name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Triangulated.TStructure.descTruncGT.congr_simp | Mathlib.CategoryTheory.Triangulated.TStructure.TruncLEGT | [
"CategoryTheory.Triangulated.TStructure.truncGT",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"Eq.rec",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Preadditive",
"CategoryTheory.Triangulated.TStructure.descTruncGT",
"C... | true |
Std.ExtTreeMap.getKey!_modify | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtTreeMap.modify",
"Inhabited.default",
"instDecidableEqOrdering",
"Std.ExtTreeMap.instDecidableMem",
"Membership.mem",
"Ordering",
"Ordering.eq",
"Std.TransCmp",
"Std.ExtTreeMap.getKey!",
"Std.ExtTreeMap",
"Std.ExtTreeMap.inner",
"Std.ExtDTreeMap.Const.getKey!_modify",
"Inhabited",
... | true |
map_rat_smul | Mathlib.Algebra.Module.Rat | [
"map_ratCast_smul",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Rat",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"AddMonoidHomClass",
"Rat.instDivisionRing",
"AddZero.toZe... | true |
_private.Mathlib.Topology.Order.MonotoneConvergence.0.Pi.supConvergenceClass._simp_2 | Mathlib.Topology.Order.MonotoneConvergence | [
"Set.Elem",
"Set.range_restrict",
"Set.image",
"Set.range",
"Set.restrict",
"Eq.symm",
"Eq",
"Set"
] | false |
NormedRing.induced._proof_13 | Mathlib.Analysis.Normed.Ring.Basic | [
"PseudoMetricSpace.toBornology",
"PartialOrder.toPreorder",
"Preorder.toLE",
"NormedRing.toNonUnitalNormedRing",
"LE.le",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"SeminormedAddGroup.toPseudoMetricSpace",
"NonUnitalSeminormedRing.toSeminormedAddCommGroup",
"NonUnitalSeminormedRing.induced._pro... | false |
CategoryTheory.Limits.coconeOfCoconeUncurryIsColimit._proof_3 | Mathlib.CategoryTheory.Limits.Fubini | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.coconeOfCoconeUncurryIsColimit._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.DiagramOfCocones.obj",
"CategoryTheory.... | false |
Polynomial.natTrailingDegree_mul' | Mathlib.Algebra.Polynomial.Degree.TrailingDegree | [
"Eq.mpr",
"HMul.hMul",
"ENat.instNatCast",
"MulZeroClass.toMul",
"Nat.cast_withTop",
"congrArg",
"MulZeroClass.zero_mul",
"instAddENat",
"id",
"Ne",
"instNatCastNat",
"Nat.cast",
"WithTop.some",
"Polynomial",
"MulZeroClass.mul_zero",
"instDistribOfSemiring",
"Polynomial.trailingCoeff... | true |
Finpartition.combine._proof_2 | Mathlib.Order.Partition.Finpartition | [
"Eq.mpr",
"Lattice",
"Lattice.toSemilatticeSup",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"id",
"Finset.biUnion",
"Finpartition.parts",
"Finset.instSetLike",
"Finset.sup_congr",
"Finset.sup",
"Fin... | false |
_private.Init.Data.BitVec.Bitblast.0.BitVec.getMsbD_umod._proof_1_1 | Init.Data.BitVec.Bitblast | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",... | false |
Commute.intCast_right | Mathlib.Data.Int.Cast.Lemmas | [
"Int.cast",
"Int.commute_cast",
"Commute",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonAssocRing",
"Int",
"AddGroupWithOne.toIntCast",
"NonAssocRing.toNonUnitalNonAssocRing",
"NonAssocRing.toAddCommGroupWithOne",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"AddCommGrou... | true |
_private.Lean.Elab.Inductive.0.Lean.Elab.Command.inductiveSyntaxToView.match_9 | Lean.Elab.Inductive | [
"Lean.Syntax",
"Prod.mk",
"Prod",
"Prod.casesOn",
"Option"
] | false |
Nat.monotone_primeCounting | Mathlib.NumberTheory.PrimeCounting | [
"Nat.instIsOrderedAddMonoid",
"Nat.monotone_primeCounting'",
"covariant_swap_add_of_covariant_add",
"Nat.primeCounting'",
"Monotone",
"Preorder.toLE",
"monotone_id",
"Monotone.comp",
"id",
"Monotone.add_const",
"instOfNatNat",
"LE.le",
"Nat.primeCounting",
"instHAdd",
"HAdd.hAdd",
"Nat... | true |
HasFPowerSeriesOnBall.pi | Mathlib.Analysis.Analytic.Constructions | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Preorder.toLT",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"HasFPowerSeriesWithinOnBa... | true |
_private.Mathlib.Algebra.SkewMonoidAlgebra.Basic.0.SkewMonoidAlgebra.smul.eq_1 | Mathlib.Algebra.SkewMonoidAlgebra.Basic | [
"Finsupp.smulZeroClass",
"instHSMul",
"SMulZeroClass",
"_private.Mathlib.Algebra.SkewMonoidAlgebra.Basic.0.SkewMonoidAlgebra.smul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"SkewMonoidAlgebra.ofFinsupp",
"AddZero.toZero",
"AddMonoid",
"SkewMonoidAlgebra",
"Eq.refl",
"HSMul.hSMul",... | true |
alexDiscEquivPreord._proof_5 | Mathlib.Topology.Order.Category.AlexDisc | [
"AlexDisc.concreteCategory",
"AlexDisc.instHasForgetToTop",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Topology.WithUpperSet.instTopologicalSpace",
"TopCat.instCategory",
"Topology.IsUpperSet.toAlexandrovDiscrete",
"ContinuousMap",
"CategoryTheory.Functor.mk... | false |
Aesop.EqualUpToIdsM.State.mk.inj | Aesop.Util.EqualUpToIds | [
"Lean.instBEqMVarId",
"Aesop.EqualUpToIdsM.State",
"Lean.MVarId",
"Lean.Expr",
"Std.HashMap",
"And",
"Lean.instHashableMVarId",
"And.intro",
"Aesop.EqualUpToIdsM.State.mk",
"Lean.instBEqLevelMVarId",
"Eq",
"Aesop.EqualUpToIdsM.State.mk.noConfusion",
"Lean.LMVarId",
"Lean.instHashableLevelM... | true |
MeasureTheory.weightedSMul_union | Mathlib.MeasureTheory.Integral.Bochner.L1 | [
"Real",
"MeasureTheory.Measure",
"ChainCompletePartialOrder.instOfCompleteLattice",
"MeasurableSet",
"NormedSpace",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Disjoint"... | true |
_private.Mathlib.RingTheory.Multiplicity.0.FiniteMultiplicity.or_of_add._simp_1_1 | Mathlib.RingTheory.Multiplicity | [
"Semigroup",
"Semigroup.toMul",
"Dvd.dvd",
"semigroupDvd",
"instHAdd",
"HAdd.hAdd",
"LeftDistribClass",
"True",
"eq_true",
"Eq",
"Add",
"dvd_add"
] | false |
Lean.Elab.Command.Structure.StructParentInfo.mk._flat_ctor | Lean.Elab.Structure | [
"Lean.Syntax",
"Lean.Elab.Command.Structure.StructParentInfo",
"Lean.Expr",
"Lean.Elab.Command.Structure.StructParentInfo.mk",
"Bool",
"Lean.Name"
] | false |
AddSubgroup.rightCosetEquivAddSubgroup._proof_5 | Mathlib.GroupTheory.Coset.Basic | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"AddMonoid.toAddSemigroup",
"AddSubgroup.rightCosetEquivAddSubgroup._proof_1",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"AddOpposite",
"Set.vaddSet",
"Set.Elem",
"SubtractionMonoid.toSubNegZeroMonoid... | false |
IsAlgebraic.inv_iff | Mathlib.RingTheory.Algebraic.Basic | [
"GroupWithZero.toMonoidWithZero",
"CommRing",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"IsAlgebraic",
"congrArg",
"inv_zero",
"Algebra",
"Classical.propDecidable",
"DivisionSemiring.toGroupWithZero",
"DivisionMonoid.toDivInvOneMonoid",
"Field.toDivisionRing",
"... | true |
Ordnode.instInsert | Mathlib.Data.Ordmap.Ordnode | [
"Ordnode",
"Ordnode.insert",
"Insert",
"LE",
"DecidableLE",
"Insert.mk"
] | true |
Lean.Meta.Grind.TopSort.State.mk.inj | Lean.Meta.Tactic.Grind.EqResolution | [
"Lean.Meta.Grind.TopSort.State",
"Lean.Meta.Grind.TopSort.State.mk",
"Lean.Expr.instBEq",
"Std.HashSet",
"Lean.Meta.Grind.TopSort.State.mk.noConfusion",
"Lean.Expr",
"Array",
"And",
"And.intro",
"Lean.Expr.instHashable",
"Eq"
] | true |
List.Sublist.reverse | Init.Data.List.Sublist | [
"Eq.mpr",
"List.Sublist.brecOn",
"congrArg",
"id",
"List.cons",
"List.reverse_cons",
"instHAppendOfAppend",
"List",
"Unit",
"List.Sublist.below",
"List.reverse",
"List.Sublist.refl",
"_private.Init.Data.List.Sublist.0.List.Sublist.reverse.match_1_7",
"List.Sublist",
"List.instAppend",
... | true |
SeparationQuotient.inseparableSetoid_eq_top_iff | Mathlib.Topology.Inseparable | [
"Lattice.toSemilatticeSup",
"Setoid.completeLattice",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"Setoid",
"inseparableSetoid",
"IndiscreteTopology",
"TopologicalSpace",
"Iff",
"OrderTop.toTop",
"Setoid.eq_top_iff",
"BoundedOr... | true |
MeasureTheory.MemLp.comp_fst | Mathlib.MeasureTheory.Function.LpSeminorm.Prod | [
"Eq.mpr",
"False",
"instHSMul",
"MeasureTheory.Measure",
"Preorder.toLT",
"instSMulOfMul",
"MeasureTheory.instSFiniteOfSigmaFinite",
"IsScalarTower.right",
"MeasureTheory.Measure.map_fst_prod",
"congrArg",
"CommSemiring.toSemiring",
"Set.univ",
"PartialOrder.toPreorder",
"MeasureTheory.IsF... | true |
Orientation.definition._proof_2._@.Mathlib.Analysis.InnerProductSpace.Orientation.2114562672._hygCtx._hyg.2 | Mathlib.Analysis.InnerProductSpace.Orientation | [
"AlternatingMap.instAddCommGroup",
"AlternatingMap",
"InnerProductSpace.toNormedSpace",
"Orientation",
"Real.partialOrder",
"Real",
"Semiring.toModule",
"Real.instRCLike",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"IsEmpty.oriented",
"NormedSpace.toModule",
"Orientation.defi... | false |
_private.Mathlib.Data.Set.Card.0.Set.three_lt_ncard._simp_1_1 | Mathlib.Data.Set.Card | [
"Exists",
"exists_and_left",
"And",
"propext",
"Eq"
] | false |
List.scanr_ne_nil | Init.Data.List.Scan.Lemmas | [
"False",
"List.scanr",
"congrArg",
"flip",
"Ne",
"List.scanl_ne_nil._simp_1",
"List",
"True",
"List.reverse",
"of_eq_true",
"congrFun'",
"not_false_eq_true",
"List.reverse_eq_nil_iff._simp_1",
"Eq",
"Not",
"List.scanl",
"Eq.trans",
"List.scanr_eq_scanl_reverse",
"List.nil"
] | true |
Mathlib.Tactic.Widget.StringDiagram.Node.id.inj | Mathlib.Tactic.Widget.StringDiagram | [
"Mathlib.Tactic.Widget.StringDiagram.Node.id.noConfusion",
"Mathlib.Tactic.Widget.StringDiagram.IdNode",
"Mathlib.Tactic.Widget.StringDiagram.Node.id",
"Eq",
"Mathlib.Tactic.Widget.StringDiagram.Node"
] | true |
IsDedekindDomain.normalizedFactorsEquivOfQuotEquiv._proof_7 | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"UniqueFactorizationMonoid.normalizedFactors",
"IsDedekindDomain.normalizedFactorsEquivOfQuotEquiv._proof_5",
"Subtype.mk.congr_simp",
"CommRing",
"Dvd.dvd",
"Semiring.toModule",
"IsScalarTower.right",
"IsDedekindDomain.idealFactorsEquivOfQuotEquiv",
"congrArg",
"CommSemiring.toSemiring",
"Submo... | false |
extDerivWithin_constOfIsEmpty | Mathlib.Analysis.Calculus.DifferentialForm.Basic | [
"ContinuousLinearMap.comp",
"LinearIsometryEquiv.instEquivLike",
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"ContinuousAlternatingMap.instAddCommGroup._proof_7",
"LinearIsometryEquiv.comp_fderivWithin",
"NormedRing.toRing",
"Equiv.instEquivLike",
"NormedSpace.toIsBoundedSM... | true |
_private.Init.Data.String.Lemmas.Pattern.Memcmp.0.String.Slice.Pattern.Internal.memcmpStr_eq_true_iff._proof_1_18 | Init.Data.String.Lemmas.Pattern.Memcmp | [
"Lean.Omega.LinearCombo.coordinate_eval_6",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"String",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"... | false |
CategoryTheory.Functor.IsLocallyDirected.recOn | Mathlib.CategoryTheory.LocallyDirected | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"Exists",
"CategoryTheory.Functor.IsLocallyDirected.rec",
"CategoryTheory.Functor.map",
"And",
"TypeCat.Fun",
"CategoryTheory.types",
"CategoryTheo... | false |
_private.Mathlib.Analysis.Calculus.ContDiff.Bounds.0.norm_iteratedFDerivWithin_comp_le._simp_1_1 | Mathlib.Analysis.Calculus.ContDiff.Bounds | [
"Membership.mem",
"Set.preimage",
"propext",
"Eq",
"Set.instMembership",
"Set.mem_preimage",
"Set"
] | false |
Int8.toInt_div | Init.Data.SInt.Lemmas | [
"instPowNat",
"Eq.mpr",
"instHDiv",
"congrArg",
"Int8.toBitVec_div",
"Int8",
"BitVec.toInt_sdiv",
"BitVec",
"Int8.toInt",
"id",
"HDiv.hDiv",
"instOfNatNat",
"Int",
"instDivInt8",
"BitVec.sdiv",
"instNatPowNat",
"Int.tdiv",
"HPow.hPow",
"Int.bmod",
"Nat",
"Int8.toInt_toBitVec"... | true |
ContinuousMultilinearMap.compAlongComposition._proof_3 | Mathlib.Analysis.Analytic.Composition | [
"FormalMultilinearSeries.applyComposition._proof_1",
"CommRing",
"Continuous",
"Pi.topologicalSpace",
"Composition.length",
"CommSemiring.toSemiring",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Continuous.comp",
"Co... | false |
Polynomial.nthRootsFinset_def | Mathlib.Algebra.Polynomial.Roots | [
"Multiset.toFinset",
"Eq.mpr",
"IsDomain",
"CommRing",
"CommSemiring.toSemiring",
"Lean.Meta.instFastSubsingletonForall",
"HEq.refl",
"Finset",
"Decidable",
"Lean.Meta.FastSubsingleton.elim",
"Multiset",
"Eq.casesOn",
"id",
"Polynomial.nthRoots",
"CommRing.toCommSemiring",
"Lean.Meta.i... | true |
DirectSum.id._proof_1 | Mathlib.Algebra.DirectSum.Basic | [
"Eq.mpr",
"Inhabited.default",
"AddMonoidHom.instAddMonoidHomClass",
"instAddCommMonoidDirectSum",
"congrArg",
"Unique",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.id",
"AddZeroClass.toAddZero",
"map_zero",
"id",
"AddCommMonoid",
"decidableEq_of_subsingleton",
"AddZero.toZero",
"Unique.in... | false |
_private.Init.Data.Vector.Erase.0.Vector.eraseIdx_append._proof_3 | Init.Data.Vector.Erase | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Om... | false |
Primrec.list_cons | Mathlib.Computability.Primrec.List | [
"List.cons",
"List",
"Primcodable",
"Primcodable.list",
"_private.Mathlib.Computability.Primrec.List.0.list_cons'",
"Primcodable.prim",
"Primrec₂"
] | true |
_private.Init.Data.Vector.OfFn.0.Vector.ofFnM.go._unary._proof_2 | Init.Data.Vector.OfFn | [
"Array.push",
"congrArg",
"instOfNatNat",
"Array",
"instHAdd",
"Nat.add_left_cancel_iff._simp_1",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"of_eq_true",
"instAddNat",
"Array.size_push",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Array.size",
"Eq.trans"
] | false |
AlgebraicGeometry.instIsStableUnderCompositionSchemeLocallyOfFiniteType | Mathlib.AlgebraicGeometry.Morphisms.FiniteType | [
"AlgebraicGeometry.Scheme",
"RingHom.FiniteType",
"CategoryTheory.MorphismProperty.IsStableUnderComposition",
"AlgebraicGeometry.HasRingHomProperty.stableUnderComposition",
"RingHom.finiteType_stableUnderComposition",
"AlgebraicGeometry.instHasRingHomPropertyLocallyOfFiniteTypeFiniteType",
"AlgebraicGeo... | true |
Pregroupoid.mk._flat_ctor | Mathlib.Geometry.Manifold.StructureGroupoid | [
"Set.univ",
"Function.comp",
"Membership.mem",
"Exists",
"id",
"Set.instInter",
"Inter.inter",
"Pregroupoid",
"TopologicalSpace",
"And",
"Set.preimage",
"IsOpen",
"Eq",
"Set.instMembership",
"Pregroupoid.mk",
"Set"
] | false |
Array.eraseIdxIfInBounds | Init.Data.Array.Basic | [
"dite",
"Array",
"Nat",
"LT.lt",
"Nat.decLt",
"instLTNat",
"Array.size",
"Not",
"Array.eraseIdx"
] | true |
ArithmeticFunction.instModule._proof_5 | Mathlib.NumberTheory.ArithmeticFunction.Defs | [
"Nat.instMulZeroClass",
"ArithmeticFunction.ext",
"instHSMul",
"ArithmeticFunction.instFunLikeNat",
"AddMonoid.toAddSemigroup",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Function.hasSMul",
"DistribSMul.toSMulZeroClass",
"SMul.mk",
"ArithmeticFunct... | false |
Set.compl_Ioc | Mathlib.Order.Interval.Set.LinearOrder | [
"Set.Ioc",
"Set.Ioi",
"Compl.compl",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Set.instUnion",
"DistribLattice.toLattice",
"Set.instCompl",
"_private.Mathlib.Order.Interval.Set.LinearOrder.0.Set.compl_Ioc._proof_1_1",
"Set.Iic",
"Union.union",
"Eq",
"instD... | true |
Finsupp.instNonUnitalNonAssocRing._proof_6 | Mathlib.Data.Finsupp.Pointwise | [
"Finsupp.instFunLike",
"NonUnitalNonAssocRing",
"NonUnitalNonAssocRing.toAddCommGroup",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"SubNegMonoid.toSub",
"instHSub",
"Pi.in... | false |
Std.ExtTreeSet.toArray | Std.Data.ExtTreeSet.Basic | [
"Ordering",
"Std.ExtTreeSet.inner",
"Std.ExtTreeMap.keysArray",
"Std.TransCmp",
"Array",
"Unit",
"Std.ExtTreeSet"
] | true |
Mathlib.Tactic.Order.AtomicFact.lt | Mathlib.Tactic.Order.CollectFacts | [
"Lean.Expr",
"Mathlib.Tactic.Order.AtomicFact.lt",
"Nat",
"Mathlib.Tactic.Order.AtomicFact"
] | true |
CategoryTheory.Limits.Cotrident.ext._proof_6 | Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers | [
"CategoryTheory.Limits.WalkingParallelFamily.one",
"CategoryTheory.Functor",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.WalkingParallelFamily",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.CoconeMorphism.ho... | false |
Array.forIn'_yield_eq_foldlM | Init.Data.Array.Monadic | [
"Iff.mpr",
"List.forIn'_yield_eq_foldlM",
"List.foldlM",
"congrArg",
"List.attachWith",
"List.attachWith_mem_toArray",
"List.forIn'_toArray",
"Monad.toApplicative",
"List.map",
"List.length_attach",
"Array.instMembership",
"Membership.mem",
"Array.foldlM_attachWith.match_1",
"Array.casesOn... | true |
Std.Sat.AIG.CacheHit.casesOn | Std.Sat.AIG.Basic | [
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.CacheHit.rec",
"Std.Sat.AIG.CacheHit",
"Std.Sat.AIG.CacheHit.mk",
"Array",
"GetElem.getElem",
"Array.instGetElemNatLtSize",
"Nat",
"LT.lt",
"instLTNat",
"Eq",
"Array.size"
] | false |
Std.Tactic.BVDecide.LRAT.Internal.Clause.eval | Std.Tactic.BVDecide.LRAT.Internal.Clause | [
"Std.Tactic.BVDecide.LRAT.Internal.Clause.instEntailsLiteral",
"Std.Tactic.BVDecide.LRAT.Internal.Clause.toList",
"Std.Tactic.BVDecide.LRAT.Internal.Entails.eval",
"Std.Tactic.BVDecide.LRAT.Internal.Clause",
"Bool",
"List.any",
"Std.Tactic.BVDecide.LRAT.Internal.Clause.instDecidableEvalLiteral",
"Deci... | true |
Std.Time.TimeZone | Std.Time.Zoned.TimeZone | [
"Std.Time.TimeZone.mk"
] | true |
Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.coreToInt.injEq | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Expr",
"And",
"Int.Linear.Expr",
"Eq.ndrec",
"Eq.refl",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.coreToInt.inj",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.coreToInt",
"Eq",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof"
] | true |
Prime.nat_prime | Mathlib.Data.Nat.Prime.Defs | [
"Iff.mpr",
"Nat.Prime",
"Nat.prime_iff",
"Prime",
"Nat",
"Nat.instCommMonoidWithZero"
] | true |
Bundle.Pretrivialization.continuousOn_continuousLinearMapCoordChange | Mathlib.Topology.VectorBundle.Hom | [
"ContinuousLinearMap.comp",
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Continuous",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousLinearMap.topologicalAddGroup",
"FiberBundle",
"Conti... | true |
Batteries.RBNode.Path.Balanced.brecOn | Batteries.Data.RBMap.Alter | [
"Batteries.RBNode",
"Batteries.RBNode.Path",
"Batteries.RBNode.Path.Balanced.below.root",
"Batteries.RBNode.Path.Balanced.below.blackR",
"instOfNatNat",
"instHAdd",
"Batteries.RBColor.red",
"HAdd.hAdd",
"Batteries.RBColor",
"Nat",
"Batteries.RBNode.Path.Balanced",
"Batteries.RBNode.Path.Balanc... | true |
CategoryTheory.Limits.BinaryBicone.ofColimitCocone._proof_8 | Mathlib.CategoryTheory.Preadditive.Biproducts | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.BinaryCofan.IsColimit.desc",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.WalkingPair.right",
"Categ... | false |
_private.Mathlib.SetTheory.Ordinal.Notation.0.ONote.exists_lt_omega0_opow' | Mathlib.SetTheory.Ordinal.Notation | [
"Iff.mpr",
"Preorder.toLT",
"Ordinal.partialOrder",
"instIsBotZeroClass",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"Order.IsSuccLimit",
"Exists.imp",
"And.casesOn",
"Ordinal.addMonoidWithOne",
"Ordinal.one",
"LT.lt.ne'",
"zero_lt_one",
"And",
... | true |
StarRingEquivClass.toStarRingEquiv.congr_simp | Mathlib.Algebra.Star.StarAlgHom | [
"Mul",
"Eq.rec",
"RingEquivClass",
"StarRingEquivClass.toStarRingEquiv",
"StarRingEquivClass",
"EquivLike",
"Star",
"Eq.refl",
"Eq",
"StarRingEquiv",
"Add"
] | true |
CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom' | Mathlib.CategoryTheory.Monoidal.Category | [
"Eq.mpr",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.IsIso.inv_hom_id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.MonoidalCategory.whis... | true |
TopCat.Path.hom₁._autoParam | Mathlib.Topology.Homotopy.TopCat.Path | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Option.forIn_yield_eq_elim | Init.Data.Option.Monadic | [
"Pure.pure",
"congrArg",
"instForInOfForIn'",
"Option.instMembership",
"Monad.toApplicative",
"Option.casesOn",
"Option.some",
"inferInstance",
"LawfulMonad.bind_pure_comp",
"LawfulApplicative.toLawfulFunctor",
"LawfulMonad",
"ForIn.forIn",
"Applicative.toPure",
"Membership",
"ForInStep"... | true |
Real.tan_arccos | Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse | [
"Eq.mpr",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"Real.pi",
"DivisionCommMonoid.toDivisionMonoid",
"Real.arcsin",
"congrArg",
"Real.instInv",
"Real.instDivInvMonoid",
"Real.instSub",
"Nat.instAtLeastTwoHAddOfNat",
"HSub.hSub",
"id",
"HDiv.hDiv",
"instOfNatNat",
"Real.tan_pi_div_tw... | true |
_private.Init.Data.Option.Lemmas.0.Option.not_rel_none_some.match_1_1 | Init.Data.Option.Lemmas | [
"False",
"Option.Rel.casesOn",
"Option.ctorIdx",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Option.some",
"Option.Rel",
"Option.none",
"Option.Rel.some",
"Eq.refl",
"HEq",
"Option.Rel.none",
"Eq",
"Option"
] | false |
Algebra.TensorProduct.mul | Mathlib.RingTheory.TensorProduct.Basic | [
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.module",
"LinearMap",
"smulCommClass_self",
"CommSemiring",
"NonUnital... | true |
CategoryTheory.ExponentiableMorphism.unit_pushforwardComp_hom_assoc | Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.ChosenPullbacksAlong",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ExponentiableMorphism.pushforward",
"CategoryTheory.Functor.category",
"CategoryTheory.Functo... | true |
ContinuousMultilinearMap.alternatization._proof_3 | Mathlib.Topology.Algebra.Module.Alternating.Basic | [
"instHSMul",
"MonoidHom.instFunLike",
"Finset.univ",
"Units.instSMulZeroClass",
"MonoidHom",
"ContinuousMultilinearMap.instAddMonoid",
"Monoid.toMulOneClass",
"congrArg",
"ContinuousMultilinearMap.domDomCongr",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Finset",
"Cont... | false |
CategoryTheory.BiconeHom.decidableEq._proof_11 | Mathlib.CategoryTheory.Limits.Bicones | [
"CategoryTheory.Bicone.right",
"HEq.refl",
"HEq",
"CategoryTheory.BiconeHom",
"CategoryTheory.Category"
] | false |
BitVec.ofNat_toNat | Init.Data.BitVec.Bootstrap | [
"instPowNat",
"BitVec.setWidth",
"congrArg",
"BitVec.eq_of_toNat_eq",
"BitVec",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"BitVec.toNat",
"BitVec.ofNat",
"instNatPowNat",
"HMod.hMod",
"BitVec.toNat_ofNat",
"HPow.hPow",
"Nat",
"congr",
"True",
"eq_self",
"of_eq_true",
"BitVec.t... | true |
AlgebraicGeometry.Scheme.instAbelianSheafEtaleSmallEtaleTopology | Mathlib.AlgebraicGeometry.Sites.AffineEtale | [
"AlgebraicGeometry.Scheme.instCategoryEtale",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.PreservesFilteredColimitsOfSize",
"CategoryTheory.sheafIsAbelian",
"CategoryTheory.Abelian",
"AlgebraicGeometry.Scheme.Etale",
"... | true |
_private.Init.Data.List.Perm.0.List.perm_middle.match_1_1 | Init.Data.List.Perm | [
"List.cons",
"List",
"List.casesOn",
"List.nil"
] | false |
Lean.Elab.Term.Do.ToTerm.Kind._sizeOf_1 | Lean.Elab.Do.Legacy | [
"Lean.Elab.Term.Do.ToTerm.Kind.rec",
"instOfNatNat",
"Nat",
"Lean.Elab.Term.Do.ToTerm.Kind",
"OfNat.ofNat"
] | false |
Filter.HasBasis.lift | Mathlib.Order.Filter.Lift | [
"Filter.instMembership",
"Sigma.exists._simp_1",
"congrArg",
"PartialOrder.toPreorder",
"Monotone",
"Membership.mem",
"Exists",
"exists_and_left._simp_1",
"CompleteLattice.toConditionallyCompleteLattice",
"HasSubset.Subset",
"Sigma.fst",
"iff_self",
"funext",
"And",
"Filter.HasBasis",
... | true |
CoalgebraStruct.mk._flat_ctor | Mathlib.RingTheory.Coalgebra.Basic | [
"CoalgebraStruct",
"Semiring.toModule",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"TensorProduct",
"Module",
"RingHom.id",
"Semiring.toNo... | false |
_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.filterMap._proof_9 | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.link",
"Std.DTreeMap.Internal.Impl.Tree.balanced_impl._simp_1",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"of_eq_true",
"instAddNat",
"OfNat.ofNat",
... | false |
CategoryTheory.ShortComplex.Homotopy.symm_h₀ | Mathlib.Algebra.Homology.ShortComplex.Preadditive | [
"NegZeroClass.toNeg",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.Homotopy",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.ShortComplex.Homotopy.symm",
"SubtractionMonoid.toSubNegZ... | true |
Convexity.map_iConvexComb | Mathlib.Geometry.Convex.ConvexSpace.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"Function.comp",
"Convexity.IsAffineMap.map_iConvexComb",
"PartialOrder",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddMonoidWithOne.toOne",
... | true |
QuadraticModuleCat.ofIso._proof_2 | Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat | [
"CommRing",
"Semiring.toModule",
"LinearEquiv.right_inv",
"QuadraticMap.IsometryEquiv.symm",
"QuadraticMap.IsometryEquiv.toIsometry",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"DFunLike.ext",
"QuadraticMap.IsometryEquiv",
"QuadraticForm",
"QuadraticModuleCat.Hom.ext",
"Categor... | false |
Batteries.CodeAction.startTacticStub | Batteries.CodeAction.Misc | [
"Lean.Elab.ElabInfo.stx",
"Pure.pure",
"Lean.FileMap.utf8RangeToLspRange",
"Lean.Server.RequestContext",
"Lean.Json",
"Lean.Server.Snapshots.Snapshot",
"Lean.Syntax.Range.mk",
"Lean.Lsp.PartialResultParams.mk",
"Lean.Server.RequestError",
"Lean.Lsp.WorkspaceEdit",
"instMonadReaderOfReaderTOfMona... | true |
PrimeMultiset.prod_dvd_prod | Mathlib.Data.PNat.Factors | [
"Iff.mpr",
"Dvd.dvd",
"instDistribLatticePrimeMultiset",
"PartialOrder.toPreorder",
"semigroupDvd",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"PrimeMultiset.prod",
"DistribLattice.toLattice",
"LE.le",
"instCommMonoidPNat",
"PrimeMultiset.prod_dvd_iff",
"CommMonoid.toMonoid",
"Monoi... | true |
AlgebraicGeometry.ExistsHomHomCompEqCompAux._sizeOf_inst | Mathlib.AlgebraicGeometry.AffineTransitionLimit | [
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"SizeOf.mk",
"AlgebraicGeometry.ExistsHomHomCompEqCompAux",
"CategoryTheory.Category.toCategoryStruct",
"AlgebraicGeometry.Scheme.instCategory",
"SizeOf"... | false |
Lean.Lsp.DocumentColorParams.workDoneToken?._inherited_default | Lean.Data.Lsp.LanguageFeatures | [
"id",
"Option.none",
"Lean.Lsp.ProgressToken",
"Option"
] | false |
_private.Std.Data.DHashMap.Internal.HashesTo.0.Std.DHashMap.Internal.List.HashesTo.containsKey_eq_false._simp_1_1 | Std.Data.DHashMap.Internal.HashesTo | [
"Membership.mem",
"Exists",
"Sigma.fst",
"Bool.true",
"List",
"Std.Internal.List.containsKey",
"And",
"BEq.beq",
"Std.Internal.List.containsKey_eq_true_iff_exists_mem",
"List.instMembership",
"propext",
"Bool",
"BEq",
"Eq",
"Sigma"
] | false |
Additive.subtractionMonoid._proof_1 | Mathlib.Algebra.Group.TypeTags.Basic | [
"Additive",
"DivisionMonoid",
"DivisionMonoid.toInvolutiveInv",
"Additive.involutiveNeg",
"InvolutiveNeg.neg_neg",
"InvolutiveNeg.toNeg",
"Eq",
"Neg.neg"
] | false |
MeasureTheory.exists_nonempty_inter_of_measure_univ_lt_sum_measure | Mathlib.MeasureTheory.Measure.MeasureSpace | [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Iff.mpr",
"Eq.mpr",
"Mathlib.Tactic.Push.not_and_eq",
"MeasureTheory.Measure",
"Preorder.toLT",
"ENNReal.instAddCommMonoid",
"Finset",
"Set.univ",
"PartialOrder.toPreorder",
"MeasureTheory.NullMeasurableSet",
"Preorder.toLE",
"Disjoint",
"Membersh... | true |
Lean.Doc.MarkdownM.Context.inLink._default | Lean.DocString.Markdown | [
"id",
"Bool",
"Bool.false"
] | false |
CategoryTheory.Limits.botSquareIsPushout | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | [
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Limits.PushoutCocone.inl",
"CategoryTheory.Limits.rightSquareIsPushout",
"CategoryTheory.Limits.PushoutCocone.pasteVert",
"CategoryTheory.Limits.WalkingPair",... | true |
Std.TreeSet.Raw.insert | Std.Data.TreeSet.Raw.Basic | [
"Unit.unit",
"Std.TreeSet.Raw.mk",
"Std.TreeMap.Raw.insertIfNew",
"Ordering",
"Std.TreeSet.Raw",
"Unit",
"Std.TreeSet.Raw.inner"
] | true |
List.min?_eq_some_iff_subtype | Init.Data.List.MinMax | [
"Iff.mpr",
"List.min?_eq_min?_attach",
"Eq.mpr",
"List.min?",
"Iff.of_eq",
"congrArg",
"Std.LawfulOrderMin",
"instInhabitedTrue",
"Subtype.forall._simp_1",
"_private.Init.Data.List.MinMax.0.List.min?_eq_some_iff_subtype._simp_1_1",
"Option.some",
"Membership.mem",
"Exists",
"exists_and_rig... | true |
Finset.disjSups_empty_left | Mathlib.Data.Finset.Sups | [
"SProd.sprod",
"congrArg",
"Finset",
"Finset.filter_empty",
"DecidableRel",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"OrderBot",
"SemilatticeSup.toMax",
"Finset.instEmptyCollection",
"Prod.fst",
"Finset.instSProd",
"Max.max",
"Finset.disjSups",
"True",
"eq_self",
"of... | true |
CategoryTheory.Functor.instLaxMonoidalMonMapAddMon._proof_6 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.AddMon.Hom.ext'",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Functor.instIsAddMonHomμ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.IsAddMonHom",
"CategoryTheory.MonoidalCategory",
"Category... | false |
_private.Mathlib.Order.Filter.AtTopBot.ModEq.0.Nat.frequently_even._simp_1_1 | Mathlib.Order.Filter.AtTopBot.ModEq | [
"Nat.instMod",
"instHMod",
"instOfNatNat",
"HMod.hMod",
"Nat",
"Even",
"propext",
"instAddNat",
"Nat.even_iff",
"OfNat.ofNat",
"Eq"
] | false |
EMetric.hausdorffEdist_union_le | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"Set.instUnion",
"ENNReal.instMax",
"LE.le",
"PseudoEMetricSpace",
"Max.max",
"Metric.hausdorffEDist",
"ENNReal.instLE",
"ENNReal",
"Metric.hausdorffEDist_union_le",
"Union.union",
"Set"
] | true |
Decidable.rec | Init.Prelude | [
"Decidable.isTrue",
"Decidable",
"Decidable.isFalse",
"Not"
] | false |
NNReal.coe_multiset_prod | Mathlib.Data.NNReal.Basic | [
"NNReal.toRealHom",
"RingHom.instRingHomClass",
"NNReal.instCommSemiring",
"Real",
"Multiset.map",
"Multiset.prod",
"RingHom",
"Real.semiring",
"Multiset",
"RingHomClass.toMonoidWithZeroHomClass",
"NNReal",
"NonAssocSemiring.toMulZeroOneClass",
"MonoidWithZeroHomClass.toMonoidHomClass",
"m... | true |
SModEq.bot | Mathlib.LinearAlgebra.SModEq.Basic | [
"Submodule.Quotient.eq",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Submodule",
"congrArg",
"sub_eq_zero",
"AddCommGroup.toAddCommMonoid",
"Submodule.mem_bot",
"Submodule.Quotient.mk",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Submodule.hasQuotient",
... | true |
imp_congr_left | Init.Core | [
"Iff.mpr",
"Function.comp",
"Iff",
"Iff.intro",
"Iff.mp"
] | true |
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