name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
Polynomial.zero_of_eval_zero | Mathlib.Algebra.Polynomial.Roots | [
"Multiset.toFinset",
"Iff.mpr",
"Polynomial.eval",
"IsDomain",
"CommRing",
"Polynomial.roots",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Polynomial.instDecidableEq",
"Finset",
"Polynomial.IsRoot",
"Classical.propDecidable",
... | true |
RingQuot.definition._@.Mathlib.Algebra.RingQuot.3673095128._hygCtx._hyg.2 | Mathlib.Algebra.RingQuot | [
"AlgHom",
"Algebra",
"RingHom",
"RingQuot.instSemiring",
"RingQuot",
"CommSemiring",
"RingQuot.instAlgebra",
"RingQuot.mkRingHom",
"AlgHom.mk",
"Semiring",
"Semiring.toNonAssocSemiring",
"RingQuot.definition._proof_1._@.Mathlib.Algebra.RingQuot.3673095128._hygCtx._hyg.2"
] | false |
Set.NPow | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"One",
"Pow",
"Set.one",
"Mul",
"npowRec",
"Pow.mk",
"Nat",
"Set.mul",
"Set"
] | true |
Std.TreeSet.Raw.instSliceableRccSlice | Std.Data.TreeSet.Raw.Slice | [
"Std.Rcc.Sliceable.mk",
"Ord.mk",
"Ordering",
"Std.TreeSet.Raw.instSliceableRccSlice._auto_1",
"Std.DTreeMap.Internal.Unit.RccSlice",
"Std.DTreeMap.Internal.Unit.RccSliceData.mk",
"Std.TreeMap.Raw.inner",
"autoParam",
"Std.TreeSet.Raw",
"Unit",
"Std.DTreeMap.Raw.inner",
"Std.Slice.mk",
"Std.... | true |
Lean.Elab.Tactic.BVDecide.Frontend.Normalize.MatchKind.enumWithDefault.elim | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Basic | [
"PULift.up",
"Lean.ConstructorVal",
"Array",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.MatchKind.enumWithDefault",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.MatchKind",
"Nat",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.MatchKind.ctorElim",
"Eq.symm",
"Lean.Elab.Tactic.BVDecide.Frontend.No... | false |
Finset.one_le_divConst_self | Mathlib.Combinatorics.Additive.DoublingConst | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"NNRat.instSemifield",
"Finset",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"NNRat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Finset.one_le_divConst",
"LE.le",
"AddMonoidWithO... | true |
Lean.Meta.StructProjDecl._sizeOf_inst | Lean.Meta.Structure | [
"SizeOf.mk",
"Lean.Meta.StructProjDecl._sizeOf_1",
"SizeOf",
"Lean.Meta.StructProjDecl"
] | false |
OpenPartialHomeomorph.ofSet_symm | Mathlib.Topology.OpenPartialHomeomorph.IsImage | [
"OpenPartialHomeomorph.ofSet",
"TopologicalSpace",
"IsOpen",
"Eq",
"OpenPartialHomeomorph",
"rfl",
"OpenPartialHomeomorph.symm",
"Set"
] | true |
Std.Time.Database.TZdb.inst.match_1 | Std.Time.Zoned.Database.TZdb | [
"Option.ctorIdx",
"String",
"Option.some",
"Nat.hasNotBit",
"Std.Time.Database.TZdb.inst._sparseCasesOn_1",
"Option"
] | false |
_private.Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous.0.MvPolynomial.weightedHomogeneousComponent_finsupp._simp_1_2 | Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous | [
"Exists",
"not_exists",
"propext",
"Eq",
"Not"
] | false |
_private.Mathlib.Topology.LocallyFinite.0.LocallyFinite.closure_iUnion._simp_1_1 | Mathlib.Topology.LocallyFinite | [
"Filter.NeBot",
"nhdsWithin",
"Membership.mem",
"mem_closure_iff_nhdsWithin_neBot",
"TopologicalSpace",
"closure",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
Std.Time.ZonedDateTime.toPlainDateTime | Std.Time.Zoned.ZonedDateTime | [
"Thunk.get",
"Std.Time.ZonedDateTime.date",
"Std.Time.PlainDateTime",
"Std.Time.ZonedDateTime"
] | true |
Multiset.decidableEq._proof_2 | Mathlib.Data.Multiset.Defs | [
"Quotient.mk",
"List",
"Iff",
"Quotient",
"HasEquiv.Equiv",
"instHasEquivOfSetoid",
"Quotient.eq_iff_equiv",
"List.isSetoid",
"Eq"
] | false |
gcd_same | Mathlib.Algebra.GCDMonoid.Basic | [
"gcd_eq_normalize",
"NormalizedGCDMonoid",
"MonoidWithZeroHom.funLike",
"GCDMonoid.dvd_gcd",
"CommMonoidWithZero.toMonoidWithZero",
"GCDMonoid.gcd",
"MonoidWithZeroHom",
"MonoidWithZero.toMulZeroOneClass",
"NormalizedGCDMonoid.toGCDMonoid",
"CommMonoidWithZero",
"NormalizedGCDMonoid.toNormalizat... | true |
Lean.Elab.InlayHintTextEdit.recOn | Lean.Elab.InfoTree.InlayHints | [
"Lean.Syntax.Range",
"String",
"Lean.Elab.InlayHintTextEdit",
"Lean.Elab.InlayHintTextEdit.rec",
"Lean.Elab.InlayHintTextEdit.mk"
] | false |
NormedAddGroupHom.coeAddHom_apply | Mathlib.Analysis.Normed.Group.Hom | [
"NormedAddGroupHom",
"SeminormedAddGroup.toAddGroup",
"SeminormedAddCommGroup",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"NormedAddGroupHom.funLike",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"AddGroup.toSubNegMonoid",
"Pi.addZeroClass",
"Eq.refl",
"NormedAddGroupHom.coeAddHom"... | true |
CategoryTheory.ShortComplex.Exact.epi_f | Mathlib.Algebra.Homology.ShortComplex.Exact | [
"CategoryTheory.ShortComplex.opcycles",
"Eq.mpr",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.p_fromOpcycles",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheo... | true |
bddAbove_Ioc | Mathlib.Order.Bounds.Basic | [
"Set.Ioc",
"Preorder.toLE",
"Set.Ioc_subset_Icc_self",
"BddAbove",
"bddAbove_Icc",
"Set.Icc",
"Preorder",
"BddAbove.mono"
] | true |
CochainComplex.HomComplex.leftHomologyData'_π | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | [
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"AddGroupWithOne.toAddMonoidWithOne",
"CochainComplex.HomComplex.instAddCommGroupCocycle",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Int",
"CochainComplex.HomComplex",
"... | true |
HomologicalComplex.shortComplexFunctor'._proof_5 | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.mk",
"HomologicalComplex.shortComplexFunctor'._proof_2",
"CategoryTheory.ShortComplex",
"HomologicalComplex",
... | false |
Measurable.lmarginal | Mathlib.MeasureTheory.Integral.Marginal | [
"dite_cond_eq_true",
"Eq.mpr",
"MeasureTheory.Measure",
"MeasureTheory.instSFiniteOfSigmaFinite",
"measurable_pi_iff",
"eq_false",
"MeasureTheory.Measure.pi.sigmaFinite",
"Function.updateFinset",
"Measurable.comp",
"congrArg",
"Finset",
"MeasureTheory.SigmaFinite",
"Measurable",
"ENNReal.m... | true |
MeasureTheory.Measure.toSphere_apply_aux | Mathlib.MeasureTheory.Constructions.HaarToSphere | [
"Set.instSProd",
"Set.image_image",
"Eq.mpr",
"Set.image2_image_right",
"Real",
"Set.Ioi",
"instHSMul",
"MeasureTheory.Measure",
"NormedSpace",
"Real.instZero",
"SProd.sprod",
"congrArg",
"DistribMulAction.toDistribSMul",
"Compl.compl",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass... | true |
CoalgHom.End._proof_3 | Mathlib.RingTheory.Coalgebra.Hom | [
"CoalgebraStruct",
"Mul.mk",
"HMul.hMul",
"CommSemiring.toSemiring",
"CoalgHom",
"CoalgHom.comp",
"AddCommMonoid",
"CommSemiring",
"Module",
"Eq",
"rfl",
"instHMul"
] | false |
InitialSeg.total | Mathlib.Order.InitialSeg | [
"InitialSeg.principalSumRelIso",
"InitialSeg.total._proof_3",
"PrincipalSeg",
"Classical.choice",
"PrincipalSeg.toRelEmbedding",
"PrincipalSeg.transRelIso",
"Sum",
"IsWellOrder",
"RelIso.symm",
"Sum.inl",
"RelEmbedding.sumLexInr",
"InitialSeg.total._proof_1",
"Sum.instIsWellOrderLex",
"Rel... | true |
Set.unit._proof_4 | Mathlib.RingTheory.DedekindDomain.SInteger | [
"Int.instAddCommGroup",
"Units.val",
"Int.instAddCommMonoid",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"_private.Mathlib.RingTheory.DedekindDomain.SInteger.0.Set.integer._simp_1",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"ValuationSubring.unitGroup",
"C... | false |
Polynomial.instIsJacobsonRing | Mathlib.RingTheory.Jacobson.Ring | [
"Iff.mpr",
"Polynomial.isJacobsonRing_polynomial_iff_isJacobsonRing",
"CommRing",
"CommSemiring.toSemiring",
"Polynomial",
"IsJacobsonRing",
"CommRing.toCommSemiring",
"Polynomial.commRing"
] | true |
_private.Mathlib.Algebra.BigOperators.Intervals.0.Finset.prod_fin_Icc_eq_prod_nat_Icc._proof_1_5 | Mathlib.Algebra.BigOperators.Intervals | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"MulOne.toOne",
"False",
"dite_congr",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"eq_false",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.ToInt.toInt",
"Mon... | false |
fintypeNodupList._simp_3 | Mathlib.Data.Fintype.List | [
"Membership.mem",
"Exists",
"Multiset",
"Multiset.instMembership",
"And",
"propext",
"Multiset.mem_bind",
"Eq",
"Multiset.bind"
] | false |
LinearMap.ofIsComplProdEquiv._proof_2 | Mathlib.LinearAlgebra.Projection | [
"CommRing",
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommRing.toCommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
IsRelPrime.neg_right | Mathlib.RingTheory.Coprime.Basic | [
"NegZeroClass.toNeg",
"CommRing",
"IsRelPrime.neg_left",
"CommSemiring.toSemiring",
"IsRelPrime",
"IsRelPrime.symm",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"CommRing.toCommSemiring",
"Ring.toAddCommGroup",
"CommRi... | true |
Mathlib.Tactic.BicategoryLike.IsoLift.mk._flat_ctor | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.Mor₂Iso",
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.IsoLift.mk",
"Mathlib.Tactic.BicategoryLike.IsoLift"
] | false |
Representation.invtSubmodule.instBoundedOrderSubtypeSubmoduleMemSublattice.match_1 | Mathlib.RepresentationTheory.Submodule | [
"Sublattice",
"Monoid",
"Representation.invtSubmodule",
"Submodule",
"Representation",
"CommSemiring.toSemiring",
"Submodule.completeLattice",
"Subtype.casesOn",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"Subtype",
"AddCommMonoid",
"Subtype.mk",
"CommSemiring",
... | false |
Equiv.Perm.IsCycle.zpowersEquivSupport.congr_simp | Mathlib.GroupTheory.Perm.Cycle.Basic | [
"Equiv.Perm.support",
"Finset",
"Membership.mem",
"Equiv",
"Subtype",
"Subgroup",
"Equiv.Perm.IsCycle.zpowersEquivSupport",
"Equiv.Perm.permGroup",
"Fintype",
"Finset.instSetLike",
"Equiv.Perm",
"Subgroup.zpowers",
"Equiv.Perm.IsCycle",
"Eq.refl",
"Eq",
"SetLike.instMembership",
"Sub... | true |
Std.TreeMap.getKey?_insertManyIfNewUnit_list_of_not_mem_of_mem | Std.Data.TreeMap.Lemmas | [
"List.Pairwise",
"instForInOfForIn'",
"Std.TreeMap.inner",
"Option.some",
"Membership.mem",
"Std.DTreeMap.Const.getKey?_insertManyIfNewUnit_list_of_not_mem_of_mem",
"Ordering",
"inferInstance",
"Ordering.eq",
"Std.TransCmp",
"Id",
"Membership",
"List",
"Unit",
"Std.TreeMap.insertManyIfNe... | true |
ModelWithCorners.continuous_invFun | Mathlib.Geometry.Manifold.IsManifold.Basic | [
"Continuous",
"NormedSpace",
"ModelWithCorners.toPartialEquiv",
"PseudoMetricSpace.toUniformSpace",
"TopologicalSpace",
"ModelWithCorners",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"PartialEquiv.invFun",
"NormedAddCommGroup... | true |
AlgEquiv.autCongr_trans | Mathlib.Algebra.Algebra.Equiv | [
"AlgEquiv.autCongr",
"Monoid.toMulOneClass",
"MulEquiv.trans",
"Algebra",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"CommSemiring",
"MulOneClass.toMulOne",
"AlgEquiv.trans",
"AlgEquiv",
"AlgEquiv.aut",
"Semiring",
"MulEquiv",
"Eq",
"rfl"
] | true |
Set.image_subset_iff | Mathlib.Data.Set.Image | [
"Membership.mem",
"HasSubset.Subset",
"Iff",
"Set.preimage",
"Set.image",
"Set.instMembership",
"Set.forall_mem_image",
"Set.instHasSubset",
"Set"
] | true |
AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem_toSpecΓ_assoc | Mathlib.AlgebraicGeometry.Stalk | [
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme.Opens.fromSpecStalkOfMem",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQui... | true |
ISize | Init.Data.SInt.Basic | [
"ISize.ofUSize"
] | true |
ContinuousMap.Homotopy.affine_apply | Mathlib.Topology.Homotopy.Affine | [
"Real",
"Semiring.toModule",
"AffineMap.instFunLike",
"ContinuousSMul",
"AddGroupWithOne.toAddGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousMap.Homotopy.affine",
"ContinuousMap",
"AddMonoid.toAddZeroClass",
"AffineMap.lineMap",
"PseudoMetricSpace.toUnifor... | true |
_private.Lean.Meta.MkIffOfInductiveProp.0.Lean.Meta.constrToProp.match_3 | Lean.Meta.MkIffOfInductiveProp | [
"Lean.Expr",
"Prod.mk",
"Nat",
"Prod",
"Prod.casesOn",
"Option"
] | false |
TensorProduct.Neg.aux | Mathlib.LinearAlgebra.TensorProduct.Basic | [
"LinearMap.id",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"TensorProduct.addCommMonoid",
"TensorProduct.Neg.aux._proof_2",
"AddCommGroup",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"TensorProduct.comm._proof_3",
"LinearMap.comp",
"LinearMap.addCommMon... | true |
CategoryTheory.eqToIso | Mathlib.CategoryTheory.EqToHom | [
"CategoryTheory.eqToHom",
"CategoryTheory.Iso",
"CategoryTheory.Iso.mk",
"CategoryTheory.eqToIso._proof_2",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.eqToIso._proof_1",
"Eq.symm",
"Eq",
"CategoryTheory.Category"
] | true |
Lean.Elab.instInhabitedDefView | Lean.Elab.DefView | [
"Lean.Elab.instInhabitedDefView.default",
"Inhabited",
"Lean.Elab.DefView",
"Inhabited.mk"
] | true |
SSet.prodStdSimplex.objEquiv._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex | [
"OrderHom.fst",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Equiv",
"OrderHom.comp",
"Prod.mk",
"instOfNatNat",
"CategoryTheory.Monoi... | false |
ZMod.charZero | Mathlib.Data.ZMod.Basic | [
"ZMod.commRing",
"AddGroupWithOne.toAddMonoidWithOne",
"instOfNatNat",
"ZMod",
"CharZero",
"_private.Mathlib.Data.ZMod.Basic.0.ZMod.charZero._proof_1",
"Nat",
"CommRing.toRing",
"OfNat.ofNat",
"Ring.toAddGroupWithOne"
] | true |
ENNReal.tendsto_inv_iff | Mathlib.Topology.Instances.ENNReal.Lemmas | [
"tendsto_inv_iff",
"InvolutiveInv.toInv",
"nhds",
"InvolutiveInv",
"TopologicalSpace",
"Iff",
"Inv.inv",
"Filter.Tendsto",
"ContinuousInv",
"Filter"
] | true |
_private.Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence.0.CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore._proof_11 | Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | [
"Lean.RArray.leaf",
"HMul.hMul",
"Int.Linear.norm_le",
"Lean.RArray.branch",
"id",
"Int.instNegInt",
"instOfNatNat",
"Int",
"LE.le",
"Int.Linear.Poly.num",
"Int.instMul",
"Int.Linear.Poly.add",
"Bool.true",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"Nat",
"Eq.substr",
"Bool",
"Int.... | false |
_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice.Pattern.Model.ForwardSliceSearcher.prefixFunctionRecurrence_eq_prefixFunction._simp_1_5 | Init.Data.String.Lemmas.Pattern.String.ForwardSearcher | [
"instOfNatNat",
"LE.le",
"instLENat",
"_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice.Pattern.Model.ForwardSliceSearcher.prefixFunction",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice.Pattern.M... | false |
Besicovitch.SatelliteConfig.mk.inj | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Besicovitch.SatelliteConfig",
"Real.instLE",
"Real",
"HMul.hMul",
"Real.instZero",
"Besicovitch.SatelliteConfig.mk",
"Real.instLT",
"instOfNatNat",
"LE.le",
"Real.instAdd",
"instHAdd",
"And",
"MetricSpace",
"HAdd.hAdd",
"Nat",
"Real.instMul",
"Fin.last",
"And.intro",
"Besicovitc... | true |
ProbabilityTheory.Kernel.withDensity_rnDeriv_of_subset_mutuallySingularSetSlice | Mathlib.Probability.Kernel.RadonNikodym | [
"ProbabilityTheory.IsFiniteKernel",
"MeasureTheory.Measure",
"MeasurableSpace.CountableOrCountablyGenerated",
"ProbabilityTheory.Kernel.instFunLike",
"HasSubset.Subset",
"MeasureTheory.measure_mono_null",
"ProbabilityTheory.Kernel.rnDeriv",
"instZeroENNReal",
"MeasurableSpace",
"ProbabilityTheory.... | true |
Hindman.FS.brecOn | Mathlib.Combinatorics.Hindman | [
"Hindman.FS.below",
"Hindman.FS.below.head'",
"AddSemigroup",
"Stream'",
"Hindman.FS.below.tail'",
"Hindman.FS.rec",
"Hindman.FS",
"Stream'.tail",
"Hindman.FS.below.cons'"
] | true |
Lean.PersistentHashMap.Entry.ctorElimType | Lean.Data.PersistentHashMap | [
"cond",
"Lean.PersistentHashMap.Entry.entry",
"Lean.PersistentHashMap.Entry",
"Nat.ble",
"Lean.PersistentHashMap.Entry.ref",
"Lean.PersistentHashMap.Entry.null",
"PULift",
"Nat"
] | false |
SimpleGraph.TripartiteFromTriangles.Graph.in₂₁_iff._simp_1 | Mathlib.Combinatorics.SimpleGraph.Triangle.Tripartite | [
"Finset",
"SimpleGraph.Adj",
"Sum3.in₂",
"Membership.mem",
"Exists",
"Sum",
"Sum3.in₁",
"Prod.mk",
"Finset.instSetLike",
"propext",
"Prod",
"Eq",
"SetLike.instMembership",
"SimpleGraph.TripartiteFromTriangles.Graph.in₂₁_iff",
"SimpleGraph.TripartiteFromTriangles.graph"
] | false |
GradeMinOrder.recOn | Mathlib.Order.Grade | [
"GradeMinOrder.mk",
"GradeMinOrder",
"Preorder.toLE",
"GradeOrder.grade",
"GradeMinOrder.rec",
"IsMin",
"Preorder",
"GradeOrder"
] | false |
Aesop.RulePatternIndex.recOn | Aesop.Index.RulePattern | [
"Aesop.RulePatternIndex.rec",
"Aesop.RulePatternIndex",
"Aesop.RulePatternIndex.mk",
"Aesop.RulePatternIndex.Entry",
"Lean.Meta.DiscrTree",
"Bool"
] | false |
CategoryTheory.GrothendieckTopology.instIsGeneratedByOneHypercovers | Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf | [
"CategoryTheory.GrothendieckTopology.OneHypercoverFamily",
"instReflLe",
"congrArg",
"CategoryTheory.PreZeroHypercover.sieve₀",
"CategoryTheory.PreOneHypercover.toPreZeroHypercover",
"PartialOrder.toPreorder",
"CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₀",
"CategoryTheory.Grothen... | true |
_private.Mathlib.Order.OrderIsoNat.0.RelEmbedding.wellFounded_iff_isEmpty.match_1_1 | Mathlib.Order.OrderIsoNat | [
"Acc",
"WellFounded.casesOn",
"WellFounded.intro",
"WellFounded"
] | false |
Polynomial.Chebyshev.S_two_mul_complex_cosh | Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Basic | [
"Int.cast",
"Polynomial.C",
"Polynomial.eval",
"GroupWithZero.toMonoidWithZero",
"False",
"Complex.sinh",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"Polynomial.Chebyshev.S_eq_U_comp_half_mul_X",
"CommRing.toNonUnitalCommRing",
"Polynomial.C... | true |
NumberField.InfinitePlace.embedding_of_isReal_apply | Mathlib.NumberTheory.NumberField.InfinitePlace.Basic | [
"Real",
"NumberField.ComplexEmbedding.IsReal",
"NumberField.InfinitePlace.isReal_iff",
"RingHom",
"Real.semiring",
"NumberField.InfinitePlace.embedding",
"NumberField.InfinitePlace.IsReal",
"Complex.ofReal",
"Field.toSemifield",
"RingHom.instFunLike",
"NumberField.ComplexEmbedding.IsReal.coe_emb... | true |
Std.HashMap.contains_keysArray | Std.Data.HashMap.Lemmas | [
"Std.HashMap.contains",
"Std.DHashMap.contains_keysArray",
"Std.HashMap",
"LawfulHashable",
"EquivBEq",
"Bool",
"Hashable",
"Std.HashMap.inner",
"BEq",
"Eq",
"Array.contains",
"Std.HashMap.keysArray"
] | true |
ContinuousInv.measurableInv | Mathlib.MeasureTheory.Constructions.BorelSpace.Basic | [
"Inv",
"BorelSpace",
"MeasurableInv.mk",
"MeasurableSpace",
"TopologicalSpace",
"BorelSpace.opensMeasurable",
"MeasurableInv",
"Inv.inv",
"ContinuousInv",
"Continuous.measurable",
"ContinuousInv.continuous_inv"
] | true |
Homotopy.compLeftId | Mathlib.Algebra.Homology.Homotopy | [
"HomologicalComplex.instCategory",
"Homotopy.ofEq",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex",
"CategoryTheory.CategoryStruct.id",
"ComplexShape",
"Homotopy.compLeftId._proof_1",
"CategoryTheory.Preadditive",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheor... | true |
CategoryTheory.Join.mapWhiskerRight_rightUnitor_hom | Mathlib.CategoryTheory.Join.Pseudofunctor | [
"CategoryTheory.Join.mapPairId_hom_app",
"CategoryTheory.Join.mapIsoWhiskerLeft",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Join.mapWhiskerRight",
"CategoryTheory.Join.id.match_1",
"CategoryTheory.Join.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Categor... | true |
Std.TreeMap.Raw._sizeOf_inst | Std.Data.TreeMap.Raw.Basic | [
"Std.TreeMap.Raw._auto_1",
"Ordering",
"autoParam",
"Std.TreeMap.Raw",
"SizeOf.mk",
"SizeOf",
"Std.TreeMap.Raw._sizeOf_1"
] | false |
OrderAddMonoidHom.instAddOfIsOrderedAddMonoid.eq_1 | Mathlib.Algebra.Order.Hom.Monoid | [
"OrderAddMonoidHom.mk",
"AddMonoidHomClass.toAddMonoidHom",
"Add.mk",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"OrderAddMonoidHom.instFunLike",
"AddCommMonoid",
"instHAdd",
"OrderAddMonoidHom.instAddOfIsOrderedAddMonoid",
"HAdd.hAdd",
"AddMonoidHom.add",
"OrderAddMonoidHom.instAdd... | true |
CategoryTheory.Limits.opProdIsoCoprod_inv_inl | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products | [
"Eq.mpr",
"CategoryTheory.Limits.opProdIsoCoprod",
"Opposite",
"Quiver.Hom.unop_op",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.prod.fst",
"Quiver.Hom.unop",
"id",
"CategoryTheory.Limit... | true |
TopologicalSpace.IsTopologicalBasis.isOpen_iff | Mathlib.Topology.Bases | [
"Filter.instMembership",
"congrArg",
"Membership.mem",
"Exists",
"nhds",
"HasSubset.Subset",
"iff_self",
"TopologicalSpace",
"And",
"Iff",
"implies_congr",
"_private.Mathlib.Topology.Bases.0.TopologicalSpace.IsTopologicalBasis.isOpen_iff._simp_1_1",
"True",
"propext",
"TopologicalSpace.I... | true |
AddCon.addMonoid._proof_1 | Mathlib.GroupTheory.Congruence.Defs | [
"AddCon",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddCon.hasAdd",
"AddCon.addSemigroup",
"Quotient.mk''",
"AddZeroClass.toAddZero",
"AddCon.zero",
"AddZeroClass.zero_add",
"Quotient.mk''_surjective",
"AddZero.toZero",
"instHAdd",
"AddCon.toSetoid",
"AddSemigroup.toAdd",
... | false |
SimpleGraph.bot_adj | Mathlib.Combinatorics.SimpleGraph.Basic | [
"False",
"SimpleGraph.Adj",
"Iff.rfl",
"Bot.bot",
"SimpleGraph",
"Iff",
"SimpleGraph.completeAtomicBooleanAlgebra",
"CompleteBooleanAlgebra.toBooleanAlgebra",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"BooleanAlgebra.toBot"
] | true |
Subring.mem_pointwise_smul_iff_inv_smul_mem | Mathlib.Algebra.Ring.Subring.Pointwise | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Subring.toSubsemiring",
"instHSMul",
"Subring.instSetLike",
"DivInvOneMonoid.toInvOneClass",
"Ring.toNonAssocRing",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Submonoid.toSubsemigroup",
"AddGroupWithOne.toAddMonoidWithOne",
"Group",... | true |
CategoryTheory.Grp.hom_one | Mathlib.CategoryTheory.Monoidal.Cartesian.Grp_ | [
"CategoryTheory.Grp.instMonoidalCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.Grp.instMonObj",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.GrpObj.toMonObj",
"CategoryTheory.Grp.grp",
"CategoryTheory.SemiCartesianMonoidalCatego... | true |
Aesop.Hyp.mk | Aesop.Forward.State | [
"Aesop.Hyp.mk",
"Aesop.Substitution",
"Lean.FVarId",
"Aesop.Hyp",
"Option"
] | true |
TypeVec.splitFun | Mathlib.Data.TypeVec | [
"TypeVec.last",
"instOfNatNat",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat",
"TypeVec.append1.match_1",
"instAddNat",
"OfNat.ofNat",
"TypeVec.drop",
"TypeVec.Arrow",
"Fin2",
"TypeVec"
] | true |
Lean.Elab.CommandContextInfo.mk.injEq | Lean.Elab.InfoTree.Types | [
"Lean.Elab.CommandContextInfo",
"Eq.propIntro",
"Lean.MetavarContext",
"Lean.FileMap",
"Lean.injEq_helper",
"List",
"And",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Lean.Elab.CommandContextInfo.mk",
"Lean.Elab.CommandContextInfo.mk.inj",
"Lean.Options",
"Eq",
"Lean.Environment",
"Lean.NameG... | true |
PowerSeries.coeff_pow | Mathlib.RingTheory.PowerSeries.Basic | [
"Finsupp.instFunLike",
"Eq.mpr",
"Semiring.toModule",
"HMul.hMul",
"Monoid.toMulOneClass",
"MvPowerSeries.instCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Finset.finsuppAntidiag",
"LinearMap.instFunLike",
"Finset.prod_range_induction",
"AddZeroClass.toAd... | true |
fderivWithin_inter | Mathlib.Analysis.Calculus.FDeriv.Basic | [
"Filter.instMembership",
"dite_congr",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Classical.propDecidable",
"Membership.mem",
"HasFDerivWithinAt",
"NormedField.toField",
"Exists",
"nhds",
"AddCommGroup",
"ContinuousLinearMap.zero",
"Set.instInter",
"Field.toSemifield",
"dite",
"Inter... | true |
_private.Mathlib.Order.Category.BoolAlg.0.BoolAlg.Hom.mk.injEq | Mathlib.Order.Category.BoolAlg | [
"BoolAlg.carrier",
"Eq.propIntro",
"_private.Mathlib.Order.Category.BoolAlg.0.BoolAlg.Hom.mk.inj",
"BoolAlg",
"BooleanAlgebra.toBoundedOrder",
"_private.Mathlib.Order.Category.BoolAlg.0.BoolAlg.Hom.mk",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"BoolAlg.str",
"Bou... | true |
HahnModule.instIsTorsionFree | Mathlib.RingTheory.HahnSeries.Multiplication | [
"Eq.mpr",
"HahnSeries.order",
"IsDomain",
"HahnSeries.instSemiring",
"instHSMul",
"Equiv.instEquivLike",
"HahnSeries.instNontrivialOfNonempty",
"Ring.toNonAssocRing",
"congrArg",
"SMulWithZero.toSMulZeroClass",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
... | true |
_private.Mathlib.Geometry.Manifold.VectorBundle.Hom.0.ContMDiffWithinAt.clm_bundle_apply._simp_1_1 | Mathlib.Geometry.Manifold.VectorBundle.Hom | [
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"Prod.normedSpace",
"chartedSpaceSelf",
"ContMDiffWithinAt",
"Prod.normedAddCommGroup",
"NormedSpace",
"ContinuousSMul",
"FiberBundle",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"... | false |
Std.ExtHashSet.contains_of_contains_insert' | Std.Data.ExtHashSet.Lemmas | [
"Unit.unit",
"Std.ExtHashSet.insert",
"Std.ExtHashSet",
"LawfulHashable",
"Std.ExtHashMap.contains_of_contains_insertIfNew'",
"Bool.true",
"And",
"BEq.beq",
"Unit",
"EquivBEq",
"Std.ExtHashSet.inner",
"Bool",
"Hashable",
"Bool.false",
"BEq",
"Eq",
"Not",
"Std.ExtHashSet.contains"
] | true |
AddCommGrpCat.epi_iff_range_eq_top | Mathlib.Algebra.Category.Grp.EpiMono | [
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.epi_of_surjective",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.range",
"AddCommGroup.toAddGroup",
"AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier",
"Ad... | true |
_private.Mathlib.Algebra.Order.Archimedean.Basic.0.archimedean_iff_nat_le.match_1_1 | Mathlib.Algebra.Order.Archimedean.Basic | [
"LinearOrder",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Preorder.toLE",
"Exists",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"AddMonoidWithOne.toNatCast",
"DivisionRing.toRing",
"LE.le",
"Nat.cast",
"Exists.casesOn",
"Nat",... | false |
Lean.Elab.Visibility.private.elim | Lean.Elab.DeclModifiers | [
"PULift.up",
"Lean.Elab.Visibility.ctorElim",
"Lean.Elab.Visibility.ctorIdx",
"Nat",
"Eq.symm",
"Eq",
"Lean.Elab.Visibility",
"Lean.Elab.Visibility.private"
] | false |
Finset.Icc_ofDual | Mathlib.Order.Interval.Finset.Defs | [
"Equiv.instEquivLike",
"OrderDual.ofDual",
"Finset",
"Finset.map",
"OrderDual.instLocallyFiniteOrder",
"Equiv",
"Finset.Icc",
"Equiv.toEmbedding",
"Finset.map_refl",
"LocallyFiniteOrder",
"OrderDual",
"Eq.symm",
"OrderDual.instPreorder",
"Function.Embedding.refl",
"Eq",
"DFunLike.coe",... | true |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable.0.EisensteinSeries.div_max_sq_ge_one._simp_1_4 | Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable | [
"le_refl",
"Preorder.toLE",
"LE.le",
"True",
"eq_true",
"Eq",
"Preorder"
] | false |
DoubleCoset.eq_of_not_disjoint | Mathlib.GroupTheory.DoubleCoset | [
"DoubleCoset.mem_doubleCoset_of_not_disjoint",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"Disjoint",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"Eq.mp",
"disjoint_comm",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"S... | true |
Mathlib.Tactic.Bicategory.naturality_inv | Mathlib.Tactic.CategoryTheory.Bicategory.PureCoherence | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Bicategory.whiskerLeftIso",
"id",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.Bicategory.whiskerLeft_inv_hom_assoc",
"CategoryTheory.... | true |
ISize.div_self | Init.Data.SInt.Lemmas | [
"instPowNat",
"Eq.mpr",
"_private.Init.Data.SInt.Lemmas.0.ISize.div_self._simp_1_1",
"Int.instDiv",
"False",
"Decidable.casesOn",
"instHDiv",
"of_decide_eq_true",
"eq_false",
"congrArg",
"instDecidableEqISize",
"Decidable",
"Int.instDecidableEq",
"id",
"HDiv.hDiv",
"Int.instNegInt",
... | true |
Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl | Mathlib.Geometry.Euclidean.Altitude | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Affine.Simplex.points",
"Nat.instMulZeroClass",
"Real",
"Real.instRCLike",
"congrArg",
"Compl.compl",
"NormedSpace.toModule",
"HSub.hSub",
"Membership.mem",
"Set.instSingletonSet",
"id",
"Affine.Simplex",
"instSubNat",
"Real.instRing",
"i... | true |
One.toOfNat1.hcongr_2 | Mathlib.GroupTheory.CoprodI | [
"One",
"HEq.refl",
"eq_of_heq",
"Eq.ndrec",
"One.toOfNat1",
"HEq",
"Eq",
"OfNat"
] | true |
CategoryTheory.RetractArrow.left_i | Mathlib.CategoryTheory.Retract | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.id",
"CategoryTheory.Retract.i",
"CategoryTheory.Arrow.leftFunc",
"CategoryTheory.instCategoryArrow",
"CategoryTheory.CommaMorphism.left",
"CategoryTheory.RetractArrow.left",
"Eq.refl",
"CategoryTheory.Category.toCateg... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Search.0.Lean.Meta.Grind.Arith.Cutsat.CooperSplit.assert.match_1 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Search | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstr",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Search.0.Lean.Meta.Grind.Arith.Cutsat.CooperSplit.assert._sparseCasesOn_1",
"Option"
] | false |
CategoryTheory.Limits.MulticospanIndex.sectionsEquiv._proof_5 | Mathlib.CategoryTheory.Limits.Types.Multiequalizer | [
"CategoryTheory.Limits.MulticospanShape.snd",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategory",
"CategoryTheory.Limits.MulticospanIndex.sections.val",
"Membership.mem",
"Set.Elem",
"CategoryTheory.Limits.MulticospanIndex",
"CategoryTheory.Limits.... | false |
Std.ExtTreeSet.self_le_max?_insert | Std.Data.ExtTreeSet.Lemmas | [
"Unit.unit",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Std.ExtTreeMap.self_le_maxKey?_insertIfNew",
"Bool.true",
"Unit",
"Option.get",
"Std.ExtTreeSet",
"Bool",
"Std.ExtTreeSet.max?",
"Ordering.isLE",
"Eq",
"Std.ExtTreeSet.insert",
"Std.ExtTreeSet.isSome_max?_insert"
] | true |
_private.Batteries.Data.Fin.Lemmas.0.Fin.exists_eq_some_of_findSome?_eq_some._proof_1_1 | Batteries.Data.Fin.Lemmas | [
"Fin.findSome?_eq_some_iff",
"False",
"eq_false",
"Lean.Grind.iff_eq",
"Classical.byContradiction",
"Option.some",
"Exists",
"Eq.mp",
"id",
"And.casesOn",
"Option.none",
"And",
"Iff",
"Exists.casesOn",
"Nat",
"Fin.findSome?",
"LT.lt",
"True",
"instLTFin",
"eq_true",
"of_eq_tr... | false |
DirectSum.Decomposition.casesOn | Mathlib.Algebra.DirectSum.Decomposition | [
"SetLike",
"DirectSum.coeAddMonoidHom",
"DirectSum.Decomposition",
"Function.LeftInverse",
"instAddCommMonoidDirectSum",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddSubmonoidClass",
"AddZeroClass.toAddZero",
"Subtype",
"AddSubmonoidClass.toAddCommMonoid",
"DirectSum.Decomposition.mk",
... | false |
_private.Init.Data.String.Basic.0.String.Slice.Pos.ofSliceFrom_le_ofSliceFrom_iff._simp_1_1 | Init.Data.String.Basic | [
"String.instLEPos_1",
"String.Slice.Pos.offset",
"String.Slice",
"LE.le",
"String.Pos.Raw",
"String.Slice.Pos.le_iff",
"String.instLERaw",
"propext",
"String.Slice.Pos",
"Eq"
] | false |
Lean.Expr.ensureHasNoMVars | Mathlib.Lean.Expr.Basic | [
"Pure.pure",
"Lean.instantiateMVars",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"String",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MessageData.instAppend",
"Lean.throwError",
"Lean.MonadQuotation.toMonadRef",
... | true |
Std.DTreeMap.Internal.Impl.Const.entryAtIdx?.eq_def | Std.Data.DTreeMap.Internal.Model | [
"Eq.mpr",
"congrArg",
"Std.DTreeMap.Internal.Impl.rec",
"HSub.hSub",
"Option.some",
"Ordering",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"id",
"Prod.mk",
"instSubNat",
"instOfNatNat",
"_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.Const.... | true |
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