name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
SetLike.instSubtypeSet | Mathlib.Data.SetLike.Basic | [
"SetLike",
"SetLike.instSubtypeSet._proof_1",
"Subtype",
"SetLike.mk",
"Subtype.val",
"Set"
] | true |
Std.IterM.anyM_filterMapM | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"Pure.pure",
"Std.IterM.filterMapM",
"Eq.mpr",
"WeaklyLawfulMonadAttach.map_attach",
"Std.Shrink.deflate",
"Classical.ofNonempty",
"instNonemptyOfMonad",
"Decidable.casesOn",
"bind_congr",
"Std.IterStep",
"Std.Iterators.Types.FilterMap.PlausibleStep.skip",
"congrArg",
"Std.Shrink",
"Lawful... | true |
Std.Do.SPred.Notation.unexpandIff | Std.Do.SPred.Notation | [
"Pure.pure",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Nam... | true |
_private.Init.Data.String.Basic.0.String.Pos.Raw.isValid_copy_iff._simp_1_6 | Init.Data.String.Basic | [
"String",
"String.Pos.le_iff",
"LE.le",
"String.Pos.Raw",
"String.instLERaw",
"propext",
"String.Pos",
"String.instLEPos",
"Eq",
"String.Pos.offset"
] | false |
MonoidAlgebra.coeff_zero | Mathlib.Algebra.MonoidAlgebra.Defs | [
"MonoidAlgebra.addCommMonoid",
"MonoidAlgebra.coeff",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"MonoidAlgebra",
"Semiring",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"Finsupp.instZero",
"OfNat.ofNat",
"Eq",
"Finsupp",
"rfl",
"MulZeroClass.toZero",
"in... | true |
CategoryTheory.Subgroupoid.Map.Arrows | Mathlib.CategoryTheory.Groupoid.Subgroupoid | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Groupoid",
"CategoryTheory.Subgroupoid",
"CategoryTheory.Category.toCategoryStruct",
"Function.Injective",
"CategoryTheory.Groupoid.toCategory",
"CategoryTheory.Functor.obj",
"CategoryTheory.Subgroupo... | true |
_private.Mathlib.Topology.ContinuousOn.0.ContinuousWithinAt.diff_iff._simp_1_1 | Mathlib.Topology.ContinuousOn | [
"Set.instUnion",
"HasSubset.Subset",
"Set.subset_union_left",
"True",
"eq_true",
"Union.union",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
Std.instDecidableEqRic.decEq | Init.Data.Range.Polymorphic.PRange | [
"Decidable.isTrue",
"Decidable",
"Std.Ric.mk",
"dite",
"_private.Init.Data.Range.Polymorphic.PRange.0.Std.instDecidableEqRic.decEq.match_1",
"Std.Ric",
"_private.Init.Data.Range.Polymorphic.PRange.0.Std.instDecidableEqRic.decEq._proof_2",
"Eq.ndrec",
"_private.Init.Data.Range.Polymorphic.PRange.0.St... | true |
_private.Batteries.Data.Fin.Coding.0.Fin.encodeProd.match_1.eq_1 | Batteries.Data.Fin.Coding | [
"Fin.encodeProd.match_1",
"Prod.mk",
"Nat",
"Eq.refl",
"Prod",
"Fin",
"Eq"
] | true |
Nat.minSqFacAux._unary | Mathlib.Data.Nat.Squarefree | [
"Dvd.dvd",
"instHDiv",
"HMul.hMul",
"Nat.decidable_dvd",
"InvImage",
"HSub.hSub",
"WellFounded.Nat.fix",
"Option.some",
"PSigma.casesOn",
"HDiv.hDiv",
"instSubNat",
"instMulNat",
"Nat.sqrt",
"instOfNatNat",
"dite",
"Nat.minSqFacAux.match_1",
"Option.none",
"instHAdd",
"instHSub",... | false |
ProbabilityTheory.Kernel.measure_eq_zero_or_one_of_indepSet_self' | Mathlib.Probability.Independence.ZeroOne | [
"MeasureTheory.ae",
"False",
"MeasureTheory.Measure",
"eq_false",
"congrArg",
"Filter.Eventually",
"setOf",
"MeasureTheory.measure_ne_top",
"Membership.mem",
"Filter.mp_mem",
"Eq.mp",
"ProbabilityTheory.Kernel.instFunLike",
"id",
"MeasurableSpace",
"MeasureTheory.IsFiniteMeasure",
"ENN... | true |
gc_coinduced_induced | Mathlib.Topology.Order | [
"PartialOrder.toPreorder",
"coinduced_le_iff_le_induced",
"TopologicalSpace.coinduced",
"TopologicalSpace",
"TopologicalSpace.induced",
"TopologicalSpace.instPartialOrder",
"GaloisConnection"
] | true |
_private.Init.Data.UInt.Bitwise.0.UInt8.shiftLeft_zero._simp_1_1 | Init.Data.UInt.Bitwise | [
"BitVec",
"instOfNatNat",
"UInt8.toBitVec",
"Nat",
"propext",
"UInt8.toBitVec_inj",
"OfNat.ofNat",
"Eq.symm",
"UInt8",
"Eq"
] | false |
MeromorphicOn.divisor_natCast | Mathlib.Analysis.Meromorphic.Divisor | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NormedRing.toRing",
"MeromorphicOn.divisor_const",
"Function.locallyFinsuppWithin.instZero",
"AddGroupWithOne.toAddMonoidWithOne",
"PseudoMetricSpace.toUniformSpace",
"Pi.instNatCast",
"MeromorphicOn.divisor",
"AddMonoidWithOne... | true |
CyclotomicField.instIsScalarTower._proof_1 | Mathlib.NumberTheory.Cyclotomic.Basic | [
"CommRing",
"CyclotomicField.instAlgebra",
"IsScalarTower",
"Algebra",
"Polynomial.cyclotomic",
"Algebra.toSMul",
"Field.toDivisionRing",
"Algebra.id",
"DivisionRing.toRing",
"Field.toSemifield",
"Field.toCommRing",
"instFieldCyclotomicField",
"CommRing.toCommSemiring",
"Semifield.toDivisi... | false |
_private.Lean.Meta.Sym.Pattern.0.Lean.Meta.Sym.processLevel.go.match_3.eq_8 | Lean.Meta.Sym.Pattern | [
"_private.Lean.Meta.Sym.Pattern.0.Lean.Meta.Sym.processLevel.go.match_3",
"Lean.Level.mvar",
"Lean.Level.param",
"Lean.Level.imax",
"Lean.Level",
"Unit",
"Lean.Level.zero",
"Lean.Name",
"Eq.refl",
"Lean.Level.succ",
"Eq",
"Lean.Level.max",
"Lean.LMVarId"
] | true |
Subalgebra.op_iSup | Mathlib.Algebra.Algebra.Subalgebra.MulOpposite | [
"iSup",
"MulOpposite.instAlgebra",
"OrderIso.map_iSup",
"MulOpposite",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Subalgebra.opEquiv",
"CompleteLattice.toConditionallyCompleteLattice",
"Subalgebra.op",
"CommSemiring",
"MulOpposite.instSemiring",
"Semiring",
"ConditionallyCompleteLa... | true |
Bool.or' | Init.Data.Bool | [
"Bool.true",
"Bool.rec",
"Bool"
] | true |
_private.Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence.0.CategoryTheory.Abelian.SpectralObject.HasSpectralSequence._proof_14 | Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | [
"Lean.RArray.leaf",
"HMul.hMul",
"Int.Linear.norm_le",
"CategoryTheory.Abelian.SpectralObject.HasSpectralSequence._proof_6",
"Preorder.toLE",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.i₀",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Int.instNegInt",
"CategoryTheory.... | false |
WithTop.coe_mono | Mathlib.Order.WithBot | [
"Iff.mpr",
"Monotone._to_dual_cast_2",
"Eq.mpr",
"WithTop.instPreorder",
"Monotone",
"Preorder.toLE",
"id",
"LE.le",
"WithTop.some",
"WithTop.coe_le_coe",
"Eq",
"WithTop.instLE",
"Preorder",
"WithTop",
"forall_congr"
] | true |
_private.Mathlib.Data.Setoid.Basic.0.Setoid.sSup_eq_eqvGen._simp_1_2 | Mathlib.Data.Setoid.Basic | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
Std.Http.instBEqVersion.beq | Std.Internal.Http.Data.Version | [
"Std.Http.Version",
"instBEqOfDecidableEq",
"BEq.beq",
"Nat",
"Bool",
"instDecidableEqNat",
"Std.Http.Version.ctorIdx"
] | true |
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimApp.evalAlts.goWithIncremental.match_16 | Lean.Elab.Tactic.Induction | [
"Option.ctorIdx",
"Option.some",
"Lean.MVarId",
"Nat.hasNotBit",
"Prod.mk",
"_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimApp.mkElimApp._sparseCasesOn_1",
"Lean.Meta.FVarSubst",
"Prod",
"Prod.casesOn",
"Option"
] | false |
Lean.Doc.Parser.listItem._unsafe_rec | Lean.DocString.Parser | [
"HAndThen.hAndThen",
"Lean.Doc.Parser.BlockCtxt.baseColumn",
"Lean.Doc.Parser.ignoreFn",
"instHAndThenOfAndThen",
"Lean.Parser.instAndThenParserFn",
"Lean.Doc.Parser.BlockCtxt.docStartPosition",
"Lean.Doc.Parser.BlockCtxt.mk",
"Lean.Doc.Parser.BlockCtxt.inLists",
"HOrElse.hOrElse",
"Lean.Doc.Parse... | false |
instLinearOrderEReal._aux_8 | Mathlib.Data.EReal.Basic | [
"Real",
"WithBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"LinearOrder.toDecidableLE",
"DistribLattice.toLattice",
"WithBot.decidableLE",
"DecidableLE",
"instPartialOrderEReal",
"WithTop.linearOrder",
"instDistribLatticeOfLinearOrder",
"Real.l... | false |
Eq.to_iff | Init.Core | [
"Iff.of_eq",
"Iff",
"Eq"
] | true |
Submodule.restrictScalars_traceDual | Mathlib.RingTheory.DedekindDomain.Different | [
"Submodule",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"IsScalarTower",
"Submodule.restrictScalars",
"Algebra",
"Algebra.toSMul",
"Field.toDivisionRing",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssoc... | true |
Int16.and_assoc | Init.Data.SInt.Bitwise | [
"Int16",
"BitVec.and_assoc",
"BitVec",
"instAndOpInt16",
"instOfNatNat",
"Nat",
"Int16.toBitVec",
"Iff.mp",
"HAnd.hAnd",
"OfNat.ofNat",
"Int16.toBitVec_inj",
"Eq",
"instHAndOfAndOp"
] | true |
Finset.indicator_biUnion_apply | Mathlib.Algebra.BigOperators.Group.Finset.Indicator | [
"Eq.mpr",
"Finset.indicator_biUnion",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Set.indicator",
"Finset",
"Set.PairwiseDisjoint",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"AddCommMonoid",
"CompleteLattice.toCompleteSemilatticeInf",
... | true |
CentroidHom.copy | Mathlib.Algebra.Ring.CentroidHom | [
"CentroidHom.copy._proof_1",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidHom.mk",
"CentroidHom.copy._proof_2",
"CentroidHom.toAddMonoidHom",
"ZeroHom.mk",
"CentroidHom.copy._proof_4",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"CentroidHom.copy._proof_3",
... | true |
Lean.PrettyPrinter.Parenthesizer.checkLineEq.parenthesizer | Lean.PrettyPrinter.Parenthesizer | [
"Pure.pure",
"Unit.unit",
"IO.RealWorld",
"Lean.PrettyPrinter.Parenthesizer",
"Applicative.toPure",
"Lean.PrettyPrinter.Parenthesizer.Context",
"Unit",
"Lean.PrettyPrinter.ParenthesizerM",
"Lean.Core.CoreM",
"StateRefT'",
"StateRefT'.instMonad",
"Lean.Core.instMonadCoreM",
"ReaderT.instAppli... | true |
Matrix.SpecialLinearGroup.fin_two_exists_eq_mk_of_apply_zero_one_eq_zero._proof_1 | Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | [
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",
"False",
"Equiv.instEquivLike",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"eq_false",
"mul_inv_cancel₀",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"sub_zero",
"Matrix",
... | false |
_private.Mathlib.MeasureTheory.Measure.Support.0.MeasureTheory.Measure.support_eq_forall_isOpen._simp_1_1 | Mathlib.MeasureTheory.Measure.Support | [
"Membership.mem",
"Iff",
"propext",
"Set.ext_iff",
"Eq",
"Set.instMembership",
"Set"
] | false |
PadicInt.subring._proof_3 | Mathlib.NumberTheory.Padics.PadicIntegers | [
"Real.instIsOrderedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"Real.instLE",
"Real",
"Nat.Prime",
"HMul.hMul",
"setOf",
"Membership.mem",
"Fact",
"Real.semiring",
"Eq.trans_le",
"Real.instMonoidWithZero",
"LE.le",
"Real.instOne",
"SeminormedAddCom... | false |
normalizedGCDMonoidOfExistsLCM._proof_2 | Mathlib.Algebra.GCDMonoid.Basic | [
"Iff.mpr",
"Dvd.dvd",
"NormalizationMonoid",
"semigroupDvd",
"MonoidWithZeroHom.funLike",
"Exists",
"SemigroupWithZero.toSemigroup",
"CommMonoidWithZero.toMonoidWithZero",
"Classical.choose_spec",
"MonoidWithZero.toSemigroupWithZero",
"And",
"MonoidWithZeroHom",
"Iff",
"MonoidWithZero.toMu... | false |
Lean.Option._sizeOf_inst | Lean.Data.Options | [
"Lean.Option",
"Lean.Option._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
Ordinal.veblen_eq_of_lt_invVeblen₁ | Mathlib.SetTheory.Ordinal.Veblen | [
"Ordinal.veblen",
"Ordinal.instLinearOrder",
"Preorder.toLT",
"LinearOrder.toDecidableEq",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"setOf",
"Membership.mem",
"Eq.mp",
"Ne",
"Decidable.not_not._simp_1",
"Ordinal.instConditionallyCompleteLinearOrderBot",
"notMem_of_lt_csInf'",
"Or... | true |
MeasureTheory.Measure.haarScalarFactor.eq_1 | Mathlib.MeasureTheory.Measure.Haar.Unique | [
"InnerProductSpace.toNormedSpace",
"instDecidableNot",
"MeasureTheory.Measure.IsHaarMeasure",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"Continuous",
"Real.instZero",
"Monoid.toMulOneClass",
"Real.instRCLike",
"CommSemiring.toSemiring",
"PseudoMetricSpace.toUniformSpace",
"Group",
"Cla... | true |
_private.Mathlib.Tactic.Linter.TextBased.0.Mathlib.Linter.TextBased.TextbasedLinter | Mathlib.Tactic.Linter.TextBased | [
"Lean.Linter.LinterOptions",
"_private.Mathlib.Tactic.Linter.TextBased.0.Mathlib.Linter.TextBased.StyleError",
"String",
"Array",
"Nat",
"Prod",
"Option"
] | true |
HasDerivAt.fun_add | Mathlib.Analysis.Calculus.Deriv.Add | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"HasDerivAt.add",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"HasDerivAt",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup"... | true |
mul_le_mul_right' | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"HMul.hMul",
"Mul",
"MulRightMono",
"LE.le",
"LE",
"mul_le_mul_left",
"instHMul"
] | true |
MonoidAlgebra.mapDomainBialgHom | Mathlib.RingTheory.Bialgebra.MonoidAlgebra | [
"MonoidAlgebra.semiring",
"Monoid",
"Coalgebra.toCoalgebraStruct",
"CommSemiring.toBialgebra",
"MonoidAlgebra.mapDomainBialgHom._proof_2",
"Semiring.toModule",
"MonoidAlgebra.instBialgebra",
"MonoidHom",
"Monoid.toMulOneClass",
"Bialgebra.toCoalgebra",
"CommSemiring.toSemiring",
"Algebra.toMod... | true |
Std.Tactic.BVDecide.LRAT.Internal.unsat_of_cons_none_unsat | Std.Tactic.BVDecide.LRAT.Internal.Convert | [
"Eq.mpr",
"List.all",
"Std.Tactic.BVDecide.LRAT.Internal.Clause.instEntails",
"Std.Tactic.BVDecide.LRAT.Internal.Clause.instDecidableEval",
"congrArg",
"Array.replicate",
"Std.Tactic.BVDecide.LRAT.Internal.Unsatisfiable",
"List.map",
"List.mem_filterMap._simp_1",
"Std.Tactic.BVDecide.LRAT.Internal... | true |
PiTensorProduct.mapL_apply | Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm | [
"PiTensorProduct.instModule",
"PiTensorProduct.instSeminormedAddCommGroup",
"SeminormedAddCommGroup",
"NormedSpace",
"PiTensorProduct.map",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"LinearMap.instFunLike",
"PseudoMetricSpac... | true |
_private.Mathlib.Topology.Inseparable.0.inseparable_iff_forall_isClosed._simp_1_4 | Mathlib.Topology.Inseparable | [
"iff_def",
"And",
"Iff",
"propext",
"Eq.symm",
"Eq"
] | false |
precMin1 | Init.Notation | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1"
] | true |
Homeomorph.toMeasurableEquiv.congr_simp | Mathlib.MeasureTheory.Function.LocallyIntegrable | [
"BorelSpace",
"Eq.rec",
"Homeomorph.toMeasurableEquiv",
"MeasurableSpace",
"TopologicalSpace",
"Homeomorph",
"Eq.refl",
"MeasurableEquiv",
"Eq"
] | true |
Circle.instMetricSpace._proof_5 | Mathlib.Analysis.Complex.Circle | [
"NormedCommRing.toSeminormedCommRing",
"Real.instLE",
"Real",
"Dist.mk",
"Circle.instMetricSpace._aux_1",
"Complex.instNormedField",
"SeminormedRing.toRing",
"Membership.mem",
"Subtype",
"LE.le",
"Real.instAdd",
"Real.instOne",
"PseudoMetricSpace.induced._proof_3",
"instHAdd",
"NormedFie... | false |
Set.mem_list_prod | Mathlib.Algebra.Group.Pointwise.Set.ListOfFn | [
"_private.Mathlib.Algebra.Group.Pointwise.Set.ListOfFn.0.Set.mem_list_prod._simp_1_7",
"Monoid",
"Eq.mpr",
"_private.Mathlib.Algebra.Group.Pointwise.Set.ListOfFn.0.Set.mem_list_prod._simp_1_6",
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg",
"Set.one",
"List.map",
"List.ofFn",
"_private.Math... | true |
PartialEquiv.refl_source | Mathlib.Logic.Equiv.PartialEquiv | [
"Set.univ",
"PartialEquiv.source",
"PartialEquiv.refl",
"Eq",
"rfl",
"Set"
] | true |
_private.Init.Data.List.ToArray.0.List.mapA.match_1.eq_2 | Init.Data.List.ToArray | [
"_private.Init.Data.List.Control.0.List.mapA.match_1",
"List.cons",
"List",
"Unit",
"Eq.refl",
"Eq",
"List.nil"
] | true |
Std.ExtHashMap.mem_of_mem_insertIfNew' | Std.Data.ExtHashMap.Lemmas | [
"Std.ExtHashMap.inner",
"Membership.mem",
"Std.ExtDHashMap.mem_of_mem_insertIfNew'",
"LawfulHashable",
"Std.ExtHashMap",
"Bool.true",
"And",
"BEq.beq",
"EquivBEq",
"Bool",
"Std.ExtHashMap.insertIfNew",
"Hashable",
"Std.ExtHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"BEq",
"Eq",
... | true |
Sum.Lex.inlLatticeHom._proof_2 | Mathlib.Data.Sum.Lattice | [
"Lattice",
"Lex",
"Sum.inlₗ",
"Sum",
"SemilatticeInf.toMin",
"Eq",
"Min.min",
"rfl",
"Lattice.toSemilatticeInf"
] | false |
DivInvOneMonoid.rec | Mathlib.Algebra.Group.Defs | [
"DivInvMonoid.toInv",
"DivInvOneMonoid.mk",
"DivInvOneMonoid",
"DivInvMonoid.toMonoid",
"DivInvMonoid",
"Inv.inv",
"One.toOfNat1",
"Monoid.toOne",
"OfNat.ofNat",
"Eq"
] | false |
CategoryTheory.GrothendieckTopology.instInhabited | Mathlib.CategoryTheory.Sites.Grothendieck | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"CategoryTheory.GrothendieckTopology.instCompleteLattice",
"OrderTop.toTop",
"CategoryTheory.GrothendieckTopology",
"BoundedOrder.toOrderTop",
"Inhabited",
"Semi... | true |
MeasureTheory.Measure.Regular.toIsFiniteMeasureOnCompacts | Mathlib.MeasureTheory.Measure.Regular | [
"MeasureTheory.Measure",
"MeasureTheory.IsFiniteMeasureOnCompacts",
"MeasureTheory.Measure.Regular",
"MeasurableSpace",
"TopologicalSpace"
] | true |
Lean.Elab.UserWidgetInfo.mk.inj | Lean.Elab.InfoTree.Types | [
"Lean.Syntax",
"Lean.Widget.WidgetInstance",
"Lean.Elab.UserWidgetInfo",
"Lean.Elab.UserWidgetInfo.mk",
"Lean.Elab.UserWidgetInfo.mk.noConfusion",
"And",
"And.intro",
"Eq"
] | true |
DividedPowers.ext | Mathlib.RingTheory.DividedPowers.Basic | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.choose",
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toSemiring",
"DividedPowers.casesOn",
"Nat.instAddMonoid",
"Membership.mem",
"id",
"Distrib.toAdd",
"AddMonoidWithOne.toNatCast",
"Ne",
"instMulNat",
"instOfNatNat",
"AddC... | true |
_private.Mathlib.Tactic.LinearCombination.0.Mathlib.Tactic.LinearCombination.expandLinearCombo.match_1 | Mathlib.Tactic.LinearCombination | [
"Unit.unit",
"Mathlib.Ineq",
"Option.casesOn",
"Option.some",
"Lean.Expr",
"Prod.mk",
"Option.none",
"Unit",
"Prod",
"Prod.casesOn",
"Option"
] | false |
IsScalarTower.toAlgHom | Mathlib.Algebra.Algebra.Hom | [
"Algebra.algebraMap",
"IsScalarTower.toAlgHom._proof_1",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"Algebra",
"RingHom",
"Algebra.toSMul",
"CommSemiring",
"AlgHom.mk",
"Semiring",
"Semiring.toNonAssocSemiring"
] | true |
_private.Mathlib.Data.Finset.Max.0.Finset.max_of_mem.match_1_1 | Mathlib.Data.Finset.Max | [
"WithBot.some",
"WithBot",
"Lattice.toSemilatticeSup",
"WithBot.instOrderBot",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"DistribLattice.toLattice",
"WithBot.semilatticeSup",
"LE.le",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.in... | false |
instPredOrderShrink | Mathlib.Order.Shrink | [
"instPreorderShrink",
"PredOrder.ofOrderIso",
"Shrink",
"orderIsoShrink",
"PredOrder",
"Preorder",
"Small"
] | true |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec.0._regBuiltin.BitVec.reduceShiftLeft.declare_163._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec.1981601135._hygCtx._hyg.14 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec | [
"IO",
"Lean.Meta.DiscrTree.Key.star",
"Lean.Meta.DiscrTree.Key",
"instOfNatNat",
"BitVec.reduceShiftLeft",
"List.toArray",
"List.cons",
"Unit",
"Nat",
"Lean.Meta.Simp.registerBuiltinDSimproc",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Lean.Meta.DiscrTree.Key.const",
"List.nil"
] | false |
exists_rat_of_not_irrational | Mathlib.NumberTheory.Real.Irrational | [
"Real",
"Real.instRatCast",
"Rat",
"Exists",
"Rat.cast",
"Irrational",
"_private.Mathlib.NumberTheory.Real.Irrational.0.exists_rat_of_not_irrational._proof_1_2",
"Eq",
"Not"
] | true |
AlgebraicGeometry.pullbackRestrictIsoRestrict_hom_ι_assoc | Mathlib.AlgebraicGeometry.Restrict | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOr... | true |
Lean.Meta.Grind.Arith.CommRing.Ring.intCastFn?._default | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Expr",
"id",
"Option.none",
"Option"
] | false |
NonUnitalStarSubalgebra.instIsSemitopologicalSemiring | Mathlib.Topology.Algebra.NonUnitalStarAlgebra | [
"NonUnitalStarSubalgebra.toNonUnitalSemiring",
"CommSemiring.toSemiring",
"Membership.mem",
"Subtype",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"TopologicalSpace",
"NonUnitalStarSubalgebra.instSetLike",
"NonUnitalSubalgebra.instI... | true |
_private.Mathlib.Algebra.QuadraticAlgebra.Defs.0.QuadraticAlgebra.instNonUnitalNonAssocSemiring._abel_5 | Mathlib.Algebra.QuadraticAlgebra.Defs | [
"QuadraticAlgebra.re",
"HMul.hMul",
"QuadraticAlgebra",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"Mathlib.Tactic.Abel.subst_into_add",
"Mathlib.Tactic.Abel.term",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Distrib.toAdd",
"instOfNatNat",
"zero_add",
"NonUnitalNonAssocSemiring.... | false |
_private.Lean.Compiler.IR.Basic.0.Lean.IR.FnBody.alphaEqv._sparseCasesOn_4 | Lean.Compiler.IR.Basic | [
"Lean.IR.Expr",
"Nat.ne_of_beq_eq_false",
"Lean.IR.Arg",
"Lean.IR.Param",
"Lean.IR.CtorInfo",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.IR.FnBody",
"Array",
"Lean.IR.VarId",
"Nat.land",
"List",
"Lean.IR.Alt.ctor",
"PUnit",
"Nat",
"Lean.IR.JoinPointId",
"Lean.IR.IRTyp... | false |
Mathlib.Tactic.LibrarySearch.«_aux_Mathlib_Tactic_Observe___macroRules_Mathlib_Tactic_LibrarySearch_tacticObserve?__:_Using__,,_1» | Mathlib.Tactic.Observe | [
"Pure.pure",
"Lean.Syntax.TSepArray.mk",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"_private.Mathlib.Tactic.Observe.0.Mathlib.Tactic.LibrarySearch.«_aux_Mathlib_Tactic_Observe___macroRules_Mathlib_Tactic_LibrarySearch_tacticObserve?__:__1».ma... | false |
ProbabilityTheory.iIndepFun.indepFun_mul_right₀ | Mathlib.Probability.Independence.Basic | [
"Unit.unit",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"HMul.hMul",
"IsScalarTower.right",
"AEMeasurable",
"MeasureTheory.Measure.const_comp",
"congrArg",
"CommSemiring.toSemiring",
"Set.univ",
"Mul",
"ProbabilityTheory.Kernel.instFunLike",
"Algebra.id",
"MeasureTheory.IsPro... | true |
Flag.casesOn | Mathlib.Order.Preorder.Chain | [
"Flag.mk",
"HasSubset.Subset",
"LE.le",
"LE",
"Flag.rec",
"Flag",
"IsChain",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
_private.Mathlib.RingTheory.Polynomial.Basic.0.Polynomial.mem_degreeLE._simp_1_4 | Mathlib.RingTheory.Polynomial.Basic | [
"Submodule",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"LinearMap.instFunLike",
"RingHom",
"Membership.mem",
"AddZeroClass.toAddZero",
"LinearMap",
"AddCommMonoid",
"LinearMap.mem_ker",
"AddZero.toZero",
"Submodule.setLike",
"propext",
"Semiring",
"Zero.toOfNat0",
"AddCommMonoid.toA... | false |
TensorProduct.tensorQuotEquivQuotSMul | Mathlib.LinearAlgebra.TensorProduct.Quotient | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"instHSMul",
"Semiring.toModule",
"TensorProduct.comm",
"TensorProduct.quotTensorEquivQuotSMul",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"TensorProduct.addCommMonoid",
"Submodule.hasQuotient",
"AddCommGroup",
"Su... | true |
_private.Mathlib.Data.Finset.Union.0.Finset.filter_biUnion._proof_1_1 | Mathlib.Data.Finset.Union | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"of_eq_false",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"forall_not_of_not_exists",
"Lean.Grind.not_not",
"Lean.Grind.not_and",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Finset",
"Classical.byContradiction",
"Lean.... | false |
_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd._simp_1_6 | Mathlib.Data.Nat.Multiplicity | [
"And",
"Iff",
"propext",
"Eq",
"iff_and_self"
] | false |
WithTop.coe_nsmul._simp_1 | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"instHSMul",
"AddMonoid.toNSMul",
"WithTop.some",
"Nat",
"AddMonoid",
"WithTop.addMonoid",
"HSMul.hSMul",
"Eq.symm",
"Eq",
"WithTop.coe_nsmul",
"WithTop"
] | false |
SheafOfModules.QuasicoherentData.IsFinitePresentation.mk | Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent | [
"CategoryTheory.Over",
"SheafOfModules.QuasicoherentData.IsFinitePresentation.isFinite_presentation._autoParam",
"AddCommGrpCat.instCategory",
"SheafOfModules.QuasicoherentData.I",
"AddMonoid.toAddZeroClass",
"RingCat.ring",
"SheafOfModules.QuasicoherentData.IsFinitePresentation.mk",
"CategoryTheory.S... | true |
CategoryTheory.Subobject.imageFactorisation._proof_3 | Mathlib.CategoryTheory.Subobject.Basic | [
"CategoryTheory.Subobject.arrow",
"CategoryTheory.Limits.HasImages.has_image",
"CategoryTheory.Subobject.underlying",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasImages",
"PartialOrder.toPreorder",
"Preorder.smallCategory",
"CategoryTheory.instPartialOrderSubobj... | false |
Finset.disjoint_range_addRightEmbedding | Mathlib.Algebra.Group.Nat.Range | [
"addLeftEmbedding",
"Eq.mpr",
"congrArg",
"Finset",
"IsCancelAdd.toIsLeftCancelAdd",
"AddCancelMonoid.toIsCancelAdd",
"AddCancelMonoid.toAddRightCancelMonoid",
"Disjoint",
"Finset.map",
"addLeftEmbedding_eq_addRightEmbedding",
"Nat.instAddCancelCommMonoid",
"id",
"Finset.partialOrder",
"Fu... | true |
neg_mul | Mathlib.Algebra.Ring.Defs | [
"HMul.hMul",
"Mul",
"HasDistribNeg",
"HasDistribNeg.neg_mul",
"HasDistribNeg.toInvolutiveNeg",
"InvolutiveNeg.toNeg",
"Eq",
"Neg.neg",
"instHMul"
] | true |
TopCat.Sheaf.existsUnique_gluing | Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing | [
"CategoryTheory.Functor",
"Opposite",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.Opens.instPartialOrder",
"iSup",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.ObjectProperty.FullSubcategory.property",
"TopologicalSpace.Opens",
"CompleteLattice.... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.deleteOne_preserves_strongAssignmentsInvariant._proof_1_6 | Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas | [
"congrArg",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.assignments",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultClause.mk",
"Option.some",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultClause.unit._proof_2",
"Membership.mem",
"Array.modify",
"Eq.rec",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultForm... | false |
Std.Internal.List.getKey!_nil | Std.Data.Internal.List.Associative | [
"Inhabited.default",
"Std.Internal.List.getKey!",
"Inhabited",
"BEq",
"Eq",
"Sigma",
"rfl",
"List.nil"
] | true |
_private.Std.Data.ExtDTreeMap.Lemmas.0.Std.ExtDTreeMap.Const.alter_eq_empty_iff_erase_eq_empty._simp_1_1 | Std.Data.ExtDTreeMap.Lemmas | [
"Ordering",
"Std.ExtDTreeMap.instEmptyCollection",
"Std.TransCmp",
"Std.ExtDTreeMap.isEmpty",
"Std.ExtDTreeMap.isEmpty_iff",
"Bool.true",
"propext",
"Std.ExtDTreeMap",
"Bool",
"EmptyCollection.emptyCollection",
"Eq.symm",
"Eq"
] | false |
CategoryTheory.Abelian.SpectralObject.p_fromOpcycles_assoc | Mathlib.Algebra.Homology.SpectralObject.Cycles | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Abelian",
"CategoryTheory.ComposableArrows",
"Eq.mp",
"id",
"CategoryThe... | true |
CategoryTheory.MonObj.ofIso._proof_2 | Mathlib.CategoryTheory.Monoidal.Mon | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.MonoidalCategory.leftUnitor_inv_comp_tensorHom_assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory... | false |
Con.comap_eq | Mathlib.GroupTheory.Congruence.Hom | [
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"MonoidHom",
"congrArg",
"Iff.rfl",
"id",
"MulOne.toMul",
"MonoidHom.comp",
"Con.mulOneClass",
"Con.Quotient",
"Con.eq",
"MulOneClass.toMulOne",
"Iff",
"Con.ker",
"MonoidHomClass.toMulHomClass",
"propext",
"Con.toQu... | true |
Std.TreeMap.Raw.getKey?_insertIfNew | Std.Data.TreeMap.Raw.Lemmas | [
"instDecidableNot",
"instDecidableEqOrdering",
"Std.TreeMap.Raw.WF.out",
"Std.TreeMap.Raw.insertIfNew",
"Option.some",
"Membership.mem",
"Ordering",
"Std.TreeMap.Raw.instMembership",
"Ordering.eq",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"And",
"... | true |
CategoryTheory.Limits.reflexiveCoforkEquivCofork_functor_obj_π | Mathlib.CategoryTheory.Limits.Shapes.Reflexive | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.Cocone.precompose",
"CategoryTheory.Limits.WalkingReflexivePair.zero",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.reflexiveCoforkEquivCofork",
"CategoryTheory.Limits.Walking... | true |
FractionalIdeal.mem_add | Mathlib.RingTheory.FractionalIdeal.Basic | [
"Eq.mpr",
"Submodule",
"CommRing",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"FractionalIdeal.instAdd",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"Submodule.completeLattice",
"Algebra",
"Membership.mem",
"Exists",
"CompleteLat... | true |
HasSubset.Subset.eq_of_not_ssubset | Mathlib.Order.RelClasses | [
"HasSSubset",
"Std.Antisymm",
"HasSSubset.SSubset",
"HasSubset.Subset",
"eq_of_subset_of_not_ssubset",
"HasSubset",
"Eq",
"IsNonstrictStrictOrder",
"Not"
] | true |
MeasureTheory.Measure.instPartialOrder._proof_1 | Mathlib.MeasureTheory.Measure.MeasureSpace | [
"MeasureTheory.Measure",
"Iff.rfl",
"LE.le",
"MeasurableSpace",
"And",
"Iff",
"ENNReal.instLE",
"ENNReal",
"DFunLike.coe",
"Not",
"MeasureTheory.Measure.instFunLike",
"Set"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_53 | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | [
"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_52",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"eq_false",
"Lean.Grind.i... | false |
Lean.Meta.Grind.GoalState.exprs | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.GoalState",
"Lean.PArray",
"Lean.Expr"
] | true |
MeasureTheory.LocallyIntegrable.congr | Mathlib.MeasureTheory.Function.LocallyIntegrable | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"MeasureTheory.IntegrableAtFilter.congr",
"MeasureTheory.LocallyIntegrable",
"nhds",
"Filter.EventuallyEq",
"ContinuousENorm",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureClass"
] | true |
IO.FS.Metadata.noConfusion | Init.System.IO | [
"IO.FS.Metadata.noConfusionType",
"IO.FS.FileType",
"UInt64",
"IO.FS.SystemTime",
"IO.FS.Metadata",
"IO.FS.Metadata.casesOn",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | false |
RingQuot.eqvGen_rel_eq | Mathlib.Algebra.RingQuot | [
"RingConGen.Rel.mul",
"RingConGen.Rel.trans",
"RingQuot.ringCon",
"RingConGen.Rel.symm",
"RingConGen.Rel",
"RingCon.mul",
"Distrib.toAdd",
"RingQuot.Rel",
"RingCon.refl",
"RingCon.trans",
"instDistribOfSemiring",
"RingConGen.Rel.refl",
"funext",
"RingConGen.Rel.of",
"Distrib.toMul",
"I... | true |
_private.Lean.Meta.Tactic.Simp.SimpCongrTheorems.0.Lean.Meta.SimpCongrTheorems.get.match_1 | Lean.Meta.Tactic.Simp.SimpCongrTheorems | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"List",
"Unit",
"Lean.Meta.SimpCongrTheorem",
"Option"
] | false |
Manifold.IsImmersionAtOfComplement.of_opens | Mathlib.Geometry.Manifold.Immersion | [
"PUnit.normedAlgebra",
"TopologicalSpace.Opens.instIsManifoldSubtypeMem",
"NormedCommRing.toSeminormedCommRing",
"PUnit.normedAddCommGroup",
"mem_chart_source",
"ContinuousLinearEquiv.prodUnique",
"NormedSpace",
"chartAt",
"continuous_subtype_val",
"congrArg",
"TopologicalSpace.Opens.instCharted... | true |
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