | |
| - MeasureTheory.Measure.restrict_eq_self | |
| - MeasureTheory.NullMeasurable.measure_preimage_eq_measure_restrict_preimage_of_ae_compl_eq_const | |
| - path: Mathlib/Data/Sym/Basic.lean | |
| theorems: | |
| - Sym.cons_equiv_eq_equiv_cons | |
| - path: Mathlib/Analysis/Convex/Function.lean | |
| theorems: | |
| - StrictConcaveOn.translate_left | |
| - path: Mathlib/Data/Finset/Basic.lean | |
| theorems: | |
| - Finset.singleton_inter_of_mem | |
| - Finset.biUnion_singleton_eq_self | |
| - Finset.left_eq_union | |
| - Finset.inter_erase | |
| - Finset.insert_union_comm | |
| - Finset.sdiff_eq_self | |
| - path: Mathlib/MeasureTheory/Integral/IntegrableOn.lean | |
| theorems: | |
| - ContinuousOn.aemeasurable | |
| - MeasurableEmbedding.integrableAtFilter_map_iff | |
| - path: Mathlib/CategoryTheory/Monoidal/Category.lean | |
| theorems: | |
| - CategoryTheory.MonoidalCategory.associator_naturality_left | |
| - CategoryTheory.MonoidalCategory.whiskerLeft_eqToHom | |
| - CategoryTheory.MonoidalCategory.id_whiskerLeft | |
| - CategoryTheory.MonoidalCategory.whiskerRight_tensor_symm | |
| - CategoryTheory.MonoidalCategory.triangle_assoc_comp_left_inv | |
| - path: Mathlib/MeasureTheory/Measure/LevyProkhorovMetric.lean | |
| theorems: | |
| - MeasureTheory.levyProkhorovDist_triangle | |
| - path: Mathlib/Data/DFinsupp/Basic.lean | |
| theorems: | |
| - DFinsupp.erase_def | |
| - DFinsupp.add_closure_iUnion_range_single | |
| - DFinsupp.support_neg | |
| - DFinsupp.filter_def | |
| - DFinsupp.single_eq_of_ne | |
| - path: Mathlib/Analysis/Convex/Jensen.lean | |
| theorems: | |
| - ConcaveOn.min_le_of_mem_Icc | |
| - path: Mathlib/Topology/EMetricSpace/Basic.lean | |
| theorems: | |
| - edist_congr_right | |
| - EMetric.mk_uniformity_basis_le | |
| - path: Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | |
| theorems: | |
| - MeasureTheory.integral_Iic_of_hasDerivAt_of_tendsto | |
| - MeasureTheory.integrableOn_Iic_of_intervalIntegral_norm_bounded | |
| - path: Mathlib/Algebra/Order/Monovary.lean | |
| theorems: | |
| - "antivaryOn_inv\u2080" | |
| - antivary_iff_forall_mul_nonpos | |
| - antivaryOn_iff_forall_mul_nonpos | |
| - path: Mathlib/Combinatorics/SetFamily/Kleitman.lean | |
| theorems: | |
| - Finset.card_biUnion_le_of_intersecting | |
| - path: Mathlib/Data/List/Nodup.lean | |
| theorems: | |
| - List.Nodup.pairwise_coe | |
| - List.inj_on_of_nodup_map | |
| - path: Mathlib/Analysis/NormedSpace/OperatorNorm/NormedSpace.lean | |
| theorems: | |
| - LinearMap.bound_of_shell | |
| - path: Mathlib/Data/Sym/Sym2.lean | |
| theorems: | |
| - Sym2.diag_injective | |
| - Sym2.mem_map | |
| - path: Mathlib/Topology/ContinuousFunction/NonUnitalFunctionalCalculus.lean | |
| theorems: | |
| - "cfc\u2099Hom_comp" | |
| - path: Mathlib/RingTheory/PowerSeries/WellKnown.lean | |
| theorems: | |
| - PowerSeries.map_exp | |
| - path: Mathlib/Algebra/Lie/Nilpotent.lean | |
| theorems: | |
| - LieModule.isNilpotent_iff_exists_ucs_eq_top | |
| - path: Mathlib/Algebra/Lie/IdealOperations.lean | |
| theorems: | |
| - LieSubmodule.lie_le_right | |
| - path: Mathlib/CategoryTheory/Quotient.lean | |
| theorems: | |
| - CategoryTheory.Quotient.compClosure_eq_self | |
| - path: Mathlib/Algebra/Module/LinearMap/Basic.lean | |
| theorems: | |
| - LinearMap.map_smul_inv | |
| - path: Mathlib/Analysis/InnerProductSpace/l2Space.lean | |
| theorems: | |
| - lp.inner_single_right | |
| - lp.inner_single_left | |
| - Orthonormal.isHilbertSum | |
| - path: Mathlib/Data/Finset/PiAntidiagonal.lean | |
| theorems: | |
| - Finset.mem_piAntidiagonal | |
| - path: Mathlib/AlgebraicGeometry/Gluing.lean | |
| theorems: | |
| - AlgebraicGeometry.Scheme.OpenCover.hom_ext | |
| - path: Mathlib/LinearAlgebra/CliffordAlgebra/EvenEquiv.lean | |
| theorems: | |
| - CliffordAlgebra.ofEven_comp_toEven | |
| - path: Mathlib/Data/Fin/Basic.lean | |
| theorems: | |
| - Fin.nontrivial_iff_two_le | |
| - Fin.liftFun_iff_succ | |
| - Fin.sub_one_lt_iff | |
| - Fin.coe_orderIso_apply | |
| - path: Mathlib/SetTheory/Cardinal/ENat.lean | |
| theorems: | |
| - Cardinal.nat_lt_ofENat | |
| - Cardinal.nat_eq_ofENat | |
| - path: Mathlib/Topology/Algebra/Module/Basic.lean | |
| theorems: | |
| - Submodule.ClosedComplemented.exists_submodule_equiv_prod | |
| - ContinuousLinearMap.map_neg | |
| - path: Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | |
| theorems: | |
| - MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp | |
| - "MeasureTheory.SimpleFunc.measure_lt_top_of_mem\u2112p_indicator" | |
| - path: Mathlib/Data/Polynomial/Reverse.lean | |
| theorems: | |
| - Polynomial.coeff_one_reverse | |
| - path: Mathlib/Data/Int/GCD.lean | |
| theorems: | |
| - Int.lcm_zero_right | |
| - path: Mathlib/Analysis/Convex/Topology.lean | |
| theorems: | |
| - Convex.openSegment_interior_closure_subset_interior | |
| - path: Mathlib/RingTheory/Etale.lean | |
| theorems: | |
| - Algebra.FormallyEtale.iff_unramified_and_smooth | |
| - path: Mathlib/Algebra/DirectLimit.lean | |
| theorems: | |
| - AddCommGroup.DirectLimit.congr_symm_apply_of | |
| - path: Mathlib/Topology/Constructions.lean | |
| theorems: | |
| - isOpen_sigma_fst_preimage | |
| - isClosedMap_sigmaMk | |
| - path: Mathlib/Order/LiminfLimsup.lean | |
| theorems: | |
| - Filter.blimsup_eq_limsup_subtype | |
| - Filter.bliminf_false | |
| - Filter.frequently_lt_of_lt_limsup | |
| - path: Mathlib/GroupTheory/Exponent.lean | |
| theorems: | |
| - Monoid.exponent_eq_iSup_orderOf' | |
| - path: Mathlib/Data/ZMod/Basic.lean | |
| theorems: | |
| - ZMod.int_cast_mod | |
| - ZMod.val_mul_of_lt | |
| - path: Mathlib/Algebra/Order/Pointwise.lean | |
| theorems: | |
| - LinearOrderedField.smul_Iic | |
| - path: Mathlib/Analysis/Complex/Basic.lean | |
| theorems: | |
| - Complex.normSq_eq_norm_sq | |
| - path: Mathlib/Data/Nat/Totient.lean | |
| theorems: | |
| - Nat.totient_prime | |
| - path: Mathlib/SetTheory/Game/PGame.lean | |
| theorems: | |
| - SetTheory.PGame.leftMoves_add_cases | |
| - SetTheory.PGame.le_neg_iff | |
| - path: Mathlib/MeasureTheory/Function/AEEqFun.lean | |
| theorems: | |
| - "MeasureTheory.AEEqFun.coeFn_comp\u2082" | |
| - path: Mathlib/Algebra/GCDMonoid/Multiset.lean | |
| theorems: | |
| - Multiset.gcd_eq_zero_iff | |
| - path: Mathlib/Analysis/BoundedVariation.lean | |
| theorems: | |
| - LocallyBoundedVariationOn.ae_differentiableWithinAt_of_mem_real | |
| - path: Mathlib/LinearAlgebra/Finsupp.lean | |
| theorems: | |
| - Finsupp.lcongr_single | |
| - Finsupp.total_comp_lmapDomain | |
| - path: Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | |
| theorems: | |
| - Real.continuousAt_log_iff | |
| - path: Mathlib/Topology/ContinuousFunction/Weierstrass.lean | |
| theorems: | |
| - continuousMap_mem_polynomialFunctions_closure | |
| - path: Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | |
| theorems: | |
| - Submodule.sub_mem_orthogonal_of_inner_left | |
| - path: Mathlib/GroupTheory/Perm/Cycle/Basic.lean | |
| theorems: | |
| - Equiv.Perm.SameCycle.conj | |
| - Equiv.Perm.IsCycle.eq_on_support_inter_nonempty_congr | |
| - path: Mathlib/Algebra/Module/LocalizedModule.lean | |
| theorems: | |
| - IsLocalizedModule.mk'_neg | |
| - path: .lake/packages/std/Std/Data/Array/Lemmas.lean | |
| theorems: | |
| - Array.size_zipWith | |
| - Array.get_extract_loop_lt | |
| - Array.data_swap | |
| - path: Mathlib/MeasureTheory/Measure/MeasureSpace.lean | |
| theorems: | |
| - MeasureTheory.Measure.AbsolutelyContinuous.smul | |
| - MeasureTheory.ae_map_mem_range | |
| - path: Mathlib/Probability/Independence/Basic.lean | |
| theorems: | |
| - ProbabilityTheory.iIndep_iff | |
| - ProbabilityTheory.iIndepSet_iff | |
| - path: Mathlib/Data/List/Forall2.lean | |
| theorems: | |
| - "List.forall\u2082_cons" | |
| - path: Mathlib/Algebra/Order/Group/PosPart.lean | |
| theorems: | |
| - leOnePart_le_one | |
| - mabs_div_eq_leOnePart_sq | |
| - one_lt_ltOnePart | |
| - path: Mathlib/Topology/MetricSpace/PiNat.lean | |
| theorems: | |
| - PiNat.mem_cylinder_iff_le_firstDiff | |
| - path: Mathlib/Analysis/Analytic/Inverse.lean | |
| theorems: | |
| - FormalMultilinearSeries.comp_rightInv_aux1 | |
| - path: Mathlib/Topology/Connected/Basic.lean | |
| theorems: | |
| - IsConnected.union | |
| - isPreconnected_of_forall_constant | |
| - QuotientMap.image_connectedComponent | |
| - path: Mathlib/MeasureTheory/Measure/Haar/Disintegration.lean | |
| theorems: | |
| - MeasureTheory.ae_ae_add_linearMap_mem_iff | |
| - path: Mathlib/Data/Multiset/Bind.lean | |
| theorems: | |
| - Multiset.bind_congr | |
| - path: Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | |
| theorems: | |
| - AlgHom.coe_range | |
| - path: Mathlib/Analysis/Convex/StrictConvexBetween.lean | |
| theorems: | |
| - Sbtw.dist_lt_max_dist | |
| - Wbtw.dist_le_max_dist | |
| - path: Mathlib/LinearAlgebra/Matrix/PosDef.lean | |
| theorems: | |
| - Matrix.PosSemidef.conjTranspose_mul_mul_same | |
| - path: Mathlib/Algebra/Homology/HomotopyCategory/HomComplex.lean | |
| theorems: | |
| - CochainComplex.HomComplex.Cochain.comp_assoc_of_first_is_zero_cochain | |
| - path: Mathlib/Order/Filter/Basic.lean | |
| theorems: | |
| - Filter.not_eventually | |
| - Filter.comap_neBot_iff | |
| - Filter.iInf_neBot_of_directed | |
| - Filter.map_const | |
| - Filter.prod_map_seq_comm | |
| - Filter.EventuallyLE.congr | |
| - path: Mathlib/MeasureTheory/Function/SimpleFunc.lean | |
| theorems: | |
| - MeasureTheory.SimpleFunc.FinMeasSupp.add | |
| - MeasureTheory.SimpleFunc.approx_apply | |
| - path: Mathlib/Analysis/InnerProductSpace/TwoDim.lean | |
| theorems: | |
| - Orientation.norm_kahler | |
| - Orientation.inner_mul_areaForm_sub' | |
| - Orientation.kahler_mul | |
| - path: Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | |
| theorems: | |
| - Real.volume_eq_stieltjes_id | |
| - path: Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | |
| theorems: | |
| - SimpleGraph.reachable_delete_edges_iff_exists_walk | |
| - path: Mathlib/RingTheory/Ideal/Operations.lean | |
| theorems: | |
| - Ideal.iInf_span_singleton | |
| - Ideal.radical_eq_iff | |
| - Ideal.sup_mul_eq_of_coprime_left | |
| - path: Mathlib/Algebra/Homology/ShortComplex/LeftHomology.lean | |
| theorems: | |
| - CategoryTheory.ShortComplex.LeftHomologyData.liftCycles_comp_cyclesIso_hom | |
| - "CategoryTheory.ShortComplex.toCycles_comp_leftHomology\u03C0" | |
| - path: Mathlib/CategoryTheory/Bicategory/Adjunction.lean | |
| theorems: | |
| - CategoryTheory.Bicategory.right_triangle_of_left_triangle | |
| - path: Mathlib/GroupTheory/Subsemigroup/Membership.lean | |
| theorems: | |
| - Subsemigroup.mem_sSup_of_mem | |
| - path: Mathlib/Algebra/Order/Hom/Monoid.lean | |
| theorems: | |
| - OrderMonoidWithZeroHom.toOrderMonoidHom_injective | |
| - path: Mathlib/MeasureTheory/Integral/Average.lean | |
| theorems: | |
| - MeasureTheory.measure_setLaverage_le_pos | |
| - MeasureTheory.laverage_eq | |
| - path: Mathlib/Algebra/Order/Floor.lean | |
| theorems: | |
| - Nat.one_le_ceil_iff | |
| - Int.fract_natCast | |
| - path: Mathlib/Data/Set/Intervals/Basic.lean | |
| theorems: | |
| - Set.right_mem_Iic | |
| - path: Mathlib/Topology/Algebra/Polynomial.lean | |
| theorems: | |
| - "Polynomial.continuous_eval\u2082" | |
| - path: Mathlib/Data/Complex/Exponential.lean | |
| theorems: | |
| - Real.cosh_sub | |
| - Real.exp_1_approx_succ_eq | |
| - Complex.cos_sq | |
| - path: Mathlib/Data/PFunctor/Multivariate/Basic.lean | |
| theorems: | |
| - MvPFunctor.const.get_map | |
| - path: Mathlib/Logic/Embedding/Basic.lean | |
| theorems: | |
| - Equiv.embeddingCongr_apply_trans | |
| - path: Mathlib/Algebra/Order/Module/Defs.lean | |
| theorems: | |
| - neg_of_smul_neg_right | |
| - smul_pos_iff_of_neg_left | |
| - PosSMulReflectLE.lift | |
| - path: Mathlib/SetTheory/Ordinal/Notation.lean | |
| theorems: | |
| - ONote.repr_sub | |
| - path: Mathlib/MeasureTheory/MeasurableSpace/Defs.lean | |
| theorems: | |
| - MeasurableSpace.measurableSpace_iSup_eq | |
| - MeasurableSpace.measurableSet_bot_iff | |
| - path: Mathlib/Combinatorics/SetFamily/Shadow.lean | |
| theorems: | |
| - Set.Sized.upShadow | |
| - path: Mathlib/GroupTheory/Submonoid/Operations.lean | |
| theorems: | |
| - Submonoid.eq_bot_of_subsingleton | |
| - path: Mathlib/RingTheory/IsAdjoinRoot.lean | |
| theorems: | |
| - IsAdjoinRootMonic.modByMonicHom_root_pow | |
| - path: Mathlib/LinearAlgebra/Matrix/Spectrum.lean | |
| theorems: | |
| - Matrix.IsHermitian.eigenvectorMatrix_apply | |
| - path: Mathlib/Algebra/GradedMonoid.lean | |
| theorems: | |
| - SetLike.pow_mem_graded | |
| - path: Mathlib/Data/ENNReal/Real.lean | |
| theorems: | |
| - ENNReal.ofReal_lt_one | |
| - path: Mathlib/Data/Nat/Log.lean | |
| theorems: | |
| - Nat.clog_eq_one | |
| - path: Mathlib/LinearAlgebra/Dual.lean | |
| theorems: | |
| - Module.forall_dual_apply_eq_zero_iff | |
| - Subspace.dualRestrict_comp_dualLift | |
| - Subspace.map_dualCoannihilator | |
| - Submodule.exists_dual_map_eq_bot_of_lt_top | |
| - path: Mathlib/Algebra/Homology/HomologicalBicomplex.lean | |
| theorems: | |
| - "HomologicalComplex\u2082.d_comm" | |
| - path: Mathlib/MeasureTheory/Function/LpSeminorm/Basic.lean | |
| theorems: | |
| - MeasureTheory.snorm'_measure_zero_of_neg | |
| - MeasureTheory.snorm_zero' | |
| - MeasureTheory.snormEssSup_mono_measure | |
| - "MeasureTheory.mem\u2112p_const" | |
| - path: Mathlib/Analysis/Calculus/LineDeriv/Basic.lean | |
| theorems: | |
| - HasLineDerivWithinAt.congr_mono | |
| - HasFDerivWithinAt.hasLineDerivWithinAt | |
| - path: Mathlib/AlgebraicTopology/SimplexCategory.lean | |
| theorems: | |
| - SimplexCategory.factorThruImage_eq | |
| - SimplexCategory.iso_eq_iso_refl | |
| - path: Mathlib/Data/Nat/Factorization/Root.lean | |
| theorems: | |
| - Nat.floorRoot_ne_zero | |
| - path: Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | |
| theorems: | |
| - DihedralGroup.orderOf_r_one | |
| - DihedralGroup.r_one_pow | |
| - path: Mathlib/Topology/Compactness/SigmaCompact.lean | |
| theorems: | |
| - CompactExhaustion.mem_diff_shiftr_find | |
| - path: Mathlib/Algebra/Function/Support.lean | |
| theorems: | |
| - Function.mulSupport_extend_one | |
| - Function.mulSupport_binop_subset | |
| - Function.range_subset_insert_image_mulSupport | |
| - path: Mathlib/Data/Set/Card.lean | |
| theorems: | |
| - Set.ncard_singleton_inter | |
| - Set.one_le_encard_iff_nonempty | |
| - Set.ncard_pair | |
| - Set.ncard_insert_le | |
| - Set.encard_eq_three | |
| - Set.fiber_ncard_ne_zero_iff_mem_image | |
| - path: Mathlib/RingTheory/WittVector/InitTail.lean | |
| theorems: | |
| - WittVector.init_init | |
| - path: Mathlib/GroupTheory/HNNExtension.lean | |
| theorems: | |
| - HNNExtension.lift_t | |
| - path: Mathlib/Data/List/BigOperators/Basic.lean | |
| theorems: | |
| - List.prod_isUnit_iff | |
| - Commute.list_prod_right | |
| - List.prod_map_neg | |
| - path: Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian.lean | |
| theorems: | |
| - WeierstrassCurve.Jacobian.equiv_of_Z_eq_zero | |
| - path: Mathlib/Data/Int/Lemmas.lean | |
| theorems: | |
| - Int.natAbs_inj_of_nonneg_of_nonneg | |
| - path: Mathlib/Data/Fintype/Basic.lean | |
| theorems: | |
| - Fintype.choose_subtype_eq | |
| - path: Mathlib/RingTheory/Valuation/Basic.lean | |
| theorems: | |
| - Valuation.map_one_sub_of_lt | |
| - path: Mathlib/Algebra/EuclideanDomain/Defs.lean | |
| theorems: | |
| - EuclideanDomain.div_add_mod' | |
| - path: Mathlib/Analysis/SpecialFunctions/Gamma/BohrMollerup.lean | |
| theorems: | |
| - Real.BohrMollerup.logGammaSeq_add_one | |
| - path: Mathlib/CategoryTheory/Localization/CalculusOfFractions.lean | |
| theorems: | |
| - CategoryTheory.Localization.essSurj_mapArrow_of_hasLeftCalculusofFractions | |
| - CategoryTheory.MorphismProperty.LeftFraction.map_ofInv_hom_id | |
| - path: Mathlib/Analysis/PSeries.lean | |
| theorems: | |
| - Real.not_summable_indicator_one_div_natCast | |
| - Finset.le_sum_condensed' | |
| - Real.summable_one_div_nat_pow | |
| - path: Mathlib/Algebra/Lie/Submodule.lean | |
| theorems: | |
| - LieSubmodule.coe_toSubmodule_mk | |
| - LieHom.mem_idealRange | |
| - path: Mathlib/MeasureTheory/MeasurableSpace/Basic.lean | |
| theorems: | |
| - measurableSet_range_inl | |
| - path: Mathlib/Data/List/Rotate.lean | |
| theorems: | |
| - List.rotate_eq_nil_iff | |
| - List.get_rotate | |
| - path: Mathlib/NumberTheory/Cyclotomic/Basic.lean | |
| theorems: | |
| - IsCyclotomicExtension.iff_union_of_dvd | |
| - IsCyclotomicExtension.of_union_of_dvd | |
| - IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_root_cyclotomic | |
| - path: Mathlib/Data/List/Lattice.lean | |
| theorems: | |
| - List.nil_bagInter | |
| - path: Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | |
| theorems: | |
| - MeasureTheory.lintegral_fn_integral_sub | |
| - path: Mathlib/Topology/Order/Basic.lean | |
| theorems: | |
| - interior_Ico | |
| - nhds_eq_iInf_abs_sub | |
| - path: Mathlib/Computability/Halting.lean | |
| theorems: | |
| - Partrec.merge' | |
| - path: Mathlib/Topology/Separation.lean | |
| theorems: | |
| - isClosed_setOf_specializes | |
| - compl_singleton_mem_nhdsSet_iff | |
| - Set.EqOn.of_subset_closure | |
| - path: Mathlib/Algebra/Homology/TotalComplexSymmetry.lean | |
| theorems: | |
| - "HomologicalComplex\u2082.totalFlipIso_hom_f_D\u2082" | |
| - path: Mathlib/Order/SuccPred/Limit.lean | |
| theorems: | |
| - Order.not_isSuccLimit_of_noMax | |
| - path: Mathlib/RingTheory/PolynomialAlgebra.lean | |
| theorems: | |
| - matPolyEquiv_map_C | |
| - path: Mathlib/RingTheory/RootsOfUnity/Minpoly.lean | |
| theorems: | |
| - IsPrimitiveRoot.minpoly_dvd_expand | |
| - path: Mathlib/CategoryTheory/Closed/Ideal.lean | |
| theorems: | |
| - CategoryTheory.bijection_natural | |
| - path: Mathlib/Algebra/Lie/Weights/Basic.lean | |
| theorems: | |
| - LieModule.exists_weightSpace_le_ker_of_isNoetherian | |
| - path: Mathlib/Analysis/LocallyConvex/AbsConvex.lean | |
| theorems: | |
| - gaugeSeminormFamily_ball | |
| - path: Mathlib/Data/Nat/Sqrt.lean | |
| theorems: | |
| - Nat.sqrt_lt_self | |
| - path: Mathlib/NumberTheory/Pell.lean | |
| theorems: | |
| - Pell.exists_of_not_isSquare | |
| - path: Mathlib/Topology/ContinuousFunction/Algebra.lean | |
| theorems: | |
| - algebraMap_apply | |
| - path: Mathlib/Algebra/Order/Rearrangement.lean | |
| theorems: | |
| - Monovary.sum_comp_perm_smul_lt_sum_smul_iff | |
| - path: Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | |
| theorems: | |
| - AffineBasis.det_smul_coords_eq_cramer_coords | |
| - path: Mathlib/Topology/UniformSpace/Basic.lean | |
| theorems: | |
| - UniformSpace.to_nhds_mono | |
| - uniformity_le_symm | |
| - path: Mathlib/Data/List/Sigma.lean | |
| theorems: | |
| - List.keys_kreplace | |
| - List.dlookup_kinsert | |
| - path: Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | |
| theorems: | |
| - GeneralizedContinuedFraction.convergents'_of_int | |
| - path: Mathlib/RingTheory/TensorProduct/Basic.lean | |
| theorems: | |
| - LinearMap.baseChange_mul | |
| - Algebra.TensorProduct.lift_comp_includeRight | |
| - Algebra.TensorProduct.lift_includeLeft_includeRight | |
| - path: Mathlib/Algebra/CharP/Basic.lean | |
| theorems: | |
| - Ring.two_ne_zero | |
| - path: Mathlib/Analysis/Complex/UpperHalfPlane/Basic.lean | |
| theorems: | |
| - UpperHalfPlane.im_inv_neg_coe_pos | |
| - path: Mathlib/Data/Option/Basic.lean | |
| theorems: | |
| - Option.guard_eq_some' | |
| - path: Mathlib/RingTheory/Ideal/Norm.lean | |
| theorems: | |
| - Ideal.absNorm_eq_zero_iff | |
| - path: Mathlib/MeasureTheory/Measure/Haar/Unique.lean | |
| theorems: | |
| - MeasureTheory.Measure.measure_isMulInvariant_eq_smul_of_isCompact_closure | |
| - MeasureTheory.Measure.isHaarMeasure_eq_of_isProbabilityMeasure | |
| - path: Mathlib/Analysis/Analytic/Composition.lean | |
| theorems: | |
| - FormalMultilinearSeries.comp_removeZero | |
| - path: Mathlib/Logic/Hydra.lean | |
| theorems: | |
| - Relation.cutExpand_fibration | |
| - Relation.cutExpand_add_left | |
| - path: Mathlib/LinearAlgebra/Matrix/ToLin.lean | |
| theorems: | |
| - LinearMap.toMatrixAlgEquiv_apply | |
| - LinearMap.toMatrixAlgEquiv_mul | |
| - LinearMap.toMatrix_basis_equiv | |
| - path: Mathlib/NumberTheory/Rayleigh.lean | |
| theorems: | |
| - Beatty.hit_or_miss | |
| - path: Mathlib/Analysis/Convolution.lean | |
| theorems: | |
| - ConvolutionExistsAt.distrib_add | |
| - path: Mathlib/Data/Finset/LocallyFinite/Basic.lean | |
| theorems: | |
| - Finset.map_add_left_Ioo | |
| - Finset.Icc_erase_right | |
| - path: Mathlib/Algebra/Group/Ext.lean | |
| theorems: | |
| - CommGroup.toGroup_injective | |
| - path: Mathlib/LinearAlgebra/AffineSpace/Combination.lean | |
| theorems: | |
| - Finset.affineCombinationSingleWeights_apply_self | |
| - path: Mathlib/GroupTheory/Perm/Fin.lean | |
| theorems: | |
| - Fin.cycleRange_symm_succ | |
| - path: Mathlib/Topology/Algebra/UniformGroup.lean | |
| theorems: | |
| - UniformContinuous.pow_const | |
| - path: Mathlib/Topology/MetricSpace/Bounded.lean | |
| theorems: | |
| - Metric.ediam_univ_eq_top_iff_noncompact | |
| - Metric.diam_triple | |
| - path: Mathlib/Algebra/Order/Field/Basic.lean | |
| theorems: | |
| - div_mul_le_div_mul_of_div_le_div | |
| - le_div_iff_of_neg' | |
| - div_pos_iff | |
| - path: Mathlib/MeasureTheory/Function/UniformIntegrable.lean | |
| theorems: | |
| - MeasureTheory.tendsto_Lp_of_tendsto_ae | |
| - path: .lake/packages/std/Std/Data/HashMap/WF.lean | |
| theorems: | |
| - Std.HashMap.Imp.Buckets.exists_of_update | |
| - path: Mathlib/RingTheory/Polynomial/ScaleRoots.lean | |
| theorems: | |
| - Polynomial.support_scaleRoots_eq | |
| - path: Mathlib/CategoryTheory/Limits/MonoCoprod.lean | |
| theorems: | |
| - CategoryTheory.Limits.MonoCoprod.mono_binaryCofanSum_inr' | |
| - path: Mathlib/Algebra/Module/Injective.lean | |
| theorems: | |
| - Module.Baer.injective | |
| - path: Mathlib/LinearAlgebra/RootSystem/Basic.lean | |
| theorems: | |
| - RootPairing.isCrystallographic_iff | |
| - path: Mathlib/RepresentationTheory/Action/Monoidal.lean | |
| theorems: | |
| - Action.rightUnitor_hom_hom | |
| - path: Mathlib/Data/Part.lean | |
| theorems: | |
| - Part.toOption_isNone | |
| - path: Mathlib/Algebra/BigOperators/Intervals.lean | |
| theorems: | |
| - Finset.prod_Ico_add' | |
| - Finset.prod_Ico_mul_eq_prod_Icc | |
| - Finset.prod_Ico_reflect | |
| - path: Mathlib/Algebra/Lie/Weights/Chain.lean | |
| theorems: | |
| - LieModule.weightSpaceChain_neg | |
| - path: Mathlib/CategoryTheory/Limits/Types.lean | |
| theorems: | |
| - CategoryTheory.Limits.Types.Image.lift_fac | |
| - path: Mathlib/Algebra/Homology/ShortComplex/RightHomology.lean | |
| theorems: | |
| - CategoryTheory.ShortComplex.RightHomologyMapData.opcyclesMap_eq | |
| - CategoryTheory.ShortComplex.opcyclesMap'_comp | |
| - path: Mathlib/Order/Filter/Lift.lean | |
| theorems: | |
| - Filter.prod_lift'_lift' | |
| - path: Mathlib/AlgebraicGeometry/Morphisms/Basic.lean | |
| theorems: | |
| - AlgebraicGeometry.targetAffineLocallyOfOpenCover | |
| - AlgebraicGeometry.AffineTargetMorphismProperty.isLocalOfOpenCoverImply | |
| - path: Mathlib/RingTheory/Norm.lean | |
| theorems: | |
| - Algebra.norm_eq_prod_embeddings_gen | |
| - path: Mathlib/Data/PNat/Prime.lean | |
| theorems: | |
| - PNat.gcd_eq_right_iff_dvd | |
| - path: Mathlib/SetTheory/Ordinal/Arithmetic.lean | |
| theorems: | |
| - Ordinal.bsup_not_succ_of_ne_bsup | |
| - Ordinal.IsNormal.eq_iff_zero_and_succ | |
| - Acc.rank_lt_of_rel | |
| - Ordinal.div_nonempty | |
| - path: Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | |
| theorems: | |
| - intervalIntegral.integral_interval_sub_interval_comm | |
| - intervalIntegral.smul_integral_comp_add_mul | |
| - intervalIntegral.integral_cases | |
| - intervalIntegral.integral_congr | |
| - IntervalIntegrable.comp_add_right | |
| - path: Mathlib/RingTheory/DedekindDomain/Ideal.lean | |
| theorems: | |
| - FractionalIdeal.mul_inv_cancel | |
| - irreducible_pow_sup_of_le | |
| - path: Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | |
| theorems: | |
| - Real.exists_rat_pow_btwn | |
| - Real.one_le_rpow | |
| - path: Mathlib/RingTheory/Subring/Basic.lean | |
| theorems: | |
| - coe_int_mem | |
| - path: Mathlib/LinearAlgebra/Matrix/Basis.lean | |
| theorems: | |
| - Basis.coePiBasisFun.toMatrix_eq_transpose | |
| - path: Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | |
| theorems: | |
| - "AlgebraicTopology.DoldKan.\u0393\u2080.Obj.map_epi_on_summand_id" | |
| - path: Mathlib/Topology/Baire/Lemmas.lean | |
| theorems: | |
| - dense_biInter_of_isOpen | |
| - path: .lake/packages/std/Std/Data/Range/Lemmas.lean | |
| theorems: | |
| - Std.Range.forIn_eq_forIn_range' | |
| - path: Mathlib/Logic/Nontrivial/Basic.lean | |
| theorems: | |
| - Function.Injective.exists_ne | |
| - path: Mathlib/MeasureTheory/OuterMeasure/Basic.lean | |
| theorems: | |
| - MeasureTheory.OuterMeasure.restrict_apply | |
| - MeasureTheory.OuterMeasure.le_trim | |
| - path: Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | |
| theorems: | |
| - ProjectiveSpectrum.basicOpen_mul_le_left | |
| - path: Mathlib/Algebra/Parity.lean | |
| theorems: | |
| - range_two_mul | |
| - path: Mathlib/Logic/Lemmas.lean | |
| theorems: | |
| - dite_dite_distrib_right | |
| - path: Mathlib/Data/Matroid/Dual.lean | |
| theorems: | |
| - Matroid.dual_dual | |
| - path: Mathlib/Data/Polynomial/Smeval.lean | |
| theorems: | |
| - Polynomial.smeval_C | |
| - path: Mathlib/Algebra/ModEq.lean | |
| theorems: | |
| - AddCommGroup.modEq_refl | |
| - path: Mathlib/Logic/Function/Conjugate.lean | |
| theorems: | |
| - Function.Semiconj.inverses_right | |
| - path: Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | |
| theorems: | |
| - summable_mul_right_iff | |
| - path: Mathlib/LinearAlgebra/Alternating/Basic.lean | |
| theorems: | |
| - AlternatingMap.curryLeft_same | |
| - path: Mathlib/RingTheory/FractionalIdeal/Operations.lean | |
| theorems: | |
| - FractionalIdeal.map_symm_map | |
| - path: Mathlib/Logic/Function/Basic.lean | |
| theorems: | |
| - Function.sometimes_spec | |
| - Function.extend_def | |
| - path: Mathlib/Algebra/Homology/Homotopy.lean | |
| theorems: | |
| - Homotopy.nullHomotopicMap'_f | |
| - path: Mathlib/Analysis/Complex/PhragmenLindelof.lean | |
| theorems: | |
| - PhragmenLindelof.right_half_plane_of_tendsto_zero_on_real | |
| - PhragmenLindelof.horizontal_strip | |
| - path: Mathlib/CategoryTheory/Comma/Presheaf.lean | |
| theorems: | |
| - "CategoryTheory.OverPresheafAux.YonedaCollection.map\u2081_fst" | |
| - path: Mathlib/LinearAlgebra/BilinearForm/Basic.lean | |
| theorems: | |
| - BilinForm.coe_injective | |
| - path: Mathlib/Data/Vector.lean | |
| theorems: | |
| - Vector.toList_drop | |
| - path: Mathlib/Data/Int/CardIntervalMod.lean | |
| theorems: | |
| - Nat.count_modEq_card | |
| - Int.Ioc_filter_modEq_card | |
| - path: Mathlib/SetTheory/Cardinal/Basic.lean | |
| theorems: | |
| - Cardinal.power_mul | |
| - Cardinal.lift_le_aleph0 | |
| - Cardinal.lift_mk_le_lift_mk_mul_of_lift_mk_preimage_le | |
| - path: Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | |
| theorems: | |
| - CategoryTheory.Limits.prod.comp_lift | |
| - path: Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | |
| theorems: | |
| - PartialHomeomorph.extend_image_nhd_mem_nhds_of_boundaryless | |
| - path: Mathlib/LinearAlgebra/Pi.lean | |
| theorems: | |
| - LinearMap.pi_zero | |
| - LinearMap.iInf_ker_proj | |
| - path: Mathlib/Data/Polynomial/Basic.lean | |
| theorems: | |
| - Polynomial.toFinsupp_sub | |
| - path: Mathlib/RingTheory/Ideal/Basic.lean | |
| theorems: | |
| - Ideal.mem_span_singleton | |
| - Ideal.eq_bot_or_top | |
| - path: Mathlib/Topology/Semicontinuous.lean | |
| theorems: | |
| - lowerSemicontinuousWithinAt_tsum | |
| - lowerSemicontinuousAt_tsum | |
| - upperSemicontinuousAt_sum | |
| - path: Mathlib/Data/Multiset/Basic.lean | |
| theorems: | |
| - Multiset.Rel.add | |
| - Multiset.cons_subset | |
| - Multiset.erase_add_right_pos | |
| - path: Mathlib/MeasureTheory/Measure/VectorMeasure.lean | |
| theorems: | |
| - MeasureTheory.Measure.toENNRealVectorMeasure_ennrealToMeasure | |
| - MeasureTheory.VectorMeasure.restrict_add | |
| - MeasureTheory.Measure.toSignedMeasure_congr | |
| - MeasureTheory.VectorMeasure.hasSum_of_disjoint_iUnion | |
| - path: Mathlib/Algebra/Order/Sub/Defs.lean | |
| theorems: | |
| - AddLECancellable.tsub_eq_of_eq_add_rev | |
| - path: Mathlib/Analysis/NormedSpace/Spectrum.lean | |
| theorems: | |
| - spectrum.differentiableOn_inverse_one_sub_smul | |
| - path: Mathlib/Computability/Partrec.lean | |
| theorems: | |
| - Computable.ofOption | |
| - path: Mathlib/CategoryTheory/Limits/Shapes/Types.lean | |
| theorems: | |
| - CategoryTheory.Limits.Types.equalizerIso_hom_comp_subtype | |
| - path: Mathlib/Control/EquivFunctor.lean | |
| theorems: | |
| - EquivFunctor.mapEquiv.injective | |
| - path: Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | |
| theorems: | |
| - MeasureTheory.MeasurePreserving.restrict_image_emb | |
| - MeasureTheory.MeasurePreserving.restrict_preimage_emb | |
| - path: Mathlib/Analysis/Calculus/Implicit.lean | |
| theorems: | |
| - ImplicitFunctionData.map_nhds_eq | |
| - path: Mathlib/Data/Finmap.lean | |
| theorems: | |
| - Finmap.keys_union | |
| - Finmap.keysLookupEquiv_symm_apply_keys | |
| - path: Mathlib/RingTheory/Ideal/Cotangent.lean | |
| theorems: | |
| - Ideal.to_quotient_square_range | |
| - path: Mathlib/Topology/Algebra/Order/Field.lean | |
| theorems: | |
| - Filter.Tendsto.div_atTop | |
| - path: Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | |
| theorems: | |
| - LiouvilleWith.int_add_iff | |
| - path: Mathlib/AlgebraicGeometry/Properties.lean | |
| theorems: | |
| - AlgebraicGeometry.basicOpen_eq_bot_iff | |
| - path: Mathlib/Order/ModularLattice.lean | |
| theorems: | |
| - eq_of_le_of_inf_le_of_sup_le | |
| - path: Mathlib/Combinatorics/SimpleGraph/Maps.lean | |
| theorems: | |
| - SimpleGraph.map_le_iff_le_comap | |
| - path: Mathlib/Data/Set/Intervals/Instances.lean | |
| theorems: | |
| - Set.Ioc.coe_eq_one | |
| - Set.Icc.one_sub_nonneg | |
| - path: Mathlib/Data/Matroid/Basic.lean | |
| theorems: | |
| - Matroid.base_compl_iff_mem_maximals_disjoint_base | |
| - path: Mathlib/Algebra/Group/Basic.lean | |
| theorems: | |
| - conj_eq_one_iff | |
| - path: Mathlib/Computability/AkraBazzi/GrowsPolynomially.lean | |
| theorems: | |
| - AkraBazziRecurrence.GrowsPolynomially.eventually_atTop_zero_or_pos_or_neg | |
| - path: Mathlib/Analysis/Convex/Intrinsic.lean | |
| theorems: | |
| - intrinsicClosure_empty | |
| - path: Mathlib/GroupTheory/Complement.lean | |
| theorems: | |
| - Subgroup.coe_transferFunction | |
| - Subgroup.IsComplement.equiv_mul_left | |
| - path: Mathlib/Analysis/Normed/Group/HomCompletion.lean | |
| theorems: | |
| - NormedAddGroupHom.ker_le_ker_completion | |
| - path: Mathlib/MeasureTheory/Constructions/Polish.lean | |
| theorems: | |
| - MeasurableSet.isClopenable | |
| - path: Mathlib/Topology/Bases.lean | |
| theorems: | |
| - Pairwise.countable_of_isOpen_disjoint | |
| - path: Mathlib/Data/List/Infix.lean | |
| theorems: | |
| - List.map_reverse_inits | |
| - path: Mathlib/Algebra/Module/Zlattice.lean | |
| theorems: | |
| - Zlattice.FG | |
| - path: Mathlib/SetTheory/ZFC/Basic.lean | |
| theorems: | |
| - Class.coe_sUnion | |
| - ZFSet.toSet_sep | |
| - ZFSet.toSet_subset_iff | |
| - path: Mathlib/Analysis/Asymptotics/Theta.lean | |
| theorems: | |
| - Asymptotics.isTheta_inv | |
| - path: Mathlib/Data/PFunctor/Univariate/M.lean | |
| theorems: | |
| - PFunctor.M.ext_aux | |
| - path: Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | |
| theorems: | |
| - WithTop.coe_iSup | |
| - path: Mathlib/NumberTheory/NumberField/CanonicalEmbedding.lean | |
| theorems: | |
| - NumberField.mixedEmbedding.convexBodySum_volume | |
| - path: Mathlib/Algebra/GCDMonoid/Basic.lean | |
| theorems: | |
| - normalize_coe_units | |
| - lcm_mul_right | |
| - Associates.dvd_out_iff | |
| - path: Mathlib/Data/Set/Image.lean | |
| theorems: | |
| - Set.forall_mem_range | |
| - Set.image_union_image_compl_eq_range | |
| - Set.image_preimage_eq_of_subset | |
| - path: Mathlib/FieldTheory/ChevalleyWarning.lean | |
| theorems: | |
| - char_dvd_card_solutions_of_fintype_sum_lt | |
| - path: .lake/packages/std/Std/Data/List/Count.lean | |
| theorems: | |
| - List.count_le_count_map | |
| - path: Mathlib/Data/Fintype/BigOperators.lean | |
| theorems: | |
| - Finset.prod_toFinset_eq_subtype | |
| - path: Mathlib/MeasureTheory/Integral/IntervalAverage.lean | |
| theorems: | |
| - interval_average_symm | |
| - path: Mathlib/Geometry/Euclidean/Basic.lean | |
| theorems: | |
| - EuclideanGeometry.dist_smul_vadd_eq_dist | |
| - EuclideanGeometry.dist_left_midpoint_eq_dist_right_midpoint | |
| - path: Mathlib/RingTheory/RingHomProperties.lean | |
| theorems: | |
| - RingHom.RespectsIso.cancel_right_isIso | |
| - path: Mathlib/Data/Set/Prod.lean | |
| theorems: | |
| - Set.range_pair_subset | |
| - path: Mathlib/LinearAlgebra/Matrix/Block.lean | |
| theorems: | |
| - Matrix.blockTriangular_stdBasisMatrix | |
| - path: Mathlib/Topology/Instances/Sign.lean | |
| theorems: | |
| - continuousAt_sign_of_pos | |
| - path: Mathlib/Data/DFinsupp/Order.lean | |
| theorems: | |
| - DFinsupp.support_tsub | |
| - path: Mathlib/Topology/MetricSpace/Basic.lean | |
| theorems: | |
| - MetricSpace.replaceBornology_eq | |
| - path: Mathlib/Data/Nat/Digits.lean | |
| theorems: | |
| - Nat.ofDigits_one_cons | |
| - path: Mathlib/NumberTheory/FLT/Four.lean | |
| theorems: | |
| - Fermat42.comm | |
| - path: Mathlib/Data/Nat/GCD/Basic.lean | |
| theorems: | |
| - Nat.coprime_pow_left_iff | |
| - path: Mathlib/Logic/Equiv/PartialEquiv.lean | |
| theorems: | |
| - PartialEquiv.refl_restr_target | |
| - path: Mathlib/Analysis/Complex/AbsMax.lean | |
| theorems: | |
| - Complex.exists_mem_frontier_isMaxOn_norm | |
| - path: Mathlib/Computability/Reduce.lean | |
| theorems: | |
| - ComputablePred.computable_of_manyOneReducible | |
| - path: Mathlib/NumberTheory/NumberField/Embeddings.lean | |
| theorems: | |
| - NumberField.InfinitePlace.exists_smul_eq_of_comap_eq | |
| - path: Mathlib/CategoryTheory/Bicategory/Basic.lean | |
| theorems: | |
| - CategoryTheory.Bicategory.leftUnitor_inv_naturality | |
| - path: Mathlib/Analysis/Calculus/Deriv/Mul.lean | |
| theorems: | |
| - HasDerivAtFilter.const_smul | |
| - path: Mathlib/CategoryTheory/Monoidal/Preadditive.lean | |
| theorems: | |
| - "CategoryTheory.leftDistributor_ext\u2082_right" | |
| - path: Mathlib/Algebra/ContinuedFractions/Translations.lean | |
| theorems: | |
| - GeneralizedContinuedFraction.first_denominator_eq | |
| - path: Mathlib/Geometry/Manifold/MFDeriv/Atlas.lean | |
| theorems: | |
| - PartialHomeomorph.MDifferentiable.symm_comp_deriv | |
| - path: Mathlib/GroupTheory/Index.lean | |
| theorems: | |
| - Subgroup.inf_relindex_left | |
| - path: Mathlib/Data/Finset/Lattice.lean | |
| theorems: | |
| - Finset.card_le_of_interleaved | |
| - Finset.sup_le_iff | |
| - path: Mathlib/RingTheory/Ideal/Over.lean | |
| theorems: | |
| - Ideal.eq_bot_of_comap_eq_bot | |
| - path: Mathlib/RingTheory/Derivation/Basic.lean | |
| theorems: | |
| - Derivation.leibniz_of_mul_eq_one | |
| - path: Mathlib/Data/List/Chain.lean | |
| theorems: | |
| - List.Chain'.infix | |
| - path: Mathlib/Data/Real/Irrational.lean | |
| theorems: | |
| - irrational_iff_ne_rational | |
| - path: Mathlib/Data/List/Zip.lean | |
| theorems: | |
| - List.unzip_zip_left | |
| - path: Mathlib/MeasureTheory/Group/Prod.lean | |
| theorems: | |
| - MeasureTheory.absolutelyContinuous_map_mul_right | |
| - path: Mathlib/CategoryTheory/Sites/Coherent/Equivalence.lean | |
| theorems: | |
| - CategoryTheory.Equivalence.precoherent_eq | |
| - path: Mathlib/MeasureTheory/Function/L1Space.lean | |
| theorems: | |
| - MeasureTheory.L1.dist_def | |
| - path: Mathlib/Analysis/SpecialFunctions/Integrals.lean | |
| theorems: | |
| - integral_sin_pow_aux | |
| - path: Mathlib/Data/Polynomial/Laurent.lean | |
| theorems: | |
| - LaurentPolynomial.T_sub | |
| - LaurentPolynomial.invert_C | |
| - path: Mathlib/Topology/Algebra/Order/Compact.lean | |
| theorems: | |
| - cocompact_le_atBot_atTop | |
| - path: Mathlib/LinearAlgebra/QuadraticForm/Prod.lean | |
| theorems: | |
| - QuadraticForm.posDef_prod_iff | |
| - path: Mathlib/MeasureTheory/Integral/Lebesgue.lean | |
| theorems: | |
| - NNReal.count_const_le_le_of_tsum_le | |
| - MeasureTheory.lintegral_indicator_le | |
| - path: Mathlib/CategoryTheory/Adjunction/Opposites.lean | |
| theorems: | |
| - CategoryTheory.Adjunction.homEquiv_leftAdjointUniq_hom_app | |
| - path: Mathlib/Topology/UniformSpace/CompactConvergence.lean | |
| theorems: | |
| - ContinuousMap.mem_compactConvergence_entourage_iff | |
| - Filter.HasBasis.compactConvergenceUniformity | |
| - path: Mathlib/Algebra/Order/Sub/Canonical.lean | |
| theorems: | |
| - AddLECancellable.tsub_lt_iff_left | |
| - path: Mathlib/MeasureTheory/Group/Integral.lean | |
| theorems: | |
| - MeasureTheory.Integrable.comp_div_right | |
| - path: Mathlib/Combinatorics/SimpleGraph/Regularity/Bound.lean | |
| theorems: | |
| - SzemerediRegularity.eps_pos | |
| - path: Mathlib/Topology/MetricSpace/PseudoMetric.lean | |
| theorems: | |
| - Real.Ioo_eq_ball | |
| - swap_dist | |
| - path: Mathlib/Order/Lattice.lean | |
| theorems: | |
| - sup_right_comm | |
| - inf_eq_right | |
| - path: Mathlib/Algebra/Module/Submodule/Bilinear.lean | |
| theorems: | |
| - "Submodule.map\u2082_flip" | |
| - "Submodule.map\u2082_eq_span_image2" | |
| - path: Mathlib/Order/WithBot.lean | |
| theorems: | |
| - WithBot.some_le_some | |
| - path: Mathlib/Geometry/Manifold/InteriorBoundary.lean | |
| theorems: | |
| - ModelWithCorners.boundary_eq_complement_interior | |
| - path: Mathlib/FieldTheory/Minpoly/MinpolyDiv.lean | |
| theorems: | |
| - natDegree_minpolyDiv_succ | |
| - path: Mathlib/LinearAlgebra/Ray.lean | |
| theorems: | |
| - eq_zero_of_sameRay_self_neg | |
| - path: Mathlib/Data/Finset/Pointwise.lean | |
| theorems: | |
| - "Finset.smul_univ\u2080" | |
| - Finset.preimage_mul_left_singleton | |
| - path: Mathlib/Data/Setoid/Partition.lean | |
| theorems: | |
| - Setoid.classes_ker_subset_fiber_set | |
| - path: Mathlib/Topology/Connected/PathConnected.lean | |
| theorems: | |
| - Path.map_trans | |
| - path: Mathlib/Algebra/Module/Submodule/Map.lean | |
| theorems: | |
| - LinearMap.map_codRestrict | |
| - path: Mathlib/NumberTheory/RamificationInertia.lean | |
| theorems: | |
| - Ideal.powQuotSuccInclusion_injective | |
| - path: Mathlib/Algebra/Homology/ShortComplex/QuasiIso.lean | |
| theorems: | |
| - CategoryTheory.ShortComplex.quasiIso_iff_isIso_descOpcycles | |
| - CategoryTheory.ShortComplex.quasiIso_opMap_iff | |
| - path: Mathlib/Data/Nat/Fib/Zeckendorf.lean | |
| theorems: | |
| - Nat.zeckendorf_succ | |
| - path: Mathlib/Geometry/Euclidean/Angle/Oriented/RightAngle.lean | |
| theorems: | |
| - EuclideanGeometry.dist_div_sin_oangle_right_of_oangle_eq_pi_div_two | |
| - Orientation.sin_oangle_sub_right_of_oangle_eq_pi_div_two | |
| - path: Mathlib/LinearAlgebra/Contraction.lean | |
| theorems: | |
| - dualTensorHomEquivOfBasis_apply | |
| - homTensorHomEquiv_toLinearMap | |
| - path: Mathlib/GroupTheory/Subgroup/Basic.lean | |
| theorems: | |
| - Subgroup.Normal.comap | |
| - mul_mem_cancel_right | |
| - Subgroup.map_eq_comap_of_inverse | |
| - path: Mathlib/Algebra/Periodic.lean | |
| theorems: | |
| - Function.Antiperiodic.neg_eq | |
| - path: Mathlib/Data/Polynomial/Splits.lean | |
| theorems: | |
| - Polynomial.splits_mul | |
| - path: Mathlib/Data/Finset/Card.lean | |
| theorems: | |
| - Finset.injOn_of_card_image_eq | |
| - path: Mathlib/Tactic/Ring/Basic.lean | |
| theorems: | |
| - Mathlib.Tactic.Ring.div_pf | |
| - Mathlib.Tactic.Ring.mul_one | |
| - path: Mathlib/Data/Set/Pairwise/Lattice.lean | |
| theorems: | |
| - Set.pairwise_sUnion | |
| - path: Mathlib/AlgebraicGeometry/StructureSheaf.lean | |
| theorems: | |
| - AlgebraicGeometry.StructureSheaf.comap_const | |
| - path: Mathlib/Geometry/Euclidean/Angle/Oriented/Basic.lean | |
| theorems: | |
| - Orientation.oangle_sign_sub_smul_right | |
| - Orientation.oangle_eq_zero_iff_sameRay | |
| - path: Mathlib/LinearAlgebra/LinearIndependent.lean | |
| theorems: | |
| - linearIndependent_sum | |
| - LinearIndependent.map' | |
| - linearIndependent_iff | |
| - path: Mathlib/RingTheory/Polynomial/Basic.lean | |
| theorems: | |
| - Polynomial.exists_irreducible_of_natDegree_pos | |
| - path: Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | |
| theorems: | |
| - MeasureTheory.Measure.mutuallySingular_singularPart | |
| - path: Mathlib/CategoryTheory/Limits/Shapes/Images.lean | |
| theorems: | |
| - "CategoryTheory.Limits.image.map_\u03B9" | |
| - path: Mathlib/Analysis/SpecialFunctions/Gamma/Basic.lean | |
| theorems: | |
| - Complex.Gamma_eq_GammaAux | |
| - path: Mathlib/Analysis/Complex/CauchyIntegral.lean | |
| theorems: | |
| - Complex.circleIntegral_div_sub_of_differentiable_on_off_countable | |
| - Complex.integral_boundary_rect_of_hasFDerivAt_real_off_countable | |
| - path: Mathlib/Algebra/Lie/Basic.lean | |
| theorems: | |
| - LieHom.ext_iff | |
| - path: Mathlib/LinearAlgebra/PiTensorProduct.lean | |
| theorems: | |
| - PiTensorProduct.tprodCoeff_eq_smul_tprod | |
| - path: Mathlib/MeasureTheory/Measure/Tilted.lean | |
| theorems: | |
| - MeasureTheory.tilted_neg_same | |
| - path: Mathlib/Data/Holor.lean | |
| theorems: | |
| - Holor.cprankMax_upper_bound | |
| - path: Mathlib/Data/Polynomial/Degree/Definitions.lean | |
| theorems: | |
| - Polynomial.degree_X_sub_C | |
| - Polynomial.leadingCoeff_quadratic | |
| - Polynomial.X_pow_add_C_ne_one | |
| - path: Mathlib/Analysis/Calculus/LHopital.lean | |
| theorems: | |
| - deriv.lhopital_zero_atBot_on_Iio | |
| - path: Mathlib/MeasureTheory/Measure/Stieltjes.lean | |
| theorems: | |
| - StieltjesFunction.iInf_Ioi_eq | |
| - StieltjesFunction.measure_singleton | |
| - StieltjesFunction.measure_Ioc | |
| - path: Mathlib/Analysis/Normed/Group/Pointwise.lean | |
| theorems: | |
| - IsCompact.closedBall_mul | |
| - div_ball_one | |
| - path: Mathlib/MeasureTheory/Group/Arithmetic.lean | |
| theorems: | |
| - List.aemeasurable_prod | |
| - path: Mathlib/Algebra/Ring/Prod.lean | |
| theorems: | |
| - RingHom.prod_unique | |
| - path: Mathlib/Algebra/Order/Archimedean.lean | |
| theorems: | |
| - existsUnique_sub_zsmul_mem_Ico | |
| - path: Mathlib/Logic/Unique.lean | |
| theorems: | |
| - unique_subtype_iff_exists_unique | |
| - path: Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | |
| theorems: | |
| - IsCyclic.ext | |
| - path: Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | |
| theorems: | |
| - QuadraticForm.associated_left_inverse | |
| - path: Mathlib/Algebra/Order/CompleteField.lean | |
| theorems: | |
| - LinearOrderedField.le_inducedMap_mul_self_of_mem_cutMap | |
| - path: Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | |
| theorems: | |
| - Matrix.nonsing_inv_mul_cancel_right | |
| - path: Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | |
| theorems: | |
| - MeasureTheory.Measure.measure_prod_null | |
| - MeasureTheory.Measure.prod_restrict | |
| - path: Mathlib/Computability/TMToPartrec.lean | |
| theorems: | |
| - Turing.PartrecToTM2.move_ok | |
| - path: Mathlib/Algebra/Homology/HomotopyCategory/MappingCone.lean | |
| theorems: | |
| - CochainComplex.mappingCone.liftCochain_descCochain | |
| - CochainComplex.mappingCone.ext_to | |
| - path: Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | |
| theorems: | |
| - MeasureTheory.FiniteMeasure.eq_of_forall_apply_eq | |
| - path: Mathlib/Data/Analysis/Topology.lean | |
| theorems: | |
| - Ctop.ofEquiv_val | |
| - path: Mathlib/NumberTheory/Modular.lean | |
| theorems: | |
| - ModularGroup.re_T_zpow_smul | |
| - path: Mathlib/RingTheory/Polynomial/Content.lean | |
| theorems: | |
| - Polynomial.primPart_mul | |
| - Polynomial.normUnit_content | |
| - path: Mathlib/Order/Sublattice.lean | |
| theorems: | |
| - Sublattice.map_symm_eq_iff_eq_map | |
| - path: Mathlib/Analysis/NormedSpace/PiLp.lean | |
| theorems: | |
| - PiLp.norm_equiv_symm_const' | |
| - path: Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | |
| theorems: | |
| - MeasureTheory.measure_eq_trim | |
| - path: Mathlib/Probability/Process/Stopping.lean | |
| theorems: | |
| - MeasureTheory.IsStoppingTime.measurableSet_lt | |
| - MeasureTheory.stronglyMeasurable_stoppedValue_of_le | |
| - path: .lake/packages/std/Std/Data/Int/Order.lean | |
| theorems: | |
| - Int.natAbs_add_le | |
| - path: Mathlib/FieldTheory/Finite/Trace.lean | |
| theorems: | |
| - FiniteField.trace_to_zmod_nondegenerate | |
| - path: Mathlib/Probability/Independence/Kernel.lean | |
| theorems: | |
| - ProbabilityTheory.kernel.iIndepFun.indepFun_mul_left | |
| - path: Mathlib/NumberTheory/ClassNumber/Finite.lean | |
| theorems: | |
| - ClassGroup.mkMMem_surjective | |
| - path: Mathlib/Algebra/GroupWithZero/Hom.lean | |
| theorems: | |
| - NeZero.of_map | |
| - path: Mathlib/LinearAlgebra/Quotient.lean | |
| theorems: | |
| - Submodule.unique_quotient_iff_eq_top | |
| - path: Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | |
| theorems: | |
| - NNReal.orderIsoRpow_symm_eq | |
| - ENNReal.top_rpow_of_pos | |
| - path: Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | |
| theorems: | |
| - InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zero | |
| - path: Mathlib/GroupTheory/Perm/Cycle/Factors.lean | |
| theorems: | |
| - Equiv.Perm.cycleFactorsFinset_injective | |
| - Equiv.Perm.IsCycle.cycleOf | |
| - path: Mathlib/LinearAlgebra/CliffordAlgebra/Conjugation.lean | |
| theorems: | |
| - CliffordAlgebra.evenOdd_comap_reverse | |
| - path: Mathlib/AlgebraicGeometry/Spec.lean | |
| theorems: | |
| - AlgebraicGeometry.Spec.sheafedSpaceMap_comp | |
| - path: Mathlib/Data/Nat/PartENat.lean | |
| theorems: | |
| - PartENat.withTopEquiv_ofNat | |
| - PartENat.get_le_get | |
| - path: Mathlib/NumberTheory/LSeries/Convergence.lean | |
| theorems: | |
| - LSeries.abscissaOfAbsConv_le_of_forall_lt_LSeriesSummable' | |
| - path: Mathlib/Data/Nat/Order/Lemmas.lean | |
| theorems: | |
| - Nat.dvd_right_iff_eq | |
| - Nat.div_eq_zero_iff | |
| - path: Mathlib/Analysis/Convex/Side.lean | |
| theorems: | |
| - AffineSubspace.sSameSide_iff_exists_left | |
| - path: Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | |
| theorems: | |
| - Real.Angle.cos_toReal | |
| - path: Mathlib/Data/Erased.lean | |
| theorems: | |
| - Erased.out_mk | |
| - path: Mathlib/Topology/EMetricSpace/Lipschitz.lean | |
| theorems: | |
| - continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWith | |
| - path: Mathlib/Algebra/Order/CauSeq/BigOperators.lean | |
| theorems: | |
| - IsCauSeq.of_abv_le | |
| - IsCauSeq.series_ratio_test | |
| - path: Mathlib/CategoryTheory/Functor/FullyFaithful.lean | |
| theorems: | |
| - CategoryTheory.preimage_comp | |
| - path: Mathlib/Analysis/Calculus/Deriv/Comp.lean | |
| theorems: | |
| - HasDerivAt.iterate | |
| - path: Mathlib/Algebra/Quandle.lean | |
| theorems: | |
| - Rack.self_distrib_inv | |
| - path: Mathlib/ModelTheory/Algebra/Field/CharP.lean | |
| theorems: | |
| - FirstOrder.Field.realize_eqZero | |
| - path: Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | |
| theorems: | |
| - Polynomial.cyclotomic_coeff_zero | |
| - path: Mathlib/Analysis/ODE/Gronwall.lean | |
| theorems: | |
| - le_gronwallBound_of_liminf_deriv_right_le | |
| - path: Mathlib/Analysis/SpecialFunctions/Exp.lean | |
| theorems: | |
| - Real.comap_exp_nhds_zero | |
| - path: Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | |
| theorems: | |
| - PrimeSpectrum.basicOpen_mul_le_left | |
| - PrimeSpectrum.vanishingIdeal_strict_anti_mono_iff | |
| - path: Mathlib/LinearAlgebra/Matrix/Transvection.lean | |
| theorems: | |
| - Matrix.det_transvection_of_ne | |
| - path: Mathlib/Data/Matrix/Basic.lean | |
| theorems: | |
| - Matrix.comp_equiv_symm_dotProduct | |
| - path: Mathlib/NumberTheory/Dioph.lean | |
| theorems: | |
| - Dioph.mod_dioph | |
| - path: Mathlib/Data/Set/Lattice.lean | |
| theorems: | |
| - Set.iInter_eq_empty_iff | |
| - Set.biInter_iUnion | |
| - Set.iUnion_setOf | |
| - path: Mathlib/RingTheory/Nullstellensatz.lean | |
| theorems: | |
| - MvPolynomial.vanishingIdeal_pointToPoint | |
| - path: Mathlib/Geometry/Manifold/IntegralCurve.lean | |
| theorems: | |
| - isIntegralCurve_iff_isIntegralCurveAt | |
| - path: Mathlib/LinearAlgebra/Lagrange.lean | |
| theorems: | |
| - Lagrange.natDegree_basisDivisor_self | |
| - path: Mathlib/ModelTheory/Algebra/Ring/Basic.lean | |
| theorems: | |
| - FirstOrder.Ring.realize_one | |
| - path: .lake/packages/std/Std/Data/Int/DivMod.lean | |
| theorems: | |
| - Int.negSucc_emod | |
| - path: Mathlib/RingTheory/DedekindDomain/SelmerGroup.lean | |
| theorems: | |
| - IsDedekindDomain.HeightOneSpectrum.valuation_of_unit_eq | |
| - path: Mathlib/Analysis/Fourier/FourierTransformDeriv.lean | |
| theorems: | |
| - Real.hasDerivAt_fourierChar | |
| - path: Mathlib/Data/Multiset/LocallyFinite.lean | |
| theorems: | |
| - Multiset.Ico_filter_lt_of_le_right | |
| - path: Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | |
| theorems: | |
| - tsum_subtype_eq_of_support_subset | |
| - hasSum_extend_zero | |
| - path: Mathlib/Topology/Homotopy/Product.lean | |
| theorems: | |
| - Path.Homotopic.prod_projLeft_projRight | |
| - path: Mathlib/Algebra/Homology/Additive.lean | |
| theorems: | |
| - HomologicalComplex.singleMapHomologicalComplex_hom_app_ne | |
| - path: Mathlib/Algebra/Group/Units.lean | |
| theorems: | |
| - eq_divp_iff_mul_eq | |
| - IsUnit.div_left_inj | |
| - path: .lake/packages/std/Std/Data/List/Lemmas.lean | |
| theorems: | |
| - List.drop_take | |
| - List.diff_cons | |
| - List.Sublist.eq_of_length | |
| - List.range'_eq_nil | |
| - path: Mathlib/Data/Nat/Order/Basic.lean | |
| theorems: | |
| - Nat.findGreatest_spec | |
| - path: Mathlib/LinearAlgebra/ExteriorAlgebra/Basic.lean | |
| theorems: | |
| - "ExteriorAlgebra.\u03B9Multi_span_fixedDegree" | |
| - path: Mathlib/LinearAlgebra/CrossProduct.lean | |
| theorems: | |
| - triple_product_eq_det | |
| - path: Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | |
| theorems: | |
| - CategoryTheory.Limits.isIso_of_source_target_iso_zero | |
| - path: Mathlib/Algebra/Divisibility/Units.lean | |
| theorems: | |
| - isRelPrime_mul_unit_left_right | |
| - path: Mathlib/Analysis/Analytic/Basic.lean | |
| theorems: | |
| - HasFPowerSeriesOnBall.eventually_eq_zero | |
| - HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn' | |
| - path: Mathlib/GroupTheory/FreeAbelianGroup.lean | |
| theorems: | |
| - FreeAbelianGroup.lift.map_hom | |
| - path: Mathlib/CategoryTheory/Limits/Presheaf.lean | |
| theorems: | |
| - CategoryTheory.final_toCostructuredArrow_comp_pre | |
| - path: Mathlib/Combinatorics/Young/SemistandardTableau.lean | |
| theorems: | |
| - SemistandardYoungTableau.ext | |
| - path: Mathlib/Data/Nat/Pow.lean | |
| theorems: | |
| - Nat.one_lt_two_pow' | |
| - path: Mathlib/CategoryTheory/Limits/FilteredColimitCommutesFiniteLimit.lean | |
| theorems: | |
| - "CategoryTheory.Limits.\u03B9_colimitLimitIso_limit_\u03C0" | |
| - path: Mathlib/Data/Stream/Init.lean | |
| theorems: | |
| - Stream'.mem_interleave_left | |
| - path: Mathlib/Data/Nat/ModEq.lean | |
| theorems: | |
| - Nat.odd_mul_odd | |
| - path: Mathlib/Data/Nat/Factorial/Basic.lean | |
| theorems: | |
| - Nat.factorial_mul_ascFactorial | |
| - path: Mathlib/CategoryTheory/Limits/HasLimits.lean | |
| theorems: | |
| - CategoryTheory.Limits.colimit.pre_post | |
| - CategoryTheory.Limits.colimit.post_post | |
| - path: Mathlib/RingTheory/DedekindDomain/Different.lean | |
| theorems: | |
| - Submodule.traceDual_top' | |
| - path: Mathlib/Topology/Order/MonotoneConvergence.lean | |
| theorems: | |
| - tendsto_atTop_ciInf | |
| - path: Mathlib/NumberTheory/SumFourSquares.lean | |
| theorems: | |
| - Int.exists_sq_add_sq_add_one_eq_mul | |
| - path: Mathlib/NumberTheory/Padics/RingHoms.lean | |
| theorems: | |
| - PadicInt.ext_of_toZModPow | |
| - path: Mathlib/RingTheory/Noetherian.lean | |
| theorems: | |
| - isNoetherian_iff_wellFounded | |
| - path: Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean | |
| theorems: | |
| - Polynomial.cyclotomic_pos_and_nonneg | |
| - path: Mathlib/Analysis/SpecialFunctions/Gamma/Deligne.lean | |
| theorems: | |
| - "Complex.Gamma\u211D_mul_Gamma\u211D_add_one" | |
| - path: Mathlib/AlgebraicGeometry/Pullbacks.lean | |
| theorems: | |
| - AlgebraicGeometry.Scheme.Pullback.cocycle_snd_fst_snd | |
| - path: Mathlib/Topology/MetricSpace/Isometry.lean | |
| theorems: | |
| - IsometryEquiv.preimage_sphere | |
| - IsometryEquiv.completeSpace_iff | |
| - path: Mathlib/Probability/Kernel/MeasureCompProd.lean | |
| theorems: | |
| - MeasureTheory.Measure.snd_dirac_unit_compProd_const | |
| - path: Mathlib/Tactic/NormNum/Pow.lean | |
| theorems: | |
| - Mathlib.Meta.NormNum.isNat_zpow_pos | |
| - path: Mathlib/Data/Polynomial/Derivative.lean | |
| theorems: | |
| - Polynomial.iterate_derivative_X_pow_eq_smul | |
| - path: Mathlib/RingTheory/FinitePresentation.lean | |
| theorems: | |
| - Algebra.FiniteType.of_finitePresentation | |
| - path: Mathlib/CategoryTheory/ComposableArrows.lean | |
| theorems: | |
| - CategoryTheory.ComposableArrows.hom_ext_succ | |
| - path: Mathlib/Algebra/GroupWithZero/Units/Basic.lean | |
| theorems: | |
| - mul_div_cancel_of_imp | |
| - path: Mathlib/LinearAlgebra/Basic.lean | |
| theorems: | |
| - LinearEquiv.ofBijective_symm_apply_apply | |
| - Submodule.map_comap_eq | |
| - path: Mathlib/Algebra/CubicDiscriminant.lean | |
| theorems: | |
| - Cubic.natDegree_of_b_eq_zero | |
| - path: Mathlib/Init/Data/Nat/Lemmas.lean | |
| theorems: | |
| - Nat.bit1_lt_bit0 | |
| - path: Mathlib/Order/CompleteSublattice.lean | |
| theorems: | |
| - CompleteSublattice.coe_sInf' | |
| - path: Mathlib/CategoryTheory/Limits/Shapes/ConcreteCategory.lean | |
| theorems: | |
| - CategoryTheory.Limits.Concrete.pullbackMk_surjective | |
| - path: Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | |
| theorems: | |
| - DoubleCentralizer.norm_fst | |
| - DoubleCentralizer.norm_fst_eq_snd | |
| - path: Mathlib/Data/Nat/MaxPowDiv.lean | |
| theorems: | |
| - Nat.maxPowDiv.go_eq | |
| - path: Mathlib/GroupTheory/Perm/Basic.lean | |
| theorems: | |
| - Equiv.mul_swap_eq_swap_mul | |
| - path: Mathlib/Topology/UniformSpace/UniformConvergence.lean | |
| theorems: | |
| - tendstoLocallyUniformlyOn_univ | |
| - path: Mathlib/NumberTheory/SmoothNumbers.lean | |
| theorems: | |
| - Nat.mem_smoothNumbers' | |
| - path: Mathlib/Tactic/NormNum/Result.lean | |
| theorems: | |
| - Mathlib.Meta.NormNum.IsRat.to_isNat | |
| - path: Mathlib/Algebra/BigOperators/Associated.lean | |
| theorems: | |
| - Associates.prod_mk | |
| - path: Mathlib/CategoryTheory/Sites/IsSheafFor.lean | |
| theorems: | |
| - CategoryTheory.Presieve.isSheafFor_arrows_iff_pullbacks | |
| - CategoryTheory.Presieve.FamilyOfElements.Compatible.pullback | |
| - path: Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | |
| theorems: | |
| - SimpleGraph.adjMatrix_pow_apply_eq_card_walk | |
| - path: Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | |
| theorems: | |
| - continuousAt_const_cpow | |
| - path: Mathlib/Algebra/Homology/HomotopyCategory/Triangulated.lean | |
| theorems: | |
| - "CochainComplex.mappingConeCompTriangleh_comm\u2081" | |
| - path: Mathlib/Algebra/Tropical/BigOperators.lean | |
| theorems: | |
| - List.trop_sum | |
| - path: Mathlib/Analysis/Seminorm.lean | |
| theorems: | |
| - Seminorm.preimage_metric_ball | |
| - path: Mathlib/FieldTheory/Minpoly/IsIntegrallyClosed.lean | |
| theorems: | |
| - Algebra.adjoin.powerBasis'_gen | |
| - path: Mathlib/Combinatorics/SetFamily/Compression/UV.lean | |
| theorems: | |
| - UV.shadow_compression_subset_compression_shadow | |
| - UV.compression_self | |
| - path: Mathlib/NumberTheory/Zsqrtd/Basic.lean | |
| theorems: | |
| - Zsqrtd.nonnegg_comm | |
| - path: Mathlib/Data/Rat/Cast/Order.lean | |
| theorems: | |
| - Rat.cast_abs | |
| - Rat.cast_pos_of_pos | |
| - path: Mathlib/Analysis/NormedSpace/FiniteDimension.lean | |
| theorems: | |
| - Basis.opNorm_le | |
| - path: Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | |
| theorems: | |
| - MeasureTheory.Measure.rnDeriv_eq_zero_of_mutuallySingular | |
| - path: Mathlib/Data/IsROrC/Basic.lean | |
| theorems: | |
| - IsROrC.re_eq_add_conj | |
| - path: Mathlib/GroupTheory/DoubleCoset.lean | |
| theorems: | |
| - Doset.eq | |
| - path: Mathlib/LinearAlgebra/Dimension/Free.lean | |
| theorems: | |
| - nonempty_linearEquiv_of_lift_rank_eq | |
| - path: Mathlib/CategoryTheory/Category/Basic.lean | |
| theorems: | |
| - CategoryTheory.whisker_eq | |
| - path: Mathlib/Algebra/Module/Submodule/LinearMap.lean | |
| theorems: | |
| - Submodule.subtype_comp_inclusion | |
| - path: Mathlib/Algebra/Algebra/Operations.lean | |
| theorems: | |
| - Submodule.le_one_toAddSubmonoid | |
| - path: Mathlib/Topology/MetricSpace/Dilation.lean | |
| theorems: | |
| - Dilation.ediam_image | |
| - path: Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | |
| theorems: | |
| - Measurable.stronglyMeasurable | |
| - path: Mathlib/LinearAlgebra/Dimension/Finite.lean | |
| theorems: | |
| - CompleteLattice.Independent.subtype_ne_bot_le_rank | |
| - path: Mathlib/Analysis/BoxIntegral/Box/Basic.lean | |
| theorems: | |
| - BoxIntegral.Box.mk'_eq_coe | |
| - path: Mathlib/Algebra/Ring/Semiconj.lean | |
| theorems: | |
| - SemiconjBy.sub_right | |
| - path: Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean | |
| theorems: | |
| - MeasureTheory.integral_divergence_of_hasFDerivWithinAt_off_countable | |
| - path: Mathlib/Data/Vector/Basic.lean | |
| theorems: | |
| - Vector.get_tail | |
| - path: Mathlib/AlgebraicGeometry/EllipticCurve/Group.lean | |
| theorems: | |
| - WeierstrassCurve.Affine.CoordinateRing.exists_smul_basis_eq | |
| - path: Mathlib/AlgebraicTopology/DoldKan/Projections.lean | |
| theorems: | |
| - AlgebraicTopology.DoldKan.Q_idem | |
| - path: Mathlib/Analysis/BoxIntegral/Partition/Split.lean | |
| theorems: | |
| - BoxIntegral.Prepartition.not_disjoint_imp_le_of_subset_of_mem_splitMany | |
| - path: Mathlib/Algebra/Category/GroupCat/FilteredColimits.lean | |
| theorems: | |
| - GroupCat.FilteredColimits.colimitInvAux_eq_of_rel | |
| - path: Mathlib/Order/CompleteLattice.lean | |
| theorems: | |
| - iSup_option_elim | |
| - "iInf\u2082_comm" | |
| - path: Mathlib/GroupTheory/Perm/Cycle/Type.lean | |
| theorems: | |
| - Equiv.Perm.cycleType_eq' | |
| - Equiv.Perm.IsThreeCycle.isCycle | |
| - path: Mathlib/RingTheory/Polynomial/Nilpotent.lean | |
| theorems: | |
| - Polynomial.isNilpotent_X_mul_iff | |
| - path: Mathlib/GroupTheory/GroupAction/Hom.lean | |
| theorems: | |
| - MulSemiringActionHom.id_comp | |
| - path: Mathlib/RingTheory/PrincipalIdealDomain.lean | |
| theorems: | |
| - IsBezout.gcd_dvd_right | |
| - path: Mathlib/Topology/DenseEmbedding.lean | |
| theorems: | |
| - DenseInducing.interior_compact_eq_empty | |
| - path: Mathlib/Algebra/Field/Basic.lean | |
| theorems: | |
| - Commute.inv_sub_inv | |
| - one_div_mul_add_mul_one_div_eq_one_div_add_one_div | |
| - path: Mathlib/Geometry/Manifold/MFDeriv/Basic.lean | |
| theorems: | |
| - mfderiv_congr_point | |
| - path: Mathlib/Topology/MetricSpace/PartitionOfUnity.lean | |
| theorems: | |
| - EMetric.exists_continuous_real_forall_closedBall_subset | |
| - path: Mathlib/Data/Finset/Image.lean | |
| theorems: | |
| - Finset.map_subset_map | |
| - path: Mathlib/Topology/MetricSpace/Infsep.lean | |
| theorems: | |
| - Set.infsep_pair_eq_toReal | |
| - path: Mathlib/CategoryTheory/Sites/Sheaf.lean | |
| theorems: | |
| - CategoryTheory.Presheaf.isSheaf_iff_isSheaf_comp | |
| - path: Mathlib/Data/Complex/Basic.lean | |
| theorems: | |
| - Complex.normSq_sub | |
| - path: Mathlib/RingTheory/Discriminant.lean | |
| theorems: | |
| - Algebra.discr_not_zero_of_basis | |
| - Algebra.discr_mul_isIntegral_mem_adjoin | |
| - path: Mathlib/Algebra/Homology/ShortComplex/SnakeLemma.lean | |
| theorems: | |
| - "CategoryTheory.ShortComplex.SnakeInput.naturality_\u03B4" | |
| - path: Mathlib/Data/Set/MemPartition.lean | |
| theorems: | |
| - memPartitionSet_eq_iff | |
| - path: Mathlib/Topology/Algebra/Module/FiniteDimension.lean | |
| theorems: | |
| - LinearMap.continuous_of_isClosed_ker | |
| - path: Mathlib/Data/Nat/PrimeFin.lean | |
| theorems: | |
| - Nat.Prime.primeFactors | |
| - path: Mathlib/Order/SymmDiff.lean | |
| theorems: | |
| - bihimp_of_le | |
| - Disjoint.symmDiff_eq_sup | |
| - symmDiff_left_comm | |
| - path: Mathlib/Algebra/Homology/HomotopyCofiber.lean | |
| theorems: | |
| - HomologicalComplex.homotopyCofiber.sndX_inrX | |
| - "HomologicalComplex.cylinder.\u03B9\u2081_\u03C0" | |
| - path: Mathlib/SetTheory/Cardinal/Ordinal.lean | |
| theorems: | |
| - Cardinal.mk_finsupp_of_infinite | |
| - path: Mathlib/Topology/Basic.lean | |
| theorems: | |
| - nhds_basis_opens' | |
| - path: Mathlib/FieldTheory/SeparableDegree.lean | |
| theorems: | |
| - Polynomial.IsSeparableContraction.natSepDegree_eq | |
| - path: Mathlib/LinearAlgebra/CliffordAlgebra/Basic.lean | |
| theorems: | |
| - "CliffordAlgebra.lift_comp_\u03B9" | |
| - path: Mathlib/ModelTheory/DirectLimit.lean | |
| theorems: | |
| - FirstOrder.Language.DirectLimit.equiv_iff | |
| - path: Mathlib/CategoryTheory/Comma/Arrow.lean | |
| theorems: | |
| - CategoryTheory.Arrow.isIso_of_isIso_left_of_isIso_right | |
| - path: Mathlib/GroupTheory/SemidirectProduct.lean | |
| theorems: | |
| - SemidirectProduct.lift_inr | |
| - path: Mathlib/Topology/SeparatedMap.lean | |
| theorems: | |
| - isLocallyInjective_iff_isOpen_diagonal | |
| - path: Mathlib/Data/Nat/Choose/Multinomial.lean | |
| theorems: | |
| - Nat.binomial_eq | |
| - path: Mathlib/Probability/Kernel/CondDistrib.lean | |
| theorems: | |
| - ProbabilityTheory.condDistrib_apply_of_ne_zero | |
| - path: Mathlib/Probability/Kernel/Disintegration/Density.lean | |
| theorems: | |
| - ProbabilityTheory.kernel.set_lintegral_density | |
| - ProbabilityTheory.kernel.density_mono_set | |
| - path: Mathlib/Data/Multiset/Fintype.lean | |
| theorems: | |
| - Multiset.toEmbedding_coeEquiv_trans | |
| - path: Mathlib/Tactic/PushNeg.lean | |
| theorems: | |
| - Mathlib.Tactic.PushNeg.not_nonempty_eq | |
| - path: Mathlib/Data/Finset/NAry.lean | |
| theorems: | |
| - "Finset.image_image\u2082_distrib" | |
| - "Finset.forall_image\u2082_iff" | |
| - path: Mathlib/CategoryTheory/Limits/Opposites.lean | |
| theorems: | |
| - CategoryTheory.Limits.PullbackCone.op_inl | |
| - path: Mathlib/Algebra/Lie/Killing.lean | |
| theorems: | |
| - LieIdeal.coe_killingCompl_top | |
| - path: Mathlib/Combinatorics/Colex.lean | |
| theorems: | |
| - Finset.Colex.toColex_sdiff_lt_toColex_sdiff' | |
| - path: Mathlib/Analysis/NormedSpace/Pointwise.lean | |
| theorems: | |
| - closedBall_add_closedBall | |
| - path: Mathlib/Combinatorics/Composition.lean | |
| theorems: | |
| - CompositionAsSet.boundary_length | |
| - path: Mathlib/Tactic/LinearCombination.lean | |
| theorems: | |
| - Mathlib.Tactic.LinearCombination.eq_of_add_pow | |
| - path: Mathlib/SetTheory/Cardinal/ToNat.lean | |
| theorems: | |
| - Cardinal.mk_toNat_of_infinite | |
| - path: .lake/packages/std/Std/Data/RBMap/WF.lean | |
| theorems: | |
| - Std.RBNode.balance2_eq | |
| - path: Mathlib/MeasureTheory/Integral/SetIntegral.lean | |
| theorems: | |
| - "integral_withDensity_eq_integral_smul\u2080" | |
| - path: Mathlib/Algebra/BigOperators/Multiset/Basic.lean | |
| theorems: | |
| - Multiset.prod_induction_nonempty | |
| - Multiset.sum_int_mod | |
| - Multiset.one_le_prod_of_one_le | |
| - path: Mathlib/RingTheory/JacobsonIdeal.lean | |
| theorems: | |
| - Ideal.eq_jacobson_iff_sInf_maximal | |
| - path: Mathlib/Data/Rat/Star.lean | |
| theorems: | |
| - NNRat.addSubmonoid_closure_range_pow | |
| - path: Mathlib/Topology/Compactness/Lindelof.lean | |
| theorems: | |
| - lindelofSpace_of_countable_subfamily_closed | |
| - path: Mathlib/Data/Finset/Fold.lean | |
| theorems: | |
| - Finset.fold_union_inter | |
| - path: Mathlib/LinearAlgebra/FiniteDimensional.lean | |
| theorems: | |
| - LinearMap.finrank_range_add_finrank_ker | |
| - path: Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | |
| theorems: | |
| - Finset.card_mul_mul_le_card_div_mul_card_div | |
| - path: Mathlib/ModelTheory/Semantics.lean | |
| theorems: | |
| - FirstOrder.Language.BoundedFormula.realize_exs | |
| - path: Mathlib/Algebra/EuclideanDomain/Basic.lean | |
| theorems: | |
| - EuclideanDomain.eq_div_of_mul_eq_right | |
| - path: Mathlib/Computability/DFA.lean | |
| theorems: | |
| - DFA.pumping_lemma | |
| - path: Mathlib/CategoryTheory/Localization/Equivalence.lean | |
| theorems: | |
| - CategoryTheory.Functor.IsLocalization.of_equivalence_source | |
| - path: Mathlib/Data/Real/Pointwise.lean | |
| theorems: | |
| - Real.sSup_smul_of_nonneg | |
| - path: Mathlib/SetTheory/Ordinal/Basic.lean | |
| theorems: | |
| - Ordinal.lift_down' | |
| - path: Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | |
| theorems: | |
| - Real.arccos_of_le_neg_one | |
| - path: Mathlib/Analysis/Calculus/FDeriv/Mul.lean | |
| theorems: | |
| - HasFDerivWithinAt.mul_const | |
| - hasStrictFDerivAt_finset_prod | |
| - path: Mathlib/MeasureTheory/Integral/DominatedConvergence.lean | |
| theorems: | |
| - MeasureTheory.hasSum_integral_of_summable_integral_norm | |
| - path: Mathlib/RingTheory/Jacobson.lean | |
| theorems: | |
| - Ideal.Polynomial.isJacobson_polynomial_of_isJacobson | |
| - path: Mathlib/Analysis/Calculus/BumpFunction/Normed.lean | |
| theorems: | |
| - ContDiffBump.measure_closedBall_div_le_integral | |
| - path: Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | |
| theorems: | |
| - Complex.isTheta_exp_arg_mul_im | |
| - path: Mathlib/Algebra/Module/Torsion.lean | |
| theorems: | |
| - Module.isTorsionBySet_singleton_iff | |
| - path: Mathlib/Algebra/Order/Group/Abs.lean | |
| theorems: | |
| - mabs_div_comm | |
| - path: Mathlib/Data/Finsupp/Defs.lean | |
| theorems: | |
| - Finsupp.update_self | |
| - path: Mathlib/Analysis/Calculus/FDeriv/Basic.lean | |
| theorems: | |
| - hasFDerivWithinAt_diff_singleton | |
| - path: Mathlib/NumberTheory/LegendreSymbol/JacobiSymbol.lean | |
| theorems: | |
| - jacobiSym.eq_zero_iff_not_coprime | |
| - path: Mathlib/SetTheory/Ordinal/Exponential.lean | |
| theorems: | |
| - Ordinal.opow_dvd_opow | |
| - path: Mathlib/RingTheory/Trace.lean | |
| theorems: | |
| - Algebra.trace_eq_zero_of_not_exists_basis | |
| - path: Mathlib/Analysis/NormedSpace/lpSpace.lean | |
| theorems: | |
| - LipschitzWith.uniformly_bounded | |
| - path: Mathlib/Data/Nat/Fib/Basic.lean | |
| theorems: | |
| - Nat.fib_two_mul_add_two | |
| - path: .lake/packages/std/Std/Data/Nat/Gcd.lean | |
| theorems: | |
| - Nat.gcd_mul_lcm | |
| - Nat.lcm_comm | |
| - path: Mathlib/Analysis/Calculus/InverseFunctionTheorem/FDeriv.lean | |
| theorems: | |
| - HasStrictFDerivAt.to_localInverse | |
| - path: Mathlib/Order/Monotone/Union.lean | |
| theorems: | |
| - StrictMonoOn.union | |
| - path: Mathlib/RingTheory/Flat/Basic.lean | |
| theorems: | |
| - Module.Flat.of_retract | |
| - path: Mathlib/Algebra/Algebra/Tower.lean | |
| theorems: | |
| - IsScalarTower.algebraMap_apply | |
| - path: Mathlib/Topology/PartialHomeomorph.lean | |
| theorems: | |
| - PartialHomeomorph.prod_eq_prod_of_nonempty | |
| - path: Mathlib/Geometry/Manifold/ContMDiff/Basic.lean | |
| theorems: | |
| - ContMDiff.comp | |
| - path: Mathlib/Data/Sign.lean | |
| theorems: | |
| - SignType.nonpos_iff_ne_one | |
| - path: Mathlib/Data/Set/Subset.lean | |
| theorems: | |
| - Set.image_val_sUnion | |
| - path: Mathlib/LinearAlgebra/Basis.lean | |
| theorems: | |
| - Basis.ext' | |
| - Basis.repr_self_apply | |
| - path: Mathlib/FieldTheory/PurelyInseparable.lean | |
| theorems: | |
| - isPurelyInseparable_of_finSepDegree_eq_one | |
| - path: Mathlib/Data/List/Join.lean | |
| theorems: | |
| - List.length_join | |
| - path: Mathlib/Data/Matrix/Rank.lean | |
| theorems: | |
| - Matrix.rank_diagonal | |
| - path: Mathlib/Combinatorics/Schnirelmann.lean | |
| theorems: | |
| - exists_of_schnirelmannDensity_eq_zero | |
| - path: Mathlib/RingTheory/IntegralClosure.lean | |
| theorems: | |
| - IsIntegral.fg_adjoin_singleton | |
| - path: Mathlib/Data/Finset/Sigma.lean | |
| theorems: | |
| - Finset.card_sigmaLift | |
| - path: Mathlib/Data/Option/NAry.lean | |
| theorems: | |
| - "Option.map_map\u2082" | |
| - path: Mathlib/MeasureTheory/Function/ConditionalExpectation/AEMeasurable.lean | |
| theorems: | |
| - MeasureTheory.AEStronglyMeasurable'.continuous_comp | |
| - path: Mathlib/LinearAlgebra/QuotientPi.lean | |
| theorems: | |
| - Submodule.piQuotientLift_single | |
| - path: Mathlib/Order/Monotone/Basic.lean | |
| theorems: | |
| - monotone_dual_iff | |
| - path: Mathlib/Order/PropInstances.lean | |
| theorems: | |
| - Pi.isCompl_iff | |
| - path: Mathlib/Data/Set/Basic.lean | |
| theorems: | |
| - Set.mem_dite_empty_right | |
| - path: Mathlib/RingTheory/Finiteness.lean | |
| theorems: | |
| - Submodule.fg_unit | |
| - path: Mathlib/Topology/MetricSpace/Lipschitz.lean | |
| theorems: | |
| - lipschitzWith_iff_dist_le_mul | |
| - path: Mathlib/Data/Complex/Module.lean | |
| theorems: | |
| - rank_real_of_complex | |
| - path: Mathlib/Data/Rat/Defs.lean | |
| theorems: | |
| - Rat.mul_add | |
| - path: Mathlib/Topology/LocallyFinite.lean | |
| theorems: | |
| - LocallyFinite.closure | |
| - path: Mathlib/Algebra/Order/Monoid/MinMax.lean | |
| theorems: | |
| - fn_min_mul_fn_max | |
| - path: Mathlib/Data/Int/Div.lean | |
| theorems: | |
| - Int.ofNat_add_negSucc_of_ge | |
| - path: Mathlib/Data/List/NodupEquivFin.lean | |
| theorems: | |
| - List.sublist_of_orderEmbedding_get?_eq | |
| - path: Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | |
| theorems: | |
| - MeasureTheory.Lp.boundedContinuousFunction_dense | |
| - path: Mathlib/Logic/Equiv/Functor.lean | |
| theorems: | |
| - Functor.mapEquiv_refl | |
| - path: Mathlib/Combinatorics/SimpleGraph/LapMatrix.lean | |
| theorems: | |
| - SimpleGraph.lapMatrix_toLin'_apply_eq_zero_iff_forall_reachable | |
| - path: Mathlib/Tactic/NormNum/DivMod.lean | |
| theorems: | |
| - Mathlib.Meta.NormNum.isInt_dvd_false | |
| - path: Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | |
| theorems: | |
| - iUnion_Ici_eq_Ioi_of_lt_of_tendsto | |
| - path: Mathlib/NumberTheory/DirichletCharacter/Basic.lean | |
| theorems: | |
| - DirichletCharacter.changeLevel_trans | |
| - path: Mathlib/Algebra/ContinuedFractions/Computation/TerminatesIffRat.lean | |
| theorems: | |
| - GeneralizedContinuedFraction.exists_rat_eq_nth_numerator | |
| - path: Mathlib/Analysis/Normed/Group/AddCircle.lean | |
| theorems: | |
| - AddCircle.norm_coe_eq_abs_iff | |
| - path: .lake/packages/std/Std/Data/AssocList.lean | |
| theorems: | |
| - Std.AssocList.contains_eq | |
| - path: Mathlib/Data/PFun.lean | |
| theorems: | |
| - PFun.coe_preimage | |
| - path: Mathlib/Data/PNat/Interval.lean | |
| theorems: | |
| - PNat.card_Ico | |
| - path: Mathlib/Data/Nat/Choose/Cast.lean | |
| theorems: | |
| - Nat.cast_choose | |
| - path: Mathlib/FieldTheory/Separable.lean | |
| theorems: | |
| - Polynomial.rootMultiplicity_le_one_of_separable | |
| - path: Mathlib/Data/Fin/Tuple/Basic.lean | |
| theorems: | |
| - Fin.insertNth_apply_succAbove | |
| - path: Mathlib/Analysis/NormedSpace/Multilinear/Curry.lean | |
| theorems: | |
| - ContinuousMultilinearMap.uncurry0_curry0 | |
| - path: Mathlib/Algebra/Order/Ring/Lemmas.lean | |
| theorems: | |
| - exists_square_le' | |
| - path: Mathlib/Data/Nat/Defs.lean | |
| theorems: | |
| - Nat.pred_sub | |
| - path: Mathlib/Analysis/Calculus/TangentCone.lean | |
| theorems: | |
| - UniqueDiffWithinAt.prod | |
| - path: Mathlib/Analysis/Normed/Field/Basic.lean | |
| theorems: | |
| - antilipschitzWith_mul_right | |
| - path: Mathlib/Combinatorics/SetFamily/FourFunctions.lean | |
| theorems: | |
| - collapse_modular | |
| - path: Mathlib/Init/Logic.lean | |
| theorems: | |
| - let_eq | |
| - path: Mathlib/Data/Finset/NoncommProd.lean | |
| theorems: | |
| - Multiset.noncommFoldr_eq_foldr | |
| - path: Mathlib/Probability/Kernel/Composition.lean | |
| theorems: | |
| - ProbabilityTheory.kernel.snd_swapRight | |
| - path: Mathlib/Data/Seq/Seq.lean | |
| theorems: | |
| - Stream'.Seq.dropn_tail | |
| - path: Mathlib/Order/LocallyFinite.lean | |
| theorems: | |
| - Finset.map_subtype_embedding_Ici | |
| - path: .lake/packages/std/Std/Data/Int/Gcd.lean | |
| theorems: | |
| - Int.gcd_neg | |
| - path: Mathlib/Algebra/Order/Ring/WithTop.lean | |
| theorems: | |
| - WithTop.distrib' | |
| - path: Mathlib/RingTheory/Kaehler.lean | |
| theorems: | |
| - Derivation.liftKaehlerDifferential_unique | |
| - path: Mathlib/CategoryTheory/Limits/Fubini.lean | |
| theorems: | |
| - "CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim_\u03B9_\u03B9\ | |
| _hom" | |
| - path: Mathlib/MeasureTheory/Covering/VitaliFamily.lean | |
| theorems: | |
| - VitaliFamily.tendsto_filterAt_iff | |
| - path: Mathlib/Combinatorics/SetFamily/Shatter.lean | |
| theorems: | |
| - Finset.shatters_empty | |
| - path: Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | |
| theorems: | |
| - "CategoryTheory.Limits.Cocone.ofCofork_\u03B9" | |
| - path: Mathlib/Order/Filter/Pi.lean | |
| theorems: | |
| - Filter.pi_mem_pi | |
| - path: Mathlib/Topology/MetricSpace/HausdorffDistance.lean | |
| theorems: | |
| - Metric.hausdorffDist_triangle' | |
| - path: Mathlib/Topology/Instances/ENNReal.lean | |
| theorems: | |
| - ENNReal.continuousOn_sub_left | |
| - path: .lake/packages/std/Std/Data/RBMap/Lemmas.lean | |
| theorems: | |
| - Std.RBNode.Stream.next?_toList | |
| - path: Mathlib/Analysis/Convex/Star.lean | |
| theorems: | |
| - StarConvex.sub | |