name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Fin.val_natAdd | Init.Data.Fin.Lemmas | [
"Fin.natAdd",
"Fin.val",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Fin",
"Eq",
"rfl"
] | true |
Set.decidableMemMul._proof_1 | Mathlib.Algebra.Group.Pointwise.Set.Finite | [
"Monoid",
"HMul.hMul",
"Monoid.toMulOneClass",
"Membership.mem",
"Exists",
"MulOne.toMul",
"MulOneClass.toMulOne",
"And",
"Iff",
"Set.mul",
"Eq",
"Set.instMembership",
"Iff.symm",
"Set.mem_mul",
"instHMul",
"Set"
] | false |
_private.Std.Time.Date.PlainDate.0.Std.Time.PlainDate.weekOfYear._proof_4 | Std.Time.Date.PlainDate | [
"Std.Time.Internal.Bounded.LE.addBounds",
"Std.Time.Internal.Bounded.LE.ediv",
"Int.instDiv",
"instHDiv",
"Std.Time.PlainDate",
"Std.Time.PlainDate.dayOfYear",
"Std.Time.Internal.Bounded.LE.subBounds",
"HSub.hSub",
"Std.Time.Year.Offset.isLeap",
"HDiv.hDiv",
"instDecidableEqBool",
"Int.ofNat",... | false |
Lean.Elab.Frontend.State | Lean.Elab.Frontend | [
"Lean.Elab.Frontend.State.mk"
] | true |
Lean.PersistentHashMap.Zipper.consCollision.inj | Lean.Data.Iterators.Producers.PersistentHashMap | [
"Subarray",
"Lean.PersistentHashMap.Zipper",
"And",
"Std.Slice.Internal.SubarrayData",
"Nat",
"And.intro",
"eq_of_heq",
"Std.Slice.size",
"Subarray.instSliceSizeSubarrayData",
"HEq",
"Lean.PersistentHashMap.Zipper.consCollision.noConfusion",
"Eq",
"Lean.PersistentHashMap.Zipper.consCollision... | true |
MeasureTheory.VectorMeasure.dirac._proof_7 | Mathlib.MeasureTheory.VectorMeasure.Basic | [
"Eq.mpr",
"False",
"ChainCompletePartialOrder.instOfCompleteLattice",
"MeasurableSet",
"eq_false",
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"and_self",
"hasSum_single",
"exists_const._simp_1",
"AddMonoid.toAddZeroClass",
"SummationFilter",
"Set.mem_i... | false |
ComplexShape.noConfusionType | Mathlib.Algebra.Homology.ComplexShape | [
"ComplexShape",
"ComplexShape.casesOn",
"HEq",
"Eq"
] | false |
Matrix.permanent.congr_simp | Mathlib.LinearAlgebra.Matrix.Permanent | [
"instSubsingletonDecidable",
"Matrix",
"Decidable",
"Eq.rec",
"Pi.instSubsingleton",
"CommSemiring",
"Fintype",
"Eq.ndrec",
"Eq.refl",
"Matrix.permanent",
"Subsingleton.elim",
"Eq",
"DecidableEq"
] | true |
GeneralizedHeytingAlgebra | Mathlib.Order.Heyting.Basic | [
"GeneralizedHeytingAlgebra.mk"
] | true |
Submodule.pow_induction_on_left | Mathlib.Algebra.Algebra.Operations | [
"Submodule",
"HMul.hMul",
"IsScalarTower.right",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Submodule.pow_induction_on_left'",
"Algebra",
"RingHom",
"Membership.mem",
"Algebra.toModule",
"Distrib.toAdd",
"instDistribOfSemiring",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMo... | true |
Set.Finite.of_inv | Mathlib.Algebra.Group.Pointwise.Set.Finite | [
"InvolutiveInv.toInv",
"Set.Finite",
"InvolutiveInv",
"Inv.inv",
"Set.finite_inv",
"Set.inv",
"Iff.mp",
"Set"
] | true |
ContinuousAffineEquiv.preimage_image | Mathlib.Topology.Algebra.ContinuousAffineEquiv | [
"ContinuousAffineEquiv.injective",
"AddCommGroup.toAddCommMonoid",
"ContinuousAffineEquiv.instFunLike",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ContinuousAffineEquiv",
"TopologicalSpace",
"Set.preimage",
"Function.Injective.preimage_image",
"AddTorsor",
"Set.image",
"Module",
"Ring.toSem... | true |
SimpleGraph.Path.loop_eq | Mathlib.Combinatorics.SimpleGraph.Paths | [
"False",
"HEq.refl",
"SimpleGraph.Adj",
"False.elim",
"Subtype.casesOn",
"SimpleGraph.Walk",
"SimpleGraph.Walk.not_nil_cons._simp_1",
"SimpleGraph.Walk.casesOn",
"Eq.mp",
"SimpleGraph.Path",
"Subtype.mk",
"SimpleGraph",
"SimpleGraph.Walk.isPath_iff_eq_nil._simp_1",
"SimpleGraph.Walk.cons",... | true |
instModuleQuotientAddSubgroupTorsion | Mathlib.GroupTheory.Torsion | [
"instModuleQuotientAddSubgroupTorsion._proof_1",
"instModuleQuotientAddSubgroupTorsion._proof_4",
"Submodule",
"Submodule.Quotient.addCommMonoid",
"instHSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"instModuleQuotientAddSubgroupTorsion._proof_6",
"AddEquiv.toAddMonoidHom",
"S... | true |
List.findRev?._unsafe_rec | Init.Data.List.Basic | [
"Option.some",
"List.findSome?.match_1",
"instDecidableEqBool",
"Bool.true",
"Option.none",
"List",
"Unit",
"List.findRev?._unsafe_rec",
"Bool",
"Eq",
"List.getLast?.match_1",
"Option",
"ite"
] | false |
LinearIsometryEquiv.withLpProdAssoc._proof_4 | Mathlib.Analysis.Normed.Lp.ProdLp | [
"WithLp",
"SeminormedAddCommGroup",
"Equiv.right_inv",
"IsometryEquiv.toEquiv",
"WithLp.instProdPseudoEMetricSpace",
"IsometryEquiv.withLpProdAssoc",
"Fact",
"Equiv.toFun",
"LE.le",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"ENNReal.instLE",
"ENNReal",
"Function.RightInverse",
"One.toO... | false |
BoxIntegral.Box.continuousOn_face_Icc | Mathlib.Analysis.BoxIntegral.Box.Basic | [
"Real",
"BoxIntegral.Box.face",
"Pi.topologicalSpace",
"BoxIntegral.Box.Icc",
"PseudoMetricSpace.toUniformSpace",
"Function.comp",
"Membership.mem",
"Fin.insertNth",
"continuousOn_const",
"BoxIntegral.Box.upper",
"instOfNatNat",
"ContinuousOn.comp",
"BoxIntegral.Box.mapsTo_insertNth_face_Icc... | true |
ContinuousMap.instInvolutiveStarOfContinuousStar | Mathlib.Topology.ContinuousMap.Star | [
"ContinuousStar",
"ContinuousMap",
"InvolutiveStar",
"TopologicalSpace",
"InvolutiveStar.toStar",
"ContinuousMap.instInvolutiveStarOfContinuousStar._proof_1",
"ContinuousMap.instStar",
"InvolutiveStar.mk"
] | true |
BarrelledSpace.mk | Mathlib.Analysis.LocallyConvex.Barrelled | [
"BarrelledSpace.mk",
"Real",
"Continuous",
"SMul",
"PseudoMetricSpace.toUniformSpace",
"Seminorm",
"Seminorm.instFunLike",
"LowerSemicontinuous",
"TopologicalSpace",
"AddGroup",
"Real.pseudoMetricSpace",
"UniformSpace.toTopologicalSpace",
"BarrelledSpace",
"DFunLike.coe",
"SeminormedRing... | true |
CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction._proof_11 | Mathlib.CategoryTheory.Monoidal.Action.Opposites | [
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_comp",
"CategoryTheory.MonoidalCategory.Mo... | false |
AlgHom.IsArithFrobAt.restrict._proof_1 | Mathlib.RingTheory.Frobenius | [
"Ideal.Quotient.commSemiring",
"MulOne.toOne",
"Ideal.instAlgebraQuotientComapRingHomAlgebraMap",
"CommRing",
"AlgHom.algHomClass",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"RingHom",
"Exists",
"NonAssocSemiring.toMulZeroO... | false |
_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.alter!.match_1.eq_1 | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Unit.unit",
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.Const.alter!.match_1",
"Unit",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | true |
Aesop.traverseUp | Aesop.Tree.Traversal | [
"Inhabited.default",
"Aesop.TreeRef",
"instInhabitedOfMonad",
"Aesop.RappRef",
"instInhabitedPUnit",
"IO.RealWorld",
"MonadLiftT",
"Aesop.GoalRef",
"Unit",
"ST",
"Bool",
"Monad",
"Aesop.MVarClusterRef"
] | true |
AddZeroClass.toAddZero | Mathlib.Algebra.Group.Defs | [
"AddZero",
"AddZeroClass"
] | true |
Subring.map_inf | Mathlib.Algebra.Ring.Subring.Basic | [
"Subring.instMin",
"Subring.instSetLike",
"Subring.map",
"RingHom",
"Set.image_inter",
"NonAssocRing",
"SetLike.coe_injective",
"RingHom.instFunLike",
"SetLike.coe",
"Subring",
"Function.Injective",
"Eq",
"DFunLike.coe",
"NonAssocRing.toNonAssocSemiring",
"Min.min"
] | true |
Mathlib.Tactic.Translate.Reorder.mk.injEq | Mathlib.Tactic.Translate.Reorder | [
"Eq.propIntro",
"Lean.injEq_helper",
"Mathlib.Tactic.Translate.Reorder.mk",
"And",
"Mathlib.Tactic.Translate.Permutation",
"Mathlib.Tactic.Translate.Reorder",
"Eq.ndrec",
"Eq.refl",
"Mathlib.Tactic.Translate.Reorder.mk.inj",
"Mathlib.Tactic.Translate.ArgReorder",
"Eq"
] | true |
Complex.instModule | Mathlib.LinearAlgebra.Complex.Module | [
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Complex.commRing",
"Module.mk",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Complex.instModule._proof_1",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocRin... | true |
forall₃_congr | Init.PropLemmas | [
"Iff",
"forall₂_congr",
"forall_congr'"
] | true |
ContinuousAt.finInsertNth | Mathlib.Topology.Constructions | [
"Fin.succAbove",
"Pi.topologicalSpace",
"ContinuousAt",
"Fin.insertNth",
"nhds",
"instOfNatNat",
"Filter.Tendsto.finInsertNth",
"TopologicalSpace",
"instHAdd",
"ContinuousAt.tendsto",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Fin"
] | true |
_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.AhlswedeZhang.infSum_compls_add_supSum._simp_1_3 | Mathlib.Combinatorics.SetFamily.AhlswedeZhang | [
"instHDiv",
"GroupWithZero.toDivInvMonoid",
"DivisionSemiring.toGroupWithZero",
"Distrib.toAdd",
"HDiv.hDiv",
"instDistribOfSemiring",
"DivisionSemiring",
"instHAdd",
"HAdd.hAdd",
"DivInvMonoid.toDiv",
"DivisionSemiring.toSemiring",
"Eq.symm",
"Eq",
"add_div"
] | false |
IsLocalization'.recOn | Mathlib.RingTheory.Localization.Defs | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"IsLocalization'.mk",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"Submonoid.IsLocalizationMap",
"RingHom.instFunLike",
"IsLocalization'",
"CommSemiring.toCommMonoid",
"Semiring.toNon... | false |
Lean.Elab.Command.Structure.StructFieldView.mk.injEq | Lean.Elab.Structure | [
"Eq.propIntro",
"Lean.Elab.Command.Structure.StructFieldViewDefault",
"Lean.Elab.Command.Structure.StructFieldView",
"Lean.injEq_helper",
"Lean.Syntax",
"And",
"Lean.Elab.Command.Structure.StructFieldView.mk.inj",
"Lean.Elab.Modifiers",
"Lean.Elab.Command.Structure.StructFieldView.mk",
"Eq.ndrec",... | true |
CommRingCat.Colimits.Relation.add_zero | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"CommRingCat",
"CommRingCat.instCategory",
"CategoryTheory.SmallCategory",
"CommRingCat.Colimits.Relation",
"CommRingCat.Colimits.Prequotient.add",
"CommRingCat.Colimits.Prequotient",
"CommRingCat.Colimits.Prequotient.zero",
"CommRingCat.Colimits.Relation.add_zero"
] | true |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.CtorHeaderResult.recOn | Lean.Elab.StructInst | [
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.CtorHeaderResult.rec",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.CtorHeaderResult.mk",
"Lean.Expr",
"Lean.Level",
"Array",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.CtorHeaderResult",
"List"
] | false |
TopologicalSpace.Opens.ext_iff | Mathlib.Topology.Sets.Opens | [
"HEq.refl",
"TopologicalSpace.Opens",
"Eq.casesOn",
"TopologicalSpace.Opens.ext",
"TopologicalSpace.Opens.instSetLike",
"TopologicalSpace",
"Iff",
"SetLike.coe",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"Set"
] | true |
Qq.Impl.MVarSynth.noConfusion | Qq.Macro | [
"Lean.MVarId",
"Lean.Expr",
"Qq.Impl.MVarSynth.casesOn",
"Eq.ndrec",
"Eq.refl",
"Qq.Impl.MVarSynth.noConfusionType",
"Eq",
"Qq.Impl.MVarSynth",
"Lean.LMVarId"
] | false |
PNat.sub_add_of_lt | Mathlib.Data.PNat.Basic | [
"Eq.mpr",
"Preorder.toLT",
"instLinearOrderPNat",
"congrArg",
"PartialOrder.toPreorder",
"HSub.hSub",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id",
"add_comm",
"instAddCommSemigroupPNat",
"instHAdd",
"instHSub",
"PNat.instSub",
"HAdd.hAdd",
"LT.lt",
"Eq.refl",
... | true |
TensorProduct.instModuleFstSnd._proof_1 | Mathlib.LinearAlgebra.TensorProduct.Graded.External | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Prod.fst",
"smulCommClass_self",
"CommRing.toCommSemiring",
"CommMonoid.toMonoid",
"Monoid.toSemigroup",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.toAddMonoid",
"Module",
"Co... | false |
_private.Lean.Meta.Tactic.Grind.Lookahead.0.Lean.Meta.Grind.lookahead.match_1 | Lean.Meta.Tactic.Grind.Lookahead | [
"Unit.unit",
"Lean.Meta.Grind.SplitStatus.notReady",
"Bool.true",
"Unit",
"Bool.casesOn",
"Lean.Meta.Grind.SplitStatus.casesOn",
"Lean.Meta.Grind.SplitStatus",
"Nat",
"Lean.Meta.Grind.SplitStatus.ready",
"Bool",
"Lean.Meta.Grind.SplitStatus.resolved",
"Bool.false"
] | false |
CategoryTheory.MorphismProperty.Arrow.changeProp | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.Comma.instCategory",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CategoryTheory.Functor.id",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf... | true |
AlgebraicGeometry.QuasiCompact.mk | Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap",
"CommR... | true |
CategoryTheory.Limits.ι_comp_colimitRightOpIsoUnopLimit_hom | Mathlib.CategoryTheory.Limits.Opposites | [
"CategoryTheory.Limits.limit.π",
"CategoryTheory.Limits.isColimitCoconeRightOpOfCone",
"CategoryTheory.Functor",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.Ha... | true |
ciSup_prod | Mathlib.Order.ConditionallyCompleteLattice.Indexed | [
"Iff.mpr",
"Eq.mpr",
"Set.mem_range",
"_private.Mathlib.Order.ConditionallyCompleteLattice.Indexed.0.ciSup_prod._proof_1_2",
"congrArg",
"iSup",
"ciSup_le_iff",
"PartialOrder.toPreorder",
"Prod.forall._simp_1",
"ConditionallyCompleteLattice",
"eq_of_forall_ge_iff",
"Preorder.toLE",
"Membersh... | true |
_private.Mathlib.Topology.Compactness.Compact.0.IsCompact.elim_directed_family_closed._simp_1_10 | Mathlib.Topology.Compactness.Compact | [
"Compl.compl",
"Membership.mem",
"Set.instCompl",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.mem_compl_iff",
"Set"
] | false |
Module.Finite.trans | Mathlib.RingTheory.Finiteness.Basic | [
"Iff.mpr",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"instHSMul",
"Submodule.restrictScalars_top",
"congrArg",
"DistribMulAction.toDistribSMul",
"Finset",
"IsScalarTower",
"Submodule.restrictScalars",
"AddMonoid.toAddZeroClass",
"Set.smul",
"Submodule.fg_def",
"Se... | true |
CategoryTheory.Functor.preimageIso | Mathlib.CategoryTheory.Functor.FullyFaithful | [
"CategoryTheory.Functor.preimage",
"CategoryTheory.Functor",
"CategoryTheory.Iso",
"CategoryTheory.Iso.mk",
"CategoryTheory.Functor.preimageIso._proof_4",
"CategoryTheory.Functor.preimageIso._proof_1",
"CategoryTheory.Iso.hom",
"CategoryTheory.Functor.Faithful",
"CategoryTheory.Iso.inv",
"Category... | true |
_private.Init.Data.Array.Sort.Lemmas.0.List.merge.match_1.eq_1 | Init.Data.Array.Sort.Lemmas | [
"List.cons",
"List",
"Eq.refl",
"_private.Init.Data.List.Sort.Basic.0.List.merge.match_1",
"Eq",
"List.nil"
] | true |
_private.Mathlib.Analysis.BoxIntegral.UnitPartition.0.BoxIntegral.unitPartition._aux_Mathlib_Analysis_BoxIntegral_UnitPartition___macroRules__private_Mathlib_Analysis_BoxIntegral_UnitPartition_0_BoxIntegral_unitPartition_termL_1 | Mathlib.Analysis.BoxIntegral.UnitPartition | [
"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.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Synta... | false |
Lean.Lsp.instFromJsonSymbolInformation | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolInformation",
"Lean.FromJson",
"Lean.FromJson.mk",
"Lean.Lsp.instFromJsonSymbolInformation.fromJson"
] | true |
_private.Mathlib.Tactic.Algebra.Basic.0.Mathlib.Tactic.Algebra.RingCompute.neg._proof_1 | Mathlib.Tactic.Algebra.Basic | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Qq.QuotedDefEq.unsafeIntro",
"List.nil"
] | false |
Real.holderConjugate_comm | Mathlib.Data.Real.ConjExponents | [
"Real",
"Real.HolderConjugate.symm",
"Iff",
"Iff.intro",
"Real.HolderConjugate"
] | true |
_private.Mathlib.Algebra.BigOperators.Group.Finset.Basic.0.Finset.eq_of_card_le_one_of_sum_eq._proof_1_1 | Mathlib.Algebra.BigOperators.Group.Finset.Basic | [
"Finset.mem_singleton",
"False",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"HEq.refl",
"Finset",
"Classical.byContradiction",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"AddCommMonoid",
"Iff",
"Exists.casesOn",
"Finset.instSetLike",
"congrFun",
"True",
"Finset.sum_singleton'",... | false |
Lean.Compiler.LCNF.CacheExtension.ctorIdx | Lean.Compiler.LCNF.CompilerM | [
"Nat",
"Hashable",
"BEq",
"Lean.Compiler.LCNF.CacheExtension"
] | false |
AddMonoidAlgebra.inhabited._aux_1 | Mathlib.Algebra.MonoidAlgebra.Defs | [
"Semiring",
"Zero.toOfNat0",
"AddMonoidAlgebra",
"Finsupp.instZero",
"OfNat.ofNat",
"Finsupp",
"MulZeroClass.toZero",
"instMulZeroClassOfSemiring"
] | false |
Filter.blimsup_congr | Mathlib.Order.LiminfLimsup | [
"Filter.eventually_inf_principal",
"Iff.mpr",
"Eq.mpr",
"Filter.blimsup_eq_limsup",
"congrArg",
"Filter.Eventually",
"setOf",
"ConditionallyCompleteLattice",
"Membership.mem",
"Filter.blimsup",
"id",
"Filter.instInf",
"Filter.limsup",
"congr",
"Filter.principal",
"Filter.limsup_congr",... | true |
Multiset.le_ndinsert_self._simp_1 | Mathlib.Data.Multiset.FinsetOps | [
"Multiset.le_ndinsert_self",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Multiset",
"LE.le",
"True",
"eq_true",
"Eq",
"Multiset.ndinsert",
"Multiset.instPartialOrder",
"DecidableEq"
] | false |
MultilinearMap.freeDFinsuppEquiv._proof_1 | Mathlib.LinearAlgebra.Multilinear.DFinsupp | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Algebra.to_smulCommClass",
"CommSemiring.toSemiring",
"instDistribSMul",
"DFinsupp.smulCommClass",
"AddMonoid.toAddZeroClass",
"DFinsupp.instSMulZeroClass",
"AddZeroClass.toAddZero",
"Algebra.id",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWithOne.to... | false |
_private.Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real.0.RealRMK.range_cut_partition._simp_1_8 | Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real | [
"HasSubset.Subset",
"Set.instInter",
"Set.inter_eq_right",
"Inter.inter",
"propext",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
Batteries.AssocList.find?.eq_def | Batteries.Data.AssocList | [
"Eq.mpr",
"Batteries.AssocList.toList.match_1",
"congrArg",
"Batteries.AssocList.find?",
"Batteries.AssocList.brecOn.eq",
"Batteries.AssocList.below",
"Option.some",
"id",
"Batteries.AssocList",
"_private.Batteries.Data.AssocList.0.Batteries.AssocList.toList.match_1.splitter",
"Batteries.AssocLi... | true |
Plausible.NamedBinder.eq_1 | Plausible.Testable | [
"String",
"Plausible.NamedBinder",
"Eq.refl",
"Eq"
] | true |
Quot.LindelofSpace | Mathlib.Topology.Compactness.Lindelof | [
"LindelofSpace",
"TopologicalSpace",
"instTopologicalSpaceQuot",
"Quot.lindelofSpace",
"Quot"
] | true |
CStarAlgebra.nnnorm_le_one_iff_of_nonneg | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order | [
"Eq.mpr",
"CStarAlgebra.toNonUnitalCStarAlgebra",
"Real.instLE",
"Real",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"NormedRing.toRing",
"CStarAlgebra.nnnorm_le_one_iff_of_nonneg._auto_1",
"congrArg",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"PartialOrder.toPreorder",
"AddGroupWithO... | true |
_private.Mathlib.Topology.Algebra.Nonarchimedean.Basic.0.NonarchimedeanGroup.prod_self_subset.match_1_1 | Mathlib.Topology.Algebra.Nonarchimedean.Basic | [
"Set.instSProd",
"OpenSubgroup",
"SProd.sprod",
"Group",
"OpenSubgroup.instSetLike",
"Exists",
"HasSubset.Subset",
"TopologicalSpace",
"Exists.casesOn",
"SetLike.coe",
"Exists.intro",
"Prod",
"Set.instHasSubset",
"Set"
] | false |
_private.Mathlib.LinearAlgebra.FixedSubmodule.0.LinearMap.fixedSubmodule_eq_top_iff._simp_1_1 | Mathlib.LinearAlgebra.FixedSubmodule | [
"LinearMap.instFunLike",
"RingHom",
"LinearMap.ext_iff",
"LinearMap",
"AddCommMonoid",
"propext",
"Semiring",
"Module",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe"
] | false |
measurable_set_iff | Mathlib.MeasureTheory.MeasurableSpace.Constructions | [
"measurable_pi_iff",
"Measurable",
"Membership.mem",
"Set.instMeasurableSpace",
"MeasurableSpace",
"Iff",
"Prop.instMeasurableSpace",
"Set.instMembership",
"Set"
] | true |
Lean.Meta.Grind.Arith.Linear.getCommRingInst | Lean.Meta.Tactic.Grind.Arith.Linear.Util | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.Grind.Arith.Linear.instMonadGetStructLinearM",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.Linear.LinearM.Context",
"Lean.Meta.Grind.State",
"ReaderT",
"String",
"Lean.Meta.State",
... | true |
TopCat.Presheaf.SubmonoidPresheaf.mk._flat_ctor | Mathlib.Topology.Sheaves.CommRingCat | [
"RingHom.instRingHomClass",
"CommRingCat.Hom.hom",
"Opposite",
"CommRingCat.carrier",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"CommRingCat",
"PartialOrder.toPreorder",
"TopologicalSpace.Ope... | false |
CommBialgCat.noConfusionType | Mathlib.Algebra.Category.CommBialgCat | [
"CommRing",
"CommSemiring.toSemiring",
"CommBialgCat.casesOn",
"CommRing.toCommSemiring",
"Bialgebra",
"HEq",
"Eq",
"CommBialgCat"
] | false |
CategoryTheory.Preadditive.toCommGrp_map | Mathlib.CategoryTheory.Preadditive.CommGrp_ | [
"CategoryTheory.CommGrp.toGrp",
"CategoryTheory.Preadditive.toCommGrp._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CommGrp.instCategory",
"CategoryTheory.Preadditive.instIsCommMonObj",
"CategoryTheory.InducedCategory.homMk",
"CategoryTheory.Grp.instCategory",
"C... | true |
_private.Mathlib.Algebra.BigOperators.Group.Multiset.Basic.0.Multiset.prod_nsmul.match_1_1 | Mathlib.Algebra.BigOperators.Group.Multiset.Basic | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Mathlib.Meta.FunProp.GeneralTheorem.mk.sizeOf_spec | Mathlib.Tactic.FunProp.Types | [
"Lean.Meta.RefinedDiscrTree.LazyEntry._sizeOf_inst",
"Mathlib.Meta.FunProp.GeneralTheorem.mk",
"instOfNatNat",
"Lean.Meta.RefinedDiscrTree.Key",
"Mathlib.Meta.FunProp.GeneralTheorem._sizeOf_inst",
"List",
"instHAdd",
"Lean.Meta.RefinedDiscrTree.LazyEntry",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Na... | true |
Lean.Grind.CommRing.Poly.denoteAsIntModuleExpr._unsafe_rec | Lean.Meta.Tactic.Grind.Arith.Linear.DenoteExpr | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.Grind.Arith.Linear.instMonadGetStructLinearM",
"Lean.Grind.CommRing.Poly",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.Linear.LinearM.Context",
"Lean.Meta.Grind.State",
"ReaderT",
"... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKey?_insertMany_list_of_contains_eq_false._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 |
PSet.brecOn.go | Mathlib.SetTheory.ZFC.PSet | [
"PSet.rec",
"PProd.mk",
"PSet.mk",
"PSet.below",
"PSet",
"PProd"
] | true |
measurableSet_iSup_of_mem_piiUnionInter | Mathlib.MeasureTheory.PiSystem | [
"piiUnionInter",
"MeasurableSpace.instLE",
"MeasurableSet",
"iSup",
"Set.iInter",
"Finset",
"le_iSup₂",
"setOf",
"Membership.mem",
"Exists",
"CompleteLattice.toConditionallyCompleteLattice",
"Finset.measurableSet_biInter",
"HasSubset.Subset",
"LE.le",
"MeasurableSpace",
"Exists.casesOn... | true |
analyticAt_pi_iff | Mathlib.Analysis.Analytic.Constructions | [
"Eq.mpr",
"analyticWithinAt_pi_iff",
"NormedSpace",
"congrArg",
"Set.univ",
"id",
"AnalyticWithinAt",
"Pi.normedAddCommGroup",
"Iff",
"Fintype",
"AnalyticAt",
"congr",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"Pi.normedSpace",
"NormedAddCommGroup.toSeminormed... | true |
Topology.WithLower.instLinearOrder | Mathlib.Topology.Order.LowerUpperTopology | [
"LinearOrder",
"Topology.WithLower"
] | true |
Matroid.isBasis_union_iff_indep_closure | Mathlib.Combinatorics.Matroid.Closure | [
"Matroid.Indep.isBasis_closure",
"Matroid.IsBasis.isBasis_subset",
"Set.subset_union_right",
"Set.instUnion",
"Matroid.Indep",
"HasSubset.Subset.trans",
"Set.instIsTransSubset",
"Matroid.subset_closure",
"HasSubset.Subset",
"Set.union_subset",
"Set.subset_union_left",
"Matroid.Indep.subset_gro... | true |
_private.Init.Data.Nat.Lemmas.0.Nat.one_mod_eq_one._proof_1_3 | Init.Data.Nat.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.combo_sat'",
"id",
"instDecidableEqBool",
"Int... | false |
Nat.unpair_add_le | Mathlib.Data.Nat.Pairing | [
"LE.le.trans_eq",
"Nat.unpair",
"LE.le",
"instLENat",
"Prod.fst",
"Nat.pair",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Nat.pair_unpair",
"instAddNat",
"Nat.add_le_pair",
"Prod.snd"
] | true |
CategoryTheory.Functor.isoSum_hom_app_inl | Mathlib.CategoryTheory.Sums.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.sum",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.isoSum",
"CategoryTheory.CategoryStruct.id",
"Sum",
"Sum.inl",
"CategoryTheory.Sum.inr_",
"CategoryT... | true |
CategoryTheory.StructuredArrow.toCostructuredArrow._proof_4 | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"Quiver.Hom.unop",
"CategoryTheory.StructuredArrow.hom",
"id",
"CategoryTheory.CostructuredArrow",
"CategoryTheory.CostructuredArrow.homMk",
"CategoryTheo... | false |
Finset.interior_iInter | Mathlib.Topology.Closure | [
"Set.iInter",
"Finset",
"Membership.mem",
"Set.Finite.interior_biInter",
"TopologicalSpace",
"SetLike.coe",
"Finset.instSetLike",
"interior",
"Finset.finite_toSet",
"Eq",
"SetLike.instMembership",
"Set"
] | true |
Equiv.Perm.not_solvable | Mathlib.GroupTheory.Solvable | [
"Eq.mpr",
"Cardinal.lift_mk_le",
"IsSolvable",
"Cardinal.mk_fin",
"Cardinal",
"congrArg",
"Nat.instAtLeastTwoHAddOfNat",
"Cardinal.lift",
"Cardinal.mk",
"id",
"Nonempty.some",
"solvable_of_solvable_injective",
"instOfNatNat",
"LE.le",
"Nat.cast",
"Cardinal.instLE",
"Function.Embeddin... | true |
Lean.Lsp.ServerCapabilities.definitionProvider._default | Lean.Data.Lsp.Capabilities | [
"id",
"Bool",
"Bool.false"
] | false |
Inseparable.specializes | Mathlib.Topology.Inseparable | [
"Specializes",
"PartialOrder.toPreorder",
"nhds",
"Eq.le",
"TopologicalSpace",
"Filter",
"Inseparable",
"Filter.instPartialOrder"
] | true |
Lean.Syntax.Range.contains | Lean.Syntax | [
"Lean.Syntax.Range",
"String.instLTRaw",
"Bool.and",
"instDecidableEqBool",
"LE.le",
"String.Pos.Raw",
"Lean.Syntax.Range.stop",
"Bool.true",
"String.instDecidableLeRaw",
"String.instDecidableLtRaw",
"LT.lt",
"String.instLERaw",
"Bool",
"Lean.Syntax.Range.start",
"optParam",
"Bool.fals... | true |
Submonoid.mem_sup_right | Mathlib.Algebra.Group.Submonoid.Membership | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"PartialOrder.toPreorder",
"SetLike.le_def",
"Preorder.toLE",
"Membership.mem",
"SemilatticeSup.toMax",
"id",
"le_sup_right",
"LE.le",
"Submonoid.instCompleteLattice",
"instIsConcreteLE",
"Max.max",
"Submono... | true |
_private.Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension.0.ExistsContDiffBumpBase.u_exists._simp_1_2 | Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | [
"Classical.not_not",
"propext",
"Eq",
"Not"
] | false |
AddMonCat.FilteredColimits.colimitZero | Mathlib.Algebra.Category.MonCat.FilteredColimits | [
"CategoryTheory.Functor",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Nonempty.some",
"CategoryTheory.SmallCategory",
"AddMonCat.str",
"AddMonCat",
"AddMonCat.instCategory",
"AddZero.toZero",
"CategoryTheory.IsFiltered.nonempty",
"Zero.mk",
"CategoryTheory.IsFiltered",
"Zero.toOfN... | true |
DirectSum.IsInternal.addSubmonoid_iSup_eq_top | Mathlib.Algebra.DirectSum.Basic | [
"AddSubmonoid.subtype",
"Eq.mpr",
"AddSubmonoid.instTop",
"DirectSum.IsInternal",
"AddMonoidHom.instAddMonoidHomClass",
"AddSubmonoid.instAddSubmonoidClass",
"AddSubmonoid.instCompleteLattice",
"congrArg",
"iSup",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.mrange_eq_top",
"Membership.mem",
"C... | true |
instCStarAlgebraProd._proof_7 | Mathlib.Analysis.CStarAlgebra.Classes | [
"CStarAlgebra.toNonUnitalCStarAlgebra",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"HMul.hMul",
"NonUnitalNonAssocRing.toMul",
"AddMonoid.toZero",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"instNonUnitalCStarAlgebraProd",
"NonUn... | false |
lpBCFₗᵢ._proof_3 | Mathlib.Analysis.Normed.Lp.LpEquiv | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"IsBoundedSMul",
"AddZeroClass.toAddZero",
... | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.ToInt.0.Lean.Meta.Grind.Arith.Cutsat.mkBinOpThms | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToInt | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.instMonadEnvOfMonadLift",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.isFinite",
"Lean.Meta.Grind.Arith.Cutsat.ToIntInfo.type",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.Cutsat.ToIntInfo",
"Lean.Meta.Grind.Arith.Cutsat.ToIntM.Context",
"Lean.Me... | true |
CategoryTheory.instIsDiscreteOpposite | Mathlib.CategoryTheory.Discrete.Basic | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsDiscrete",
"CategoryTheory.obj_ext_of_isDiscrete",
"CategoryTheory.IsDiscrete.mk",
"inferInstance",
"CategoryTheory.subsingleton_of_unop",
"Opposite.op",
"Opposite.casesOn",
"Eq.ndrec",
"CategoryTheory.Catego... | true |
_private.Mathlib.Data.Finsupp.MonomialOrder.DegLex.0.Finsupp.DegLex.single_strictAnti._simp_1_2 | Mathlib.Data.Finsupp.MonomialOrder.DegLex | [
"Nat.instMulZeroClass",
"Preorder.toLT",
"Equiv.instEquivLike",
"Lex",
"LinearOrder",
"PartialOrder.toPreorder",
"Finsupp.instLTLex",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Equiv",
"Finsupp.Lex.single_lt_iff",
"instOfNatNat",
"Nat",
"LT.lt",
"propext",
"instLTNat... | false |
_private.Init.Data.List.Erase.0.List.eraseP_sublist.match_1_1 | Init.Data.List.Erase | [
"Membership.mem",
"Exists",
"Or.casesOn",
"List.cons",
"And.casesOn",
"Bool.true",
"instHAppendOfAppend",
"List",
"And",
"Exists.casesOn",
"List.instMembership",
"And.intro",
"Exists.intro",
"Bool",
"Or.inl",
"Or",
"List.instAppend",
"List.eraseP",
"Eq",
"Not",
"HAppend.hAppe... | false |
AlgebraicGeometry.UniversallyOpen.rec | Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.UniversallyOpen",
"IsOpenMap",
"AlgebraicGeometry.UniversallyOpen.mk",
"CategoryTheory.MorphismProperty.universally",
"AlgebraicGeometry.topologically",
"CategoryTheory.Category.toCategoryStruct",
... | false |
Hyperreal.infinitePos_abs_iff_infinite | Mathlib.Analysis.Real.Hyperreal | [
"Hyperreal.instField",
"AddGroupWithOne.toAddGroup",
"abs",
"Hyperreal.infinite_abs_iff",
"Field.toDivisionRing",
"Hyperreal.InfinitePos",
"DistribLattice.toLattice",
"Hyperreal.instLinearOrder",
"DivisionRing.toRing",
"Hyperreal.infinitePos_abs_iff_infinite_abs",
"Iff",
"Hyperreal.Infinite",
... | true |
AlgebraicGeometry.Scheme.IdealSheafData.glueDataT'Aux._proof_1 | Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme | [
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme.homOfLE",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjι",
"AlgebraicGeometry.PresheafedSpace.carrier",
"AlgebraicGeometry.Scheme.IdealSheaf... | false |
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