name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
εNFA.stepSet | Mathlib.Computability.EpsilonNFA | [
"Option.some",
"Membership.mem",
"εNFA.step",
"Set.instMembership",
"εNFA",
"Set.iUnion",
"εNFA.εClosure",
"Set"
] | true |
CategoryTheory.Functor.hasPointwiseRightKanExtensionAt_of_equivalence | Mathlib.CategoryTheory.Functor.KanExtension.Pointwise | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Functor.HasPointwiseRightKanExtensionAt",
"CategoryTheory.Equivalence.full_functor",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence.faithful_functor",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"Categ... | true |
CategoryTheory.Subobject.inf_comp_right_assoc | Mathlib.CategoryTheory.Subobject.Lattice | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Subobject.arrow",
"CategoryTheory.Subobject.underlying",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.Subobject.ofLE",
"Eq.mp",
"id",
"Preorder.smallCategory",
"Mathlib.Tactic.Rea... | true |
Turing.TM2to1.StAct.push.sizeOf_spec | Mathlib.Computability.TuringMachine.StackTuringMachine | [
"instOfNatNat",
"Turing.TM2to1.StAct.push",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"SizeOf",
"Turing.TM2to1.StAct._sizeOf_inst",
"OfNat.ofNat",
"Turing.TM2to1.StAct",
"Eq"
] | true |
Std.Do.SPred.and_or_elim_l | Std.Do.SPred.DerivedLaws | [
"Std.Do.SPred.entails",
"Std.Do.SPred.or",
"Std.Do.SPred.imp",
"List",
"Std.Do.SPred.imp_elim",
"Std.Do.SPred.imp_intro",
"Std.Do.SPred",
"Std.Do.SPred.and",
"Std.Do.SPred.or_elim"
] | true |
differentiableWithinAt_sub_const_iff | Mathlib.Analysis.Calculus.FDeriv.Add | [
"NormedSpace",
"congrArg",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"differentiableWithinAt_add_const_iff._simp_1",
"iff_self",
"SubNegMonoid.toSub",
"funext",
... | true |
Continuous.measurable | Mathlib.MeasureTheory.Constructions.BorelSpace.Basic | [
"Continuous",
"OpensMeasurableSpace.borel_le",
"BorelSpace.measurable_eq",
"MeasurableSpace.instPartialOrder",
"PartialOrder.toPreorder",
"Measurable",
"BorelSpace",
"borel",
"Continuous.borel_measurable",
"MeasurableSpace",
"TopologicalSpace",
"OpensMeasurableSpace",
"le_of_eq",
"Measurab... | true |
CategoryTheory.Discrete.functor_obj_eq_as | Mathlib.CategoryTheory.Discrete.Basic | [
"CategoryTheory.Discrete.functor",
"CategoryTheory.Discrete.as",
"CategoryTheory.discreteCategory",
"Eq",
"CategoryTheory.Functor.obj",
"rfl",
"CategoryTheory.Category",
"CategoryTheory.Discrete"
] | true |
Lean.IR.IRType._sizeOf_3_eq | Lean.Compiler.IR.Basic | [
"congrArg",
"instOfNatNat",
"List.rec",
"List.cons",
"List",
"instHAdd",
"List.cons.sizeOf_spec",
"HAdd.hAdd",
"Nat",
"List._sizeOf_inst",
"SizeOf.sizeOf",
"Lean.IR.IRType",
"instAddNat",
"Eq.refl",
"Lean.IR.IRType._sizeOf_inst",
"Lean.IR.IRType._sizeOf_3",
"OfNat.ofNat",
"Eq.symm"... | false |
CategoryTheory.Under.isLeftAdjoint_post | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Functor",
"CategoryTheory.Under.postAdjunctionLeft",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.Functor.id",
"CategoryTheory.Under",
"Nonempty.intro",
"CategoryTheory.Functor.IsLeftAdjoint",
"_private.Mathlib... | true |
Lean.Parser.Term.show._regBuiltin.Lean.Parser.Term.show.parenthesizer_11 | Lean.Parser.Term | [
"Lean.Name.mkStr5",
"Lean.Parser.Term.show.parenthesizer",
"IO",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.PrettyPrinter.parenthesizerAttribute",
"Unit",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
_private.Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer.0.CategoryTheory.Limits.WalkingMulticospan.functor_ext._proof_1_1 | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategory",
"CategoryTheory.Limits.MulticospanShape.fst",
"CategoryTheory.Limits.WalkingMulticospan",
"CategoryTheory.Limits.MulticospanShape",
"CategoryTheory.Limits.WalkingMulticospa... | false |
groupHomology.cyclesOfIsCycle₁._proof_1 | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"Iff.mpr",
"Submodule",
"Rep.V",
"CommRing",
"Representation",
"MonoidHom.instFunLike",
"Finsupp.module",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"AddMonoid.toAddZeroCla... | false |
Finset.sum_indicator_subset | Mathlib.Algebra.BigOperators.Group.Finset.Indicator | [
"Set.indicator",
"Finset",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"id",
"HasSubset.Subset",
"Finset.sum_indicator_subset_of_eq_zero",
"AddCommMonoid",
"AddZero.toZero",
"SetLike.coe",
"Finset.instSetLike",
"Finset.instHasSubset",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",... | true |
SupHom.mk.sizeOf_spec | Mathlib.Order.Hom.Lattice | [
"Max",
"instOfNatNat",
"Max.max",
"Nat",
"SizeOf.sizeOf",
"SupHom._sizeOf_inst",
"Eq.refl",
"SizeOf",
"SupHom",
"OfNat.ofNat",
"Eq",
"SupHom.mk"
] | true |
KStar | Mathlib.Algebra.Order.Kleene | [
"KStar.mk"
] | true |
_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.natCast_image_Iio._proof_1_1 | Mathlib.SetTheory.Ordinal.Arithmetic | [
"instLawfulOrderLT_mathlib",
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"of_eq_false",
"False",
"Set.mem_Iio",
"Ordinal.instLinearOrder",
"forall_not_of_not_exists",
"Preorder.toLT",
"Lean.Grind.not_not",
"Lean.Grind.not_and",
"eq_false",
"Lean.Grind.iff_eq",
"Ordina... | false |
HahnSeries.support_embDomain_subset | Mathlib.RingTheory.HahnSeries.Basic | [
"HahnSeries.support",
"Eq.mpr",
"HahnSeries.embDomain",
"Classical.not_not",
"congrArg",
"PartialOrder.toPreorder",
"HahnSeries.embDomain_notin_image_support",
"Preorder.toLE",
"Membership.mem",
"PartialOrder",
"id",
"HasSubset.Subset",
"Ne",
"Mathlib.Tactic.Contrapose.contrapose₁",
"pro... | true |
Matrix.twoBlockTriangular_det | Mathlib.LinearAlgebra.Matrix.Block | [
"Eq.mpr",
"instDecidableNot",
"Matrix.fromBlocks",
"CommRing",
"instFintypeSum",
"HMul.hMul",
"outParam",
"congrArg",
"CommSemiring.toSemiring",
"HMul",
"Matrix",
"HEq.refl",
"Matrix.toBlock",
"instDecidableEqSum",
"Subtype.fintype",
"Sum",
"Eq.casesOn",
"id",
"Subtype",
"instD... | true |
Finset.intervalGapsWithin.snd.congr_simp | Mathlib.Order.Interval.Finset.Gaps | [
"Finset",
"LinearOrder",
"Eq.rec",
"instOfNatNat",
"Finset.intervalGapsWithin.snd",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Finset.card",
"Eq.ndrec",
"instAddNat",
"Eq.refl",
"Prod",
"OfNat.ofNat",
"Fin",
"Eq"
] | true |
Mathlib.Tactic.Sat.buildProof.match_5 | Mathlib.Tactic.Sat.FromLRAT | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Expr",
"Option.none",
"Unit",
"Option"
] | false |
ClosedSubgroup.instSetLike | Mathlib.Topology.Algebra.Group.ClosedSubgroup | [
"SetLike",
"ClosedSubgroup.toSubgroup",
"Group",
"Subgroup",
"SetLike.mk",
"TopologicalSpace",
"SetLike.coe",
"ClosedSubgroup",
"ClosedSubgroup.instSetLike._proof_1",
"Subgroup.instSetLike"
] | true |
_private.Mathlib.Analysis.SpecialFunctions.Artanh.0.Real.strictMonoOn_artanh._proof_1_4 | Mathlib.Analysis.SpecialFunctions.Artanh | [
"instLawfulOrderLT_mathlib",
"GroupWithZero.toMonoidWithZero",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
"Set.mem_Ioo",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
"R... | false |
CategoryTheory.Localization.Construction.natTransExtension | Mathlib.CategoryTheory.Localization.Construction | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.Q",
"CategoryTheory.Functor.category",
"CategoryTheory.Localization.Construction.NatTransExtension.app",
"CategoryTheory.Functor.comp",
"CategoryTheor... | true |
Computability.instDecidableEqΓ'.decEq._proof_6 | Mathlib.Computability.Encoding | [
"False",
"False.elim",
"noConfusion_of_Nat",
"Computability.Γ'.blank",
"Computability.Γ'.ctorIdx",
"Computability.Γ'.comma",
"Eq",
"Not",
"Computability.Γ'"
] | false |
_private.Init.Data.String.Pattern.Basic.0.String.Slice.Pattern.ToBackwardSearcher.DefaultBackwardSearcher.finitenessRelation._proof_2 | Init.Data.String.Pattern.Basic | [
"Iff.mpr",
"Eq.mpr",
"String.Slice.Pattern.BackwardPattern",
"String.Slice.Pos.lt_endPos_iff",
"String.instLEPos_1",
"Option.some.noConfusion",
"Std.IterStep",
"String.Slice.Pattern.StrictBackwardPattern.ne_endPos",
"Std.IterStep.successor",
"String.Slice.Pos.ofSliceTo",
"String.Slice.Pos.prev",... | false |
ModuleFilterBasis.smul_right' | Mathlib.Topology.Algebra.FilterBasis | [
"CommRing",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Filter.Eventually",
"AddGroupFilterBasis.toFilterBasis",
"AddMonoid.toAddZeroClass",
"ModuleFilterBasis.toAddGroupFilterBasis",
"AddCommGroup.toAddGroup",
"Membership.mem",
"n... | true |
Homeomorph.isCompact_image | Mathlib.Topology.Homeomorph.Lemmas | [
"Homeomorph.isEmbedding",
"Topology.IsEmbedding.isCompact_iff",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Iff",
"Homeomorph",
"Set.image",
"DFunLike.coe",
"Iff.symm",
"IsCompact",
"EquivLike.toFunLike",
"Set"
] | true |
topologicalNilradical._proof_1 | Mathlib.Topology.Algebra.TopologicallyNilpotent | [
"CommRing",
"CommSemiring.toSemiring",
"IsTopologicallyNilpotent",
"TopologicalSpace",
"CommRing.toCommSemiring",
"MonoidWithZero.toMulZeroOneClass",
"Zero.toOfNat0",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"MulZeroClass.toZero",
"IsTopologicallyNilpotent.zero",
"Semiring.toMonoidWith... | false |
Std.Rio.length_iter | Std.Data.Iterators.Lemmas.Producers.Range | [
"Eq.mpr",
"Std.PRange.UpwardEnumerable",
"Std.Rxo.LawfulHasSize",
"congrArg",
"Std.PRange.LawfulUpwardEnumerableLT",
"Std.Rxo.Iterator.instIteratorLoop",
"Std.Rxo.instIteratorIteratorIdOfUpwardEnumerableOfDecidableLT",
"Std.Iter.size_toArray_eq_length",
"id",
"Std.Iter.length",
"Std.Rxo.Iterator... | true |
Std.Iter.filterMapWithPostcondition_eq_toIter_filterMapWithPostcondition_toIterM | Init.Data.Iterators.Lemmas.Combinators.FilterMap | [
"Monad.toApplicative",
"MonadLiftT.monadLift",
"Std.Iter.toIterM",
"Id",
"Applicative.toPure",
"Std.Iterator",
"Std.Iter.filterMapWithPostcondition",
"Std.Iterators.Types.FilterMap",
"Std.Iter",
"Std.IterM.filterMapWithPostcondition",
"Std.Iterators.PostconditionT",
"Std.IterM",
"Monad",
"... | true |
MulArchimedeanClass.instLinearOrder._proof_19 | Mathlib.Algebra.Order.Archimedean.Class | [
"AntisymmRel.setoid",
"Preorder.toLT",
"instPartialOrderAntisymmetrization._proof_2",
"IsOrderedMonoid",
"Quot.recOnSubsingleton._proof_1",
"LinearOrder",
"PartialOrder.toPreorder",
"Decidable",
"Classical.propDecidable",
"Preorder.toLE",
"MulArchimedeanClass._proof_1",
"SemilatticeInf.toParti... | false |
Char.reduceToString._regBuiltin.Char.reduceToString.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Char.2368443037._hygCtx._hyg.18 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Char | [
"IO",
"Bool.true",
"Unit",
"Sum.inr",
"Lean.Meta.Simp.DSimproc",
"Char.reduceToString",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.addSimprocBuiltinAttr",
"Lean.Meta.Simp.Simproc"
] | false |
nontrivial_iff_exists_ne | Mathlib.Logic.Nontrivial.Defs | [
"Nontrivial",
"Exists",
"exists_ne",
"nontrivial_of_ne",
"Ne",
"_private.Mathlib.Logic.Nontrivial.Defs.0.nontrivial_iff_exists_ne.match_1_1",
"Iff",
"Iff.intro"
] | true |
instDecidableEqNum.decEq._proof_4 | Mathlib.Data.Num.Basic | [
"False",
"False.elim",
"noConfusion_of_Nat",
"Num.ctorIdx",
"Num",
"Num.pos",
"PosNum",
"Eq",
"Not",
"Num.zero"
] | false |
Lean.Meta.MVarRenaming | Lean.Meta.Match.MVarRenaming | [
"Lean.Meta.MVarRenaming.mk"
] | true |
_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.typeHasRecFun.match_4 | Lean.Elab.MutualDef | [
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.getPendingMVarErrorMessage._sparseCasesOn_1",
"Lean.Expr.fvar",
"Lean.Expr.ctorIdx",
"_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.typeHasRecFun._sparseCasesOn_1",
"Option"... | false |
CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanShape_L | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.Functor.PreOneHypercoverDenseData",
"Eq.refl",
"Eq",
"CategoryTheory.Functor.PreOneHypercoverDenseData.I₀",
"CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanShape",
"CategoryTheory.Category"
] | true |
_private.Lean.Data.NameTrie.0.Lean.toKey.loop._f | Lean.Data.NameTrie | [
"Lean.Name.below",
"String",
"Lean.Name.num",
"Lean.NamePart",
"Lean.Name.str",
"List.cons",
"Lean.Name.anonymous",
"List",
"_private.Lean.Data.NameTrie.0.Lean.toKey.match_1",
"Nat",
"Lean.NamePart.num",
"Lean.Name",
"Lean.NamePart.str"
] | false |
List.zipWith_map_left | Init.Data.List.Zip | [
"List.zipWith",
"congrArg",
"List.map",
"List.rec",
"List.cons",
"List",
"congr",
"True",
"List.casesOn",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"congrFun'",
"List.zipWith_nil_right",
"Eq.symm",
"Eq",
"Eq.trans",
"List.nil"
] | true |
Lean.Lsp.CompletionItemKind.value.sizeOf_spec | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.CompletionItemKind._sizeOf_inst",
"instOfNatNat",
"Lean.Lsp.CompletionItemKind",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Lsp.CompletionItemKind.value"
] | true |
Lean.PrefixTreeNode.brecOn_3.eq | Lean.Data.PrefixTree | [
"Lean.PrefixTreeNode.below_3",
"Lean.PrefixTreeNode.below_1",
"Lean.PrefixTreeNode",
"Std.DTreeMap.Internal.Impl.casesOn",
"Lean.PrefixTreeNode.below_2",
"Ordering",
"Std.DTreeMap.Internal.Impl.inner",
"Lean.PrefixTreeNode.brecOn_3.go",
"Lean.PrefixTreeNode.below",
"Std.TreeMap.Raw",
"Std.DTreeM... | true |
SimpleGraph.lapMatrix_ker_basis | Mathlib.Combinatorics.SimpleGraph.LapMatrix | [
"Pi.Function.module",
"Submodule",
"Real",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Pi.addCommMonoid",
"Matrix.module",
"CommSemiring.toSemiring",
"Matrix",
"Submodule.addCommMonoid",
"SimpleGraph.Adj",
"DecidableRel",
"Function.smulCommClass",
"LinearMap.ker",
"SimpleGraph.lapM... | true |
isClopen_connectedComponent | Mathlib.Topology.Connected.LocallyConnected | [
"connectedComponent",
"isOpen_connectedComponent",
"IsClosed",
"TopologicalSpace",
"And.intro",
"IsOpen",
"isClosed_connectedComponent",
"IsClopen",
"LocallyConnectedSpace"
] | true |
NONote.ofNat | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.NF",
"ONote.ofNat",
"NONote.ofNat._proof_1",
"Subtype.mk",
"Nat",
"NONote",
"ONote"
] | true |
ContinuousOpenMapClass.casesOn | Mathlib.Topology.Hom.Open | [
"ContinuousMapClass",
"IsOpenMap",
"ContinuousOpenMapClass.rec",
"TopologicalSpace",
"DFunLike.coe",
"ContinuousOpenMapClass",
"FunLike",
"ContinuousOpenMapClass.mk"
] | false |
Matrix.IsHermitian.charpoly_cfc_eq | Mathlib.Analysis.Matrix.HermitianFunctionalCalculus | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"Polynomial.C",
"Matrix.instStar",
"NormedCommRing.toSeminormedCommRing",
"Matrix.smul",
"MulOne.toOne",
"Matrix.IsHermitian.cfc_eq",
"IsSelfAdjoint",
"Semigroup.toMul",
"Real",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",... | true |
compl_bihimp_self | Mathlib.Order.SymmDiff | [
"Lattice.toSemilatticeSup",
"hnot_symmDiff_self",
"Compl.compl",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"GeneralizedHeytingAlgebra.toHImp",
"Bot.bot",
"SemilatticeInf.toMin",
"bihimp",
"GeneralizedHeytingAlgebra.toLattice",
"HeytingAlgebra.toGeneralizedHeytingAlgebra",
... | true |
_private.Std.Sync.Notify.0.Std.Notify.notify.match_1 | Std.Sync.Notify | [
"Option.ctorIdx",
"Std.Notify.Consumer",
"Option.some",
"Nat.hasNotBit",
"Prod.mk",
"Unit",
"_private.Std.Sync.Notify.0.Std.Notify.notify._sparseCasesOn_1",
"Std.Queue",
"Prod",
"Prod.casesOn",
"Option"
] | false |
instGradedAlgebraRestrictScalars._proof_3 | Mathlib.RingTheory.GradedAlgebra.Basic | [
"DirectSum.coeAddMonoidHom",
"Submodule",
"instAddCommMonoidDirectSum",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Algebra",
"Membership.mem",
"GradedRing.toDecomposition",
"AddZeroClass.toAddZero",
"Algebra.toModule",
"Subtype",
"AddSubmonoidClass.toAddCommMonoid",
"CommSemirin... | false |
Aesop.UnsafeRuleInfo.successProbability | Aesop.Rule | [
"Aesop.UnsafeRuleInfo",
"Aesop.Percent"
] | true |
Lean.Parser.ppAllowUngrouped.parenthesizer | Lean.Parser.Extra | [
"Lean.PrettyPrinter.Parenthesizer.skip.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer"
] | true |
Stream'.WSeq.mem_think | Mathlib.Data.WSeq.Basic | [
"False",
"Option.some.noConfusion",
"Option.ctorIdx",
"False.elim",
"Subtype.casesOn",
"noConfusion_of_Nat",
"Option.some",
"Membership.mem",
"id",
"Or.resolve_left",
"Stream'.mem_cons_of_mem",
"Subtype.mk",
"Stream'",
"Option.none",
"Iff",
"Stream'.IsSeq",
"Stream'.instMembership",
... | true |
Bitraversable.id_tsnd | Mathlib.Control.Bitraversable.Lemmas | [
"Pure.pure",
"Bitraversable",
"Monad.toApplicative",
"LawfulBitraversable",
"Bitraversable.tsnd",
"Id",
"Applicative.toPure",
"Id.instMonad",
"Eq",
"LawfulBitraversable.id_bitraverse"
] | true |
_private.Lean.Meta.Offset.0.Lean.Meta.getOffset | Lean.Meta.Offset | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.instInhabitedMetaM",
"Nat",
"Prod"
] | true |
Lean.Meta.Grind.PendingSolverPropagations._sizeOf_inst | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.PendingSolverPropagations",
"SizeOf.mk",
"SizeOf",
"Lean.Meta.Grind.PendingSolverPropagations._sizeOf_1"
] | false |
MvPFunctor.wRec_eq | Mathlib.Data.PFunctor.Multivariate.W | [
"MvPFunctor",
"PFunctor.B",
"instOfNatNat",
"MvPFunctor.A",
"instHAdd",
"HAdd.hAdd",
"Nat",
"MvPFunctor.B",
"MvPFunctor.last",
"instAddNat",
"MvPFunctor.wRec",
"MvPFunctor.drop",
"OfNat.ofNat",
"MvPFunctor.wMk",
"TypeVec.Arrow",
"MvPFunctor.W",
"Eq",
"rfl",
"TypeVec"
] | true |
Lean.Meta.Grind.Arith.isNatAdd? | Lean.Meta.Tactic.Grind.Arith.Util | [
"Lean.Meta.Grind.Arith.isInstAddNat",
"Unit.unit",
"Lean.Expr.isApp",
"Lean.Expr.cleanupAnnotations",
"Option.some",
"Lean.Expr",
"instDecidableEqBool",
"Prod.mk",
"Lean.Expr.appArg",
"Lean.Expr.appFnCleanup",
"dite",
"Bool.true",
"Option.none",
"Unit",
"Bool",
"Lean.Name.mkStr2",
"L... | true |
Lean.SMap.mk.injEq | Lean.Data.SMap | [
"Eq.propIntro",
"Lean.PHashMap",
"Lean.injEq_helper",
"Lean.SMap.mk.inj",
"Std.HashMap",
"Lean.SMap.mk",
"And",
"Lean.SMap",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Hashable",
"BEq",
"Eq"
] | true |
Finset.mk_mem_sigmaLift | Mathlib.Data.Finset.Sigma | [
"Eq.mpr",
"congrArg",
"HEq.refl",
"Finset",
"Finset.map",
"Membership.mem",
"Exists",
"Eq.rec",
"Sigma.mk.noConfusion",
"dif_pos",
"Eq.casesOn",
"id",
"Sigma.fst",
"Finset.instEmptyCollection",
"dite",
"Function.Embedding",
"And.casesOn",
"And",
"Function.Embedding.sigmaMk",
"I... | true |
DMatrix.map_zero | Mathlib.Data.Matrix.DMatrix | [
"DMatrix",
"DMatrix.map",
"congrArg",
"True",
"eq_self",
"of_eq_true",
"DMatrix.ext",
"Zero.toOfNat0",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Eq.trans",
"DMatrix.instZero",
"Zero"
] | true |
List.continuous_prod | Mathlib.Topology.List | [
"Iff.mpr",
"MulOne.toOne",
"Continuous",
"ContinuousAt",
"MulOne.toMul",
"TopologicalSpace",
"List",
"MulOneClass.toMulOne",
"ContinuousMul",
"List.tendsto_prod",
"MulOneClass",
"instTopologicalSpaceList",
"continuous_iff_continuousAt",
"List.prod"
] | true |
WeierstrassCurve.preΨ₄._proof_1 | Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
MDifferentiableAt.prodMap | Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | [
"Set.instSProd",
"Eq.mpr",
"Prod.normedSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"mdifferentiableWithinAt_univ",
"SProd.sprod",
"congrArg",
"HEq.refl",
"Set.univ",
"instTopologicalSpaceProd",
"MDifferentiableAt",
"Eq.mp",
"Eq.casesOn",
"id",
"instTopologicalSpaceModelProd",
"... | true |
AddChar.starComp_apply | Mathlib.NumberTheory.LegendreSymbol.AddCharacter | [
"Eq.mpr",
"CommRing",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Complex.commRing",
"congrArg",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"RingHom",
"AddChar",
"DivisionMonoid.toDivInvOneMonoid",
"id",
"instOfNatNat",
"CommGroup.toDivisi... | true |
Lean.Compiler.LCNF.UnreachableBranches.Value.bot.elim | Lean.Compiler.LCNF.ElimDeadBranches | [
"PULift.up",
"Lean.Compiler.LCNF.UnreachableBranches.Value.bot",
"Nat",
"Eq.symm",
"Lean.Compiler.LCNF.UnreachableBranches.Value.ctorIdx",
"Eq",
"Lean.Compiler.LCNF.UnreachableBranches.Value",
"Lean.Compiler.LCNF.UnreachableBranches.Value.ctorElim"
] | false |
CategoryTheory.SimplicialObject.Splitting.IndexSet.epiComp_fst | Mathlib.AlgebraicTopology.SimplicialObject.Split | [
"Opposite",
"CategoryTheory.Epi",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SimplicialObject.Splitting.IndexSet",
"Quiver.Hom.unop",
"Subtype",
"Sigma.fst",
"SimplexCategory",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"SimplexCate... | true |
Set.mem_vadd_set_iff_neg_vadd_mem | Mathlib.Algebra.Group.Action.Pointwise.Set.Basic | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"Membership.mem",
"Set.vaddSet",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
"Iff"... | true |
Lean.SyntaxNodeKinds | Init.Prelude | [
"List",
"Lean.SyntaxNodeKind"
] | true |
WeierstrassCurve.Projective.polynomial.eq_1 | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | [
"Finsupp.instAddZeroClass",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"Finsupp.instAddMonoid",
"MvPolynomial.X",
"Nat.instAddMonoid",
"RingHom",
"Weierstras... | true |
ULift.instLinearOrder._proof_3 | Mathlib.Order.Lattice | [
"LinearOrder",
"ULift",
"ULift.down_inf",
"ULift.instMin_mathlib",
"LinearOrder.toMin",
"Eq",
"ULift.down",
"Min.min"
] | false |
Std.DTreeMap.Internal.Impl.Equiv.constModify | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.Equiv.impl",
"Ord",
"Std.instLawfulBEqOrd",
"beqOfOrd",
"Std.DTreeMap.Internal.Impl.Ordered.distinctKeys",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.Ordered",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.WF.ordered",
"List.Perm.congr_... | true |
MonTypeEquivalenceMon.inverse._proof_12 | Mathlib.CategoryTheory.Monoidal.Internal.Types.Basic | [
"MonTypeEquivalenceMon.inverse._proof_4",
"MulOne.toOne",
"MonoidHom.instFunLike",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CategoryTheory.ConcreteCategory.hom",
"MonTypeEquivalence... | false |
nnnorm_eq_zero' | Mathlib.Analysis.Normed.Group.Basic | [
"Norm.norm",
"Eq.mpr",
"Real",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Real.instZero",
"congrArg",
"coe_nnnorm'",
"NormedGroup",
"NNNorm.nnnorm",
"Iff.rfl",
"NNReal.coe_eq_zero",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"norm_eq_zero'",
"id",
"NNRe... | true |
UInt16.toNat_xor | Init.Data.UInt.Bitwise | [
"UInt16.toBitVec",
"Nat.instXorOp",
"BitVec.instXorOp",
"congrArg",
"UInt16.toBitVec_xor",
"BitVec",
"instOfNatNat",
"BitVec.toNat",
"UInt16",
"Nat",
"True",
"HXor.hXor",
"eq_self",
"of_eq_true",
"UInt16.toNat",
"congrFun'",
"instXorOpUInt16",
"OfNat.ofNat",
"Eq",
"instHXorOfXo... | true |
List.countP_lt_length_iff._simp_1 | Mathlib.Data.List.Count | [
"List.countP",
"Membership.mem",
"Exists",
"List.countP_lt_length_iff",
"List",
"And",
"List.instMembership",
"Nat",
"LT.lt",
"propext",
"Bool",
"instLTNat",
"Bool.false",
"Eq",
"List.length"
] | false |
ZeroAtInftyContinuousMap.instAddZeroClass._proof_2 | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"ZeroAtInftyContinuousMap.coe_zero",
"AddZeroClass.toAddZero",
"ZeroAtInftyContinuousMap.instFunLike",
"TopologicalSpace",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
"ZeroAtInftyContinuousMap.instZero",
"Pi.addZeroClass",
"DFunLike.coe_injective",
"Function.Injective.addZeroCla... | false |
CompleteLatticeHomClass.toFrameHomClass | Mathlib.Order.Hom.CompleteLattice | [
"sSupHomClass.map_sSup",
"CompleteLattice.toLattice",
"CompleteLatticeHomClass",
"InfTopHomClass",
"FrameHomClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toBoundedOrder",
"SemilatticeInf.toMin",
"OrderTop.toTop",
"BoundedOrder.toOrderTop"... | true |
zpow_right_strictAnti | Mathlib.Algebra.Order.Group.Basic | [
"Eq.mpr",
"Preorder.toLT",
"InvOneClass.toOne",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"IsOrderedMonoid",
"Monoid.toMulOneClass",
"IsLeftCancelMul.mulLeftStrictMono_of_mulLeftMono",
"congrArg",
"PartialOrder.toPreorder",
"DivInvMonoid.toZPow",
"P... | true |
ProperlyDiscontinuousVAdd.rec | Mathlib.Topology.Algebra.ConstMulAction | [
"setOf",
"Set.Finite",
"VAdd",
"Set.instInter",
"HVAdd.hVAdd",
"Inter.inter",
"TopologicalSpace",
"Set.Nonempty",
"ProperlyDiscontinuousVAdd.mk",
"instHVAdd",
"Set.image",
"IsCompact",
"ProperlyDiscontinuousVAdd",
"Set"
] | false |
instDecidableEqQuadraticAlgebra.decEq.match_1 | Mathlib.Algebra.QuadraticAlgebra.Defs | [
"QuadraticAlgebra",
"QuadraticAlgebra.mk",
"QuadraticAlgebra.casesOn"
] | false |
CategoryTheory.Functor.relativelyRepresentable.w | Mathlib.CategoryTheory.MorphismProperty.Representable | [
"CategoryTheory.Functor.relativelyRepresentable.fst",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.relativelyRepresentable.isPullback",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Functor.relativelyRep... | true |
Set.zero_smul_set_subset | Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set | [
"Iff.mpr",
"instHSMul",
"SMulWithZero.toSMulZeroClass",
"Membership.mem",
"HasSubset.Subset",
"Set.zero",
"zero_smul",
"Set.preimage",
"Zero.toOfNat0",
"Set.image",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"Set.image_subset_iff",
"SMulWithZero",
"OfNat.ofNat",
"Set.instMembership",
"Se... | true |
Algebra.FormallyUnramified.of_surjective | Mathlib.RingTheory.Unramified.Basic | [
"Eq.mpr",
"CommRing",
"DFunLike.congr_fun",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AlgHom.comp_apply",
"Algebra",
"Algebra.FormallyUnramified",
"Exists",
"Eq.rec",
"Algebra.id",
"id",
"instOfNatNat",
"Bot.bot",
"AlgHom.ext",
"DFun... | true |
Int.bmod_eq_self_sub_bdiv_mul | Init.Data.Int.DivMod.Lemmas | [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"id",
"Int.add_sub_cancel",
"Int",
"Nat.cast",
"Int.instMul",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Int.bmod",
"Nat",
"Int.instAdd",
"Eq.refl",
"Int.instSub",
"Int.bdiv",
"instNatCastInt",
"Eq.symm",
"Eq",
"Int.bmod_add_bdiv'"... | true |
LieAdmissibleAlgebra.toModule | Mathlib.Algebra.NonAssoc.LieAdmissible.Defs | [
"LieAdmissibleAlgebra",
"CommRing",
"CommSemiring.toSemiring",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"LieAdmissibleRing.toNonUnitalNonAssocRing",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
"LieAdmissibleRing",
"Module"
] | true |
CategoryTheory.Abelian.SpectralObject.kernelSequenceE._proof_2 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Abelian",
"CategoryTheory.ComposableArrows",
"CategoryTheory.Limits.HasBinaryBiprod... | false |
_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM0to1.tr.match_3.eq_1 | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Turing.TM0to1.Λ'.act",
"Turing.TM0.Stmt.move",
"Turing.TM0to1.Λ'",
"Eq.refl",
"Turing.TM0to1.tr.match_3",
"Turing.TM0to1.Λ'.normal",
"Eq",
"Turing.Dir",
"Turing.TM0.Stmt.write"
] | true |
Bundle.Trivialization.piecewise._proof_1 | Mathlib.Topology.FiberBundle.Trivialization | [
"Eq.mpr",
"frontier",
"congrArg",
"instTopologicalSpaceProd",
"id",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"Set.preimage",
"Bundle.Trivialization",
"Bundle.Trivialization.frontier_preimage",
"PartialEquiv.source",
"Eq.refl",
"Prod",
"Bundle.Trivialization.baseSet",
"OpenPa... | false |
Std.TreeSet.Raw.max?_le_max?_insert | Std.Data.TreeSet.Raw.Lemmas | [
"Unit.unit",
"Std.TreeSet.Raw.max?",
"Std.TreeSet.Raw.WF.out",
"Option.some",
"Ordering",
"Std.TransCmp",
"Std.TreeSet.Raw.isSome_max?_insert",
"Bool.true",
"Std.TreeSet.Raw.insert",
"Std.TreeSet.Raw",
"Unit",
"Option.get",
"Std.TreeMap.Raw.maxKey?_le_maxKey?_insertIfNew",
"Bool",
"Order... | true |
ContinuousOn.cpow | Mathlib.Analysis.SpecialFunctions.Pow.Continuity | [
"NormedCommRing.toSeminormedCommRing",
"ContinuousWithinAt.cpow",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"Complex.instPow",
"Membership.mem",
"TopologicalSpace",
"HPow.hPow",
"SeminormedCommRing.toSeminormedRing",
"ContinuousOn",
"instHPow",
"SeminormedRing.toPseudoMetr... | true |
AddCircle.equivIco | Mathlib.Topology.Instances.AddCircle.Defs | [
"AddCircle.equivIco._proof_1",
"Preorder.toLT",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Fact",
"AddCommGroup",
"Set.Elem",
"DistribLattice.toLattice",
"Equiv",
"SubtractionMonoid.toSubNegZeroMonoid",
"AddCircle",
"SubNegZe... | true |
_private.Std.Time.Date.ValidDate.0.PSigma.casesOn._arg_pusher | Std.Time.Date.ValidDate | [
"PSigma.casesOn",
"PSigma.mk",
"Eq.refl",
"PSigma",
"Eq"
] | false |
MvPolynomial.expand_char | Mathlib.RingTheory.MvPolynomial.Expand | [
"Finsupp.instAddZeroClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommSemiring.toSemiring",
"AlgHom",
"MvPolynomial.map_frobenius_expand",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",... | true |
Mathlib.Util.«_aux_Mathlib_Util_CompileInductive___elabRules_Mathlib_Util_commandCompile_def%__1» | Mathlib.Util.CompileInductive | [
"Pure.pure",
"Lean.instMonadEnvOfMonadLift",
"Lean.TSyntax",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Command.CommandElab",
"Lean.Elab.Command.liftTermElabM",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.instMonadMacroAda... | false |
Int32.toInt_not | Init.Data.SInt.Bitwise | [
"instPowNat",
"congrArg",
"Int32.toInt_sub",
"HSub.hSub",
"Int.instNegInt",
"Int.bmod_sub_bmod",
"instOfNatNat",
"Int",
"Int32.toInt",
"instSubInt32",
"instNatPowNat",
"instHSub",
"HPow.hPow",
"instOfNat",
"Int.bmod",
"Nat",
"True",
"Complement.complement",
"eq_self",
"Int32.to... | true |
PointedCone.lineal._proof_4 | Mathlib.Geometry.Convex.Cone.Pointed | [
"IsOrderedRing.toPosMulMono",
"IsOrderedRing",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"instDistribOfSemiring",
"PosMulMono",
"Distrib.toMul",
"Ring.toSemiring",
"Ring",
"instDistribLatticeOfLinearOrder",
"MulZeroClass.toZero",
... | false |
SubMulAction.subtype_eq_val | Mathlib.GroupTheory.GroupAction.SubMulAction | [
"SubMulAction.instSetLike",
"SMul",
"Membership.mem",
"id",
"Subtype",
"instFunLikeMulActionHom",
"SubMulAction.subtype",
"MulActionHom",
"SubMulAction.instSMulSubtypeMem",
"Subtype.val",
"Eq",
"SubMulAction",
"DFunLike.coe",
"SetLike.instMembership",
"rfl"
] | true |
Lean.Elab.Term.State.mk.injEq | Lean.Elab.Term.TermElabM | [
"Lean.Elab.Term.LevelMVarErrorInfo",
"Eq.propIntro",
"Lean.Elab.Term.State.mk",
"Lean.MVarIdMap",
"Lean.injEq_helper",
"Lean.MVarId",
"Lean.Elab.Term.MVarErrorInfo",
"List",
"And",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Lean.Elab.Term.State",
"Lean.Elab.Term.State.mk.inj",
"Eq",
"Lean.El... | true |
Encodable.decode₂_is_partial_inv | Mathlib.Logic.Encodable.Basic | [
"Function.IsPartialInv",
"Encodable.decode₂",
"Nat",
"Encodable.encode",
"Encodable",
"Encodable.decode₂_isPartialInv"
] | true |
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