name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Matrix.replicateCol_zero | Mathlib.LinearAlgebra.Matrix.RowCol | [
"Matrix",
"Matrix.replicateCol",
"Pi.instZero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Matrix.zero",
"rfl",
"Zero"
] | true |
_private.Mathlib.GroupTheory.FreeGroup.Orbit.0.FreeGroup.startsWith.disjoint_iff_ne._simp_1_6 | Mathlib.GroupTheory.FreeGroup.Orbit | [
"And",
"propext",
"not_and",
"Eq",
"Not"
] | false |
FirstOrder.Language.Hom.homClass | Mathlib.ModelTheory.Basic | [
"FirstOrder.Language.Hom",
"FirstOrder.Language.Hom.map_fun'",
"FirstOrder.Language.Structure",
"FirstOrder.Language.HomClass",
"FirstOrder.Language.HomClass.mk",
"FirstOrder.Language",
"FirstOrder.Language.Hom.map_rel'",
"FirstOrder.Language.Hom.instFunLike"
] | true |
MonCat.Colimits.monoidColimitType._proof_1 | Mathlib.Algebra.Category.MonCat.Colimits | [
"MonCat.Colimits.Relation.mul_2",
"CategoryTheory.Functor",
"Mul.mk",
"One.mk",
"HMul.hMul",
"MonCat.Colimits.colimitSetoid",
"MonCat.Colimits.Prequotient",
"Semigroup.mk",
"Quotient.map₂",
"MonCat",
"npowRecAuto",
"instOfNatNat",
"Quotient.ind₂",
"Quotient.ind",
"MonCat.instCategory",
... | false |
Thunk.fn | Init.Core | [
"Unit",
"Thunk"
] | true |
_private.Mathlib.Combinatorics.Derangements.Finite.0.card_derangements_fin_eq_numDerangements._proof_1_1 | Mathlib.Combinatorics.Derangements.Finite | [
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"congrArg",
"Classical.byContradiction",
"HSub.hSub",
"Nat.Linear.ExprCnstr.eq_true_of_isValid",
"Lean.Grind.Nat.lt_eq",
"id",
"False.casesOn",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Bool.true",
"instHAdd",
"instHSub",
... | false |
PFunctor.W | Mathlib.Data.PFunctor.Univariate.Basic | [
"PFunctor",
"PFunctor.A",
"WType",
"PFunctor.B"
] | true |
_private.Mathlib.Topology.Filter.0.Filter.sInter_nhds._simp_1_1 | Mathlib.Topology.Filter | [
"Filter.instMembership",
"Filter.le_principal_iff",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"propext",
"Filter.principal",
"Eq",
"Filter",
"Filter.instPartialOrder",
"Set"
] | false |
CategoryTheory.LocalizerMorphism.LeftResolution.Hom.ext_iff | Mathlib.CategoryTheory.Localization.Resolution | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.LocalizerMorphism.LeftResolution",
"CategoryTheory.LocalizerMorphism.LeftResolution.Hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.LocalizerMorphism.LeftResolution.X₁",
"Eq.casesOn",
"CategoryTheory.Localiz... | true |
BooleanRing.mul_one_add_self | Mathlib.Algebra.Ring.BooleanRing | [
"Distrib.leftDistribClass",
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"BooleanRing.mul_self",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"id",
"MulOne.toMul",
"Distrib.toAdd",
"BooleanRing.add_self",
"BooleanRing.toRing",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"ins... | true |
CategoryTheory.Abelian.SpectralObject.EIsoH_hom_naturality._auto_5 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.ComposableArrows.fourδ₃Toδ₂._proof_2 | Mathlib.CategoryTheory.ComposableArrows.Four | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ComposableArrows.map'._proof_8",
"PartialOrder.toPreorder",
"CategoryTheory.CategoryStruct.id",
"Fin.mk",
"CategoryTheory.ComposableArrows.homMk₁._proof_4",
"Preorder.smallCategory",
"instOfNatNat",
"CategoryTheo... | false |
SimpleGraph.Walk.head_support._proof_1 | Mathlib.Combinatorics.SimpleGraph.Walk.Basic | [
"False",
"congrArg",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Ne",
"SimpleGraph.Walk.support_ne_nil._simp_1",
"SimpleGraph",
"List",
"True",
"of_eq_true",
"not_false_eq_true",
"Eq",
"Not",
"Eq.trans",
"List.nil"
] | false |
CategoryTheory.SimplicialObject.Splitting.toNondegComplex_fromNondegComplex_assoc | Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject | [
"CategoryTheory.Category.assoc",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddRightCancelSemigroup.toAddSemigroup",
"CategoryTheory.SimplicialObject.Splitting",
"AddCancelMonoid.toAddRightCancelMonoid",
... | true |
CategoryTheory.Functor.Monoidal.toUnit_ε | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unique",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.LaxMonoidal.ε",
"id",
"CategoryTheory.cancel_mono",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidal... | true |
Filter.rcomap'_sets | Mathlib.Order.Filter.Partial | [
"SetRel",
"Filter.rcomap'",
"setOf",
"Filter.sets",
"HasSubset.Subset",
"Filter.rcomap.match_1",
"SetRel.image",
"SetRel.preimage",
"Prod",
"Eq",
"Filter",
"rfl",
"Set.instHasSubset",
"Set"
] | true |
Set.image2_iInter_subset_right | Mathlib.Data.Set.Lattice.Image | [
"Eq.mpr",
"Set.iInter",
"_private.Mathlib.Data.Set.Lattice.Image.0.Set.image2_iInter_subset_right._simp_1_2",
"Membership.mem",
"id",
"HasSubset.Subset",
"_private.Mathlib.Data.Set.Lattice.Image.0.Set.image2_iInter_subset_right._simp_1_1",
"implies_congr",
"Set.image2",
"Eq.refl",
"Set.mem_image... | true |
Lean.Compiler.LCNF.Probe.filterByUnreach | Lean.Compiler.LCNF.Probing | [
"Lean.Compiler.LCNF.Decl",
"Lean.Expr",
"Lean.Compiler.LCNF.Decl.value",
"Lean.Compiler.LCNF.Purity",
"_private.Lean.Compiler.LCNF.Probing.0.Lean.Compiler.LCNF.Probe.filterByUnreach.go",
"Lean.Compiler.LCNF.DeclValue.isCodeAndM",
"Lean.Compiler.LCNF.instMonadCompilerM",
"Lean.Compiler.LCNF.Probe",
"... | true |
AddMonoidHom.mulRight₃._proof_2 | Mathlib.Algebra.Ring.Associator | [
"add_mul",
"HMul.hMul",
"congrArg",
"AddMonoidHom.compr₂",
"AddMonoid.toAddZeroClass",
"Distrib.rightDistribClass",
"AddZeroClass.toAddZero",
"AddMonoidHom.mul",
"AddMonoidHom.instAddCommMonoid",
"AddMonoidHom.ext",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"Distrib.toMul",
... | false |
_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_32 | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | [
"HSub.hSub",
"Lean.Grind.Nat.lt_eq",
"SimpleGraph.Walk",
"instSubNat",
"instOfNatNat",
"SimpleGraph.Dart",
"LE.le",
"instLENat",
"SimpleGraph",
"SimpleGraph.Walk.darts",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
... | false |
_private.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.0.wrapped._proof_1._@.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.588747923._hygCtx._hyg.2 | Mathlib.MeasureTheory.Measure.Typeclasses.Finite | [
"MeasureTheory.Measure",
"SecondCountableTopology",
"setOf",
"MeasurableSpace",
"TopologicalSpace",
"definition._@.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.588747923._hygCtx._hyg.2",
"MeasureTheory.IsLocallyFiniteMeasure",
"IsOpen",
"Eq",
"rfl",
"MeasureTheory.Measure.FiniteSpanningSetsI... | false |
SimpleGraph.Walk.getVert_comp_val_eq_get_support | Mathlib.Combinatorics.SimpleGraph.Walk.Traversal | [
"List.get",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Function.comp",
"Fin.val",
"SimpleGraph",
"Nat",
"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Traversal.0.SimpleGraph.Walk.getVert_comp_val_eq_get_support._proof_1_3",
"Fin",
"Eq",
"List.length",
"SimpleGraph.Walk.getVert"
] | true |
UniformSpace.Completion.isDenseInducing_coe | Mathlib.Topology.UniformSpace.Completion | [
"UniformSpace",
"UniformSpace.Completion.coe'",
"IsDenseInducing.mk",
"IsUniformInducing.isInducing",
"UniformSpace.Completion.denseRange_coe",
"IsDenseInducing",
"Topology.IsInducing",
"UniformSpace.Completion.uniformSpace",
"UniformSpace.toTopologicalSpace",
"UniformSpace.Completion",
"Uniform... | true |
CategoryTheory.Functor.instLaxMonoidalMonMapAddMon._proof_3 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.instIsAddMonHomμ",
"CategoryTheory.Functor.addMonObjObj",
"CategoryTheory.AddMon.instAddMonObjTensorObj",
"CategoryTheory.IsAddMonHom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.LaxBraided.toLaxMonoidal",
"CategoryTheory.BraidedCategor... | false |
instFinitePresentationForall | Mathlib.Algebra.Module.FinitePresentation | [
"Pi.Function.module",
"Semiring.toModule",
"Pi.addCommMonoid",
"Ring.toNonAssocRing",
"AddCommGroup.toAddCommMonoid",
"Finite",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonAssocRing.toNonUnitalNonAssocRing",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Module.Finite.self",
"Module.... | true |
AffineIsometry.norm_map | Mathlib.Analysis.Normed.Affine.Isometry | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Real",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"LinearMap.instFunLike",
"LinearMap",
"NormedField",
"SeminormedAddCommGroup.toNorm",
"PseudoMetricSpace",
"NormedAddTor... | true |
Lean.IR.CollectMaps.collectDecl | Lean.Compiler.IR.EmitUtil | [
"Lean.IR.CollectMaps.collectParams",
"_private.Lean.Compiler.IR.EmitUtil.0.Lean.IR.CollectMaps.collectDecl.match_1",
"Lean.IR.Param",
"Function.comp",
"id",
"Lean.IR.CollectMaps.Collector",
"Lean.IR.DeclInfo",
"Lean.IR.FnBody",
"Array",
"Lean.IR.CollectMaps.collectFnBody",
"Lean.IR.FunId",
"Le... | true |
IsLocalization.tensorProductEquivOfMapIncludeRight._proof_9 | Mathlib.RingTheory.Localization.BaseChange | [
"Algebra.to_smulCommClass",
"IsLocalization.tensorProductEquivOfMapIncludeRight._proof_7",
"CommSemiring.toSemiring",
"Algebra.TensorProduct.map",
"IsScalarTower",
"IsScalarTower.toAlgHom",
"AlgHom.id",
"Algebra",
"Algebra.TensorProduct.instCommSemiring",
"Algebra.toSMul",
"Algebra.toModule",
... | false |
Finset.instGradeMinOrder_nat | Mathlib.Data.Finset.Grade | [
"Finset.card_strictMono",
"GradeMinOrder.mk",
"GradeMinOrder",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finset.partialOrder",
"GradeOrder.mk",
"Nat.instPreorder",
"Nat",
"Finset.card",
"IsMin",
"Finset.instGradeMinOrder_nat._proof_1",
"CovBy.card_finset"
] | true |
ZeroAtInftyContinuousMap.instFunLike | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"DFunLike.mk",
"ZeroAtInftyContinuousMap.instFunLike._proof_1",
"TopologicalSpace",
"ContinuousMap.toFun",
"ZeroAtInftyContinuousMap",
"ZeroAtInftyContinuousMap.toContinuousMap",
"Eq",
"FunLike",
"Zero"
] | true |
Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof.dvdTight.sizeOf_spec | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.LeCnstr._sizeOf_inst",
"instOfNatNat",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstr",
"instHAdd",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstr._sizeOf_inst",
"HAdd.hAdd",
"Lean.Meta.Grind.Arith.Cutsat.LeCnstr",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Lean.Meta.Grind... | true |
ValuationRing.commGroupWithZero._proof_9 | Mathlib.RingTheory.Valuation.ValuationRing | [
"ValuationRing.instInvValueGroup",
"Mul.mk",
"CommRing",
"instHDiv",
"One.mk",
"HMul.hMul",
"ValuationRing.commGroupWithZero._proof_4",
"ValuationRing.ValueGroup",
"Semigroup.mk",
"Algebra",
"ValuationRing.commGroupWithZero._proof_5",
"ValuationRing.commGroupWithZero._proof_3",
"HDiv.hDiv",
... | false |
HOrElse.ctorIdx | Init.Prelude | [
"outParam",
"HOrElse",
"Nat"
] | false |
AddCon.comap_eq | Mathlib.GroupTheory.Congruence.Hom | [
"AddCon.instFunLikeForallProp",
"AddCon.eq",
"AddCon",
"Eq.mpr",
"AddCon.ext",
"AddMonoidHom.instAddMonoidHomClass",
"AddCon.addZeroClass",
"congrArg",
"Iff.rfl",
"AddZeroClass.toAddZero",
"id",
"AddCon.comap",
"AddZeroClass",
"Iff",
"AddMonoidHomClass.toAddHomClass",
"propext",
"Add... | true |
Lean.Elab.Structural.RecArgCandidates.noConfusionType | Lean.Elab.PreDefinition.Structural.FindRecArg | [
"Lean.MessageData",
"Lean.Elab.Structural.RecArgCandidates",
"Array",
"Lean.Elab.Structural.RecArgCandidate",
"Eq",
"Lean.Elab.Structural.RecArgCandidates.casesOn"
] | false |
Finmap.insert | Mathlib.Data.Finmap | [
"AList.insert",
"AList",
"Finmap.liftOn",
"Finmap.insert._proof_1",
"AList.toFinmap",
"Finmap",
"DecidableEq"
] | true |
Polynomial.fourierCoeff_toAddCircle | Mathlib.Analysis.Polynomial.Fourier | [
"_private.Mathlib.Analysis.Polynomial.Fourier.0.Polynomial.fourierCoeff_toAddCircle._simp_1_1",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"fourierCoeff",
"Int.instIsStrictOrderedRing",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"... | true |
Std.Internal.List.Const.getValueD_filter | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"Option.pfilter",
"congrArg",
"Std.Internal.List.containsKey_eq_isSome_getValue?",
"Option.getD",
"Option.getD.match_1",
"Option.some",
"Sigma.fst",
"Bool.true",
"Std.Internal.List.getKey",
"List",
"Std.Internal.List.containsKey",
"Unit",
"EquivBEq",
"St... | true |
Matrix.nondegenerate_iff_det_ne_zero | Mathlib.LinearAlgebra.Matrix.ToLinearEquiv | [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Eq.mpr",
"IsDomain",
"Mathlib.Tactic.Push.not_and_eq",
"False",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Matrix.Nondegenerate",
"dotProduct",
"congrArg",
"CommSemiring.toSemiring",
"Matrix.nondege... | true |
AlgebraicGeometry.StructureSheaf.const_mul | Mathlib.AlgebraicGeometry.StructureSheaf | [
"AlgebraicGeometry.StructureSheaf.Localizations",
"CategoryTheory.Functor",
"CommRing",
"Opposite",
"HMul.hMul",
"PrimeSpectrum.basicOpen",
"AlgebraicGeometry.StructureSheaf.const._proof_1",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"LocalizedModule.mk_mul_mk",
"Algeb... | true |
IsCoercive.continuousLinearEquivOfBilin | Mathlib.Analysis.InnerProductSpace.LaxMilgram | [
"InnerProductSpace.toNormedSpace",
"IsCoercive.continuousLinearEquivOfBilin._proof_3",
"Real",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"Semiring.toModule",
"IsCoercive.continuousLinearEquivOfBilin._proof_1",
"ContinuousLinearMap.topologicalSpace"... | true |
Lean.Meta.Tactic.Cbv.CbvSimprocOLeanEntry.noConfusion | Lean.Meta.Tactic.Cbv.CbvSimproc | [
"Lean.Meta.Tactic.Cbv.CbvSimprocPhase",
"Lean.Meta.DiscrTree.Key",
"Lean.Meta.Tactic.Cbv.CbvSimprocOLeanEntry.noConfusionType",
"Array",
"Lean.Meta.Tactic.Cbv.CbvSimprocOLeanEntry.casesOn",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq",
"Lean.Meta.Tactic.Cbv.CbvSimprocOLeanEntry"
] | false |
Bundle.Pretrivialization.linearEquivAt | Mathlib.Topology.VectorBundle.Basic | [
"Bundle.Pretrivialization.IsLinear",
"LinearEquiv.mk",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Bundle.TotalSpace.mk",
"AddZeroClass.toAddZero",
"Bundle.Pretrivialization.linearEquivAt._proof_4",
"Bundle.Pretrivialization.toFun'",
"AddCommMonoid",
"Bundle.Pretrivialization",
"TopologicalSp... | true |
HasSubset.Subset.trans | Mathlib.Order.RelClasses | [
"subset_trans",
"HasSubset.Subset",
"IsTrans",
"HasSubset"
] | true |
Units.mul_right_inj | Mathlib.Algebra.Group.Units.Basic | [
"Monoid",
"Units.val",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Units",
"Eq.mp",
"MulOne.toMul",
"congr_arg",
"MulOneClass.toMulOne",
"Iff",
"Inv.inv",
"congr",
"Iff.intro",
"Eq",
"Units.instInv",
"instHMul",
"Units.inv_mul_cancel_left"
] | true |
Derivation.liftOfSurjective.congr_simp | Mathlib.RingTheory.Derivation.Basic | [
"Derivation",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Algebra",
"Eq.rec",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Derivation.instFunLike",
"AlgHomClass",
"C... | true |
NormedSpace.inclusionInDoubleDualWeak._proof_11 | Mathlib.Analysis.Normed.Module.DoubleDual | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Algebra.to_smulCommClass",
"Continuous",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddCommGroup",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace",
"Pi.topologicalSpace",
"ContinuousLinearMap.topologi... | false |
RingTheory.LinearMap._aux_Mathlib_Algebra_Algebra_Bilinear___macroRules_RingTheory_LinearMap_termμ_1 | Mathlib.Algebra.Algebra.Bilinear | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkSt... | false |
ProbabilityTheory.Kernel.borelMarkovFromReal.congr_simp | Mathlib.Probability.Kernel.Disintegration.StandardBorel | [
"StandardBorelSpace",
"Real",
"Eq.rec",
"ProbabilityTheory.Kernel.borelMarkovFromReal",
"MeasurableSpace",
"Real.measurableSpace",
"Nonempty",
"Eq.refl",
"Eq",
"ProbabilityTheory.Kernel"
] | true |
Equiv.pemptyArrowEquivPUnit | Mathlib.Logic.Equiv.Defs | [
"Equiv.arrowPUnitOfIsEmpty",
"Equiv",
"PEmpty",
"PUnit",
"PEmpty.instIsEmpty"
] | true |
CategoryTheory.Cat.FreeRefl.lift | Mathlib.CategoryTheory.Category.ReflQuiv | [
"CategoryTheory.Functor",
"CategoryTheory.Cat.FreeRefl.instCategory",
"CategoryTheory.catToReflQuiver",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"CategoryTheory.ReflPrefunctor",
"CategoryTheory.Cat.FreeRefl.lift._proof_1",
"CategoryTheory.Cat.FreeRefl",
"CategoryTheory.ReflPrefu... | true |
PerfectClosure.instNeg | Mathlib.FieldTheory.PerfectClosure | [
"NegZeroClass.toNeg",
"CommRing",
"Nat.Prime",
"Neg.mk",
"AddGroupWithOne.toAddMonoidWithOne",
"Fact",
"Quot.lift",
"Prod.mk",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Prod.fst",
"Neg",
"PerfectClosure.mk",
"... | true |
CategoryTheory.LocalizerMorphism.RightResolution._sizeOf_1 | Mathlib.CategoryTheory.Localization.Resolution | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.LocalizerMorphism.RightResolution",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.LocalizerMorphism.RightResolution.rec",
"instSizeOfDefault",
"instOfNatNat",
"CategoryTheory.LocalizerMorphism.functor",
"instHAdd",
"HAdd.... | false |
AddSubsemigroup.coe_op | Mathlib.Algebra.Group.Subsemigroup.MulOpposite | [
"AddSubsemigroup.instSetLike",
"AddOpposite",
"AddOpposite.instAdd",
"AddSubsemigroup.op",
"SetLike.coe",
"Set.preimage",
"AddSubsemigroup",
"Eq.refl",
"AddOpposite.unop",
"Eq",
"Add",
"Set"
] | true |
Polynomial.mapRingHom_comp_C | Mathlib.Algebra.Polynomial.Eval.Defs | [
"Polynomial.C",
"Polynomial.ext",
"congrArg",
"RingHom",
"Polynomial",
"Polynomial.coeff",
"RingHom.ext",
"RingHom.comp",
"RingHom.instFunLike",
"Polynomial.mapRingHom",
"Polynomial.semiring",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Semiring",
"congrFun'",
"Polynomial.map_C",
"S... | true |
CategoryTheory.instBicategoryMonoidalSingleObj._proof_6 | Mathlib.CategoryTheory.Bicategory.SingleObj | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.id_whiskerLeft",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"CategoryTheory.MonoidalSingleObj",
"infer... | false |
_private.Init.Data.List.Basic.0.List.getLastD.match_1.eq_1 | Init.Data.List.Basic | [
"List.cons",
"List",
"Eq.refl",
"List.getLastD.match_1",
"Eq",
"List.nil"
] | true |
VectorBundleCore.moduleFiber._proof_3 | Mathlib.Topology.VectorBundle.Basic | [
"Semigroup.toMul",
"instHSMul",
"HMul.hMul",
"VectorBundleCore.Fiber",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"VectorBundleCore.moduleFiber._aux_1",
"Field.toSemifield",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"SeminormedAddC... | false |
Aesop.Script.Tactic.sTactic? | Aesop.Script.Tactic | [
"Aesop.Script.STactic",
"Aesop.Script.Tactic",
"Option"
] | true |
_private.Lean.Parser.Term.Doc.0.Lean.Parser.Term.Doc.recommendedSpellingByNameExt.match_1 | Lean.Parser.Term.Doc | [
"Lean.Parser.Term.Doc.RecommendedSpelling",
"Prod.mk",
"Array",
"Lean.Name",
"Prod",
"Prod.casesOn"
] | false |
Real.convexOn_log_Gamma | Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | [
"Iff.mpr",
"Real.instIsOrderedRing",
"Not.intro",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"Real.Gamma_pos_of_pos",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Real.instPow",
"Real.partialOrder",
"Real.rpow_pos_of_pos",
"Rea... | true |
Array.beq_eq_decide | Init.Data.Array.DecidableEq | [
"congrArg",
"Array.instBEq",
"Eq.rec",
"instDecidableEqBool",
"dite",
"Array",
"GetElem.getElem",
"Bool.true",
"BEq.beq",
"Array.instGetElemNatLtSize",
"Nat",
"LT.lt",
"True",
"eq_self",
"Bool",
"of_eq_true",
"congrFun'",
"instDecidableEqNat",
"Array.isEqv_eq_decide",
"instLTNa... | true |
CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp | Mathlib.CategoryTheory.Localization.Monoidal.Functor | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp._proof_1",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Localization.Lifting.iso",
"CategoryTheory.Functor.comp",
"CategoryTheory.Locali... | true |
SimpleGraph.le_chromaticNumber_iff_coloring | Mathlib.Combinatorics.SimpleGraph.Coloring.VertexColoring | [
"ENat.instNatCast",
"congrArg",
"LE.le",
"instLENat",
"Nat.cast",
"Nonempty.forall._simp_1",
"instLEENat",
"SimpleGraph.Coloring",
"SimpleGraph",
"iff_self",
"Iff",
"_private.Mathlib.Combinatorics.SimpleGraph.Coloring.VertexColoring.0.SimpleGraph.le_chromaticNumber_iff_coloring._simp_1_1",
"... | true |
Subgroup.Commensurable.eq_1 | Mathlib.GroupTheory.Commensurable | [
"Group",
"Subgroup",
"Ne",
"instOfNatNat",
"Subgroup.relIndex",
"And",
"Nat",
"Subgroup.Commensurable",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
Unitization.instNonAssocRing._proof_9 | Mathlib.Algebra.Algebra.Unitization | [
"AddMonoidWithOne.natCast_zero._autoParam",
"NonUnitalNonAssocRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup"... | false |
Std.Iter.toIter_toIterM | Init.Data.Iterators.Basic | [
"Std.IterM.toIter",
"Std.Iter.toIterM",
"Std.Iter",
"Eq",
"rfl"
] | true |
LinearIsometry.strictConvexSpace_range | Mathlib.Analysis.Convex.LinearIsometry | [
"LinearIsometry",
"Iff.mpr",
"NormedCommRing.toNormedRing",
"Submodule",
"RingHomSurjective.ids",
"instSMulOfMul",
"NormedRing.toRing",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"LinearIsometry.instFunLike",
"Membership.mem",
"NormedField.toField",
"PartialOrde... | true |
monotoneOn_of_le_add_one | Mathlib.Algebra.Order.SuccPred | [
"Eq.mpr",
"Preorder.toLT",
"One",
"Order.succ",
"Order.succ_eq_add_one",
"congrArg",
"SuccAddOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"PartialOrder",
"Eq.mp",
"id",
"not_isMax_iff._simp_1",
"LE.le",
"forall_exists_index._simp_1",
"monotoneOn_o... | true |
Lean.Environment.Visibility._sizeOf_inst | Lean.Environment | [
"Lean.Environment.Visibility",
"Lean.Environment.Visibility._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
ContinuousAlternatingMap.ofSubsingleton_toAlternatingMap | Mathlib.Topology.Algebra.Module.Alternating.Basic | [
"AlternatingMap",
"ContinuousAlternatingMap.toAlternatingMap",
"Equiv.instEquivLike",
"Equiv",
"ContinuousLinearMap.toLinearMap",
"ContinuousAlternatingMap.ofSubsingleton",
"LinearMap",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"Semiring",
"Subsingleton",
"Module",
"Alter... | true |
_private.Mathlib.AlgebraicTopology.ExtraDegeneracy.0.CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.homotopy._proof_40 | Mathlib.AlgebraicTopology.ExtraDegeneracy | [
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"Lean.Grind.ToInt.toInt",
"Classical.byContradiction",
"Nat.ToInt.add_congr",
"Eq.mp",
"Lean.RArray.branch",
"Fin.mk",
"Int.Linear.Expr.add",
"Nat.Linear.ExprCnstr.eq_of_toNormPoly_eq",
"id",
"Lean.RArray",
"Int.instNegInt",
"in... | false |
Filter.bliminf_or_le_inf_aux_right._simp_1 | Mathlib.Order.LiminfLimsup | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toConditionallyCompleteLattice",
"Filter.bliminf",
"LE.le",
"True",
"eq_true",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"Or",
"Filter.bliminf_or_le_inf_a... | false |
definition._@.Mathlib.Analysis.InnerProductSpace.PiL2.1554134833._hygCtx._hyg.2 | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"Submodule",
"Submodule.addSubmonoidClass",
"DirectSum.IsInternal",
"NormedRing.toRing",
"AddCommGroup.toAddCommMonoid",
"Submodule.innerProductSpace",
"Submodule.addCommMonoid",
"NormedSpace.toModule",
"Fintype.equivFinOfCardEq",... | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof.0.Lean.Meta.Grind.Arith.Cutsat.EqCnstr.collectDecVars.match_1 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof | [
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.mul",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.coreToInt",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.core0",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.ofLeGe",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.defnNat",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.div... | false |
ProofWidgets.RpcEncodablePacket.«_@».ProofWidgets.Component.Basic.2277670097._hygCtx._hyg.1.noConfusion | ProofWidgets.Component.Basic | [
"Lean.Json",
"ProofWidgets.RpcEncodablePacket.«_@».ProofWidgets.Component.Basic.2277670097._hygCtx._hyg.1.casesOn",
"ProofWidgets.RpcEncodablePacket.«_@».ProofWidgets.Component.Basic.2277670097._hygCtx._hyg.1.noConfusionType",
"Eq.ndrec",
"Eq.refl",
"Eq",
"ProofWidgets.RpcEncodablePacket._@.ProofWidgets... | false |
Lean.guardMsgsPositions | Init.Notation | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.ParserDescr.nodeWithAntiquot",
"Lean.ParserDescr.binary",
"Lean.guardMsgsPositionsArg",
"Lean.ParserDescr",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Bool.false",
"Lean.Name.mkStr1"
] | true |
subset_tangentConeAt_prod_left | Mathlib.Analysis.Calculus.TangentCone.Prod | [
"Set.instSProd",
"Eq.mpr",
"instHSMul",
"LinearMap.inl",
"AddMonoid.toAddSemigroup",
"SProd.sprod",
"congrArg",
"and_self",
"DistribMulAction.toDistribSMul",
"tendsto_const_nhds",
"subset_closure",
"AddCommGroup.toAddCommMonoid",
"Set.mem_prod._simp_1",
"Filter.NeBot",
"Filter.Eventually... | true |
AlgebraicGeometry.Scheme.kerAdjunction_counit_app | Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme | [
"CategoryTheory.Over",
"AlgebraicGeometry.Scheme",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.comp",
"AlgebraicGeometry.Scheme.Hom.toImage",
"CategoryTheory.Functor.id",
"Preorder.sm... | true |
ZFSet.card_empty | Mathlib.SetTheory.ZFC.Cardinal | [
"Cardinal.mk_eq_zero",
"Eq.mpr",
"False",
"ZFSet.instEmptyCollection",
"Cardinal.lift_zero",
"Cardinal",
"congrArg",
"ZFSet",
"Cardinal.lift",
"Cardinal.mk",
"Membership.mem",
"id",
"Subtype",
"funext",
"Cardinal.lift_inj",
"congr",
"True",
"eq_self",
"propext",
"of_eq_true",
... | true |
SeparatelyContinuousMul.rec | Mathlib.Topology.Algebra.Monoid.Defs | [
"Continuous",
"HMul.hMul",
"Mul",
"TopologicalSpace",
"SeparatelyContinuousMul",
"SeparatelyContinuousMul.mk",
"instHMul"
] | false |
Subring.mem_toSubsemiring._simp_1 | Mathlib.Algebra.Ring.Subring.Defs | [
"Subring.toSubsemiring",
"Subsemiring.instSetLike",
"Subring.instSetLike",
"Subring.mem_toSubsemiring",
"Membership.mem",
"NonAssocRing",
"Subsemiring",
"Subring",
"propext",
"Eq",
"NonAssocRing.toNonAssocSemiring",
"SetLike.instMembership"
] | false |
Lean.Syntax.ident.inj | Init.Core | [
"Lean.Syntax.ident",
"Lean.SourceInfo",
"Lean.Syntax",
"Substring.Raw",
"List",
"And",
"Lean.Syntax.Preresolved",
"And.intro",
"Lean.Name",
"Eq",
"Lean.Syntax.ident.noConfusion"
] | true |
CliffordAlgebra.reverse_mem_evenOdd_iff | Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation | [
"Submodule",
"CommRing",
"CliffordAlgebra.reverse",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"instAlgebraCliffordAlgebra",
"QuadraticForm",
"LinearMap.instFunLike",
"Membership.mem",
"AddCommGroup",
"Algebra.toModule",
"CliffordAl... | true |
_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.State.rec | Lean.Meta.LetToHave | [
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.State.mk",
"Std.HashMap",
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.Result",
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.State",
"Nat",
"Lean.ExprStructEq.instHashable",
"Lean.ExprStructEq.instBEq",
"Lean.ExprStructEq"
] | false |
QuadraticAlgebra.algebraMap_norm_eq_mul_star | Mathlib.Algebra.QuadraticAlgebra.Basic | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"QuadraticAlgebra.re",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"RingHom.instRingHomCl... | true |
Module.DirectLimit.addCommGroup._proof_12 | Mathlib.Algebra.Colimit.Module | [
"ModuleCon.instAddCommGroupQuotient._proof_1",
"Module.DirectLimit.addCommGroup._aux_6",
"AddMonoid.toAddSemigroup",
"instAddCommMonoidDirectSum",
"DirectSum.instModule",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"SubNegMonoid.mk",
"AddMonoid.toAddZeroClass",
"Neg.mk",
"M... | false |
_private.Mathlib.Order.Filter.Bases.Finite.0.Filter.hasBasis_generate._simp_1_1 | Mathlib.Order.Filter.Bases.Finite | [
"Filter.instMembership",
"Set.Finite",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"And",
"propext",
"Filter.mem_generate_iff",
"Filter.generate",
"Eq",
"Set.sInter",
"Filter",
"Set.instHasSubset",
"Set"
] | false |
HahnSeries.orderTop_embDomain | Mathlib.RingTheory.HahnSeries.Basic | [
"HahnSeries.support",
"Eq.mpr",
"HahnSeries.embDomain",
"congrArg",
"HahnSeries.orderTop_eq_top._simp_1",
"WithTop.coe_untop",
"LinearOrder",
"HahnSeries.orderTop",
"PartialOrder.toPreorder",
"WithTop.map",
"Preorder.toLE",
"Set.mem_of_subset_of_mem",
"Set.mem_image",
"Membership.mem",
"... | true |
orthogonalFamily_iff_pairwise | Mathlib.Analysis.InnerProductSpace.Orthogonal | [
"LinearIsometry",
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"Submodule",
"NormedRing.toRing",
"Function.onFun",
"Inner.inner",
"AddCommGroup.toAddCommMonoid",
"Submodule.innerProductSpace",
"NormedSpace.toModule",
"forall₃_congr",
"LinearIsometry.instFunLike",
"Member... | true |
ProofWidgets.MakeEditLinkProps.ctorIdx | ProofWidgets.Component.MakeEditLink | [
"Nat",
"ProofWidgets.MakeEditLinkProps"
] | false |
Int.zsmul_eq_mul | Mathlib.Algebra.Group.Int.Defs | [
"instHSMul",
"HMul.hMul",
"Int",
"Int.instMul",
"AddGroup.toSubNegMonoid",
"Int.instAddGroup",
"HSMul.hSMul",
"Eq",
"rfl",
"instHMul",
"SubNegMonoid.toZSMul"
] | true |
_private.Lean.Elab.PreDefinition.Structural.FindRecArg.0.Lean.Elab.Structural.nonIndicesFirst.match_1 | Lean.Elab.PreDefinition.Structural.FindRecArg | [
"Prod.mk",
"Array",
"Lean.Elab.Structural.RecArgInfo",
"Prod",
"Prod.casesOn"
] | false |
MeromorphicOn.neg | Mathlib.Analysis.Meromorphic.Basic | [
"NegZeroClass.toNeg",
"Pi.instNeg",
"NormedSpace",
"Membership.mem",
"MeromorphicOn",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"MeromorphicAt.neg",
"NontriviallyNormedField",
"NormedAddCommGroup.toAddCommGroup",
"No... | true |
List.nil_lt_cons | Init.Data.List.Lex | [
"List.Lex.nil",
"List.instLT",
"List.cons",
"List",
"LT.lt",
"LT",
"List.nil"
] | true |
_private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.instBEqMon.beq.match_1.eq_1 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Power",
"Unit.unit",
"Lean.Grind.CommRing.Mon.mult",
"Unit",
"Lean.Grind.CommRing.instBEqMon.beq.match_1",
"Eq.refl",
"Eq",
"Lean.Grind.CommRing.Mon",
"Lean.Grind.CommRing.Mon.unit"
] | true |
enorm_mul_le' | Mathlib.Analysis.Normed.Group.Basic | [
"ESeminormedMonoid",
"ENNReal.instAdd",
"HMul.hMul",
"ESeminormedMonoid.toContinuousENorm",
"Monoid.toMulOneClass",
"MulOne.toMul",
"ESeminormedMonoid.toMonoid",
"LE.le",
"TopologicalSpace",
"instHAdd",
"MulOneClass.toMulOne",
"ENorm.enorm",
"ContinuousENorm.toENorm",
"HAdd.hAdd",
"ENNRe... | true |
CategoryTheory.Bicategory.postcomposing._proof_2 | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.Bicategory.whisker_exchange",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory.postcomp",
"CategoryTheory.Functor.map",
"CategoryTheory.Bicategory",
... | false |
Finset.Ioi_nonempty | Mathlib.Order.Interval.Finset.Basic | [
"Eq.mpr",
"LocallyFiniteOrderTop",
"Finset.Ioi",
"congrArg",
"Finset",
"Preorder.toLE",
"id",
"Finset.Ioi_eq_empty",
"Finset.instEmptyCollection",
"Iff",
"Finset.not_nonempty_iff_eq_empty._simp_1",
"Finset.Nonempty",
"congrFun'",
"EmptyCollection.emptyCollection",
"Mathlib.Tactic.Contrap... | true |
ContinuousStar.rec | Mathlib.Topology.Algebra.Star | [
"Continuous",
"ContinuousStar",
"ContinuousStar.mk",
"TopologicalSpace",
"Star",
"Star.star"
] | false |
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