| 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: <path-to-repo>/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" | |