name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Matrix.emptyRows_isTotallyUnimodular | Mathlib.LinearAlgebra.Matrix.Determinant.TotallyUnimodular | [
"SignType.cast",
"Eq.mpr",
"NegZeroClass.toNeg",
"instNeZeroNatHAdd_1",
"SignType.coe_one",
"CommRing",
"Matrix.submatrix",
"SignType.instOne",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"False.elim",
"instDecidableEqFin",
"Matrix.submatrix_empty",
"AddGroupWithOne.toAddMonoidWithO... | true |
Complex.abs_arg_lt_pi_div_two_iff | Mathlib.Analysis.SpecialFunctions.Complex.Arg | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"False",
"_private.Mathlib.Analysis.SpecialFunctions.Complex.Arg.0.Complex.abs_arg_lt_pi_div_two_iff._simp_1_2",
"Real.instLE",
"Real",
"Preorder.toLT",
"instHDiv",
"Real.pi",
"Real.lattice",
"eq_false",
"Complex.neg_pi_div_two_... | true |
Real.rpow_sub_intCast | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"NegZeroClass.toNeg",
"Real.instPow",
"Real",
"instHDiv",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Real.instZero",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Real.instDivInvMonoid",
"... | true |
Lean.Lsp.InlayHintTooltip.plaintext.injEq | Lean.Data.Lsp.LanguageFeatures | [
"Eq.propIntro",
"Lean.Lsp.InlayHintTooltip.plaintext",
"String",
"Lean.Lsp.InlayHintTooltip",
"Eq.ndrec",
"Eq.refl",
"Lean.Lsp.InlayHintTooltip.plaintext.inj",
"Eq"
] | true |
CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex | Mathlib.CategoryTheory.Sites.MayerVietorisSquare | [
"NegZeroClass.toNeg",
"CategoryTheory.Functor",
"CategoryTheory.Square.f₂₄",
"Opposite",
"AddCommGrpCat.free",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"CategoryTheory.Limits.biprod.desc",
"CategoryTheory.ShortComplex.mk",
"CategoryTheory.HasSheafify"... | true |
Int.rec | Init.Data.Int.Basic | [
"Int.ofNat",
"Int",
"Nat",
"Int.negSucc"
] | false |
BddDistLat.Iso.mk._proof_7 | Mathlib.Order.Category.BddDistLat | [
"BddDistLat.isBoundedOrder",
"BddDistLat.instDistribLatticeCarrier",
"PartialOrder.toPreorder",
"Preorder.toLE",
"BddDistLat",
"SemilatticeInf.toPartialOrder",
"DistLat.str",
"DistribLattice.toLattice",
"OrderIso",
"OrderIso.instEquivLike",
"OrderIso.instOrderIsoClass",
"OrderTop.toTop",
"in... | false |
HomotopicalAlgebra.instWeakEquivalenceMapOfIsWeakFactorizationSystemTrivialCofibrationsFibrations | Mathlib.AlgebraicTopology.ModelCategory.Instances | [
"Eq.mpr",
"HomotopicalAlgebra.isStableUnderCoproductsOfShape_trivialCofibrations",
"HomotopicalAlgebra.fibrations",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HomotopicalAlgebra.weakEquivalence_iff",
"CategoryTheory.Discrete.functor",
"id",
"HomotopicalAlgebra.Cofibration... | true |
_private.Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone.0.NumberField.mixedEmbedding.fundamentalCone.mem_idealSet._simp_1_8 | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone | [
"Submodule",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Algebra",
"Membership.mem",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"MulZeroOneClass.toMulOneClass",
"FractionalIdeal.instSetLike... | false |
Sym2.mem_iff_mem._simp_1 | Mathlib.Data.Sym.Sym2 | [
"Membership.mem",
"Sym2.instSetLike",
"propext",
"Eq",
"Sym2",
"SetLike.instMembership",
"Sym2.Mem",
"Sym2.mem_iff_mem"
] | false |
Matrix.linfty_opNorm_eq_opNorm | Mathlib.Analysis.Matrix.Normed | [
"Norm.norm",
"Pi.Function.module",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Semiring.toModule",
"Pi.addCommMonoid",
"Pi.topologicalSpace",
"CommSemiring.toSemiring",
"Matrix",
"SeminormedAddGroup.toNNNorm",
"ContinuousLinearMap.mk",
"NNNorm.nnnorm",
"Matrix.linfty_opNNNorm_eq_opNNNorm... | true |
CategoryTheory.Equivalence.congrRight._proof_4 | Mathlib.CategoryTheory.Equivalence | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.rightUnitor",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.... | false |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.toList_rco_eq_cons_iff._simp_1_1 | Init.Data.Range.Polymorphic.NatLemmas | [
"eq_comm",
"propext",
"Eq"
] | false |
Lean.mkLitEx | Lean.Expr | [
"Lean.Expr",
"Lean.Literal",
"Lean.mkLit"
] | true |
Topology.IsEmbedding.comapMetricSpace._proof_1 | Mathlib.Topology.MetricSpace.Basic | [
"PseudoMetricSpace.toUniformSpace",
"TopologicalSpace",
"MetricSpace",
"Topology.IsEmbedding.injective",
"Topology.IsEmbedding",
"MetricSpace.toPseudoMetricSpace",
"Function.Injective",
"UniformSpace.toTopologicalSpace"
] | false |
MeasureTheory.VectorMeasure.transpose.eq_1 | Mathlib.MeasureTheory.VectorMeasure.Integral | [
"LinearMap.toAddMonoidHom",
"MeasureTheory.VectorMeasure.transpose._proof_8",
"Real",
"NormedSpace",
"MeasureTheory.VectorMeasure.transpose._proof_5",
"ContinuousLinearMap.topologicalSpace",
"Real.denselyNormedField",
"AddCommGroup.toAddCommMonoid",
"MeasureTheory.VectorMeasure.transpose._proof_7",
... | true |
Lean.Parser.Tactic.MCasesPat.parse.goAlts | Std.Tactic.Do.Syntax | [
"Lean.TSyntax",
"Inhabited.default",
"List.cons",
"instInhabitedOption",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr4",
"Lean.Parser.Tactic.MCasesPat",
"List.nil",
"Option"
] | true |
PointwiseConvergenceCLM.seminorm._proof_4 | Mathlib.Analysis.LocallyConvex.PointwiseConvergence | [
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"SeminormedRing.toNorm",
"Real",
"instHSMul",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"norm_smul",
"PointwiseConvergenceCLM",
"NormedSpace",
"UniformConvergenceCLM.instAddCommGroup",
... | false |
CategoryTheory.Presheaf.isLimitOfIsSheaf | Mathlib.CategoryTheory.Sites.Sheaf | [
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"CategoryTheory.Limits.IsLimit.mk",
"Opposite",
"CategoryTheory.Presheaf.isLimitOfIsSheaf._proof_1",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategory",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Presheaf.IsSh... | true |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.toList_roo_add_right_eq_map._proof_1_1 | Init.Data.Range.Polymorphic.NatLemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.... | false |
QuotientGroup.congr_mk' | Mathlib.GroupTheory.QuotientGroup.Defs | [
"MulEquiv.instEquivLike",
"MonoidHom.instFunLike",
"MonoidHom",
"Subgroup.map",
"Monoid.toMulOneClass",
"MulEquiv.instMulEquivClass",
"Group",
"MulOne.toMul",
"MonoidHomClass.toMonoidHom",
"QuotientGroup.instHasQuotientSubgroup",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
... | true |
Complex.UnitDisc.instMulActionCircle._aux_1 | Mathlib.Analysis.Complex.UnitDisc.Basic | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"Complex.instNormedField",
"instSMulElemClosedBallOfNatRealBall",
"NormedField.toField",
"Set.Elem",
"Metric.ball",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
... | false |
Turing.TM1to1.trNormal.eq_5 | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Turing.TM1to1.read",
"List.Vector",
"Turing.TM1to1.trNormal",
"Turing.TM1to1.Λ'",
"Turing.TM1to1.Λ'.normal",
"Nat",
"Bool",
"Eq.refl",
"Turing.TM1.Stmt.goto",
"Eq",
"Turing.TM1.Stmt"
] | true |
AlgebraicGeometry.Scheme.Opens.ι.eq_1 | Mathlib.AlgebraicGeometry.Restrict | [
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"TopCat.instCategory",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"CommRingCat.instCategory",
"Preo... | true |
_private.Mathlib.Algebra.Group.Pointwise.Set.Card.0.Set.natCard_mul_le._simp_1_2 | Mathlib.Algebra.Group.Pointwise.Set.Card | [
"Preorder.toLT",
"HMul.hMul",
"Cardinal",
"PartialOrder.toPreorder",
"Cardinal.instMul",
"Cardinal.aleph0",
"And",
"Cardinal.partialOrder",
"Cardinal.mul_lt_aleph0_iff",
"LT.lt",
"propext",
"Zero.toOfNat0",
"Or",
"OfNat.ofNat",
"Eq",
"Cardinal.instZero",
"instHMul"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.good_vertices_triangle_card._simp_1_7 | Mathlib.Combinatorics.SimpleGraph.Triangle.Counting | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"not_lt",
"LT.lt",
"propext",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
_private.Mathlib.Data.Set.NAry.0.Set.image2_subset_iff_right._simp_1_2 | Mathlib.Data.Set.NAry | [
"Membership.mem",
"Set.preimage",
"propext",
"Eq",
"Set.instMembership",
"Set.mem_preimage",
"Set"
] | false |
CategoryTheory.LaxFunctor.mapId' | Mathlib.CategoryTheory.Bicategory.Functor.Lax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.PrelaxFunctorStruct.map₂",
"CategoryTheory.LaxFunctor.mapId'._proof_1",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruc... | true |
FundamentalGroupoid.map._proof_2 | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ContinuousMap",
"CategoryTheory.CategoryStruct.id",
"Path.Homotopic.Quotient.map",
"TopologicalSpace",
"FundamentalGroupoid",
"FundamentalGroupoid.mk",
"FundamentalGroupoid.as",
"FundamentalGroupoid.instGroupoid",
"CategoryTheory.Category.... | false |
Matrix.mul_apply' | Mathlib.Data.Matrix.Mul | [
"HMul.hMul",
"dotProduct",
"Matrix",
"Matrix.instHMulOfFintypeOfMulOfAddCommMonoid",
"Mul",
"AddCommMonoid",
"Fintype",
"Eq",
"rfl"
] | true |
Std.DHashMap.Internal.Raw₀.Const.get.congr_simp | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Internal.Raw₀.contains",
"Eq.rec",
"Bool.true",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Hashable",
"BEq",
"Eq",
"Std.DHashMap.Internal.Raw₀",
"Std.DHashMap.Internal.Raw₀.Const.get"
] | true |
_private.Lean.Meta.Tactic.UnifyEq.0.Lean.Meta.toOffset?.match_1 | Lean.Meta.Tactic.UnifyEq | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Nat",
"Option"
] | false |
Function.RightInverse.comp | Mathlib.Logic.Function.Basic | [
"Function.comp",
"Function.RightInverse",
"Function.LeftInverse.comp"
] | true |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.0._regBuiltin.Nat.reduceAdd.declare_26._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.2624385985._hygCtx._hyg.19 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat | [
"IO",
"Lean.Meta.DiscrTree.Key.star",
"Nat.reduceAdd",
"Lean.Meta.DiscrTree.Key",
"instOfNatNat",
"List.toArray",
"List.cons",
"Unit",
"Nat",
"Lean.Meta.Simp.registerBuiltinDSimproc",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.Meta.DiscrTree.Key.const",
"List.nil"
] | false |
PrimeSpectrum.piLocalizationToMaximalEquiv._proof_1 | Mathlib.RingTheory.Spectrum.Maximal.Localization | [
"MaximalSpectrum.asIdeal",
"MulOne.toOne",
"Function.LeftInverse",
"OreLocalization.instAlgebra",
"PrimeSpectrum.isPrime",
"CommSemiring.toSemiring",
"Localization.AtPrime",
"MaximalSpectrum.mk",
"RingHom",
"PrimeSpectrum.PiLocalization",
"Algebra.id",
"Localization",
"NonAssocSemiring.toMul... | false |
_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic.0.AlgebraicGeometry.Proj.fromOfGlobalSections_preimage_basicOpen._simp_1_1 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic | [
"Membership.mem",
"Set.preimage",
"propext",
"Eq",
"Set.instMembership",
"Set.mem_preimage",
"Set"
] | false |
Lean.Meta.Grind.Params.config | Lean.Meta.Tactic.Grind.Main | [
"Lean.Meta.Grind.Params",
"Lean.Grind.Config"
] | true |
_private.Batteries.Data.MLList.Basic.0.MLList.Spec.ctorIdx | Batteries.Data.MLList.Basic | [
"Nat",
"_private.Batteries.Data.MLList.Basic.0.MLList.Spec"
] | false |
CategoryTheory.Sheaf.instMonoidalFunctorOppositePresheafToSheaf._aux_1 | Mathlib.CategoryTheory.Sites.Monoidal | [
"CategoryTheory.Localization.Monoidal.leftUnitor_hom_app",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.IsMonoidal",
"CategoryTheory.Functor.CoreMonoidal.εIso",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functo... | false |
QuaternionAlgebra.equivTuple_symm_apply | Mathlib.Algebra.Quaternion | [
"Equiv.instEquivLike",
"QuaternionAlgebra.equivTuple._proof_3",
"QuaternionAlgebra.mk",
"QuaternionAlgebra",
"Fin.instOfNat",
"Equiv",
"instOfNatNat",
"QuaternionAlgebra.equivTuple",
"Nat",
"Eq.refl",
"Equiv.symm",
"OfNat.ofNat",
"Fin",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Representation.linearizeTrivial_def | Mathlib.RepresentationTheory.Action | [
"LinearMap.id",
"Monoid",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Representation",
"MonoidHom.instFunLike",
"Action.trivial",
"Representation.linearize_single",
"Semiring.toModule",
"Finsupp.module",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"CategoryTheory.ConcreteCat... | true |
CategoryTheory.Localization.Construction.NatTransExtension.app_eq | Mathlib.CategoryTheory.Localization.Construction | [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.MorphismProperty.Q",
"CategoryTheory.Functor.category",
"CategoryTheory.Localization.Construction.NatTransExtension.a... | true |
_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.analyticAt_relation_zero | Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass | [
"iteratedDeriv_zero",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"CharP.cast_eq_zero",
"Iff.mpr",
"NormedCommRing.toNormedRing",
"Monoid",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"iteratedDeriv_fun_add",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"Nat.instCanonicallyOrder... | true |
Measurable.fun_const_vadd | Mathlib.MeasureTheory.Group.Arithmetic | [
"MeasurableConstVAdd",
"Measurable",
"VAdd",
"id",
"Measurable.const_vadd",
"HVAdd.hVAdd",
"MeasurableSpace",
"instHVAdd"
] | true |
ZeroHom.withBotMap._proof_1 | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"Eq.mpr",
"ZeroHom.funLike",
"WithBot.some",
"WithBot",
"congrArg",
"WithBot.zero",
"map_zero",
"id",
"ZeroHom.zeroHomClass",
"ZeroHom",
"Zero.toOfNat0",
"Eq.refl",
"OfNat.ofNat",
"WithBot.map",
"Eq",
"DFunLike.coe",
"WithBot.map_zero",
"WithBot.coe_zero",
"Zero"
] | false |
CategoryTheory.PreGaloisCategory.IsGalois.mk | Mathlib.CategoryTheory.Galois.GaloisObjects | [
"CategoryTheory.GaloisCategory.toPreGaloisCategory",
"CategoryTheory.PreGaloisCategory.instFiniteAutOfIsConnected",
"CategoryTheory.Aut.toEnd",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.SingleObj.functor",
"CategoryTheory.Limits.IsTerminal",
"CategoryTheory.PreGaloisCategor... | true |
Lean.Lsp.LeanModuleQuery.mk._flat_ctor | Lean.Data.Lsp.Internal | [
"Lean.Lsp.LeanModuleQuery.mk",
"String",
"Array",
"Lean.Lsp.OpenNamespace",
"Lean.Lsp.LeanModuleQuery"
] | false |
instToStringId._aux_1 | Init.Data.ToString.Basic | [
"id",
"ToString"
] | false |
CategoryTheory.Limits.IsColimit.fac_assoc | Mathlib.CategoryTheory.Limits.IsLimit | [
"CategoryTheory.Limits.IsColimit.fac",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"Eq.mp",
"CategoryTheory.Limits.IsColimit",
"id",
"Mathlib.Ta... | true |
Lean.Meta.SimpTheorems.mk | Lean.Meta.Tactic.Simp.SimpTheorems | [
"Lean.PHashMap",
"Lean.Meta.instHashableOrigin",
"Lean.Meta.instBEqOrigin",
"Lean.PHashSet",
"Array",
"Lean.Meta.SimpTheoremTree",
"Lean.Meta.SimpTheorems",
"Lean.Name",
"Lean.Meta.Origin",
"Lean.Name.instBEq",
"Lean.Meta.SimpTheorems.mk",
"Lean.instHashableName"
] | true |
integral_sin | Mathlib.Analysis.SpecialFunctions.Integrals.Basic | [
"Mathlib.Tactic.Ring.Common.neg_zero",
"Real.differentiableAt_cos._simp_1",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Real",
"Mathlib.Meta.NormNum.instAddMonoidWithOne",
"NonUnitalCommRing.to... | true |
AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_fst_assoc | Mathlib.AlgebraicGeometry.Gluing | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.pullback.snd",
"AlgebraicGeometry.Scheme.Cover.gluedCoverT'_fst_fst",
"Alg... | true |
HasCompl.casesOn | Mathlib.Order.Notation | [
"HasCompl.mk",
"HasCompl",
"HasCompl.rec"
] | false |
interior_closure_idem | Mathlib.Topology.Closure | [
"interior_mono",
"isOpen_interior",
"Set.instAntisymmSubset",
"TopologicalSpace",
"IsOpen.subset_interior_closure",
"closure",
"HasSubset.Subset.antisymm",
"IsClosed.closure_interior_subset",
"interior",
"isClosed_closure",
"Eq",
"Set.instHasSubset",
"Set"
] | true |
UInt8.toBitVec_ofBitVec | Init.Data.UInt.Lemmas | [
"BitVec",
"instOfNatNat",
"UInt8.toBitVec",
"Nat",
"OfNat.ofNat",
"UInt8.ofBitVec",
"Eq",
"rfl"
] | true |
_private.Mathlib.Algebra.Homology.ExactSequenceFour.0.CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac._proof_8 | Mathlib.Algebra.Homology.ExactSequenceFour | [
"_private.Mathlib.Algebra.Homology.ExactSequenceFour.0.CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac._proof_5",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CategoryTheory.ComposableArrows.map'._proof_2",
"Fin.mk",
"instOfNatNat",
"LE.le",
"instLENat",
"autoParam",
"CategoryTheor... | false |
BoundedContinuousFunction.coe_toContinuousMap | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"BoundedContinuousFunction.instFunLike",
"TopologicalSpace",
"PseudoMetricSpace",
"UniformSpace.toTopologicalSpace",
"Eq",
"ContinuousMap.instFunLike",
"DFunLike.coe",
"BoundedContinuousFunction",
"rfl",
"BoundedContinuousFunction.toContinuo... | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.tdiv_le_tdiv._simp_1_1 | Init.Data.Int.DivMod.Lemmas | [
"Int.add_assoc",
"Int",
"instHAdd",
"HAdd.hAdd",
"Int.instAdd",
"Eq.symm",
"Eq"
] | false |
Nat.one_add_le_iff | Init.Data.Nat.Lemmas | [
"congrArg",
"instOfNatNat",
"LE.le",
"instLENat",
"iff_self",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Nat",
"LT.lt",
"True",
"_private.Init.Data.Nat.Lemmas.0.Nat.one_add_le_iff._simp_1_1",
"of_eq_true",
"instAddNat",
"congrFun'",
"instLTNat",
"OfNat.ofNat",
"Eq.trans",
"Nat.add_comm"
] | true |
CategoryTheory.SheafOfTypes.balanced | Mathlib.CategoryTheory.Sites.LeftExact | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.HasSheafify",
"CategoryTheory.Functor.category",
"inferInstance",
"CategoryTheory.balanced_of_strongMonoCategory",
"CategoryTheory.SheafOfTypes.adhesive",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.types",
"CategoryTheory.Category.o... | true |
_private.Mathlib.Computability.AkraBazzi.SumTransform.0.AkraBazziRecurrence.eventually_atTop_sumTransform_le._simp_1_3 | Mathlib.Computability.AkraBazzi.SumTransform | [
"HSub.hSub",
"OrderedSub",
"LE.le",
"tsub_le_iff_right",
"LE",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"propext",
"Eq",
"Add",
"Sub"
] | false |
MultilinearMap.mkContinuousLinear_norm_le' | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"le_max_right",
"NormedCommRing.toNormedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"ContinuousMultilinearMap.seminorm._proof_2",
"Real.instLE",
"Real",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"UniformContinuousConstSMul.to_cont... | true |
OrderDual.instSemilatticeSup | Mathlib.Order.Lattice | [
"SemilatticeSup.mk",
"SemilatticeInf.inf_le_right",
"SemilatticeInf.inf_le_left",
"SemilatticeInf.toPartialOrder",
"SemilatticeInf.inf",
"SemilatticeInf.le_inf",
"SemilatticeInf",
"OrderDual.instPartialOrder",
"OrderDual",
"SemilatticeSup"
] | true |
Polynomial.Monic.mul_right_ne_zero | Mathlib.Algebra.Polynomial.Monic | [
"not_le",
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.instOne",
"Nat.instMulZeroClass",
"WithBot",
"Preorder.toLT",
"WithBot.instLT",
"HMul.hMul",
"congrArg",
"Polynomial.instDecidableEq",
"PartialOrder.toPreorder",
"WithBot.bot_neg._simp_1",
"WithBot.zero",
"lt_trans",
"Classical.pr... | true |
_private.Mathlib.Combinatorics.Enumerative.Composition.0.List.splitWrtCompositionAux.match_3.eq_1 | Mathlib.Combinatorics.Enumerative.Composition | [
"List.cons",
"List",
"List.splitWrtCompositionAux.match_3",
"Nat",
"Eq.refl",
"Eq",
"List.nil"
] | true |
Module.Basis.coord_toDualEquiv_symm_apply | Mathlib.LinearAlgebra.Dual.Basis | [
"Finsupp.instFunLike",
"LinearEquiv.symm",
"Semiring.toModule",
"Finsupp.module",
"Module.Basis.coord",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Finite",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"Module... | true |
irrational_natCast_sub_iff._simp_1 | Mathlib.NumberTheory.Real.Irrational | [
"Real",
"Real.instSub",
"HSub.hSub",
"Nat.cast",
"irrational_natCast_sub_iff",
"instHSub",
"Irrational",
"Nat",
"propext",
"Eq",
"Real.instNatCast"
] | false |
CommRingCat.Colimits.ColimitType.instAdd._proof_1 | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"CommRingCat",
"CommRingCat.Colimits.Relation.add_2",
"CommRingCat.instCategory",
"CategoryTheory.SmallCategory",
"CommRingCat.Colimits.colimitSetoid",
"CommRingCat.Colimits.Prequotient.add",
"CommRingCat.Colimits.Prequotient",
"HasEquiv.Equiv",
"instHasEquivOfSetoid",
... | false |
TensorAlgebra.instNontrivial | Mathlib.LinearAlgebra.TensorAlgebra.Basic | [
"Nontrivial",
"Function.LeftInverse.injective",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Function.Injective.nontrivial",
"RingHom",
"Algebra.id",
"TensorAlgebra",
"instSemiringTensorAlgebra",
"IsScalarTower.left",
"AddCommMonoid",
"instAlgebra",
"Comm... | true |
FreeAddGroup.map.mk | Mathlib.GroupTheory.FreeGroup.Basic | [
"List.map",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Prod.mk",
"FreeAddGroup.mk",
"FreeAddGroup.map",
"Prod.fst",
"List",
"AddGroup.toSubNegMonoid",
"Bool",
"SubNegMonoid.toAddMonoid",
"AddMonoidHom",
"Prod",
"FreeAddGroup",
"AddMonoidHom.instFunLike",
"Eq",
"Prod.snd",... | true |
Matroid.IsCocircuit.isCircuit | Mathlib.Combinatorics.Matroid.Circuit | [
"Matroid.dual",
"Matroid.IsCircuit",
"Matroid.IsCocircuit",
"Matroid",
"Set"
] | true |
Lean.Meta.SynthInstance.instInhabitedConsumerNode | Lean.Meta.SynthInstance | [
"Lean.Meta.SynthInstance.ConsumerNode",
"Lean.Meta.SynthInstance.instInhabitedConsumerNode.default",
"Inhabited",
"Inhabited.mk"
] | true |
String.reduceOfList._regBuiltin.String.reduceOfList.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.String.1479931662._hygCtx._hyg.17 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.String | [
"IO",
"Bool.true",
"Unit",
"Lean.Meta.Simp.addSEvalprocBuiltinAttr",
"Sum.inr",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"String.reduceOfList",
"Lean.Meta.Simp.Simproc"
] | false |
AddConjClasses.map.eq_1 | Mathlib.Algebra.Group.Conj | [
"AddConjClasses.map",
"AddConjClasses.mk",
"AddMonoid.toAddZeroClass",
"Function.comp",
"AddZeroClass.toAddZero",
"AddConjClasses",
"AddConjClasses.map._proof_1",
"AddMonoid",
"Eq.refl",
"Quotient.lift",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"Eq",
"DFunLike.coe",
"IsAddConj.setoid"... | true |
BotHom.dual_symm_apply_apply | Mathlib.Order.Hom.Bounded | [
"TopHom.instFunLike",
"Equiv.instEquivLike",
"OrderBot.toBot",
"BotHom.dual",
"OrderBot",
"Equiv",
"LE",
"BotHom.instFunLike",
"TopHom",
"Eq.refl",
"OrderDual",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"OrderDual.instTopOfBot",
"BotHom",
"EquivLike.toFunLike"
] | true |
AddLocalization.mk_self | Mathlib.GroupTheory.MonoidLocalization.Basic | [
"AddCon.instFunLikeForallProp",
"AddCon",
"Eq.mpr",
"AddOreLocalization.instZero",
"congrArg",
"Prod.instAdd",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"Subtype",
"AddSubmonoid.add",
"Prod.mk",
"AddSubmonoid",
"AddLocalization.zero_rel",
"AddCommMon... | true |
Lean.instToExprDeclarationRange | Lean.Data.DeclarationRange | [
"Lean.mkAppN",
"Lean.Position.instToExpr",
"Lean.DeclarationRange.endCharUtf16",
"Lean.Name.mkStr3",
"Lean.Expr",
"Lean.Level",
"Lean.Position",
"Lean.DeclarationRange.endPos",
"List.toArray",
"Lean.mkConst",
"List.cons",
"Lean.instToExprNat",
"Lean.DeclarationRange",
"Lean.ToExpr.toExpr",... | true |
MeasureTheory.Measure.instIsScalarTower | Mathlib.MeasureTheory.Measure.MeasureSpace | [
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"MeasurableSet",
"smul_assoc",
"CommSemiring.toSemiring",
"IsScalarTower",
"SMul",
"MeasureTheory.OuterMeasure",
"MeasureTheory.Measure.instSMul",
"ENNReal.instCommSemiring",
"instDistribOfSemiring",
"MeasurableSpace",
"MeasureTheory.M... | true |
AddOpposite.op_surjective | Mathlib.Algebra.Opposites | [
"AddOpposite",
"AddOpposite.op_bijective",
"Function.Bijective.surjective",
"Function.Surjective",
"AddOpposite.op"
] | true |
IsPurelyInseparable.exponent_def | Mathlib.FieldTheory.PurelyInseparable.Exponent | [
"CommRing",
"Subring.instSetLike",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"ringExpChar",
"Algebra",
"Classical.propDecidable",
"IsPurelyInseparable.HasExponent.has_exponent",
"Membership.mem",
"CommRing.toNonAssocCommRing",
"Monoid.toPow",
... | true |
UpperSet.instAdd._proof_1 | Mathlib.Algebra.Order.UpperLower | [
"UpperSet.upper'",
"IsUpperSet.add_right",
"UpperSet",
"AddCommGroup.toAddCommMonoid",
"UpperSet.instSetLike",
"AddMonoid.toAddZeroClass",
"IsUpperSet",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"instHAdd",
"UpperSet.carrier",
"Set.add",
"AddGr... | false |
_private.Mathlib.Data.List.Lattice.0.List.count_bagInter._proof_1_11 | Mathlib.Data.List.Lattice | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"List.filter",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Decidable.decide",
"Eq",
"List.length",
"DecidableEq"
] | false |
Std.DHashMap.Raw.Const.get_insert | Std.Data.DHashMap.RawLemmas | [
"Iff.mpr",
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Eq.mpr",
"dite_congr",
"congrArg",
"Std.DHashMap.Raw.Const.get",
"Bool.eq_false_iff",
"Std.DHashMap.Raw",
"Membership.mem",
"id",
"instDecidableEqBool",
"Ne",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_bu... | true |
LinearMap.continuousLinearMapClassOfFiniteDimensional | Mathlib.Topology.Algebra.Module.FiniteDimension | [
"NormedCommRing.toSeminormedCommRing",
"CompleteSpace",
"ContinuousSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedDivisionRing.toDivisionRing",
"No... | true |
OrderEmbedding.addLeft.eq_1 | Mathlib.Algebra.Order.Monoid.Basic | [
"Preorder.toLT",
"OrderEmbedding.addLeft",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"OrderEmbedding.addLeft._proof_1",
"instHAdd",
"AddLeftStrictMono",
"OrderEmbedding.ofStrictMono",
"HAdd.hAdd",
"Eq.refl",
"Ord... | true |
_private.Lean.Elab.Tactic.Split.0.Lean.Elab.Tactic.evalSplit.throwTermUnsupported | Lean.Elab.Tactic.Split | [
"Pure.pure",
"Option.isNone",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.LocalContext.findFromUserName?",
"Lean.Synta... | true |
Filter.Realizer.inf._proof_1 | Mathlib.Data.Analysis.Filter | [
"CFilter.inf",
"CompleteLattice.toConditionallyCompleteLattice",
"HasSubset.Subset",
"Set.inter_subset_inter",
"Set.instInter",
"Prod.fst",
"Inter.inter",
"Filter.Realizer.F",
"CompleteBooleanAlgebra.toCompleteLattice",
"CFilter.inf_le_left",
"ConditionallyCompletePartialOrderSup.toPartialOrder"... | false |
_private.Mathlib.FieldTheory.Finite.Basic.0.ZMod.pow_card_sub_one._simp_1_1 | Mathlib.FieldTheory.Finite.Basic | [
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"OrderedSub",
"tsub_eq_zero_iff_le",
"LE.le",
"CanonicallyOrderedAdd",
"AddCommMonoid",
"AddZero.toZero",
"instHSub",
"propext",
"Zero.toOfNat0",
"AddCommMonoi... | false |
_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.dist_mem_candidates._simp_1_3 | Mathlib.Topology.MetricSpace.GromovHausdorffRealized | [
"Metric.metricSpaceSum",
"Real.instLE",
"Real",
"_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.maxVar_bound",
"PseudoMetricSpace.toUniformSpace",
"Sum",
"LE.le",
"CompactSpace",
"MetricSpace",
"True",
"eq_true",
"_private.Mathlib.Topology.MetricSpace.GromovHau... | false |
Lean.Lsp.SymbolKind.string.sizeOf_spec | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolKind.string",
"Lean.Lsp.SymbolKind._sizeOf_inst",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Lean.Lsp.SymbolKind",
"Eq"
] | true |
LatticeCon.sup | Mathlib.Order.Lattice.Congruence | [
"Lattice",
"Lattice.toSemilatticeSup",
"SemilatticeSup.toMax",
"Max.max",
"LatticeCon.toSetoid",
"Setoid.r",
"LatticeCon"
] | true |
AnalyticOnNhd.eqOn_zero_or_eventually_ne_zero_of_preconnected | Mathlib.Analysis.Analytic.IsolatedZeros | [
"Filter.instMembership",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"False",
"_private.Mathlib.Analysis.Analytic.IsolatedZeros.0.AnalyticOnNhd.eqOn_zero_or_eventually_ne_zero_of_preconnected._simp_1_1",
"NormedSpace",
"eq_false",
"congrArg",
"Compl.compl",
"Filter.instCompleteLatticeFilter",... | true |
BddBelow.of_upperClosure | Mathlib.Order.UpperLower.Closure | [
"bddBelow_upperClosure",
"UpperSet",
"UpperSet.instSetLike",
"upperClosure",
"Preorder.toLE",
"SetLike.coe",
"BddBelow",
"Iff.mp",
"Preorder",
"Set"
] | true |
SimpleGraph.Walk.dropUntil_first | Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | [
"dite_cond_eq_true",
"Eq.mpr",
"SimpleGraph.Walk.takeUntil.match_1",
"SimpleGraph.Walk.dropUntil._proof_1",
"congrArg",
"HEq.refl",
"SimpleGraph.Adj",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Membership.mem",
"id",
"dite",
"SimpleGraph",
"SimpleGraph.Walk.cons",
"List",
"_priva... | true |
contDiff_omega_iff_analyticOnNhd | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"NormedSpace",
"Set.univ",
"AnalyticOnNhd",
"AnalyticOnNhd.contDiff",
"ContDiff",
"Iff",
"WithTop.top",
"ENat",
"Iff.intro",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"Top.top",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"NormedAddCommGroup",
"ContDiff.analy... | true |
DedekindCut.principal_le_principal._simp_1 | Mathlib.Order.Completion | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"DedekindCut.principal",
"Concept.instPartialOrder",
"DedekindCut",
"LE.le",
"DedekindCut.principal_le_principal",
"propext",
"Eq",
"Preorder"
] | false |
Lean.Compiler.LCNF.Simp.FunDeclInfo.recOn | Lean.Compiler.LCNF.Simp.FunDeclInfo | [
"Lean.Compiler.LCNF.Simp.FunDeclInfo.rec",
"Lean.Compiler.LCNF.Simp.FunDeclInfo",
"Lean.Compiler.LCNF.Simp.FunDeclInfo.once",
"Lean.Compiler.LCNF.Simp.FunDeclInfo.many",
"Lean.Compiler.LCNF.Simp.FunDeclInfo.mustInline"
] | false |
cocompact_eq_atTop | Mathlib.Topology.Order.Compact | [
"Preorder.toLT",
"ClosedIciTopology",
"NoMaxOrder",
"LinearOrder",
"cocompact_le_atTop",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"SemilatticeInf.toPartialOrder",
"LE.le.antisymm",
"DistribLattice.toLattice",
"Filter.cocompact",
"Filter.atTop",
"TopologicalSpace",
"atTop_l... | true |
_private.Init.Data.List.Sort.Impl.0.List.MergeSort.Internal.mergeSortTR.run.match_1.splitter | Init.Data.List.Sort.Impl | [
"instHDiv",
"Subtype",
"HDiv.hDiv",
"Prod.mk",
"instOfNatNat",
"_private.Init.Data.List.Sort.Impl.0.List.MergeSort.Internal.mergeSortTR.run.match_1",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Nat.instDiv",
"instAddNat",
"Prod",
"OfNat.ofNat",
"Eq",
"List.length"
] | true |
CategoryTheory.Equivalence.instMonoidalInverseTrans._proof_9 | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Equivalence.instMonoidalInverseTrans._aux_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Equivalence",
"CategoryTheo... | false |
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