name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Finset.prod_range_div_prod_range | Mathlib.Algebra.BigOperators.Intervals | [
"Eq.mpr",
"Preorder.toLT",
"instHDiv",
"congrArg",
"Finset",
"Finset.ext",
"Preorder.toLE",
"Nat.instLocallyFiniteOrder",
"Membership.mem",
"Eq.rec",
"id",
"Finset.Ico",
"HDiv.hDiv",
"_private.Mathlib.Algebra.BigOperators.Intervals.0.Finset.prod_range_div_prod_range._simp_1_3",
"LE.le",
... | true |
ModularForm.coe_mcast | Mathlib.NumberTheory.ModularForms.Basic | [
"ModularForm",
"Real",
"Matrix",
"instDecidableEqFin",
"Real.semiring",
"Subgroup",
"instOfNatNat",
"Int",
"Units.instGroup",
"autoParam",
"Fin.fintype",
"UpperHalfPlane",
"Nat",
"Semiring.toMonoid",
"Eq.refl",
"Matrix.GeneralLinearGroup",
"Matrix.semiring",
"Complex",
"OfNat.ofN... | true |
Set.union_add_inter_subset | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Set.instUnion",
"HasSubset.Subset",
"Set.instInter",
"add_comm",
"Inter.inter",
"instHAdd",
"Set.add",
"HAdd.hAdd",
"AddCommSemigroup.toAddCommMagma",
"Union.union",
"AddCommSemigroup",
"AddCommMagma.toAdd",
"Set.image2_union_inter_subset",
"Set.instHasSubset",
"Set"
] | true |
Ordnode.Bounded.weak_right | Mathlib.Data.Ordmap.Invariants | [
"WithBot",
"Ordnode.Bounded.weak_right._f",
"Ordnode",
"WithTop.top",
"Ordnode.brecOn",
"Ordnode.Bounded",
"Top.top",
"Preorder",
"WithTop"
] | true |
SetLike.gmodule | Mathlib.Algebra.Module.GradedModule | [
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"DirectSum.GdistribMulAction.mk",
"AddMonoid.toAddSemigroup",
"DistribMulAction.toDistribSMul",
"GradedMonoid.GMulAction.mk",
"SetLike.GradedSMul",
"SetLike.gMonoid",
"AddMonoid.toAddZeroClass",
"SetLike.gdistribMulAction",
"Se... | true |
Ideal.span_pow_eq_top | Mathlib.RingTheory.Ideal.Basic | [
"Ideal.span_le",
"Iff.mpr",
"one_pow",
"Finsupp.instFunLike",
"LinearMap.id",
"Set.singleton_subset_iff",
"Eq.mpr",
"Ideal.subset_span",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"MulOne.toOne",
"Semigroup.toMul",
"Dvd.dvd",
"Semiring.toModule",
"Finsupp.module",
"HMul.hM... | true |
Matroid.rankPos_nonempty | Mathlib.Combinatorics.Matroid.Basic | [
"Matroid.subset_ground",
"Matroid.E",
"False.elim",
"Membership.mem",
"Exists",
"Matroid.IsBase",
"Matroid.RankPos.empty_not_isBase",
"Or.casesOn",
"Set.eq_empty_or_nonempty",
"Matroid.RankPos",
"Set.Nonempty",
"Exists.casesOn",
"Matroid.exists_isBase",
"Exists.intro",
"Set.instEmptyColl... | true |
_private.Std.Internal.Http.Data.Body.Stream.0.Std.Http.Body.Channel.State.casesOn | Std.Internal.Http.Data.Body.Stream | [
"Std.Http.Chunk",
"Std.Internal.IO.Async.Waiter",
"_private.Std.Internal.Http.Data.Body.Stream.0.Std.Http.Body.Channel.State",
"_private.Std.Internal.Http.Data.Body.Stream.0.Std.Http.Body.Channel.State.rec",
"_private.Std.Internal.Http.Data.Body.Stream.0.Std.Http.Body.Channel.Producer",
"Bool",
"Std.Htt... | false |
Vector.replace_toArray | Init.Data.Vector.Lemmas | [
"Array.replace",
"Vector",
"Vector.replace",
"Array",
"Nat",
"BEq",
"Eq",
"Vector.toArray",
"rfl"
] | true |
ContinuousMultilinearMap.flipLinear._proof_3 | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"NormedCommRing.toSeminormedCommRing",
"MultilinearMap.mk",
"instHSMul",
"SeminormedAddCommGroup",
"Function.update",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"congrArg",
"DistribMulAction.toDistrib... | false |
Lean.Meta.DiscrTree.Key.other.elim | Lean.Meta.DiscrTree.Types | [
"PULift.up",
"Lean.Meta.DiscrTree.Key.ctorElim",
"Lean.Meta.DiscrTree.Key",
"Nat",
"Lean.Meta.DiscrTree.Key.other",
"Lean.Meta.DiscrTree.Key.ctorIdx",
"Eq.symm",
"Eq"
] | false |
ENat.map_natCast_strictMono | Mathlib.Data.ENat.Basic | [
"Iff.mpr",
"StrictMono",
"AddMonoid.toAddSemigroup",
"WithTop.instPreorder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddLeftMono",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"instPreorderENat",
"ZeroLEOneClass",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"E... | true |
AddGroupExtension._sizeOf_1 | Mathlib.GroupTheory.GroupExtension.Defs | [
"AddMonoidHom._sizeOf_inst",
"AddGroupExtension",
"AddMonoid.toAddZeroClass",
"instSizeOfDefault",
"AddMonoidHom.range",
"AddZeroClass.toAddZero",
"instOfNatNat",
"AddSubgroup",
"instHAdd",
"AddGroup",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"SizeO... | false |
ModuleCon.instAddMonoidQuotient | Mathlib.Algebra.Module.Congruence.Defs | [
"ModuleCon.instAddSemigroupQuotient",
"AddMonoid.toAddSemigroup",
"SMul",
"AddMonoid.toAddZeroClass",
"AddMonoid.mk",
"AddZeroClass.toAddZero",
"ModuleCon.instAddMonoidQuotient._proof_6",
"ModuleCon.instAddMonoidQuotient._proof_5",
"ModuleCon.instAddMonoidQuotient._proof_2",
"AddZero.toZero",
"A... | true |
LieSubalgebra.normalizer._proof_1 | Mathlib.Algebra.Lie.Normalizer | [
"LieAlgebra.toModule",
"instIsLieTower",
"LieSubalgebra.lieAlgebra",
"LieSubmodule.instSetLike",
"Eq.mpr",
"NegZeroClass.toNeg",
"leibniz_lie",
"CommRing",
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"Submodule.toAddSubmonoid",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGrou... | false |
Batteries.RBNode.Path.Ordered.eq_3 | Batteries.Data.RBMap.Alter | [
"Batteries.RBNode",
"Batteries.RBNode.Path",
"Ordering",
"Batteries.RBNode.cmpLT",
"Batteries.RBNode.Path.RootOrdered",
"And",
"Batteries.RBColor",
"Eq.refl",
"Batteries.RBNode.Path.right",
"Batteries.RBNode.Path.Ordered",
"Batteries.RBNode.All",
"Eq",
"Batteries.RBNode.Ordered"
] | true |
Subring.smul_sup | Mathlib.Algebra.Ring.Subring.Pointwise | [
"Monoid",
"instHSMul",
"Lattice.toSemilatticeSup",
"Ring.toNonAssocRing",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"MulSemiringAction.toRingHom",
"Subring",
"Max.max",
"MulSemiringAction",
"Monoid.toSemigroup",
"Subring.instCompleteLattice",
"HSMul.hSMul",
... | true |
_private.Lean.Compiler.IR.Basic.0.Lean.IR.FnBody.alphaEqv._sparseCasesOn_9 | Lean.Compiler.IR.Basic | [
"Lean.IR.FnBody.case",
"Lean.IR.FnBody.jdecl",
"Lean.IR.Expr",
"Nat.ne_of_beq_eq_false",
"Lean.IR.FnBody.uset",
"Lean.IR.FnBody.ret",
"Lean.IR.FnBody.inc",
"Lean.IR.Arg",
"Lean.IR.Param",
"Lean.IR.CtorInfo",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.IR.FnBody.rec",
"Lean.I... | false |
AddSubsemigroup.map_map | Mathlib.Algebra.Group.Subsemigroup.Operations | [
"Set.image_image",
"AddSubsemigroup.instSetLike",
"AddHom",
"AddHom.funLike",
"SetLike.coe_injective",
"SetLike.coe",
"AddSubsemigroup",
"AddHom.comp",
"Eq",
"DFunLike.coe",
"Add",
"AddSubsemigroup.map"
] | true |
List.takeWhile₂TR.go._sunfold | Batteries.Data.List.Basic | [
"cond",
"List.takeWhile₂TR.go",
"Prod.mk",
"List.takeWhile₂TR.go.match_1",
"List.cons",
"List",
"List.reverse",
"Bool",
"Prod"
] | false |
CompHausLike.toCompHausLike._proof_1 | Mathlib.Topology.Category.CompHausLike.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopCat.instCategory",
"ContinuousMap",
"CategoryTheory.CategoryStruct.id",
"id",
"CompHausLike",
"TopCat.str",
"CompHausLike.is_compact",
"TopCat.carrier",
"CategoryTheory.ConcreteCategory.ofHom",
"TopCat.Hom.hom",
"CompHausLike.catego... | false |
Bicategory.Opposite.opFunctor | Mathlib.CategoryTheory.Bicategory.Opposites | [
"CategoryTheory.Functor",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"Bicategory.Opposite.opFunctor._proof_1",
"CategoryTheory.Functor.mk",
"CategoryTheory.Bicategory.toCategoryStruct",
"Bicategory.Opposite.op2",
"CategoryTheory.Bicate... | true |
FunLike.commSemigroup.eq_1 | Mathlib.Data.FunLike.Group | [
"FunLike.commSemigroup._proof_1",
"FunLike.semigroup._proof_1",
"FunLike.commSemigroup",
"Mul",
"CommMagma.toMul",
"IsMulApply",
"CommSemigroup",
"Function.Injective.commSemigroup",
"CommSemigroup.toCommMagma",
"Pi.commSemigroup",
"Eq.refl",
"Eq",
"DFunLike.coe",
"FunLike"
] | true |
Lean.Lsp.DidOpenTextDocumentParams.mk | Lean.Data.Lsp.TextSync | [
"Lean.Lsp.DidOpenTextDocumentParams",
"Lean.Lsp.TextDocumentItem",
"Lean.Lsp.DidOpenTextDocumentParams.mk"
] | true |
_private.Mathlib.Data.List.Destutter.0.List.le_length_destutter'_cons._simp_1_3 | Mathlib.Data.List.Destutter | [
"Nat.le_succ",
"LE.le",
"instLENat",
"Nat",
"True",
"eq_true",
"Nat.succ",
"Eq"
] | false |
ProbabilityTheory.Kernel.Indep.eq_1 | Mathlib.Probability.Independence.Kernel.Indep | [
"MeasureTheory.Measure",
"MeasurableSet",
"ProbabilityTheory.Kernel.Indep",
"setOf",
"ProbabilityTheory.Kernel.IndepSets",
"MeasurableSpace",
"Eq.refl",
"Eq",
"ProbabilityTheory.Kernel",
"Set"
] | true |
Filter.Germ.instSemifield._proof_1 | Mathlib.Order.Filter.FilterProduct | [
"DivisionSemiring.div_eq_mul_inv",
"Semigroup.toMul",
"Filter.Germ.instDivisionSemiring",
"instHDiv",
"HMul.hMul",
"DivisionSemiring.toInv",
"Semifield",
"HDiv.hDiv",
"DivisionSemiring.toDiv",
"Inv.inv",
"Semifield.toDivisionSemiring",
"Filter.Germ",
"Semiring.toMonoid",
"Monoid.toSemigrou... | false |
_private.Mathlib.Data.Set.Prod.0.Set.univ_pi_singleton._simp_1_1 | Mathlib.Data.Set.Prod | [
"funext_iff",
"propext",
"Eq"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.isEmpty_filter_eq_false_iff._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
Matrix.conjTranspose_intCast_smul | Mathlib.LinearAlgebra.Matrix.ConjTranspose | [
"Int.cast",
"Matrix.smul",
"instHSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Matrix",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"Int",
"AddGroupWithOne.toIntCast"... | true |
Algebra.TensorProduct.tensorQuotientEquiv_apply_tmul | Mathlib.RingTheory.TensorProduct.Quotient | [
"Submodule.Quotient.addCommMonoid",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Algebra.TensorProduct.instCommRing",
"Ideal.Quotient.mk",
"AlgHom",
"IsScalarTower",
"AlgHom.... | true |
Lean.Elab.Term.MutualClosure.ClosureState.mk.noConfusion | Lean.Elab.MutualDef | [
"Lean.Elab.Term.MutualClosure.ClosureState",
"Lean.Elab.Term.MutualClosure.ClosureState.mk",
"Lean.Expr",
"id",
"Array",
"Lean.Elab.Term.MutualClosure.ClosureState.noConfusion",
"Lean.LocalDecl",
"Eq"
] | false |
HomotopicalAlgebra.mem_trivialCofibrations_iff | Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Iff.rfl",
"HomotopicalAlgebra.weakEquivalence_iff",
"id",
"HomotopicalAlgebra.Cofibration",
"And",
"Iff",
"HomotopicalAlgebra.CategoryWithWeakEquivalences",
"propext",
"HomotopicalAlgebra.cofibrations",
"Homotop... | true |
instMetricSpaceEmpty._proof_2 | Mathlib.Topology.MetricSpace.Defs | [
"Real",
"Real.instZero",
"ENNReal.ofReal",
"NNReal",
"NNReal.instZero",
"Empty",
"ENNReal.coe_nnreal_eq",
"ENNReal",
"Zero.toOfNat0",
"ENNReal.instZero",
"OfNat.ofNat",
"Eq"
] | false |
Lean.Elab.Tactic.BVDecide.Frontend.evalBvDecide._regBuiltin.Lean.Elab.Tactic.BVDecide.Frontend.evalBvDecide_1 | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide | [
"Lean.Elab.Tactic.tacticElabAttribute",
"IO",
"Unit",
"Lean.Elab.Tactic.Tactic",
"Lean.Elab.Tactic.BVDecide.Frontend.evalBvDecide",
"Lean.Name.mkStr6",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
_private.Mathlib.LinearAlgebra.Matrix.Irreducible.Defs.0.Matrix.isIrreducible_transpose_iff._simp_1_3 | Mathlib.LinearAlgebra.Matrix.Irreducible.Defs | [
"Exists",
"propext",
"Classical.not_forall",
"Eq",
"Not"
] | false |
Lean.Grind.LinarithConfig.mk.inj | Init.Grind.Config | [
"Lean.Grind.LinarithConfig.mk.noConfusion",
"Lean.Grind.LinarithConfig.mk",
"Lean.Grind.NoopConfig",
"Lean.Grind.LinarithConfig",
"Eq"
] | true |
SimpleGraph.Walk.isTrail_rotate | Mathlib.Combinatorics.SimpleGraph.Paths | [
"Eq.mpr",
"congrArg",
"SimpleGraph.Walk.rotate_edges",
"SimpleGraph.Walk.isTrail_def",
"Iff.rfl",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Membership.mem",
"id",
"SimpleGraph.Walk.rotate",
"List.Perm.nodup_iff",
"SimpleGraph",
"List.Nodup",
"List",
"Iff",
"List.instMembership",... | true |
TendstoLocallyUniformlyOn.mul₀ | Mathlib.Topology.MetricSpace.Algebra | [
"instSMulOfMul",
"HMul.hMul",
"TendstoLocallyUniformlyOn",
"PseudoMetricSpace.toUniformSpace",
"Mul",
"IsBoundedSMul",
"TopologicalSpace",
"PseudoMetricSpace",
"Pi.instMul",
"ContinuousOn",
"TendstoLocallyUniformlyOn.smul₀",
"UniformSpace.toTopologicalSpace",
"Filter",
"instHMul",
"Zero"... | true |
CategoryTheory.Limits.limit.post.eq_1 | Mathlib.CategoryTheory.Limits.HasLimits | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Limits.limit.post",
"Quiver.Hom",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.HasLimit",
"CategoryTheory.Limits.limit.cone",
"CategoryTheory.Limits.limit",
"Eq.refl",
"CategoryTheory.Limits.limit.lift",
... | true |
Filter.pureMulHom | Mathlib.Order.Filter.Pointwise | [
"Pure.pure",
"MulHom",
"Mul",
"Filter.instMul",
"Filter.pureMulHom._proof_1",
"Filter.instPure",
"MulHom.mk",
"Filter"
] | true |
AnalyticWithinAt.mul | Mathlib.Analysis.Analytic.Constructions | [
"NormedRing.toRing",
"HMul.hMul",
"NormedSpace",
"NormedRing.toNonUnitalNormedRing",
"AnalyticWithinAt",
"Prod.mk",
"AnalyticAt.comp₂_analyticWithinAt",
"Prod.fst",
"instDistribOfSemiring",
"NonUnitalNormedRing.toNormedAddCommGroup",
"Distrib.toMul",
"NormedAlgebra.toNormedSpace",
"NormedRin... | true |
CategoryTheory.Pretriangulated.Triangle.π₁._proof_1 | Mathlib.CategoryTheory.Triangulated.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTheory.CategoryStruct.id",
"id",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Triangle",
"CategoryTheory.Pretriangulated.triangleCategory",
"Eq.refl",
"CategoryTheory.P... | false |
WithTop.tendsto_nhds_top_iff | Mathlib.Topology.Order.WithTop | [
"Pure.pure",
"Eq.mpr",
"WithTop.instPartialOrder",
"OrderTopology",
"Set.Ioi",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Set.forall_mem_range",
"WithTop.instPreorder",
"congrArg",
"TopologicalSpace.instOrderTopologyWithTop",
"LinearOrder",
"Filter.Eventually",
"Filter.tendsto_pure._sim... | true |
CStarAlgebra.isUnit_of_le | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order | [
"Nontrivial",
"Iff.mpr",
"Eq.mpr",
"CStarAlgebra.toNonUnitalCStarAlgebra",
"MulOne.toOne",
"CFC.exists_pos_algebraMap_le_iff",
"Real.instStarOrderedRing",
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"NormedRing.toRing",
... | true |
unexpandSubtype | Init.NotationExtra | [
"Pure.pure",
"cond",
"Lean.Syntax.node",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.matchesIdent",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Array.... | true |
_private.Lean.Elab.Tactic.Grind.Lint.0.Lean.Elab.Tactic.Grind.mkParams | Lean.Elab.Tactic.Grind.Lint | [
"Pure.pure",
"Lean.Meta.Grind.Params",
"Lean.Meta.Grind.Params.normProcs",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.Meta.Grind.Params.symPrios",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.PersistentEnvExtensionState",
"Lean.Grind.Config",
"instMonadExceptOfMonadExceptOf",
"Lean.Meta.Grind.Par... | true |
SimplexCategory.const_apply | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"PartialOrder.toPreorder",
"instOfNatNat",
"instHAdd",
"OrderHom.instFunLike",
"Fin.instPartialOrder",
"SimplexCategory.const",
"HAdd.hAdd",
"Nat",
"SimplexCategory",
"SimplexCategory.Hom.toOrderHom",
"instAddNat",
"OfNat.ofNat",
"Fin",
"Eq",
"DFunLike.coe",
"OrderHom",
"rfl",
"Sim... | true |
_private.Lean.Environment.0.Lean.Environment.PromiseCheckedResult.mk.inj | Lean.Environment | [
"_private.Lean.Environment.0.Lean.Environment.PromiseCheckedResult.mk.noConfusion",
"Lean.Kernel.Environment",
"_private.Lean.Environment.0.Lean.Environment.PromiseCheckedResult.mk",
"And",
"And.intro",
"IO.Promise",
"Lean.Environment.PromiseCheckedResult",
"Eq",
"Lean.Environment"
] | true |
PredOrder.ofCore.eq_1 | Mathlib.Order.SuccPred.Basic | [
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"PredOrder.ofCore",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"DistribLattice.toLattice",
"PredOrder.mk",
"LE.le",
"PredOrder.ofCore._proof_3",
"Iff",
"LT.lt",
"Eq.refl",
"SemilatticeSup.toPartialOrder",
"PredOrder",
"Eq",
... | true |
ModuleCat.limitModule._proof_8 | Mathlib.Algebra.Category.ModuleCat.Limits | [
"Submodule",
"CategoryTheory.Functor",
"instHSMul",
"Pi.addCommMonoid",
"ModuleCat.instSmallSubtypeForallCarrierObjMemSubmoduleSectionsSubmodule",
"CategoryTheory.Limits.Types.Small.limitCone",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Pi.module",
"AddMonoid.toAddZ... | false |
Mathlib.TacticAnalysis.Config.mk.noConfusion | Mathlib.Tactic.TacticAnalysis | [
"Mathlib.TacticAnalysis.Config",
"Mathlib.TacticAnalysis.Config.mk",
"Mathlib.TacticAnalysis.Config.noConfusion",
"id",
"Array",
"Unit",
"Lean.Elab.Command.CommandElabM",
"Eq",
"Mathlib.TacticAnalysis.TacticNode"
] | false |
CategoryTheory.Limits.Concrete.widePullback_ext | Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory | [
"CategoryTheory.Limits.limit.π",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Limits.widePullback",
"CategoryTheory.Limits.WidePullbackShape",
"Option.casesOn",
"CategoryTheory.Limits.WidePullba... | true |
ProofWidgets.Penrose.RpcEncodablePacket.mk.«_@».ProofWidgets.Component.PenroseDiagram.3621647104._hygCtx._hyg.1.noConfusion | ProofWidgets.Component.PenroseDiagram | [
"ProofWidgets.Penrose.RpcEncodablePacket.mk._@.ProofWidgets.Component.PenroseDiagram.3621647104._hygCtx._hyg.1",
"Lean.Json",
"id",
"ProofWidgets.Penrose.RpcEncodablePacket._@.ProofWidgets.Component.PenroseDiagram.3621647104._hygCtx._hyg.1",
"ProofWidgets.Penrose.RpcEncodablePacket.«_@».ProofWidgets.Compone... | false |
_private.Mathlib.Tactic.CancelDenoms.Core.0.Mathlib.Tactic._aux_Mathlib_Tactic_CancelDenoms_Core___elabRules_Mathlib_Tactic_tacticCancel_denoms__1.match_1 | Mathlib.Tactic.CancelDenoms.Core | [
"Lean.TSyntax",
"_private.Mathlib.Tactic.CancelDenoms.Core.0.Mathlib.Tactic.CancelDenoms.cancelDenominatorsInType._sparseCasesOn_5",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"List.cons",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr4",
"List.nil",
"Option"
] | false |
CategoryTheory.SimplicialObject.augmentOfIsTerminal | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"CategoryTheory.Limits.IsTerminal.from",
"Opposite",
"CategoryTheory.SimplicialObject.const",
"CategoryTheory.Limits.IsTerminal",
"CategoryTheory.SimplicialObject.augmentOfIsTerminal._proof_2",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"CategoryTheory.NatTrans.mk",
"SimplexCate... | true |
_private.Mathlib.CategoryTheory.Galois.Prorepresentability.0.CategoryTheory.PreGaloisCategory.AutGalois.π_surjective._proof_1_1 | Mathlib.CategoryTheory.Galois.Prorepresentability | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"CategoryTheory.Functor",
"CategoryTheory.PreGaloisCategory.instFiniteAutOfIsConnected",
"GrpCat",
"MonoidHom.instFunLike",
"MonoidHom",
"GrpCat.str",
"Monoid.toMulOneClass",
"CategoryTheory.PreGaloisCategory.PointedGaloisObject.instCategory",
"Finite... | false |
Mathlib.Deriving.Encodable.mkEncodableInstance | Mathlib.Tactic.DeriveEncodable | [
"Pure.pure",
"Lean.mkNullNode",
"Lean.NameSet.ofList",
"Lean.MonadError.mk",
"Lean.Elab.Command.liftTermElabM",
"bne",
"_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.mkEncodableCmds",
"Array.push",
"instForInOfForIn'",
"ReaderT",
"Lean.NameSet",
"Lean.Elab.Command.elabCo... | true |
Array.scanl_singleton | Batteries.Data.Array.Scan | [
"Array.scanl",
"instOfNatNat",
"Array.toList",
"List.toArray",
"List.cons",
"Array",
"List",
"Nat",
"Iff.mp",
"Array.toList_inj",
"_private.Batteries.Data.Array.Scan.0.Array.scanl_singleton._proof_1_1",
"OfNat.ofNat",
"Eq",
"Array.size",
"List.nil"
] | true |
Bundle.Trivialization.proj_surjOn_baseSet | Mathlib.Topology.FiberBundle.Trivialization | [
"Set.SurjOn",
"instTopologicalSpaceProd",
"TopologicalSpace",
"Bundle.Trivialization",
"Nonempty",
"PartialEquiv.source",
"Prod",
"Bundle.Trivialization.baseSet",
"OpenPartialHomeomorph.toPartialEquiv",
"Bundle.Trivialization.toPretrivialization",
"Bundle.Pretrivialization.proj_surjOn_baseSet",
... | true |
Std.DHashMap.Internal.Raw₀.Const.mem_toArray_iff_get?_eq_some | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.Const.toList",
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Internal.Raw₀.Const.get?",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.Const.toArray",
"Array.instMembership",
"Option.some",
"LawfulBEq",
"Membership.mem",
"List.mem_toArray._simp_1",
"Prod.mk",
"instOfNatNat",
"L... | true |
HomotopicalAlgebra.Precylinder.LeftHomotopy.refl_h | Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.Precylinder.I",
"HomotopicalAlgebra.Precylinder.π",
"HomotopicalAlgebra.Precylinder.LeftHomotopy.h",
"HomotopicalAlgebra.Precylinder",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruc... | true |
_private.Init.Ext.0.PProd.ext.match_1 | Init.Ext | [
"PProd.mk",
"PProd.casesOn",
"PProd"
] | false |
WellFounded.prop_min | Mathlib.Order.WellFounded | [
"WellFounded.min_mem",
"setOf",
"Exists",
"WellFounded.min",
"WellFounded"
] | true |
Lean.Lsp.SemanticTokenType.class | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SemanticTokenType",
"Lean.Lsp.SemanticTokenType.class"
] | true |
MeasureTheory.integral_coe_le_of_lintegral_coe_le | Mathlib.MeasureTheory.Integral.Bochner.Basic | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real.instLE",
"Real",
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"Real.instZero",
"congrArg",
"MeasureTheory.integral_undef",
"PseudoMetricSpace.toUniformSpace",
"Classical.propDecidable",
"MeasureTheory.Integrable",
"SeminormedAddGroup.toC... | true |
Quiver.Arborescence.mk._flat_ctor | Mathlib.Combinatorics.Quiver.Arborescence | [
"Quiver.Arborescence",
"Unique",
"Quiver.Path",
"Quiver",
"Quiver.Arborescence.mk"
] | false |
_private.Mathlib.Data.Setoid.Partition.Card.0.Setoid.IsPartition.ncard_eq_finsum._simp_1_16 | Mathlib.Data.Setoid.Partition.Card | [
"Subtype.coe_inj",
"Subtype",
"propext",
"Eq.symm",
"Subtype.val",
"Eq"
] | false |
ArithmeticFunction.carmichael_dvd | Mathlib.NumberTheory.ArithmeticFunction.Carmichael | [
"ZMod.unitsMap_surjective",
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"instNeZeroNatHAdd_1",
"Nat.instMulZeroClass",
"ZMod.unitsMap",
"Dvd.dvd",
"MonoidHom.instFunLike",
"ArithmeticFunction.instFunLikeNat",
"_private.Mathlib.NumberTheory.ArithmeticFunction.Carmichael.0.ArithmeticFunction.carmichae... | true |
Finset.sum_Ico_Ico_comm | Mathlib.Algebra.BigOperators.Intervals | [
"Eq.mpr",
"_private.Mathlib.Algebra.BigOperators.Intervals.0.Finset.sum_Ico_Ico_comm._proof_1_4",
"Preorder.toLT",
"_private.Mathlib.Algebra.BigOperators.Intervals.0.Finset.sum_Ico_Ico_comm._proof_1_5",
"congrArg",
"Finset",
"Preorder.toLE",
"Nat.instLocallyFiniteOrder",
"Membership.mem",
"Finset.... | true |
PowerSeries.derivative_subst | Mathlib.RingTheory.PowerSeries.Derivative | [
"Derivation",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"PowerSeries.coeff_trunc",
"CommRing",
"instHSMul",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Nat.instOne",
"instReflLe",
"MvPowerSe... | true |
_private.Aesop.Forward.LevelIndex.0.Aesop.instBEqLevelIndex.beq.match_1 | Aesop.Forward.LevelIndex | [
"Aesop.LevelIndex.mk",
"Aesop.LevelIndex",
"Nat",
"Aesop.LevelIndex.casesOn"
] | false |
GroupNormClass.eq_one_of_map_eq_zero | Mathlib.Algebra.Order.Hom.Basic | [
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"outParam",
"AddMonoid.toAddZeroClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"AddZeroClass.toAddZero",
"PartialOrder",
"GroupNormClass",
"AddCommMonoid",
"AddZero.toZero",
"One.toOfNat1",
"Zero.toOfNat0... | true |
Std.Tactic.BVDecide.BVExpr.eval_extract | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"Std.Tactic.BVDecide.BVExpr.extract",
"BitVec.extractLsb'",
"Std.Tactic.BVDecide.BVExpr.eval",
"BitVec",
"Nat",
"Eq.refl",
"Std.Tactic.BVDecide.BVExpr",
"Std.Tactic.BVDecide.BVExpr.Assignment",
"Eq"
] | true |
QuasiconvexOn | Mathlib.Analysis.Convex.Quasiconvex | [
"SMul",
"setOf",
"Membership.mem",
"PartialOrder",
"LE.le",
"LE",
"AddCommMonoid",
"And",
"Convex",
"Semiring",
"Set.instMembership",
"Set"
] | true |
CategoryTheory.AreEqualizedByLocalization.map_eq | Mathlib.CategoryTheory.Localization.Predicate | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.areEqualizedByLocalization_iff",
"CategoryTheory.Functor.map",
"CategoryTheory.Functor.IsLocalization",
"CategoryTheory.AreEqualizedByLocalization",
"Iff.mp",
"Categ... | true |
_private.Mathlib.Topology.Continuous.0.DenseRange.mem_nhds.match_1_1 | Mathlib.Topology.Continuous | [
"Membership.mem",
"Exists",
"TopologicalSpace",
"Exists.casesOn",
"interior",
"Exists.intro",
"Set.instMembership",
"Set"
] | false |
Module.Basis.mkFinCons._proof_1 | Mathlib.LinearAlgebra.Basis.Fin | [
"Set.range_comp",
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"LinearMap.instFunLike",
"Function.comp",
"Membership.mem",
"AddCommGroup",
"id",
"Subtype",
"Submodule.instTop",
"Submodule.module",
"Module.Basis.i... | false |
SSet.Truncated.HomotopyCategory.BinaryProduct.curriedInverse._proof_5 | Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal | [
"SSet.Truncated.Edge",
"SSet.Truncated.Edge.CompStruct.tensor",
"Eq.mpr",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"SSet.Truncated.HomotopyCateg... | false |
MoritaEquivalence.mk.sizeOf_spec | Mathlib.RingTheory.Morita.Basic | [
"MoritaEquivalence",
"MoritaEquivalence._sizeOf_inst",
"MoritaEquivalence.linear._autoParam",
"ModuleCat",
"CommSemiring.toSemiring",
"CategoryTheory.Functor.Linear",
"instSizeOfDefault",
"CategoryTheory.Equivalence",
"Algebra",
"ModuleCat._sizeOf_inst",
"CategoryTheory.Equivalence.functor",
"... | true |
_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._proof_299 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"instOfNatNat",
"LE.le",
"instLENat",
"Nat",
"Decidable.byContradiction",
"_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._proof_289",
"OfNat.ofNat",
"Not",
"Nat.decLe"
] | false |
LinearMap.continuous_of_isClosed_graph | Mathlib.Analysis.Normed.Operator.Banach | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"LinearMap.id",
"NormedCommRing.toSeminormedCommRing",
"Submodule",
"ContinuousLinearEquiv.symm",
"RingHomSurjective.ids",
"instUniformSpaceProd",
"LinearEquiv.ofLeftInverse",
"LinearEquiv.symm",
"Function.LeftInverse",
"IsComplete",
"Prod.normedSpac... | true |
CategoryTheory.Limits.IndObjectPresentation.mk.injEq | Mathlib.CategoryTheory.Limits.Indization.IndObject | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Eq.propIntro",
"CategoryTheory.Functor.category",
"Lean.injEq_helper",
"CategoryTheory.Functor.comp",
"CategoryTheory.yoneda",
"HEq.homo_ndrec",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Lim... | true |
Int.ediv_lt_of_lt_mul | Init.Data.Int.DivMod.Lemmas | [
"Int.instDiv",
"instHDiv",
"Int.lt_of_not_ge",
"HMul.hMul",
"Int.mul_le_of_le_ediv",
"mt",
"HDiv.hDiv",
"Int",
"LE.le",
"Int.instMul",
"Int.instLTInt",
"instOfNat",
"LT.lt",
"OfNat.ofNat",
"Int.not_le_of_gt",
"Int.instLEInt",
"instHMul"
] | true |
_private.Mathlib.Topology.UniformSpace.AbstractCompletion.0.AbstractCompletion._aux_Mathlib_Topology_UniformSpace_AbstractCompletion___macroRules__private_Mathlib_Topology_UniformSpace_AbstractCompletion_0_AbstractCompletion_termHatβ_1_1 | Mathlib.Topology.UniformSpace.AbstractCompletion | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr... | false |
Lean.Meta.Grind.Arith.Linear.OfNatModuleM.Context.natStructId | Lean.Meta.Tactic.Grind.Arith.Linear.OfNatModule | [
"Lean.Meta.Grind.Arith.Linear.OfNatModuleM.Context",
"Nat"
] | true |
IsCompactOpenCovered.of_finite_of_isSpectralMap | Mathlib.Topology.Sets.CompactOpenCovered | [
"subset_refl._simp_1",
"Eq.mpr",
"IsCompact.preimage_of_isOpen",
"Iff.of_eq",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"Finite",
"Set.mem_image._simp_1",
"Set.mem_iUnion._simp_1",
"IsSpectralMap",
"TopologicalSpace.Opens",
"Set.Finite",
"Membership.mem",
"Exists",
"IsCompactOpen... | true |
NeZero.nat_of_neZero | Mathlib.Data.Nat.Cast.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"congrArg",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"RingHomClass.toMonoidWithZeroHomClass",
"AddMonoidWithOne.toNatCast",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Nat.cast",
"NeZero.of_map",
"NonAssocSemiring"... | true |
Ordnode.eraseMax.eq_2 | Mathlib.Data.Ordmap.Invariants | [
"Ordnode",
"Ordnode.node",
"Ordnode.eraseMax",
"Nat",
"Ordnode.nil",
"Eq.refl",
"Eq"
] | true |
LightProfinite.continuous_iff_convergent | Mathlib.Topology.Category.LightProfinite.Sequence | [
"Continuous",
"OnePoint.infty",
"SecondCountableTopology",
"instTopologicalSpaceNat",
"OnePoint.some",
"nhds",
"TotallyDisconnectedSpace",
"LightProfinite.NatUnionInfty",
"Filter.atTop",
"TopologicalSpace",
"TopCat.str",
"And",
"Iff",
"TopCat.carrier",
"Filter.Tendsto",
"Nat.instPreord... | true |
_private.Mathlib.NumberTheory.ModularForms.QExpansion.0.UpperHalfPlane.qExpansion_coeff_eq_intervalIntegral._simp_1_11 | Mathlib.NumberTheory.ModularForms.QExpansion | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
Finsupp.lex_def | Mathlib.Data.Finsupp.Lex | [
"Finsupp.instFunLike",
"Iff.rfl",
"Exists",
"And",
"Iff",
"Finsupp.Lex",
"Eq",
"DFunLike.coe",
"Finsupp",
"Zero"
] | true |
MeasureTheory.tendsto_zero_of_hasDerivAt_of_integrableOn_Iic | Mathlib.MeasureTheory.Integral.IntegralEqImproper | [
"Filter.instMembership",
"Real.instIsOrderedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"UniformSpace.Completion.coe'",
"Real.partialOrder",
"Real",
"MeasureTheory.Measure",
"Real.instArchimedean",
"NormedSpace.toIsBoundedSMul",
"instZeroCompletion",
"NormedSpace",
"ContinuousLin... | true |
LocallyConstant.coe_smul | Mathlib.Topology.LocallyConstant.Algebra | [
"LocallyConstant.smul",
"instHSMul",
"SMul",
"Function.hasSMul",
"LocallyConstant",
"TopologicalSpace",
"HSMul.hSMul",
"LocallyConstant.instFunLike",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
StarAlgHom.continuous_realContinuousMapOfNNReal | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | [
"NNReal.instTopologicalSpace",
"Continuous.comp'",
"Continuous.neg",
"IsSemitopologicalRing.toIsTopologicalAddGroup",
"NNReal.instCommSemiring",
"Real",
"Continuous",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSem... | true |
Lean.Meta.Grind.Entry.casesOn | Lean.Meta.Tactic.Grind.Extension | [
"Lean.Meta.Grind.Entry.funCC",
"Lean.Meta.Grind.InjectiveTheorem",
"Lean.Meta.Grind.Entry.ext",
"Lean.Meta.Grind.Entry.ematch",
"Lean.Meta.Grind.EMatchTheorem",
"Lean.Meta.Grind.Entry.inj",
"Lean.Meta.Grind.Entry.rec",
"Lean.Meta.Grind.Entry",
"Bool",
"Lean.Name",
"Lean.Meta.Grind.Entry.cases"
] | false |
exists_exists_and_eq_and._simp_1 | Mathlib.Logic.Basic | [
"Exists",
"And",
"exists_exists_and_eq_and",
"propext",
"Eq"
] | false |
CategoryTheory.Functor.mapTriangleIdIso._proof_8 | Mathlib.CategoryTheory.Triangulated.Functor | [
"CategoryTheory.Pretriangulated.TriangleMorphism.hom₂",
"CategoryTheory.Functor.mapTriangleIdIso._proof_6",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.CommShift.id",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTh... | false |
vieta_formula_quadratic | Mathlib.Algebra.Ring.Basic | [
"sub_add",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"neg_sub",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"mul_sub",
"sub_self",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"HSub.hSub",
"NonUnitalNonAssocSem... | true |
Filter.Germ.instNonAssocRing._proof_4 | Mathlib.Order.Filter.Germ.Basic | [
"AddMonoid.toAddSemigroup",
"NonAssocSemiring.toOne",
"instOfNatNat",
"NonAssocRing",
"Filter.Germ.instNonAssocSemiring",
"NatCast.natCast",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Filter.Germ"... | false |
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