name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.subterminalsEquivMonoOverTerminal._proof_7 | Mathlib.CategoryTheory.Subterminal | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Over",
"CategoryTheory.instCategorySubterminals",
"CategoryTheory.subterminalsEquivMonoOverTerminal._proof_4",
"CategoryTheory.subterminalsEquivMonoOverTerminal._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Categ... | false |
CategoryTheory.Limits.MonoFactorisation.mk._flat_ctor | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.MonoFactorisation.mk",
"autoParam",
"CategoryTheory.Limits.MonoFactorisation",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.MonoFactorisat... | false |
_private.Lean.Meta.WHNF.0.Lean.Meta.unfoldProjInstWhenInstances?._sparseCasesOn_1 | Lean.Meta.WHNF | [
"Lean.Meta.TransparencyMode.ctorIdx",
"Nat.ne_of_beq_eq_false",
"Lean.Meta.TransparencyMode.none",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Meta.TransparencyMode",
"Lean.Meta.TransparencyMode.default",
"Lean.Meta.TransparencyMode.all",
"Nat.land",
"Lean.Meta.TransparencyMode.inst... | false |
_private.Mathlib.Algebra.SkewMonoidAlgebra.Support.0.SkewMonoidAlgebra.support_mul_single_eq_image._simp_1_1 | Mathlib.Algebra.SkewMonoidAlgebra.Support | [
"Finset.mem_image",
"Finset",
"Membership.mem",
"Exists",
"And",
"Finset.instSetLike",
"propext",
"Eq",
"Finset.image",
"SetLike.instMembership",
"DecidableEq"
] | false |
_private.Mathlib.RingTheory.HahnSeries.Summable.0.HahnSeries.instField._simp_4 | Mathlib.RingTheory.HahnSeries.Summable | [
"ZeroHom.funLike",
"HahnSeries.single_zero_nnratCast",
"NNRatCast",
"HahnSeries.single",
"PartialOrder",
"HahnSeries.instZero",
"NNRat",
"ZeroHom",
"Zero.toOfNat0",
"HahnSeries.instNNRatCast",
"OfNat.ofNat",
"Eq.symm",
"NNRat.cast",
"HahnSeries",
"Eq",
"DFunLike.coe",
"Zero"
] | false |
SimpleGraph.isBridge_iff | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"SimpleGraph.deleteEdges",
"Sym2.mk",
"SimpleGraph.Adj",
"Iff.rfl",
"Set.instSingletonSet",
"SimpleGraph.IsBridge",
"SimpleGraph",
"And",
"Iff",
"Singleton.singleton",
"Sym2",
"Not",
"SimpleGraph.Reachable",
"Set"
] | true |
ProofWidgets.Html.ofComponent | ProofWidgets.Data.Html | [
"ProofWidgets.Html",
"ProofWidgets.Html.component",
"String",
"ProofWidgets.Component",
"instHashableString",
"Array",
"Lean.Server.RpcEncodable",
"Hashable.hash",
"Lean.Server.RpcEncodable.rpcEncode",
"Lean.Widget.Module.javascript",
"ProofWidgets.Component.toModule",
"ProofWidgets.Component.... | true |
ENat.map | Mathlib.Data.ENat.Basic | [
"WithTop.map",
"Nat",
"ENat",
"WithTop"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.size_insertIfNew._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
Std.DTreeMap.Raw.get?_filterMap | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.get?",
"Std.DTreeMap.Raw.filterMap",
"Std.DTreeMap.Internal.Impl.get?_filterMap!",
"Ord.mk",
"Ordering",
"Option.bind",
"Std.TransCmp",
"Std.DTreeMap.Raw.WF.out",
"Std.LawfulEqCmp",
"Std.DTreeMap.Raw.inner",
"Eq",
"Std.DTreeMap.Raw.WF",
"Option",
"Std.DTreeMap.Raw"
] | true |
HomotopicalAlgebra.Fibration | Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Category.toCategoryStruct",
"HomotopicalAlgebra.Fibration.mk",
"CategoryTheory.Category",
"HomotopicalAlgebra.CategoryWithFibrations"
] | true |
ONote.addAux.match_3 | Mathlib.SetTheory.Ordinal.Notation | [
"Unit.unit",
"ONote.oadd",
"namedPattern",
"ONote.zero",
"Unit",
"Eq.refl",
"Eq",
"ONote",
"ONote.casesOn",
"PNat"
] | false |
_private.Lean.Server.InfoUtils.0.Lean.Elab.InfoTree.foldInfoTree.go._unsafe_rec | Lean.Server.InfoUtils | [
"Lean.Elab.InfoTree",
"Lean.MVarId",
"Lean.Elab.PartialContextInfo",
"Lean.Elab.Info.updateContext?",
"instOfNatNat",
"Lean.Elab.PartialContextInfo.mergeIntoOuter?",
"Lean.PersistentArray",
"Lean.PersistentArray.foldl",
"Lean.Elab.ContextInfo",
"_private.Lean.Server.InfoUtils.0.Lean.Elab.InfoTree.... | false |
CategoryTheory.StructuredArrow.commaMapEquivalenceInverse._proof_4 | Mathlib.CategoryTheory.Comma.StructuredArrow.CommaMap | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.C... | false |
Real.stronglyMeasurable_sinc | Mathlib.MeasureTheory.Function.SpecialFunctions.Sinc | [
"Real",
"Measurable.stronglyMeasurable",
"Real.measurable_sinc",
"PseudoMetricSpace.toUniformSpace",
"PseudoEMetricSpace.pseudoMetrizableSpace",
"Real.sinc",
"EMetricSpace.toPseudoEMetricSpace",
"BorelSpace.opensMeasurable",
"Real.measurableSpace",
"Real.metricSpace",
"instSecondCountableTopolog... | true |
GroupFilterBasis.nhds_one_hasBasis | Mathlib.Topology.Algebra.FilterBasis | [
"Eq.mpr",
"GroupFilterBasis.nhds_one_eq",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"FilterBasis.hasBasis",
"Group",
"GroupFilterBasis",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"nhds",
"id",
"Filter.HasBasis",
"GroupFilterBa... | true |
Unitization.mem_unitsFstOne | Mathlib.Algebra.Algebra.Spectrum.Quasispectrum | [
"Units.val",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Units",
"AddZeroClass.toAddZero",
"Unitization.instMonoid",
"DistribSMul.toSMulZero... | true |
CategoryTheory.Functor.whiskeringLeft₃Map._proof_4 | Mathlib.CategoryTheory.Whiskering | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.whiskerLeft",
"id",
"CategoryTheory.Functor.whiskeringLeft₃Map._proof_2",
"CategoryTheory.Functor.map",
"Catego... | false |
Matrix.diagonal_mul | Mathlib.Data.Matrix.Mul | [
"HMul.hMul",
"Matrix",
"Matrix.instHMulOfFintypeOfMulOfAddCommMonoid",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"diagonal_dotProduct",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Fintype",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"NonUnitalNonAssocSemiring",
"Eq",
"Matrix.d... | true |
Submodule.instSemilatticeSupSubtypeFG | Mathlib.RingTheory.Finiteness.Basic | [
"SemilatticeSup.mk",
"Submodule",
"Lattice.toSemilatticeSup",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"Subtype",
"Submodule.instPartialOrder",
"Submodule.instSemilatticeSupSubtypeFG._proof_... | true |
CategoryTheory.SmallObject.SuccStruct.extendToSucc.objIso._proof_1 | Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | [
"Order.succ",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Set.Elem",
"DistribLattice.toLattice",
"LE.le",
"Set.Iic",
"Order.le_succ",
"LE.le.trans",
"SuccOrder",
"Subtype.val",
"Set.instMembership",
"instDistribLatticeO... | false |
Lean.Meta.Tactic.TryThis.SuggestionText.string.noConfusion | Lean.Meta.TryThis | [
"String",
"Lean.Meta.Tactic.TryThis.SuggestionText.noConfusion",
"id",
"Lean.Meta.Tactic.TryThis.SuggestionText",
"Lean.Meta.Tactic.TryThis.SuggestionText.string",
"Eq"
] | false |
Std.DTreeMap.Raw.isSome_minKey?_of_mem | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Internal.Impl.isSome_minKey?_of_mem",
"Std.DTreeMap.Raw.instMembership",
"Ord.mk",
"Std.DTreeMap.Raw.minKey?",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Bool",
"Option.isSome",
"Eq",
"Std.DTreeMap.Raw.WF",... | true |
Complex.dist_le_dist_of_mapsTo_ball | Mathlib.Analysis.Complex.Schwarz | [
"GroupWithZero.toMonoidWithZero",
"False",
"Real.instLE",
"Real",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"NormedSpace",
"eq_false",
"Real.instZero",
"congrArg",
"Real.instDivInvMonoid",
"NormedSpace.toModule",
"C... | true |
CategoryTheory.Paths.induction | Mathlib.CategoryTheory.PathCategory.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"CategoryTheory.CategoryStruct.id",
"Prefunctor.map",
"CategoryTheory.CategoryStruct.comp",
"Quiver",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Paths.induction_fi... | true |
PosNum.noConfusionType | Mathlib.Data.Num.Basic | [
"PosNum.casesOn",
"PosNum.one.elim",
"PosNum.ctorIdx",
"PosNum.bit0.elim",
"PosNum.bit1.elim",
"dite",
"Nat",
"Nat.decEq",
"PosNum",
"Eq",
"Not"
] | false |
Aesop.Queue.recOn | Aesop.Search.Queue.Class | [
"Aesop.Queue.mk",
"Array",
"Aesop.GoalRef",
"Aesop.Queue",
"Aesop.Queue.rec",
"Prod",
"BaseIO",
"Option"
] | false |
FirstOrder.Language.Substructure.Simps.coe | Mathlib.ModelTheory.Substructures | [
"FirstOrder.Language.Substructure.instSetLike",
"FirstOrder.Language.Substructure",
"FirstOrder.Language.Structure",
"SetLike.coe",
"FirstOrder.Language",
"Set"
] | true |
WithConv.symm_congrLinearEquiv | Mathlib.Algebra.WithConv | [
"LinearEquiv.symm",
"AddCommMonoid",
"WithConv.instModule",
"RingHomInvPair.ids",
"WithConv.congrLinearEquiv",
"LinearEquiv",
"Semiring",
"WithConv",
"Module",
"RingHom.id",
"WithConv.instAddCommMonoid",
"Semiring.toNonAssocSemiring",
"Eq",
"rfl"
] | true |
DirectedOn.sSup_le | Mathlib.Order.CompletePartialOrder | [
"lowerBounds",
"DirectedOn.isLUB_sSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"DirectedOn",
"Membership.mem",
"upperBounds",
"LE.le",
"And.right",
"CompletePartialOrder.toSupSet",
"Set.instMembership",
"CompletePartialOrder.toPartialOrder",
"SupSet.sSup",
"CompletePartialOrder",
"S... | true |
Lean.LocalContext.mkLambda | Lean.LocalContext | [
"Lean.Expr",
"Array",
"Bool.true",
"Lean.LocalContext.mkBinding",
"Bool",
"optParam",
"Bool.false",
"Lean.LocalContext"
] | true |
UniformEquiv.prodComm | Mathlib.Topology.UniformSpace.Equiv | [
"UniformSpace",
"instUniformSpaceProd",
"Equiv.prodComm",
"Equiv",
"UniformEquiv.mk",
"UniformEquiv.prodComm._proof_1",
"Prod",
"UniformEquiv.prodComm._proof_2",
"UniformEquiv"
] | true |
Std.ExtDTreeMap.getKey!_eq_default_of_contains_eq_false | Std.Data.ExtDTreeMap.Lemmas | [
"Inhabited.default",
"Std.DTreeMap",
"Ordering",
"Std.DTreeMap.getKey!_eq_default_of_contains_eq_false",
"Std.TransCmp",
"Std.ExtDTreeMap.getKey!",
"Std.ExtDTreeMap.contains",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Bool",
"Inhabited",
"Bool.false",
"Eq"
] | true |
Lean.Meta.Grind.Arith.Linear.EqCnstrProof.neg.elim | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"PULift.up",
"Lean.Meta.Grind.Arith.Linear.EqCnstr",
"Lean.Meta.Grind.Arith.Linear.EqCnstrProof.ctorIdx",
"Nat",
"Lean.Meta.Grind.Arith.Linear.EqCnstrProof",
"Lean.Meta.Grind.Arith.Linear.EqCnstrProof.neg",
"Lean.Meta.Grind.Arith.Linear.EqCnstrProof.ctorElim",
"Eq.symm",
"Eq"
] | false |
SkewMonoidAlgebra.domCongrAlg.congr_simp | Mathlib.Algebra.SkewMonoidAlgebra.Lift | [
"Monoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"MulEquiv.instEquivLike",
"Monoid.toMulOneClass",
"DistribMulAction.toDistribSMul",
"SkewMonoidAlgebra.domCongrAlg",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"Eq.rec",
"AddZeroClass.toAddZero",
"MulOne.toMul",
... | true |
OpenPartialHomeomorph.lift_openEmbedding_source | Mathlib.Topology.OpenPartialHomeomorph.Constructions | [
"TopologicalSpace",
"Topology.IsOpenEmbedding",
"Nonempty",
"PartialEquiv.source",
"Set.image",
"OpenPartialHomeomorph.toPartialEquiv",
"Eq",
"OpenPartialHomeomorph",
"rfl",
"OpenPartialHomeomorph.lift_openEmbedding",
"Set"
] | true |
ArithmeticFunction.coe_zeta_mul_comm | Mathlib.NumberTheory.ArithmeticFunction.Zeta | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"ArithmeticFunction.ext",
"instHDiv",
"HMul.hMul",
"Nat.divisorsAntidiagonal",
"ArithmeticFunction.instFunLikeNat",
"ArithmeticFunction.instMul",
"congrArg",
"ArithmeticFunction.zeta",
"Finset",
"AddMonoid.toAddZero... | true |
_private.Mathlib.Analysis.MeanInequalities.0.ENNReal.inner_le_weight_mul_Lp_of_nonneg._simp_1_5 | Mathlib.Analysis.MeanInequalities | [
"Real",
"ENNReal.instPowReal",
"NNReal",
"ENNReal.toNNReal",
"ENNReal.toNNReal_rpow",
"HPow.hPow",
"NNReal.instPowReal",
"ENNReal",
"instHPow",
"Eq.symm",
"Eq"
] | false |
Lean.Meta.ApplyConfig.synthAssignedInstances | Init.Meta.Defs | [
"Lean.Meta.ApplyConfig",
"Bool"
] | true |
FrameHom.id_apply | Mathlib.Order.Hom.CompleteLattice | [
"FrameHom",
"FrameHom.instFunLike",
"CompleteLattice",
"Eq",
"DFunLike.coe",
"rfl",
"FrameHom.id"
] | true |
_private.Mathlib.RingTheory.DividedPowerAlgebra.Init.0.DividedPowerAlgebra.dp_mul._simp_1_2 | Mathlib.RingTheory.DividedPowerAlgebra.Init | [
"instHSMul",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"Nat",
"AddMonoid",
"HSMul.hSMul",
"Eq.symm",
"map_nsmul",
"Eq",
"DFunLike.coe",
"FunLike"
] | false |
NNReal.Lp_add_le | Mathlib.Analysis.MeanInequalities | [
"add_mul",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"False",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"instReflLe",
"congrArg",
"Finset.sum_add_distri... | true |
groupHomology.chainsMap₃ | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"Rep.V",
"CommRing",
"MonoidHom.instFunLike",
"Finsupp.module",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"AddMonoid.toAddZeroClass",
"Group",
"Rep.instCa... | true |
Lean.Elab.Command.elabPrint._regBuiltin.Lean.Elab.Command.elabPrint.declRange_3 | Lean.Elab.Print | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"IO",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk",
"Lean.Name.mkStr4"
] | false |
_private.Mathlib.RingTheory.FreeCommRing.0.FreeCommRing.exists_finite_support.match_1_1 | Mathlib.RingTheory.FreeCommRing | [
"FreeCommRing.IsSupported",
"FreeCommRing",
"Set.Finite",
"Exists",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"Set"
] | false |
MeasureTheory.«term∫⋯∫⁻__,_» | Mathlib.MeasureTheory.Integral.Marginal | [
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
_private.Mathlib.Analysis.Calculus.Rademacher.0.LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul._simp_1_2 | Mathlib.Analysis.Calculus.Rademacher | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
OrderEmbedding.supIrredLowerSet_apply | Mathlib.Order.Birkhoff | [
"Lattice.toSemilatticeSup",
"LowerSet.completeLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toConditionallyCompleteLattice",
"PartialOrder",
"Subtype",
"LowerSet.instPartialOrder",
"Subtype.mk",
"OrderEmbedding",
"ConditionallyCompleteLattice.toLattice",
"LowerSet",
... | true |
AlgHom.norm_apply_le_self_mul_norm_one | Mathlib.Analysis.Normed.Algebra.Spectrum | [
"Norm.norm",
"Real.instLE",
"Real",
"CompleteSpace",
"NormedRing.toRing",
"HMul.hMul",
"AlgHom.apply_mem_spectrum",
"spectrum.norm_le_norm_mul_of_mem",
"AddGroupWithOne.toAddMonoidWithOne",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Field.instIsLocalRing",
"Algebra.id",
"N... | true |
RootPairing.InvariantForm.mk.sizeOf_spec | Mathlib.LinearAlgebra.RootSystem.RootPositive | [
"CommRing",
"Semiring.toModule",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"RootPairing.InvariantForm",
"instSizeOfDefault",
"LinearMap.IsOrthogonal",
"AddCommGroup",
"Ne",
"instOfNatNat",
"LinearMap.module",
"RootPairing.Inv... | true |
CategoryTheory.Bicategory.congr_whiskerLeft | Mathlib.CategoryTheory.Bicategory.EqToHom | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Bicategory.congr_whiskerLeft._proof_1",
"CategoryTheory.CategoryStruct.id",
"Eq.rec",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Category.comp_id",
"CategoryTheory.Bicat... | true |
_private.Mathlib.Algebra.Homology.CochainComplexOpposite.0.CochainComplex.homotopyUnop_hom_eq._proof_1_1 | Mathlib.Algebra.Homology.CochainComplexOpposite | [
"Lean.RArray.leaf",
"False",
"congrArg",
"Classical.byContradiction",
"Lean.RArray.branch",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Int.Linear.Poly.num",
"Int.Linear.Poly.add",
"Int.Linear.norm_eq",
"Int.Linear.diseq_unsat",
"Bool.true",
"instHAdd",
"instOfNat"... | false |
RestrictGermPredicate._proof_1 | Mathlib.Topology.Germ | [
"Iff.mpr",
"Eq.mpr",
"Filter.Germ.ofFun",
"congrArg",
"Filter.Eventually",
"Filter.Eventually.eventually_nhds",
"nhds",
"Filter.Eventually.and",
"Filter.EventuallyEq",
"id",
"Filter.Germ.coe_eq",
"And.casesOn",
"Filter.Eventually.mono",
"TopologicalSpace",
"And",
"Filter.Germ",
"Eq",... | false |
nhdsKer_prod | Mathlib.Topology.NhdsKer | [
"Set.instSProd",
"Eq.mpr",
"_private.Mathlib.Topology.NhdsKer.0.nhdsKer_prod._simp_1_1",
"Trans.trans",
"SProd.sprod",
"congrArg",
"HEq.refl",
"instTopologicalSpaceProd",
"Membership.mem",
"Set.biUnion_of_singleton",
"Eq.rec",
"Set.instSingletonSet",
"Eq.casesOn",
"id",
"Prod.mk",
"Set... | true |
_private.Mathlib.Algebra.Module.ZLattice.Basic.0.ZSpan.fundamentalDomain_ae_parallelepiped._simp_1_1 | Mathlib.Algebra.Module.ZLattice.Basic | [
"SetLike",
"neg_mem_iff",
"Membership.mem",
"InvolutiveNeg",
"NegMemClass",
"propext",
"InvolutiveNeg.toNeg",
"Eq",
"SetLike.instMembership",
"Neg.neg"
] | false |
Lean.Widget.instInhabitedMsgEmbed | Lean.Widget.InteractiveDiagnostic | [
"Lean.Widget.instInhabitedMsgEmbed.default",
"Lean.Widget.MsgEmbed",
"Inhabited",
"Inhabited.mk"
] | true |
deriv_abs | Mathlib.Analysis.Calculus.Deriv.Abs | [
"SignType.cast",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"Semiring.toModule",
"Real.lattice",
"Real.denselyNormedField",
"Real.instZero",
"Real.instRCLike",
"abs",
"congrArg",
"deriv",
"PartialOrder.toPreorder",
"HasDerivAt.deriv",
"Real.decidableLT",
"SignType.instLinearO... | true |
_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.checkNextPatternTypes | Lean.Meta.Match.Match | [
"Pure.pure",
"Lean.Meta.Match.Alt.fvarDecls",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.Match.Problem.vars",
"Lean.Meta.Match.Alt",
"Lean.Meta.Match.Alt.ref",
"instForInOfForIn'",
"instMonadControlTOfPure",
"String",
"Lean.Meta.... | true |
ball_div | Mathlib.Analysis.Normed.Group.Pointwise | [
"Real",
"DivInvMonoid.toInv",
"instHSMul",
"instHDiv",
"instSMulOfMul",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"SeminormedCommGroup.toPseudoMetricSpace",
"ball_mul",
"DivisionMonoid.toDivInvOneMonoid",
"MulOn... | true |
CategoryTheory.ShortComplex.HomologyData.rec | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.RightHomologyData",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.RightHomologyData.H",
"CategoryTheory.Iso",
"... | false |
CategoryTheory.Abelian.SpectralObject.dHomologyData_iso_hom | Mathlib.Algebra.Homology.SpectralObject.Homology | [
"CategoryTheory.ComposableArrows.fourδ₄Toδ₃",
"CategoryTheory.ShortComplex.Exact.gIsCokernel",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.Exact.fIsKernel",
"CategoryTheory.Abelian.SpectralObject.E",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.ComposableArrows.fourδ₁... | true |
ProbabilityTheory.isProbabilityMeasure_gammaMeasure | Mathlib.Probability.Distributions.Gamma | [
"MeasureTheory.Measure.withDensity",
"Real",
"MeasureTheory.Measure",
"ProbabilityTheory.gammaMeasure",
"MeasurableSet",
"ProbabilityTheory.gammaPDF",
"Real.instZero",
"congrArg",
"Set.univ",
"MeasureTheory.MeasureSpace.toMeasurableSpace",
"Real.instLT",
"Real.measureSpace",
"MeasureTheory.M... | true |
CategoryTheory.Abelian.SpectralObject.d_map_fourδ₄Toδ₃._auto_1 | Mathlib.Algebra.Homology.SpectralObject.EpiMono | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
instAddCommMonoidLex.eq_1 | Mathlib.Algebra.Order.Group.Synonym | [
"instAddCommMonoidLex",
"Lex",
"AddCommMonoid",
"Eq.refl",
"Eq"
] | true |
DirectSum.ext_component_iff | Mathlib.Algebra.DirectSum.Module | [
"Eq.mpr",
"instAddCommMonoidDirectSum",
"DirectSum.instModule",
"congrArg",
"LinearMap.instFunLike",
"DirectSum.component",
"id",
"LinearMap",
"AddCommMonoid",
"Iff",
"Iff.intro",
"Semiring",
"Eq.refl",
"DirectSum.ext_component",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",... | true |
_private.Mathlib.Data.Finset.Lattice.Prod.0.Finset.prodMk_sup'_sup'._simp_1_2 | Mathlib.Data.Finset.Lattice.Prod | [
"SProd.sprod",
"Finset",
"Membership.mem",
"Prod.fst",
"And",
"Finset.instSProd",
"Finset.instSetLike",
"propext",
"Prod",
"Eq",
"Prod.snd",
"Finset.mem_product",
"SetLike.instMembership"
] | false |
CategoryTheory.Limits.end_.condition_assoc | Mathlib.CategoryTheory.Limits.Shapes.End | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.end_.π",
"CategoryTheory.Limits.end_.condition",
"Eq.mp",
"id",
"Mathlib.Tacti... | true |
Nat.ceil_lt_add_one | Mathlib.Algebra.Order.Floor.Semiring | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Eq.ge",
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Nat.lt_succ_self",
"Distrib.toAdd",
"Nat.ceil_add_one",
"AddMonoidWithOne.toNat... | true |
Submodule.botEquivPUnit._proof_1 | Mathlib.Algebra.Module.Submodule.Lattice | [
"Submodule",
"Function.LeftInverse",
"Membership.mem",
"Subtype",
"Bot.bot",
"AddCommMonoid",
"Submodule.instBot",
"PUnit",
"Submodule.setLike",
"Semiring",
"Zero.toOfNat0",
"Submodule.zero",
"PUnit.unit",
"Module",
"OfNat.ofNat",
"SetLike.instMembership",
"Submodule.bot_ext"
] | false |
Lean.Meta.DefEqArgsFirstPassResult.failed.sizeOf_spec | Lean.Meta.ExprDefEq | [
"instOfNatNat",
"Lean.Meta.DefEqArgsFirstPassResult._sizeOf_inst",
"Lean.Meta.DefEqArgsFirstPassResult.failed",
"Nat",
"SizeOf.sizeOf",
"Lean.Meta.DefEqArgsFirstPassResult",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Util.FormatTable.0.formatTable.match_3 | Mathlib.Util.FormatTable | [
"Alignment",
"Prod.mk",
"Nat",
"Prod",
"Prod.casesOn"
] | false |
Lean.Widget.RpcEncodablePacket.mk.sizeOf_spec._@.Lean.Widget.Types.2243429567._hygCtx._hyg.1 | Lean.Widget.Types | [
"Lean.Json",
"Lean.Widget.RpcEncodablePacket.mk._@.Lean.Widget.Types.2243429567._hygCtx._hyg.1",
"instOfNatNat",
"Lean.Json._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Lean.Widget.RpcEncodablePacket._sizeOf_inst._@.Lean.Widget.Types.2243429567._hygCtx._hyg.1",
"instAddNat",
... | false |
CategoryTheory.Functor.isLeftDerivedFunctor_iff_of_inverts | Mathlib.CategoryTheory.Functor.Derived.PointwiseLeftDerived | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.IsLeftDerivedFunctor",
"CategoryTheory.Functor.isLeftDerivedFunctor_o... | true |
Sum.LiftRel.inr | Init.Data.Sum.Basic | [
"Sum.LiftRel.inr",
"Sum.LiftRel",
"Sum.inr"
] | true |
IsLocalRing.instCommRingResidueField | Mathlib.RingTheory.LocalRing.ResidueField.Defs | [
"IsLocalRing.instCommRingResidueField._proof_46",
"IsLocalRing.instCommRingResidueField._aux_4",
"Ring.mk",
"Mul.mk",
"IsLocalRing.instCommRingResidueField._proof_47",
"CommRing",
"One.mk",
"IsLocalRing.instCommRingResidueField._proof_31",
"IsLocalRing.instCommRingResidueField._proof_24",
"CommSem... | true |
Lean.Meta.Sym.Simp.Context.initialLCtxSize | Lean.Meta.Sym.Simp.SimpM | [
"Nat",
"Lean.Meta.Sym.Simp.Context"
] | true |
_private.Init.Data.Array.Lemmas.0.Array.getElem_eq_getElem_reverse._proof_1_1 | Init.Data.Array.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",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"Lean.Omega.Int.ofNat_sub_sub",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lea... | false |
ENNReal.add_eq_top | Mathlib.Data.ENNReal.Operations | [
"ENNReal.instAdd",
"Distrib.toAdd",
"NNReal",
"WithTop.add_eq_top",
"instDistribOfSemiring",
"instHAdd",
"Iff",
"HAdd.hAdd",
"ENNReal",
"NNReal.instSemiring",
"ENNReal.instTop",
"Or",
"Top.top",
"Eq"
] | true |
StrongDual.toLpₗ._proof_7 | Mathlib.Probability.Moments.CovarianceBilinDual | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"SeparatelyContinuousMul.to_continuousSMul",
"IsTopologicalDivisionRing.toIsTopologicalRing",
"PseudoMetricSpace.toUniformSpace",
"NormedDivisio... | false |
ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction._proof_4 | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | [
"LinearEquiv.symm",
"instHSMul",
"Semiring.toModule",
"SemilinearMapClass.toMulActionSemiHomClass",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat.coextendScalars",
"ModuleCat",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"DistribMulAction.toDistribSMul"... | false |
AddOpposite.opUniformEquivLeft.eq_1 | Mathlib.Topology.Algebra.IsUniformGroup.Basic | [
"AddOpposite.opUniformEquivLeft._proof_1",
"AddOpposite",
"AddOpposite.opUniformEquivLeft",
"AddOpposite.instTopologicalSpaceAddOpposite",
"AddOpposite.opEquiv",
"UniformEquiv.mk",
"TopologicalSpace",
"instIsTopologicalAddGroupAddOpposite",
"AddGroup",
"AddOpposite.instAddGroup",
"Eq.refl",
"A... | true |
DilationEquiv.smulTorsor_apply | Mathlib.Analysis.Normed.Affine.AddTorsor | [
"instHSMul",
"SeminormedAddCommGroup",
"AddMonoid.toAddSemigroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedDivisionRing.toNorm",
"AddMonoid.toAddZeroClass",
"DilationEquiv.instEquivLike",
"AddCommGroup.toAddGroup",
"NormedDivisionRing.toDivisionRing",
"DivisionRi... | true |
QuasispectrumRestricts.nnreal_of_nonneg | Mathlib.Analysis.Real.Spectrum | [
"NNReal.instTopologicalSpace",
"Iff.mpr",
"NNReal.instCommSemiring",
"Real.partialOrder",
"Real.instLE",
"Real",
"QuasispectrumRestricts.nnreal_iff",
"instSMulOfMul",
"Real.instZero",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"ContinuousMap",
"AddMonoid.... | true |
Std.TreeMap.getKey?_ofList_of_mem | Std.Data.TreeMap.Lemmas | [
"List.Pairwise",
"List.map",
"Option.some",
"Membership.mem",
"Ordering",
"Ordering.eq",
"Std.DTreeMap.Const.getKey?_ofList_of_mem",
"Std.TransCmp",
"Prod.fst",
"List",
"List.instMembership",
"Std.TreeMap.ofList",
"Std.TreeMap.getKey?",
"Prod",
"Eq",
"Not",
"Option"
] | true |
TannakaDuality.FiniteGroup.leftRegular._proof_1 | Mathlib.RepresentationTheory.Tannaka | [
"AddHom.mk.congr_simp",
"Pi.Function.module",
"MulOne.toOne",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"InvOneClass.toOne",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"DivInvOneMonoid.toInvOneClass",
"inv_one",
"Mo... | false |
Lean.Doc.option | Lean.Elab.DocString.Builtin | [
"Pure.pure",
"Lean.instMonadEnvOfMonadLift",
"Lean.Doc.Context",
"Lean.Parser.identWithPartialTrailingDot",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.TSyntax.getId",
"Subarray",
"_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.throwOrNest",
"Lean.ElabInline.mk",
"Lean.E... | true |
CongruenceSubgroup.IsCongruenceSubgroup.finiteIndex | Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | [
"Nat.instMulZeroClass",
"CongruenceSubgroup.instFiniteIndexGamma",
"NeZero.mk",
"Matrix.SpecialLinearGroup",
"Subgroup.FiniteIndex",
"PartialOrder.toPreorder",
"instDecidableEqFin",
"CongruenceSubgroup.Gamma",
"Preorder.toLE",
"Matrix.SpecialLinearGroup.instGroup",
"Subgroup",
"Ne",
"instOfN... | true |
Sat.Clause.reify.casesOn | Mathlib.Tactic.Sat.FromLRAT | [
"Sat.Clause.reify",
"Sat.Clause",
"Sat.Clause.reify.mk",
"Sat.Valuation",
"Sat.Clause.reify.rec",
"Not",
"Sat.Valuation.satisfies"
] | false |
Std.DTreeMap.Internal.Impl.Const.getEntryGE!_eq_get!_getEntryGE? | Std.Data.DTreeMap.Internal.Model | [
"Ord",
"Option.get!",
"Std.DTreeMap.Internal.Impl.Const.getEntryGE!",
"Std.DTreeMap.Internal.Impl.Const.getEntryGE?",
"Inhabited",
"Prod",
"Eq",
"Std.DTreeMap.Internal.Impl",
"rfl"
] | true |
Std.ExtTreeSet.get?_insert | Std.Data.ExtTreeSet.Lemmas | [
"Unit.unit",
"instDecidableNot",
"instDecidableEqOrdering",
"Option.some",
"Membership.mem",
"Ordering",
"Std.ExtTreeSet.inner",
"Ordering.eq",
"Std.TransCmp",
"And",
"Unit",
"Std.ExtTreeSet.instMembershipOfTransCmp",
"Std.ExtTreeMap.getKey?_insertIfNew",
"Std.ExtTreeSet",
"instDecidable... | true |
Nat.toList_roc_eq_singleton_iff | Init.Data.Range.Polymorphic.NatLemmas | [
"Eq.mpr",
"Nat.toList_rco_eq_nil_iff._simp_1",
"congrArg",
"Nat.toList_rco_eq_cons_iff._simp_1",
"id",
"Std.Roc.toList",
"Std.PRange.instIsAlwaysFiniteNat_1",
"instOfNatNat",
"LE.le",
"Nat.add_lt_add_iff_right._simp_1",
"instLENat",
"Nat.add_le_add_iff_right._simp_1",
"Nat.toList_roc_eq_toLi... | true |
CategoryTheory.Equivalence.sheafCongr.counitIso_inv_app_hom_app | Mathlib.CategoryTheory.Sites.Equivalence | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Equivalence.op",
"CategoryTheory.Equivalence... | true |
Lean.Meta.Grind.Arith.CommRing.PolyDerivation.normEq0.inj | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Grind.CommRing.Poly",
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation.normEq0",
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation.normEq0.noConfusion",
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation",
"And",
"And.intro",
"Lean.Meta.Grind.Arith.CommRing.EqCnstr",
"Eq"
] | true |
Lean.Server.Watchdog.WaitForILeanRequest.id | Lean.Server.Watchdog | [
"Lean.JsonRpc.RequestID",
"Lean.Server.Watchdog.WaitForILeanRequest"
] | true |
AlgebraicGeometry.PresheafedSpace.Hom.ext | Mathlib.Geometry.RingedSpace.PresheafedSpace | [
"AlgebraicGeometry.PresheafedSpace.Hom",
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"congrArg",
"TopCat.instCategory",
"TopCat.i... | true |
Std.DHashMap.Const.get_ofList_of_mem | Std.Data.DHashMap.Lemmas | [
"List.Pairwise",
"Std.DHashMap.Internal.Raw₀.Const.get_insertMany_emptyWithCapacity_list_of_mem",
"Membership.mem",
"Std.DHashMap.instMembership",
"Prod.mk",
"LawfulHashable",
"Prod.fst",
"Bool.true",
"List",
"BEq.beq",
"EquivBEq",
"List.instMembership",
"Std.DHashMap.Const.ofList",
"Bool"... | true |
Lean.ImportState._sizeOf_1 | Lean.Environment | [
"Std.HashMap._sizeOf_inst",
"Lean.ImportState.rec",
"instOfNatNat",
"Std.HashMap",
"Array._sizeOf_inst",
"Array",
"_private.Lean.Environment.0.Lean.ImportedModule._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Name",
"_private.L... | false |
CategoryTheory.Limits.bicone_ι_π_ne_assoc | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.Bicone.pt",
"Eq.mp",
"id",
"Ne",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Limits.Bicone.π",
"CategoryTheory.Limits.... | true |
CategoryTheory.InjectiveResolution.Hom.ι_f_zero_comp_hom_f_zero | Mathlib.CategoryTheory.Preadditive.Injective.Resolution | [
"CategoryTheory.InjectiveResolution.Hom",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.InjectiveResolution.Hom.hom",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.single₀",
"Categor... | true |
instAddCommGroupPolynomialModule._proof_19 | Mathlib.Algebra.Polynomial.Module.Basic | [
"instAddCommGroupPolynomialModule._proof_11",
"CommRing",
"instAddCommGroupPolynomialModule._proof_7",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Add.mk",
"Finsupp.instAddGroup._proof_2",
"AddMonoid.toZero",
"AddMonoid.mk",
"instAddCommGroupPolynomialModule._aux_4",
"AddCommGrou... | false |
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