name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.SetTheory.ZFC.Basic.0.ZFSet.mem_image.match_1_1 | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"PSet.Func",
"Membership.mem",
"ZFSet.Definable₁",
"ZFSet.Definable₁.out",
"PSet.mk",
"Quotient.mk",
"PSet",
"PSet.setoid",
"Exists.casesOn",
"ZFSet.image",
"Exists.intro",
"PSet.image",
"ZFSet.instSetLike",
"SetLike.instMembership",
"PSet.Type",
"PSet.Equiv"
] | false |
AddUnits.val_vadd | Mathlib.Algebra.Group.Action.Units | [
"AddUnits.val",
"AddMonoid.toAddSemigroup",
"instVAddOfAdd",
"AddUnits.addAction'",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
"AddSemigroupAction.toVAdd",
"AddGroup.toSubNegMonoid",
"AddMonoid",
"instHVAd... | true |
CategoryTheory.TwoSquare.equivNatTrans | Mathlib.CategoryTheory.Functor.TwoSquare | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.TwoSquare.mk",
"CategoryTheory.TwoSquare.equivNatTrans._proof_1",
"Equiv.mk",
"Equiv",
"CategoryTheory.TwoSquare.equivNatTrans._proof_... | true |
AddEquiv.cast | Mathlib.Algebra.Group.Equiv.Defs | [
"congrArg",
"Equiv.cast",
"Equiv",
"AddEquiv.mk",
"AddEquiv.cast._proof_1",
"AddEquiv",
"Eq",
"Add"
] | true |
Lean.Meta.Split.initFn._@.Lean.Meta.Tactic.Split.806046213._hygCtx._hyg.2 | Lean.Meta.Tactic.Split | [
"IO",
"Lean.registerInternalExceptionId",
"Lean.InternalExceptionId",
"Lean.Name.mkStr1"
] | false |
List.prod_pair | Batteries.Data.List.Lemmas | [
"Std.LawfulRightIdentity.right_id",
"One",
"HMul.hMul",
"Std.LawfulRightIdentity",
"congrArg",
"Mul",
"List.cons",
"True",
"eq_self",
"of_eq_true",
"One.toOfNat1",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Eq.trans",
"List.prod",
"instHMul",
"List.nil"
] | true |
Finset.eraseInduction | Mathlib.Data.Finset.Card | [
"Finset",
"HasSSubset.SSubset",
"Membership.mem",
"Finset.instSetLike",
"Finset.instHasSSubset",
"Finset.erase",
"Finset.erase_ssubset",
"Finset.strongInduction",
"SetLike.instMembership",
"DecidableEq"
] | true |
_private.Lean.Elab.PreDefinition.Eqns.0.Lean.Elab.Eqns.mkEqnProof.go._unsafe_rec | Lean.Elab.PreDefinition.Eqns | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Array.mkEmpty",
"Lean.Meta.TacticResultCNM",
"Lean.PersistentArrayNode.node",
"Lean.instMonadAlwaysExceptStateRefT'",
"Lean.instExceptToTraceResult",
"L... | false |
_private.Mathlib.Data.Complex.Basic.0.Complex.horizontalSegment_eq._simp_1_2 | Mathlib.Data.Complex.Basic | [
"Set.instSProd",
"SProd.sprod",
"Membership.mem",
"Prod.fst",
"Set.mem_prod",
"And",
"propext",
"Prod",
"Eq",
"Set.instMembership",
"Prod.snd",
"Set"
] | false |
_private.Mathlib.SetTheory.Cardinal.HasCardinalLT.0.hasCardinalLT_subtype_iSup.match_1_1 | Mathlib.SetTheory.Cardinal.HasCardinalLT | [
"Subtype.casesOn",
"Subtype",
"Subtype.mk",
"Sigma.mk",
"Sigma.casesOn",
"Sigma"
] | false |
_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore.match_1.splitter | Mathlib.Data.Nat.Digits.Defs | [
"_private.Init.Data.Repr.0.Nat.toDigitsCore.match_1",
"instOfNatNat",
"List",
"Nat",
"Char",
"OfNat.ofNat",
"Nat.succ"
] | true |
Real.not_summable_one_div_natCast | Mathlib.Analysis.PSeries | [
"MulOne.toOne",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"Monoid.toMulOneClass",
"congrArg",
"Real.instInv",
"Real.instDivInvMonoid",
"SummationFilter",
"PseudoMetricSpace.toUniformSpace",
"Eq.mp",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"inv_eq_one_div",
"Nat.cast",
"Real.instOne",
"... | true |
Lean.Elab.GoalsAtResult.priority | Lean.Server.InfoUtils | [
"Nat",
"Lean.Elab.GoalsAtResult"
] | true |
_private.Mathlib.Analysis.Convex.Side.0.AffineSubspace.wSameSide_comm.match_1_3 | Mathlib.Analysis.Convex.Side | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"IsStrictOrderedRing",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Exists",
"PartialOrder",
"AddCommGroup",
"AddTorsor.toVSub",
"VSub.vsub",
"And.casesOn",
"AffineSubspace.instSetLike",
"And",
"CommRing.toCommSemiri... | false |
OrderEmbedding.withTopMap.eq_1 | Mathlib.Order.Hom.WithTopBot | [
"RelEmbedding.mk",
"WithTop.instPreorder",
"WithTop.map",
"Preorder.toLE",
"Function.Embedding.mk",
"LE.le",
"OrderEmbedding._proof_5",
"OrderEmbedding.withTopMap",
"Eq.refl",
"OrderEmbedding.withTopMap._proof_1",
"OrderEmbedding",
"OrderEmbedding.withTopMap._proof_2",
"Eq",
"DFunLike.coe"... | true |
LinearMap.baseChange_tmul | Mathlib.LinearAlgebra.TensorProduct.Tower | [
"LinearMap.baseChange",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"LinearMap.instFunLike",
"Algebra",
"Algebra.toModule",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemir... | true |
_private.Lean.Server.InfoUtils.0.Lean.Elab.Info.fmtHover?.match_3 | Lean.Server.InfoUtils | [
"Prod.mk",
"Lean.FormatWithInfos",
"Std.Format",
"Prod",
"Prod.casesOn",
"Option"
] | false |
Mathlib.Tactic.ITauto.Proof.curry.elim | Mathlib.Tactic.ITauto | [
"Mathlib.Tactic.ITauto.AndKind",
"PULift.up",
"Mathlib.Tactic.ITauto.Proof.ctorElim",
"Mathlib.Tactic.ITauto.Proof",
"Nat",
"Eq.symm",
"Eq",
"Mathlib.Tactic.ITauto.Proof.curry",
"Mathlib.Tactic.ITauto.Proof.ctorIdx"
] | false |
ProbabilityTheory.«_aux_Mathlib_Probability_Independence_Conditional___macroRules_ProbabilityTheory_term_⟂ᵢ[_,_;_]__1» | Mathlib.Probability.Independence.Conditional | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.node5",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSynta... | false |
antitoneOn_of_add_one_le | Mathlib.Algebra.Order.SuccPred | [
"Eq.mpr",
"Preorder.toLT",
"One",
"Order.succ",
"Order.succ_eq_add_one",
"congrArg",
"SuccAddOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"PartialOrder",
"Eq.mp",
"id",
"not_isMax_iff._simp_1",
"LE.le",
"forall_exists_index._simp_1",
"antitoneOn_o... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.card_edgeFinset._proof_1_2 | Mathlib.Combinatorics.SimpleGraph.Acyclic | [
"Inhabited.default",
"Lean.RArray.leaf",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"SimpleGraph.Walk.length",
"False.elim",
"Nat.ToInt.add_congr",
"SimpleGraph.Walk",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
"Lean.RArray",
"Int.instNegInt",
"instOfNat... | false |
norm_eq_sqrt_re_inner | Mathlib.Analysis.InnerProductSpace.Basic | [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Real",
"Trans.trans",
"SeminormedAddCommGroup",
"AddMonoid.toAddSemigroup",
"Inner.inner",
"Real.instAddMonoid",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"NormedField.toField",
"AddZeroClass.toAddZero",
"instOfNatNat",
"Field.toCommRing",
... | true |
SemiRingCat.FilteredColimits.semiringObj._proof_7 | Mathlib.Algebra.Category.Ring.FilteredColimits | [
"SemiRingCat.instConcreteCategoryRingHomCarrier",
"SemiRingCat.FilteredColimits.semiringObj._aux_1",
"CategoryTheory.Functor",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"AddMonoid.add_zero",
"CategoryTheory.Functor.comp",
"RingHom",
"SemiRingCat.carrier",
"SemiRingCat.hasForg... | false |
List.decidableSubperm | Batteries.Data.List.Perm | [
"decidable_of_iff",
"List.isSubperm",
"DecidableRel",
"LawfulBEq",
"instDecidableEqBool",
"Bool.true",
"List",
"List.Subperm",
"Bool",
"BEq",
"Eq",
"List.isSubperm_iff"
] | true |
ProbabilityTheory.Kernel.definition._@.Mathlib.Probability.Kernel.RadonNikodym.743833221._hygCtx._hyg.2 | Mathlib.Probability.Kernel.RadonNikodym | [
"ProbabilityTheory.Kernel.IsSFiniteKernel.add",
"Real",
"ENNReal.ofNNReal",
"HMul.hMul",
"CommSemiring.toSemiring",
"Real.instSub",
"HSub.hSub",
"ProbabilityTheory.IsSFiniteKernel",
"MeasurableSpace.CountableOrCountablyGenerated",
"ProbabilityTheory.Kernel.instAdd",
"ENNReal.instCommSemiring",
... | false |
CategoryTheory.Functor.curry₃ObjProdComp._proof_4 | Mathlib.CategoryTheory.Functor.CurryingThree | [
"CategoryTheory.Functor",
"CategoryTheory.prod",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Prod.mkHom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.curry₃ObjProdComp._proof_2",
... | false |
_private.Mathlib.CategoryTheory.Sites.Coverage.0.CategoryTheory.Coverage.saturate_iff_saturate_toPrecoverage._proof_1_4 | Mathlib.CategoryTheory.Sites.Coverage | [
"CategoryTheory.Presieve",
"congrArg",
"Eq.symm",
"Eq",
"CategoryTheory.Category"
] | false |
ContinuousOn.cfc_nnreal'._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
FinEnum.Finset.enum.eq_1 | Mathlib.Data.FinEnum | [
"Finset",
"Finset.instEmptyCollection",
"FinEnum.Finset.enum",
"List.cons",
"List",
"Eq.refl",
"EmptyCollection.emptyCollection",
"Eq",
"List.nil",
"DecidableEq"
] | true |
List.findIdx.go | Init.Data.List.Basic | [
"List.brecOn",
"List",
"Nat",
"Bool",
"List.findIdx.go._f"
] | true |
ContMDiffAt.finsum_section_of_locallyFinite | Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | [
"Eq.mpr",
"Prod.normedSpace",
"ContMDiffWithinAt",
"Prod.normedAddCommGroup",
"NormedSpace",
"FiberBundle",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"finsum",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"AddCommGroup",
"Eq.mp",
"id",
"instTopologicalSpaceMode... | true |
«_aux_Init_Notation___macroRules_term_$___1» | Init.Notation | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Array.push",
"Lean.Syntax.getArgs",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Array.mkArray0",
"Lean.TSy... | false |
List.support_formPerm_le | Mathlib.GroupTheory.Perm.List | [
"Eq.mpr",
"Equiv.Perm.support",
"Equiv.instEquivLike",
"congrArg",
"Finset",
"List.coe_toFinset",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Eq.mp",
"id",
"Ne",
"Finset.partialOrder",
"LE.le",
"List.toFinset",
"List.mem_toFinset._simp_1",
"List.formPerm... | true |
_private.Mathlib.CategoryTheory.Limits.Shapes.Reflexive.0.CategoryTheory.Limits.reflexivePair.match_1.eq_2 | Mathlib.CategoryTheory.Limits.Shapes.Reflexive | [
"Unit.unit",
"CategoryTheory.Limits.WalkingReflexivePair.zero",
"CategoryTheory.Limits.WalkingReflexivePair.one",
"Unit",
"Eq.refl",
"Eq",
"CategoryTheory.Limits.WalkingReflexivePair",
"CategoryTheory.Limits.reflexivePair.match_1"
] | true |
Lean.Elab.Tactic.BVDecide.LRAT.trim.M.mapStep | Lean.Elab.Tactic.BVDecide.LRAT.Trim | [
"Pure.pure",
"Std.Tactic.BVDecide.LRAT.Action.addEmpty",
"instInhabitedOfMonad",
"Lean.Elab.Tactic.BVDecide.LRAT.trim.State",
"Std.Tactic.BVDecide.LRAT.IntAction",
"Std.Tactic.BVDecide.LRAT.Action",
"panicWithPosWithDecl",
"ReaderT.instMonad",
"Std.Tactic.BVDecide.LRAT.Action.addRat",
"Prod.mk",
... | true |
_private.Mathlib.CategoryTheory.Limits.Cones.0.CategoryTheory.Limits.ConeMorphism.hom_inv_id._simp_1_1 | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Limits.ConeMorphism",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Limits.ConeMorphism.hom",
"CategoryTheory.Limits.Cone.category_comp_hom",
"CategoryTheory.CategoryStr... | false |
_private.Mathlib.LinearAlgebra.Matrix.Circulant.0.Matrix.circulant_single._simp_1_1 | Mathlib.LinearAlgebra.Matrix.Circulant | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
_private.Std.Sync.Broadcast.0.Std.Bounded.mk.inj | Std.Sync.Broadcast | [
"_private.Std.Sync.Broadcast.0.Std.Bounded",
"_private.Std.Sync.Broadcast.0.Std.Bounded.mk",
"Std.Mutex",
"eq_of_heq",
"HEq",
"_private.Std.Sync.Broadcast.0.Std.Bounded.mk.noConfusion",
"Eq",
"_private.Std.Sync.Broadcast.0.Std.Bounded.State"
] | true |
AlgebraicGeometry.Proj.pullbackAwayιIso.congr_simp | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic | [
"SetLike",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Spec",
"CommRing",
"AlgebraicGeometry.Scheme",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"HomogeneousLocalization.homogeneousLocalizationCommRing",
"AlgebraicGeometry.Proj",
"Nat.instAddMonoid",
"Member... | true |
Rep.instEpiModuleCatToModuleCatHom | Mathlib.RepresentationTheory.Rep.Basic | [
"Monoid",
"Rep.V",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"Rep.hV2",
"Rep.instCategory",
"Rep.hV1",
"ModuleCat.of",
"Rep",
"_private.Mathlib.RepresentationTheory.Rep.Basic.0.Rep.instEpiModuleCatToModuleCatHom._proof_1",
"ModuleCat.moduleCat... | true |
_private.Std.Data.ExtHashSet.Lemmas.0.Std.ExtHashSet.erase_eq_empty_iff._simp_1_1 | Std.Data.ExtHashSet.Lemmas | [
"Std.ExtHashSet",
"Std.ExtHashMap",
"Unit",
"Std.ExtHashSet.inner",
"propext",
"Hashable",
"BEq",
"Eq",
"_private.Std.Data.ExtHashSet.Lemmas.0.Std.ExtHashSet.ext_iff"
] | false |
Module.End.invtSubmodule_inf_invtSubmodule_le_invtSubmodule_add | Mathlib.Algebra.Module.Submodule.Invariant | [
"Sublattice",
"Submodule",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"LinearMap.instFunLike",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"LinearMap.instAdd",
"LE.le",
"LinearMap",
"AddCommMonoid",
"instHAdd",
"SetLike.coe",
"Submodu... | true |
_private.Mathlib.Analysis.InnerProductSpace.Projection.Minimal.0.norm_eq_iInf_iff_real_inner_le_zero.match_1_1 | Mathlib.Analysis.InnerProductSpace.Projection.Minimal | [
"Norm.norm",
"Real",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Set.Elem",
"SubNegMonoid.toSub",
"instHSub",
"Exists.casesOn",
"AddGroup.toSubNegMonoid",
"NormedAddCommGroup.toNorm",
"Exists.intro",
"NormedAddCommGroup.toAddCommGroup",
"Set.range",
"Subtype.val",
"Eq",
... | false |
AlgebraicGeometry.IsOpenImmersion.forgetCreatesPullbackOfLeft._proof_2 | Mathlib.AlgebraicGeometry.OpenImmersion | [
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme.Hom.toLRSHom",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullback_snd_of_left",
"AlgebraicGeometry.LocallyRi... | false |
Int.Linear.Poly.denote_insert | Init.Data.Int.Linear | [
"Nat.blt",
"HMul.hMul",
"congrArg",
"Int.add_left_comm",
"Int.add_assoc",
"Int.Linear.Poly.insert",
"Int.instDecidableEq",
"Eq.mp",
"Int.Linear.Var.denote",
"Nat.beq_eq",
"id",
"Nat.beq",
"Int.instLawfulBEq",
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.num",
"Int.add_comm",
"instBEqO... | true |
CategoryTheory.Bicategory.Strict.associator_eqToIso._autoParam | Mathlib.CategoryTheory.Bicategory.Strict.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Multiset.sub_le_sub_right | Mathlib.Data.Multiset.AddSub | [
"Iff.mpr",
"Multiset.sub_le_iff_le_add'",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"Multiset",
"Multiset.le_add_sub",
"LE.le",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"LE.le.trans",
"Multiset.instAdd",
"Multiset.instSub",
"Multiset.instPartialOrder",
"DecidableEq"
] | true |
Function.fromTypes_nil_equiv_apply | Mathlib.Logic.Function.FromTypes | [
"Equiv.instEquivLike",
"Function.FromTypes",
"Equiv",
"instOfNatNat",
"Function.fromTypes_nil_equiv",
"Nat",
"Matrix.vecEmpty",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
_private.Mathlib.AlgebraicGeometry.Gluing.0.AlgebraicGeometry.Scheme.IsLocallyDirected.t_id._simp_1_3 | Mathlib.AlgebraicGeometry.Gluing | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso.inv_comp_eq",
"CategoryTheory.Iso",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",
"Eq",
"CategoryTheory.Iso.inv",
"CategoryTheory.Category"
] | false |
Std.instStreamSubarray._proof_2 | Init.Data.Stream | [
"Subarray",
"Subarray.stop",
"Nat",
"Subarray.stop_le_array_size",
"LT.lt",
"instLTNat",
"Subarray.start",
"Nat.lt_of_lt_of_le",
"Array.size",
"Subarray.array"
] | false |
Std.DHashMap.Internal.Raw₀.get!_insertIfNew | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"dite_congr",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw.WF.out",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.get!_eq_getValueCast!",
"cast",
"Std.DHashMap... | true |
Aesop.PhaseSpec.casesOn | Aesop.Builder.Basic | [
"Aesop.SafeRuleInfo",
"Aesop.PhaseSpec.unsafe",
"Aesop.UnsafeRuleInfo",
"Aesop.PhaseSpec.safe",
"Aesop.PhaseSpec.rec",
"Aesop.PhaseSpec.norm",
"Aesop.PhaseSpec",
"Aesop.NormRuleInfo"
] | false |
Mathlib.Tactic.BicategoryLike.Normalize.Result._sizeOf_1 | Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence | [
"Mathlib.Tactic.BicategoryLike.NormalizedHom._sizeOf_inst",
"Mathlib.Tactic.BicategoryLike.NormalizedHom",
"Mathlib.Tactic.BicategoryLike.Mor₂Iso",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Mathlib.Tactic.BicategoryLike.Normalize.Result",
"Mathlib.Tactic.Bic... | false |
Set.toFinset_smul_set | Mathlib.Algebra.Group.Pointwise.Finset.Scalar | [
"instHSMul",
"Finset",
"SMul",
"Finset.smulFinset",
"Set.Elem",
"Set.toFinset_image",
"Set.toFinset",
"Fintype",
"HSMul.hSMul",
"Eq",
"Set.smulSet",
"DecidableEq",
"Set"
] | true |
LinearEquiv.domMulActCongrRight._proof_2 | Mathlib.Algebra.Module.Equiv.Basic | [
"DomMulAct",
"instHSMul",
"Equiv.instEquivLike",
"LinearMap.ext",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"RingHom",
"AddZeroClass.toAddZero",
"RingHomCompTriple",
"Equiv",
"DistribSMul.toSMulZeroClass",
"LinearMap.instAdd",
"Equiv.toFun",
"... | false |
OrderIso.neg | Mathlib.Algebra.Order.Group.OrderIso | [
"AddGroup.toSubtractionMonoid",
"OrderDual.instLE",
"OrderDual.toDual",
"SubtractionMonoid.toInvolutiveNeg",
"RelIso.mk",
"Equiv.trans",
"Equiv.neg",
"AddMonoid.toAddZeroClass",
"AddLeftMono",
"AddRightMono",
"AddZeroClass.toAddZero",
"Equiv",
"OrderIso",
"LE.le",
"LE",
"AddGroup",
"... | true |
PreconnectedSpace.isPreconnected_univ | Mathlib.Topology.Connected.Basic | [
"Set.univ",
"PreconnectedSpace",
"TopologicalSpace",
"IsPreconnected"
] | true |
Matrix.submatrixEquivInvertible | Mathlib.LinearAlgebra.Matrix.NonsingularInverse | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Matrix.submatrix",
"Equiv.instEquivLike",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
"AddGroupWithOne.toAddMonoidWithOne",
"Invertible.invOf",
"Matrix.submatrixEquivI... | true |
generatePiSystem.casesOn | Mathlib.MeasureTheory.PiSystem | [
"generatePiSystem.base",
"Membership.mem",
"generatePiSystem.rec",
"Set.instInter",
"Inter.inter",
"Set.Nonempty",
"Set.instMembership",
"generatePiSystem",
"generatePiSystem.inter",
"Set"
] | false |
List.append_right_inj | Init.Data.List.Lemmas | [
"congrArg",
"instHAppendOfAppend",
"List",
"Iff",
"Nat",
"Iff.intro",
"List.append_inj_right",
"List.instAppend",
"Eq",
"List.length",
"HAppend.hAppend",
"rfl"
] | true |
_private.Mathlib.Data.Num.ZNum.0.castNum.match_1.eq_2 | Mathlib.Data.Num.ZNum | [
"castNum.match_1",
"Num",
"Unit",
"Num.pos",
"Eq.refl",
"PosNum",
"Eq",
"Num.zero"
] | true |
CategoryTheory.down_comp | Mathlib.CategoryTheory.Category.ULift | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.instSmallCategoryAsSmall",
"CategoryTheory.AsSmall",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"ULift.down",
"rfl",
"CategoryTheory.Category"
] | true |
Std.Iterators.PostconditionT.operation_map | Init.Data.Iterators.PostconditionMonad | [
"Iff.mpr",
"Functor",
"Exists",
"Std.Iterators.PostconditionT.Property",
"Subtype",
"Std.Iterators.PostconditionT.property_map",
"Std.Iterators.PostconditionT.operation",
"Subtype.mk",
"And",
"And.intro",
"Exists.intro",
"Std.Iterators.PostconditionT",
"Eq.refl",
"Subtype.val",
"Eq",
"... | true |
Set.Finite.nonempty_fintype | Mathlib.Data.Set.Finite.Basic | [
"Set.Finite",
"Set.Elem",
"Fintype",
"Iff.mp",
"Nonempty",
"Set.finite_def",
"Set"
] | true |
_private.Mathlib.Tactic.TermCongr.0.Mathlib.Tactic.TermCongr.congrHoleIndex | Mathlib.Tactic.TermCongr | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Nat",
"Lean.Name",
"OfNat.ofNat"
] | true |
TopModuleCat.instHasLimitsOfShapeOfModuleCat | Mathlib.Algebra.Category.ModuleCat.Topology.Basic | [
"TopModuleCat.instCategory",
"TopModuleCat.instHasForget₂ContinuousLinearMapIdCarrierModuleCatLinearMap",
"CategoryTheory.Functor",
"TopModuleCat.hasLimit_of_hasLimit_forget₂",
"ModuleCat",
"CategoryTheory.Limits.HasLimitsOfShape",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"Line... | true |
Std.Internal.IO.Async.System.OSInfo.release | Std.Internal.Async.System | [
"Std.Internal.IO.Async.System.OSInfo",
"String"
] | true |
String.Pos.Raw.utf8GetAux._unsafe_rec | Init.Data.String.Basic | [
"Inhabited.default",
"String.Pos.Raw.utf8GetAux._unsafe_rec",
"String.Pos.Raw.utf8GetAux.match_1",
"String.Pos.Raw",
"Char.instInhabited",
"List",
"instDecidableEqRaw",
"HAdd.hAdd",
"Char",
"Eq",
"String.instHAddRawChar",
"ite"
] | false |
CategoryTheory.ShiftedHom.comp_add | Mathlib.CategoryTheory.Shift.ShiftedHom | [
"Eq.mpr",
"CategoryTheory.Functor",
"AddMonoid.toAddSemigroup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.ShiftedHom.comp... | true |
MulAction.selfEquivSigmaOrbits._proof_1 | Mathlib.GroupTheory.GroupAction.Defs | [
"Quotient.out_eq'",
"MulAction.orbitRel.Quotient.orbit",
"Group",
"Quotient.out",
"DivInvMonoid.toMonoid",
"MulAction.orbitRel",
"Group.toDivInvMonoid",
"MulAction.orbit",
"MulAction.orbitRel.Quotient",
"MulAction",
"Monoid.toSemigroup",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction... | false |
Void.nonemptyType | Init.System.ST | [
"Inhabited.default",
"NonemptyType",
"instInhabitedNonemptyType"
] | true |
MeasureTheory.addContent_accumulate | Mathlib.MeasureTheory.Measure.AddContent | [
"Eq.mpr",
"Nat.recAux",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Finset",
"Set.accumulate_succ",
"AddMonoid.toAddZeroClass",
"Set.disjoint_accumulate",
"Nat.instAddMonoid",
"Disjoint",
"Membership.mem... | true |
Real.tan_mul_cos | Mathlib.Analysis.Complex.Trigonometric | [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"div_mul_cancel₀",
"Real",
"instHDiv",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"MulZeroClass.toMul",
"Real.instZero",
"Real.cos",
"congrArg",
"Real.instDivInvMonoid",
"DivisionSemiring.toGroupWithZero",
"id",
"HDiv.hDiv",
"Ne",
"Field.... | true |
toModuleCatFromModuleCatLinearEquiv._proof_8 | Mathlib.RingTheory.Morita.Matrix | [
"Matrix.scalar",
"instHSMul",
"ModuleCat",
"ZeroHom.toFun",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Matrix",
"AddMonoid.toAddZeroClass",
"MatrixModCat.toModuleCatObj._proof_3",
"AddGroupWithOne.toAddMonoidWithOne",
"LinearMap.instFunLike",
"AddCommGroup.toAddGroup",
... | false |
hasStrictDerivAt_exp_zero | Mathlib.Analysis.SpecialFunctions.Exponential | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"RCLike.toNormedAlgebra",
"IsTopologicalRing.toIsTopologicalSemiring",
"IsTopologicalSemiring.toContinuousMu... | true |
LinearOrderedCommMonoidWithZero.toDecidableEq._inherited_default | Mathlib.Algebra.Order.GroupWithZero.Canonical | [
"LT.mk",
"Preorder.mk",
"decidableEqOfDecidableLE",
"id",
"And",
"DecidableLE",
"Iff",
"LE.mk",
"Eq",
"Not",
"PartialOrder.mk",
"DecidableEq"
] | false |
_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.checkMVar | Lean.Meta.LetToHave | [
"Pure.pure",
"Unit.unit",
"Subarray",
"Lean.instMonadMCtxOfMonadLift",
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.Context",
"instMonadReaderOfReaderTOfMonad",
"instForInOfForIn'",
"ReaderT",
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.M",
"Lean.Meta.State",
"Std.Stream.next?",
... | true |
Polynomial.natDegree_mul_leadingCoeff_inv | Mathlib.Algebra.Polynomial.Degree.Lemmas | [
"Polynomial.C",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"Polynomial.degree_mul_leadingCoeff_inv",
"DivInvOneMonoid.toInvOneClass",
"DivisionSemiring.toGroupWithZero",
"RingHom",
"DivisionMonoid.toDivInvOneMonoid",
"DivisionRing.toDivisionSemiring",
"Polynomial.leadingCoeff",
"Ne",
"Poly... | true |
MvPolynomial.coe_expand | Mathlib.Algebra.MvPolynomial.Expand | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"MvPolynomial.X",
"AddMonoidAlgebra.commSemiring",
"Nat.instAddMonoid",
"MvPolynomial.eval₂",
"Algebra.id",
"Pi.instPow",
"Finsup... | true |
Lean.Elab.Command.Structure.StructFieldView.declName | Lean.Elab.Structure | [
"Lean.Elab.Command.Structure.StructFieldView",
"Lean.Name"
] | true |
NormedAddGroupHom.noConfusionType | Mathlib.Analysis.Normed.Group.Hom | [
"Norm.norm",
"Real.instLE",
"Real",
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"HMul.hMul",
"AddCommGroup.toAddCommMonoid",
"NormedAddGroupHom.casesOn",
"Exists",
"LE.le",
"SeminormedAddCommGroup.toNorm",
"instHAdd",
"HAdd.hAdd",
"SeminormedAddCommGroup.toAddCommGroup",
"Real.instMul... | false |
Lean.Server.Test.Runner.Client.SubexprInfo | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.SubexprInfo.mk"
] | true |
_private.Mathlib.Algebra.Lie.Engel.0.LieAlgebra.isEngelian_of_isNoetherian._simp_1_1 | Mathlib.Algebra.Lie.Engel | [
"LieAlgebra.toModule",
"Submodule",
"CommRing",
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieSubalgebra.mem_toSubmodule",
"Membership.mem",
"LieRing",
"CommRing.toCommSemiring",
"Submodule.setLike",
"propext",
"LieSub... | false |
IsDedekindDomain.instCommRingFiniteAdeleRing._aux_13 | Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing | [
"Int.instAddCommGroup",
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"CommRing",
"IsDedekindDomain.FiniteAdeleRing",
"HMul.hMul",
"Int.instLinearOrder",
"IsFractionRing",
"Filter.Eventually",
"PartialOrder.toPreorder",
"IsDedekindDomain.HeightOneSpectrum",
"IsTopologicalDivisionRing.... | false |
GroupFilterBasis.one' | Mathlib.Topology.Algebra.FilterBasis | [
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Group",
"GroupFilterBasis",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"FilterBasis.sets",
"One.toOfNat1",
"GroupFilterBasis.toFilterBasis",
"OfNat.ofNat",
"Set.instMembership",
"Set"
] | true |
_private.Init.Data.Fin.Lemmas.0.Fin.coe_sub_iff_le._proof_1_4 | Init.Data.Fin.Lemmas | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.ev... | false |
_private.Mathlib.Tactic.Algebra.Lemmas.0.Mathlib.Tactic.Algebra.rat_ofNat_smul_2._simp_1_1 | Mathlib.Tactic.Algebra.Lemmas | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.rawCast",
"CommSemiring.toSemiring",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Mathlib.Tactic.Algebra.nat_rawCast_2",
"CommSemiring",
"Nat",
"OfNat.ofNat",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Eq",
"instOfN... | false |
AddMonoidHom.surjective_of_surjective_of_surjective_of_injective | Mathlib.Algebra.FiveLemma | [
"Function.Exact.apply_apply_eq_zero",
"Function.Exact",
"AddGroup.toSubtractionMonoid",
"DFunLike.congr_fun",
"AddMonoidHom.instAddMonoidHomClass",
"map_sub",
"sub_self",
"congrArg",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"Eq.mp",
"... | true |
NNReal.lt_iff_exists_rat_btwn | Mathlib.Data.NNReal.Defs | [
"Rat.instOfNat",
"Real.instLE",
"Real",
"Preorder.toLT",
"Real.instArchimedean",
"DivisionRing.toRatCast",
"Real.instZero",
"congrArg",
"and_self",
"Real.instRatCast",
"Rat",
"PartialOrder.toPreorder",
"lt_trans",
"Real.instLT",
"le_of_lt",
"Preorder.toLE",
"Exists",
"Field.toDivis... | true |
EuclideanDomain.gcd._unary._proof_2 | Mathlib.Algebra.EuclideanDomain.Defs | [
"invImage",
"EuclideanDomain.r",
"PSigma.casesOn",
"id",
"instHMod",
"HMod.hMod",
"EuclideanDomain.wellFoundedRelation",
"EuclideanDomain.instMod",
"EuclideanDomain",
"PSigma.mk",
"PSigma"
] | false |
_private.Lean.Server.Completion.SyntheticCompletion.0.Lean.Server.Completion.isSyntheticTacticCompletion.isEmpty.match_1 | Lean.Server.Completion.SyntheticCompletion | [
"Lean.Syntax.node",
"Unit.unit",
"Lean.Syntax.ident",
"Lean.Syntax.missing",
"String",
"Lean.SourceInfo",
"Lean.Syntax.casesOn",
"Lean.Syntax.atom",
"Lean.Syntax",
"Substring.Raw",
"Array",
"List",
"Unit",
"Lean.Syntax.Preresolved",
"Lean.Name",
"Lean.SyntaxNodeKind"
] | false |
_private.Init.Data.Nat.Fold.0.Nat.all_eq_allTR._proof_1_1 | Init.Data.Nat.Fold | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.LinearCombo.coordinate_eva... | false |
WithZero.isOrderedMonoid | Mathlib.Algebra.Order.GroupWithZero.Canonical | [
"CommMonoidWithZero.toCommMonoid",
"Semigroup.toMul",
"CommMonoid.toCommSemigroup",
"IsOrderedMonoid",
"Monoid.toMulOneClass",
"Preorder.toLE",
"MulOne.toMul",
"LE.le",
"WithZero.instMulLeftMono",
"WithZero.instCommSemigroup",
"IsOrderedMonoid._proof_1",
"MulOneClass.toMulOne",
"CommSemigrou... | true |
concaveOn_of_slope_anti_adjacent | Mathlib.Analysis.Convex.Slope | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Mathlib.Tactic.Ring.Common.div_congr",
"le_refl",
"Mathlib.Meta.NormNum.instAddMonoidWithOne",
"Preorde... | true |
SimpleGraph.chromaticNumber_mono | Mathlib.Combinatorics.SimpleGraph.Coloring.VertexColoring | [
"SimpleGraph.chromaticNumber_le_of_forall_imp",
"LE.le",
"instLEENat",
"SimpleGraph",
"SimpleGraph.Colorable.mono_left",
"Nat",
"ENat",
"SimpleGraph.chromaticNumber",
"SimpleGraph.instLE"
] | true |
CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Functor.LaxMonoidal.associativity_assoc",
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryThe... | true |
_private.Mathlib.Topology.Filter.0.Filter.mem_closure._simp_1_8 | Mathlib.Topology.Filter | [
"and_comm",
"And",
"propext",
"Eq"
] | false |
AddSubgroup.IsComplement.rightQuotientEquiv_apply | Mathlib.GroupTheory.Complement | [
"Subtype.coe_mk",
"Iff.mpr",
"Equiv.instEquivLike",
"Quotient.mk''",
"Membership.mem",
"Set.Elem",
"Equiv",
"Subtype",
"Subtype.ext_iff",
"Subtype.mk",
"AddSubgroup",
"AddGroup",
"Quotient",
"Exists.intro",
"Iff.mp",
"Set.range",
"Equiv.symm",
"Eq.symm",
"Subtype.val",
"Eq",
... | true |
ContinuousMap.Homotopy.refl._proof_1 | Mathlib.Topology.Homotopy.Basic | [
"Continuous.comp'",
"Real",
"Continuous",
"Continuous.snd",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"continuous_id'",
"instTopologicalSpaceProd",
"Membership.mem",
"ContinuousMap.instContinuousMapClass",
"Set.Elem",
"TopologicalSpace",
"Real.pseudoMetricSpace",
"instTopologica... | false |
ModuleCat.FilteredColimits.colimitModule._proof_3 | Mathlib.Algebra.Category.ModuleCat.FilteredColimits | [
"ModuleCat.FilteredColimits.colimitSMulWithZero",
"CategoryTheory.Functor",
"instHSMul",
"ModuleCat",
"SMulWithZero.toSMulZeroClass",
"CategoryTheory.SmallCategory",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"AddCommGrpC... | false |
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