name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
List.all_flatten | Init.Data.List.Lemmas | [
"List.all",
"congrArg",
"Bool.and",
"List.rec",
"List.cons",
"List.all_append",
"Bool.true",
"instHAppendOfAppend",
"List",
"True",
"eq_self",
"Bool",
"of_eq_true",
"congrFun'",
"List.instAppend",
"Eq",
"HAppend.hAppend",
"Eq.trans",
"List.flatten"
] | true |
ArithmeticFunction.IsMultiplicative.multiplicative_factorization | Mathlib.NumberTheory.ArithmeticFunction.Defs | [
"CommMonoidWithZero.toCommMonoid",
"Nat.Coprime",
"MulOne.toOne",
"Nat.instMulZeroClass",
"HMul.hMul",
"ArithmeticFunction.instFunLikeNat",
"MulZeroClass.toMul",
"Nat.instMonoid",
"Ne",
"instMulNat",
"instOfNatNat",
"CommMonoidWithZero.toMonoidWithZero",
"MulZeroOneClass.toMulOneClass",
"M... | true |
_private.Init.Data.Array.Lemmas.0.Array.forIn'.loop.match_3.eq_1 | Init.Data.Array.Lemmas | [
"instOfNatNat",
"LE.le",
"instLENat",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"Array.forIn'.loop.match_3",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Array.size"
] | true |
Matrix.blockDiagonal_conjTranspose | Mathlib.Data.Matrix.Block | [
"Eq.mpr",
"Matrix.blockDiagonal_transpose",
"Matrix.blockDiagonal",
"congrArg",
"Matrix",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Matrix.blockDiagonal_map",
"id",
"StarAddMonoid.toInvolutiveStar",
"AddZero.toZero",
"Matrix.transpose",
"star_zero",
"AddMonoid",
"Matrix.map"... | true |
Std.DTreeMap.Internal.Impl.WF.inter! | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Eq.mpr",
"Ord",
"congrArg",
"Std.TransOrd",
"id",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Std.DTreeMap.Internal.Impl.inter!",
"Std.DTreeMap.Internal.Impl.inter_eq_inter!",
"Std.DTreeMap.Internal.Impl.inter",
"Eq.symm",
"Eq",
"Std.DTreeMap.Internal.Impl",
... | true |
Batteries.Tactic.CollectOpaques.collect | Batteries.Tactic.PrintOpaques | [
"Inhabited.default",
"Batteries.Tactic.CollectOpaques.State",
"instInhabitedOfMonad",
"instInhabitedPUnit",
"Lean.Meta.MetaM",
"Batteries.Tactic.CollectOpaques.M",
"Unit",
"Lean.Meta.instMonadMetaM",
"Lean.Name",
"StateT.instMonad",
"StateT",
"instInhabitedReaderT",
"Lean.Environment"
] | true |
_private.Mathlib.Analysis.Convex.BetweenList.0.List.sbtw_triple._simp_1_3 | Mathlib.Analysis.Convex.BetweenList | [
"Membership.mem",
"List.cons",
"List",
"List.instMembership",
"propext",
"Or",
"List.mem_cons",
"Eq"
] | false |
CategoryTheory.IsIso.inv_eq_of_inv_hom_id | Mathlib.CategoryTheory.Iso | [
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.inv",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category",
"_private.Mathlib.CategoryTheor... | true |
Aesop.OrderedHashSet.ctorIdx | Aesop.Util.OrderedHashSet | [
"Aesop.OrderedHashSet",
"Nat",
"Hashable",
"BEq"
] | false |
_private.Mathlib.Tactic.Widget.LibraryRewrite.0.Mathlib.Tactic.LibraryRewrite.rpc.match_1 | Mathlib.Tactic.Widget.LibraryRewrite | [
"Lean.SubExpr.GoalLocation.ctorIdx",
"Lean.FVarId",
"Nat.hasNotBit",
"Lean.SubExpr.Pos",
"Lean.SubExpr.GoalLocation",
"Lean.SubExpr.GoalLocation.hypValue",
"_private.Mathlib.Tactic.Widget.LibraryRewrite.0.Mathlib.Tactic.LibraryRewrite.rpc._sparseCasesOn_1"
] | false |
DivisibleHull.mk_eq_mk | Mathlib.GroupTheory.DivisibleHull | [
"PNat.val",
"Eq.mpr",
"instHSMul",
"Equiv.instEquivLike",
"Submonoid.mul",
"instLinearOrderPNat",
"Equiv.exists_congr_left",
"LocalizedModule",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LocalizedModule.mk_eq",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"Partia... | true |
Dvd.elim | Mathlib.Algebra.Divisibility.Basic | [
"Semigroup",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"semigroupDvd",
"Eq",
"Exists.elim",
"instHMul"
] | true |
Vector.toArray_swapAt! | Init.Data.Vector.Lemmas | [
"Array.swapAt!",
"Vector",
"Prod.mk",
"Prod.fst",
"Array",
"Vector.swapAt!",
"Nat",
"Prod",
"Eq",
"Prod.snd",
"Vector.toArray",
"rfl"
] | true |
NonUnitalNonAssocCommSemiring.ext | Mathlib.Algebra.Ring.Ext | [
"HMul.hMul",
"NonUnitalNonAssocCommSemiring",
"Distrib.toAdd",
"NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring_injective",
"instHAdd",
"Distrib.toMul",
"HAdd.hAdd",
"NonUnitalNonAssocSemiring.ext",
"NonUnitalNonAssocCommSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocSemiring.t... | true |
Lean.Elab.Tactic.BVDecide.Frontend.ReflectionResult.casesOn | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide | [
"Lean.Elab.Tactic.BVDecide.Frontend.ReflectionResult",
"Lean.instBEqFVarId",
"Lean.Elab.Tactic.BVDecide.Frontend.ReflectionResult.rec",
"Std.HashSet",
"Lean.Expr",
"Lean.FVarId",
"Lean.instHashableFVarId",
"Lean.Elab.Tactic.BVDecide.Frontend.M",
"Std.Tactic.BVDecide.BVLogicalExpr",
"Lean.Elab.Tact... | false |
CategoryTheory.Triangulated.SpectralObject.Hom.ext_iff | Mathlib.CategoryTheory.Triangulated.SpectralObject | [
"CategoryTheory.Functor",
"CategoryTheory.Triangulated.SpectralObject",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Triangulated.SpectralObject.Hom",
"CategoryTheory.Triangulated.SpectralObject.Hom.hom",
"PartialOrder.toPreor... | true |
_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformFun.uniformSpace_eq_iInf_precomp_of_cover.match_1_1 | Mathlib.Topology.UniformSpace.UniformConvergenceTopology | [
"Equiv.instEquivLike",
"Set.iInter",
"Function.comp",
"Membership.mem",
"Set.Elem",
"Equiv",
"UniformFun.gen",
"Prod.mk",
"Sigma.fst",
"Prod.map",
"UniformFun.toFun",
"Set.preimage",
"UniformFun",
"Sigma.mk",
"Prod",
"Prod.casesOn",
"Sigma.snd",
"Subtype.val",
"Set.instMembership... | false |
CategoryTheory.ShortComplex.SnakeInput.δ_apply | Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory | [
"CategoryTheory.Functor.preservesFiniteLimits_of_preservesHomology",
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Functor",
"CategoryTheory.ShortComplex.SnakeInput.L₃",
"CategoryTheory.Limits.PreservesFiniteLimits",
"CategoryTheory.Limits.Concrete... | true |
Set.Ici_inj | Mathlib.Order.Interval.Set.Basic | [
"Set.Ici",
"PartialOrder.toPreorder",
"Function.Injective.eq_iff",
"PartialOrder",
"Iff",
"Set.Ici_injective",
"Eq",
"Set"
] | true |
Function.Surjective.semiring._proof_2 | Mathlib.Algebra.Ring.InjSurj | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Monoid.npow",
"Semigroup.toMul",
"One",
"HMul.hMul",
"Pow",
"Function.Surjective.monoidWithZero",
"Mul",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instDistribOfSemiring",
"Monoid.toPow",
"AddMonoidWithOne.toOne",
"instHAdd",
"... | false |
Matroid.ofExistsFiniteIsBase._proof_4 | Mathlib.Combinatorics.Matroid.IndepAxioms | [
"Eq.mpr",
"Matroid.existsMaximalSubsetProperty_of_bdd",
"Set.encard",
"Matroid.ExchangeProperty",
"ENat.instNatCast",
"Matroid.ExistsMaximalSubsetProperty",
"congrArg",
"Set.Finite",
"Exists",
"id",
"HasSubset.Subset",
"LE.le",
"Nat.cast",
"instLEENat",
"And.casesOn",
"Set.encard_mono"... | false |
RingHom.locally_iff_finite | Mathlib.RingTheory.RingHom.Locally | [
"_private.Mathlib.RingTheory.RingHom.Locally.0.RingHom.locally_iff_finite.match_1_1",
"CommRing",
"Semiring.toModule",
"Algebra.algebraMap",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"Finset",
"Ideal.span_eq_top_iff_finite",
"Localization.Away",
"RingHom",
"Membership.mem",
"Ex... | true |
_private.Mathlib.NumberTheory.WellApproximable.0.AddCircle.addWellApproximable_ae_empty_or_univ._simp_1_3 | Mathlib.NumberTheory.WellApproximable | [
"Lattice.toSemilatticeSup",
"Set.sup_eq_union",
"Set.instUnion",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"Set.instDistribLattice",
"Max.max",
"Union.union",
"Eq.symm",
"Eq",
"Set"
] | false |
NNDist.casesOn | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"NNDist",
"NNReal",
"NNDist.rec",
"NNDist.mk"
] | false |
_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.map._simp_3 | Mathlib.Data.Analysis.Filter | [
"Filter.instMembership",
"Filter.mem_sets",
"Membership.mem",
"Filter.sets",
"propext",
"Eq",
"Set.instMembership",
"Filter",
"Set"
] | false |
_private.Lean.Elab.BuiltinNotation.0.Lean.Elab.Term.expandCDot?.go.match_3 | Lean.Elab.BuiltinNotation | [
"Lean.Syntax.node",
"Lean.Syntax.ctorIdx",
"Lean.SourceInfo",
"Lean.Syntax",
"Nat.hasNotBit",
"Array",
"_private.Lean.Elab.BuiltinNotation.0.Lean.Elab.Term.hasCDot._sparseCasesOn_1",
"Lean.SyntaxNodeKind"
] | false |
Lean.MetavarContext.MkBinding.Context.binderInfoForMVars | Lean.MetavarContext | [
"Lean.BinderInfo",
"Lean.MetavarContext.MkBinding.Context"
] | true |
Lean.Grind.Semiring.mul_one | Init.Grind.Ring.Basic | [
"HMul.hMul",
"Lean.Grind.Semiring.toMul",
"Lean.Grind.Semiring.ofNat",
"Lean.Grind.Semiring",
"OfNat.ofNat",
"Eq",
"instHMul"
] | true |
SimpleGraph.IsContained.lineGraph | Mathlib.Combinatorics.SimpleGraph.LineGraph | [
"SimpleGraph.IsContained",
"SimpleGraph.Copy",
"Set.Elem",
"Nonempty.some",
"Nonempty.intro",
"SimpleGraph.edgeSet",
"SimpleGraph",
"SimpleGraph.Copy.lineGraph",
"SimpleGraph.lineGraph",
"Sym2"
] | true |
_private.Mathlib.Algebra.GroupWithZero.Basic.0.IsNilpotent.pow_succ.match_1_1 | Mathlib.Algebra.GroupWithZero.Basic | [
"Monoid.toPow",
"MonoidWithZero",
"Exists.casesOn",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Nat",
"Exists.intro",
"Zero.toOfNat0",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"IsNilpotent",
"Eq",
"MonoidWithZero.toMonoid",
"MulZeroClass.toZero"
] | false |
Float32.mk | Init.Data.Float32 | [
"Float32.mk",
"FloatSpec.float",
"float32Spec",
"Float32"
] | true |
_private.Batteries.Tactic.HelpCmd.0.Batteries.Tactic.elabHelpCats.match_1 | Batteries.Tactic.HelpCmd | [
"Lean.Parser.ParserCategory",
"Prod.mk",
"Lean.Name",
"Prod",
"Prod.casesOn"
] | false |
MeasureTheory.Measure.AbsolutelyContinuous.null_mono | Mathlib.MeasureTheory.Measure.AbsolutelyContinuous | [
"MeasureTheory.Measure",
"MeasureTheory.Measure.AbsolutelyContinuous",
"MeasurableSpace",
"ENNReal",
"Zero.toOfNat0",
"ENNReal.instZero",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"MeasureTheory.Measure.instFunLike",
"Set"
] | true |
Submonoid.ext | Mathlib.Algebra.Group.Submonoid.Defs | [
"Membership.mem",
"Iff",
"SetLike.ext",
"Submonoid.instSetLike",
"MulOneClass",
"Eq",
"SetLike.instMembership",
"Submonoid"
] | true |
Lean.Compiler.specializeAttr._regBuiltin.Lean.Compiler.specializeAttr.declRange_3 | Lean.Compiler.Specialize | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"IO",
"Lean.Name.mkStr3",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk"
] | false |
ConGen.Rel | Mathlib.GroupTheory.Congruence.Defs | [
"ConGen.Rel.mul",
"Mul",
"ConGen.Rel.trans",
"ConGen.Rel.symm",
"ConGen.Rel.refl",
"ConGen.Rel.of"
] | true |
LinearEquiv.mapMatrix._proof_2 | Mathlib.Data.Matrix.Basic | [
"instHSMul",
"Matrix.module",
"DistribMulAction.toDistribSMul",
"Matrix",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.toAddHom",
"Matrix.addCommMonoid",
"AddCommMonoid",
"RingHomInvPair",
"AddZero.toZero",
"RingHom.instFunLike"... | false |
_private.Mathlib.MeasureTheory.Integral.IntegralEqImproper.0.MeasureTheory.tendsto_limUnder_of_hasDerivAt_of_integrableOn_Ioi._simp_1_2 | Mathlib.MeasureTheory.Integral.IntegralEqImproper | [
"Set.Ici",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"Set.mem_Ici",
"propext",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | false |
Plausible.SampleableExt.noConfusionType | Plausible.Sampleable | [
"Plausible.Arbitrary",
"Plausible.Shrinkable",
"Plausible.SampleableExt.casesOn",
"HEq",
"Repr",
"Eq",
"Plausible.SampleableExt"
] | false |
CategoryTheory.NatTrans.removeRightOp | Mathlib.CategoryTheory.Opposites | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.NatTrans.removeRightOp._proof_2",
"Quiver.Hom.unop",
"CategoryTheory.NatTrans.mk",
"CategoryTheory.Category.opposite",
"CategoryTheory.Category.toCategor... | true |
SheafOfModules.pushforwardOver.eq_1 | Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous | [
"CategoryTheory.Functor.op",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.GrothendieckTopology.instIsContinuousOverStarOver",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Functor.category",
"CategoryTheory.Sheaf.over",
"... | true |
WithTop.untopA.eq_1 | Mathlib.Order.WithBot | [
"Classical.arbitrary",
"Nonempty",
"Eq.refl",
"WithTop.untopD",
"WithTop.untopA",
"Eq",
"WithTop"
] | true |
AlgebraicGeometry.Scheme.isoOfEq_hom | Mathlib.AlgebraicGeometry.Restrict | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme.homOfLE",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"Partial... | true |
OnePoint.IsZeroAt.smul_iff | Mathlib.NumberTheory.ModularForms.BoundedAtCusp | [
"smul_left_cancel_iff._simp_2",
"OnePoint.instGLAction",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"Equiv.instEquivLike",
"HMul.hMul",
"OnePoint.infty",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"Matrix",
"instDecidableEqFin",
"Compl... | true |
CategoryTheory.Functor.instIsHomologicalCompOfIsTriangulated | Mathlib.CategoryTheory.Triangulated.HomologicalFunctor | [
"CategoryTheory.Functor.IsTriangulated",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Functor",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Abelian",
"Membership.mem",
"CategoryTheory.Functor.IsHomological",
"CategoryT... | true |
Mathlib.Meta.FunProp.LambdaTheorems | Mathlib.Tactic.FunProp.Theorems | [
"Mathlib.Meta.FunProp.LambdaTheorems.mk"
] | true |
instNonAssocRingWithConvMatrix._proof_3 | Mathlib.LinearAlgebra.Matrix.WithConv | [
"HMul.hMul",
"Matrix",
"NonAssocSemiring.one_mul",
"NonAssocSemiring.toOne",
"NonUnitalNonAssocSemiring.toMul",
"instNonAssocSemiringWithConvMatrix",
"NonAssocRing",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"One.toOfNat1",
"WithConv",
"OfNat.ofNat",
"Eq",
"NonAssocRing.toNonAssocSemir... | false |
OrderDual.instPow_1 | Mathlib.Algebra.Order.Group.Synonym | [
"Pow",
"OrderDual"
] | true |
_private.Lean.Meta.Tactic.Simp.Main.0.Lean.Meta.simpGoal.match_3 | Lean.Meta.Tactic.Simp.Main | [
"Lean.MVarId",
"Lean.FVarId",
"Prod.mk",
"Array",
"Prod",
"Prod.casesOn"
] | false |
affineHomeomorph._proof_3 | Mathlib.Topology.Algebra.Field | [
"Continuous",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSeparatelyContinuousAddOfContinuousAdd",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"continuous_id'",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Fi... | false |
SSet.Truncated.Path₁.arrow_tgt | Mathlib.AlgebraicTopology.SimplicialSet.Path | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"SimplexCategory.Truncated.Hom.tr",
"CategoryTheory.CategoryStruct.toQuiver",
"Fin.succ",
"CategoryTheory.ConcreteCategory.hom",
"Quiver.Hom.op",
"SSet.Truncated",
"TypeCat.instFunLikeFun",
"SimplexCategory.δ",
"SSet.Truncated.Path₁... | true |
Nat.toList_roo_eq_if | Init.Data.Range.Polymorphic.NatLemmas | [
"Eq.mpr",
"congrArg",
"id",
"Std.PRange.instIsAlwaysFiniteNat_1",
"instOfNatNat",
"List.cons",
"List",
"instHAdd",
"HAdd.hAdd",
"Std.PRange.instUpwardEnumerableNat",
"Nat",
"congr",
"LT.lt",
"Std.PRange.instLawfulUpwardEnumerableNat",
"Std.Rco.toList",
"Nat.decLt",
"instAddNat",
"E... | true |
TensorProduct.piRightHom._proof_1 | Mathlib.LinearAlgebra.TensorProduct.Pi | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZer... | false |
induced_to_pi | Mathlib.Topology.Constructions | [
"Eq.mpr",
"iInf",
"Pi.topologicalSpace",
"congrArg",
"Function.comp",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"inferInstance",
"id",
"induced_compose",
"TopologicalSpace",
"funext",
"TopologicalSpace.induced",
"eq_self",
"of_eq_true",
"... | true |
CategoryTheory.Limits.HasImages.mk | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasImages",
"CategoryTheory.Limits.HasImages.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.HasImage",
"CategoryTheory.Category"
] | true |
Lean.Syntax.isNodeOf | Init.Prelude | [
"Lean.Syntax.isOfKind",
"Lean.Syntax.getNumArgs",
"Lean.Syntax",
"Bool.and",
"instBEqOfDecidableEq",
"BEq.beq",
"Nat",
"Bool",
"instDecidableEqNat",
"Lean.SyntaxNodeKind"
] | true |
Lean.Sym.Fin.eq_eq_true | Init.Sym.Lemmas | [
"congrArg",
"instDecidableEqFin",
"Eq.mp",
"id",
"Bool.true",
"Nat",
"True",
"eq_self",
"Bool",
"of_eq_true",
"congrFun'",
"decide_eq_true_eq",
"Fin",
"Decidable.decide",
"Eq",
"Eq.trans"
] | true |
Order.isSuccPrelimitRecOn_of_isSuccPrelimit | Mathlib.Order.SuccPred.Limit | [
"Preorder.toLT",
"Order.succ",
"Order.IsSuccPrelimit",
"PartialOrder.toPreorder",
"Order.isSuccPrelimitRecOn._proof_1",
"Classical.propDecidable",
"Preorder.toLE",
"cast",
"Order.isSuccPrelimitRecOn._proof_3",
"PartialOrder",
"dif_pos",
"And",
"Classical.choose",
"Order.isSuccPrelimitRecOn... | true |
Lean.PrettyPrinter.Delaborator.SubExpr.withAppFn | Lean.PrettyPrinter.Delaborator.SubExpr | [
"Lean.PrettyPrinter.Delaborator.SubExpr.descend",
"MonadWithReaderOf",
"Lean.Expr",
"instOfNatNat",
"Lean.Expr.appFn!",
"Nat",
"Monad.toBind",
"Bind.bind",
"Lean.PrettyPrinter.Delaborator.SubExpr.getExpr",
"Lean.SubExpr",
"OfNat.ofNat",
"Monad",
"MonadReaderOf"
] | true |
SemicontinuousAt | Mathlib.Topology.Semicontinuity.Defs | [
"Filter.Eventually",
"nhds",
"TopologicalSpace"
] | true |
Real.contDiff_fourier | Mathlib.Analysis.Fourier.FourierTransformDeriv | [
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"measureSpaceOfInnerProductSpace",
"HMul.hMul",
"NormedSpace",
"ENat.instNatCast",
"Real.denselyNormedField",
"Real.instRCLike",
"innerSL",
"NormedSpace.toModule",
"MeasureTheory.MeasureSpace.toMea... | true |
OrderHom.monotone' | Mathlib.Order.Hom.Basic | [
"Monotone",
"OrderHom.toFun",
"OrderHom",
"Preorder"
] | true |
MeasureTheory.integral_divergence_prod_Icc_of_hasFDerivAt_off_countable_of_le | Mathlib.MeasureTheory.Integral.DivergenceTheorem | [
"instWeaklyLocallyCompactSpaceOfLocallyCompactSpace",
"Fin.forall_fin_two",
"Iff.mpr",
"HasFDerivAt",
"Set.instSProd",
"MeasurableEquiv.instEquivLike",
"Real.instIsOrderedRing",
"Fin.succAbove",
"Eq.mpr",
"Pi.Function.module",
"MeasurableEquiv.measurableEmbedding",
"Set.Ioc",
"InnerProductSp... | true |
CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanMapIso._proof_3",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategory",
"CategoryTheory.Funct... | true |
Std.ExtHashSet.filter_eq_self_iff | Std.Data.ExtHashSet.Lemmas | [
"Std.ExtHashSet.get",
"Std.ExtHashSet",
"Membership.mem",
"LawfulHashable",
"Std.ExtHashMap",
"Std.ExtHashMap.filter_eq_self_iff",
"Bool.true",
"Unit",
"Iff",
"EquivBEq",
"Std.ExtHashSet.filter",
"Std.ExtHashSet.inner",
"Iff.trans",
"Bool",
"Hashable",
"Std.ExtHashSet.instMembershipOfE... | true |
«_aux_Init_Notation___macroRules_term_<*__1» | Init.Notation | [
"Pure.pure",
"Lean.TSyntax",
"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",... | false |
MeasureTheory.lconvolution_comm | Mathlib.Analysis.LConvolution | [
"neg_add_rev",
"Eq.mpr",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"MeasureTheory.Measure",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"MeasureTheory.lintegral_neg_eq_s... | true |
UpperHalfPlane.smulFDeriv.eq_1 | Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | [
"ContinuousLinearMap.comp",
"instInnerProductSpaceRealComplex",
"Units.val",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"UpperHalfPlane.smulFDeriv._proof_1",
"Real",
"MonoidHom.instFunLike",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toM... | true |
InfTopHom.top_apply | Mathlib.Order.Hom.BoundedLattice | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"InfTopHom.instFunLike",
"SemilatticeInf.toMin",
"OrderTop",
"Min",
"SemilatticeInf",
"OrderTop.toTop",
"InfTopHom.instPartialOrder",
"InfTopHom",
"InfTopHom.instOrderTop",
"Top.top",
"Eq",
"DFunLike.coe",
"To... | true |
_private.Mathlib.Geometry.Manifold.Riemannian.PathELength.0.Manifold.riemannianEDist_comm._simp_1_1 | Mathlib.Geometry.Manifold.Riemannian.PathELength | [
"chartedSpaceSelf",
"NormedSpace",
"ContMDiff",
"PseudoMetricSpace.toUniformSpace",
"contMDiff_iff_contDiff",
"ContDiff",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"ENat",
"propext",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"modelWithCornersSelf",
"NormedAddCom... | false |
_private.Init.Data.List.Sort.Impl.0.List.MergeSort.Internal.mergeSortTR.run._unary._proof_1 | Init.Data.List.Sort.Impl | [
"instDecidableNot",
"Int.instDiv",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"instHDiv",
"HMul.hMul",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Int.natCast_ediv",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"InvImage",
"Int.add_one_le_of_lt",
... | false |
_private.Mathlib.Topology.Algebra.Valued.ValuedField.0.Valued.continuous_valuation_of_surjective._simp_1_1 | Mathlib.Topology.Algebra.Valued.ValuedField | [
"setOf",
"HasSubset.Subset",
"Set.setOf_subset_setOf",
"propext",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
finrank_vectorSpan_insert_le_set | Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional | [
"Eq.mpr",
"Submodule",
"direction_affineSpan",
"vectorSpan",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"finrank_vectorSpan_insert_le",
"AddCommGroup.toAddGroup",
"Membership.mem",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"id",
"Subtype",
"Insert.ins... | true |
_private.Plausible.Gen.0.Plausible.Gen.printSamples.match_1 | Plausible.Gen | [
"String",
"Nat.hasNotBit",
"IO.Error.ctorIdx",
"_private.Plausible.Gen.0.Plausible.Gen.printSamples._sparseCasesOn_1",
"IO.Error",
"IO.Error.userError"
] | false |
CategoryTheory.Limits.opProductIsoCoproduct_inv_comp_lift | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products | [
"Eq.mpr",
"CategoryTheory.Limits.HasProduct",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.Fan.op",
"CategoryTheory.Limits.Fan.mk",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"HEq.refl",
"CategoryThe... | true |
Equiv.subtypeEquivCodomain.match_1 | Mathlib.Logic.Equiv.Basic | [
"Subtype.casesOn",
"Subtype",
"Subtype.mk",
"Eq"
] | false |
ProofWidgets.GetExprPresentationParams.mk.sizeOf_spec | ProofWidgets.Presentation.Expr | [
"Lean.Server.WithRpcRef",
"ProofWidgets.GetExprPresentationParams",
"ProofWidgets.GetExprPresentationParams._sizeOf_inst",
"instOfNatNat",
"ProofWidgets.ExprWithCtx._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Name",
"Eq.refl",
... | true |
List.getLast?_eq_none_iff._simp_1 | Init.Data.List.Lemmas | [
"List.getLast?",
"Option.none",
"List",
"propext",
"Eq",
"List.getLast?_eq_none_iff",
"List.nil",
"Option"
] | false |
Lean.PrettyPrinter.Formatter.rawIdentNoAntiquot.formatter | Lean.PrettyPrinter.Formatter | [
"Lean.PrettyPrinter.Formatter.pushToken",
"Lean.PrettyPrinter.Formatter.instMonadTraverserFormatterM",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.PrettyPrinter.Formatter",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.PrettyPrinter.Formatter.getExprPos?",
"Lean.Syntax.ident",
"Lean.PrettyPrinte... | true |
noncompact_univ | Mathlib.Topology.Compactness.Compact | [
"Set.univ",
"NoncompactSpace.noncompact_univ",
"TopologicalSpace",
"Not",
"NoncompactSpace",
"IsCompact"
] | true |
Std.Rii.toList_eq_match_roi | Init.Data.Range.Polymorphic.Lemmas | [
"Std.Rci.mk",
"Std.Roi.toList",
"Std.PRange.UpwardEnumerable",
"congrArg",
"Std.Rci.toList",
"Std.Rxc.Iterator.toList_eq_match.match_1",
"Std.Rxi.instIteratorIteratorIdOfUpwardEnumerable",
"Std.Rii.toList_eq_match_rci",
"Std.Roi.mk",
"Std.Rci.lower",
"Std.Rci.toList_eq_toList_roi",
"List.cons"... | true |
_private.Mathlib.NumberTheory.MahlerMeasure.0.Polynomial.card_mahlerMeasure._proof_1_5 | Mathlib.NumberTheory.MahlerMeasure | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"instConditionallyCompleteLinearOrder",
"Complex.commRing",
"Lean.Grind.CommRing.Expr.var",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"IntCast... | false |
Set.Ioi_subset_Ioc_union_Ici | Mathlib.Order.Interval.Set.LinearOrder | [
"Set.Ioi_subset_Ioo_union_Ici",
"Set.Ioc",
"Set.Ioi",
"Set.Ici",
"Set.Subset.trans",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Set.instUnion",
"DistribLattice.toLattice",
"HasSubset.Subset",
"Set.Ioo_subset_Ioc_self",
"Set.union_subset_union_left",
"Union.... | true |
TopologicalSpace.NonemptyCompacts.locallyCompactSpace_iff | Mathlib.Topology.Sets.VietorisTopology | [
"Filter.instMembership",
"Set.singleton_subset_iff",
"TopologicalSpace.NonemptyCompacts.instSetLike",
"Set.iUnion₂_subset",
"mem_interior_iff_mem_nhds",
"TopologicalSpace.NonemptyCompacts",
"congrArg",
"TopologicalSpace.NonemptyCompacts.isCompact_biUnion_coe_of_isCompact",
"isOpen_interior",
"setO... | true |
_private.Init.Data.List.ToArray.0.Array.findSomeM?.match_1.eq_2 | Init.Data.List.ToArray | [
"Eq.mpr",
"False",
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"congrArg",
"Array.findSomeM?._sparseCasesOn_1.else_eq",
"False.elim",
"Nat.shiftRight",
"Option.some",
"_private.Init.Data.List.ToArray.0.Array.findSomeM?.match_1.splitter._sparseCasesOn_2",
"id",
"Nat.hasNotBit",
"Option.rec",
... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Clause.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultClause.ofArray._proof_1 | Std.Tactic.BVDecide.LRAT.Internal.Clause | [
"False",
"Lean.Grind.not_not",
"instLawfulBEq",
"Lean.Grind.iff_eq",
"congrArg",
"Std.HashMap.mem_toList_iff_getElem?_eq_some",
"Lean.Grind.not_or",
"False.elim",
"Classical.byContradiction",
"noConfusion_of_Nat",
"Option.some",
"Membership.mem",
"Std.HashMap.toList",
"Eq.mp",
"id",
"P... | false |
GrpCat.FilteredColimits.G.mk_eq | Mathlib.Algebra.Category.Grp.FilteredColimits | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"Quot.eqvGen_sound",
"CategoryTheory.Functor",
"GrpCat",
"MonoidHom.instFunLike",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"GrpCat.str",
"Monoid.toMulOneClass",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Fun... | true |
_private.Lean.Compiler.LCNF.SimpleGroundExpr.0.Lean.Compiler.LCNF.compileToSimpleGroundExpr.compileStrArg | Lean.Compiler.LCNF.SimpleGroundExpr | [
"Pure.pure",
"OptionT.instMonad",
"Lean.instMonadEnvOfMonadLift",
"Lean.instBEqFVarId",
"OptionT",
"_private.Lean.Compiler.LCNF.SimpleGroundExpr.0.Lean.Compiler.LCNF.SimpleGroundValue",
"Lean.Compiler.LCNF.Arg",
"StateRefT'.instAlternativeOfMonad",
"_private.Lean.Compiler.LCNF.SimpleGroundExpr.0.Lea... | true |
WeakDual.CharacterSpace.equivAlgHom.congr_simp | Mathlib.Analysis.CStarAlgebra.GelfandDuality | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"NormedRing.toRing",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AlgHom",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"SeparatelyContinuousMul.to_continuousSMul",
"NormedSpace.t... | true |
CategoryTheory.Limits.parallelPair_initial_mk | Mathlib.CategoryTheory.Limits.Final.ParallelPair | [
"CategoryTheory.Limits.parallelPair_initial_mk'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Functor.Initial",
"CategoryTheory.Limits.WalkingParallelPair.one",
"Exists",
"CategoryTheory.CostructuredArrow.hom",
"CategoryTheory.... | true |
IsCornerFree.image | Mathlib.Combinatorics.Additive.Corner.Defs | [
"Iff.mpr",
"Set.instSProd",
"SProd.sprod",
"HasSubset.Subset",
"Prod.map",
"instOfNatNat",
"isCornerFree_image",
"AddCommMonoid",
"IsCornerFree",
"Nat",
"IsAddFreimanIso",
"Set.image",
"Prod",
"OfNat.ofNat",
"Set.instHasSubset",
"Set"
] | true |
PSigma.exists | Mathlib.Data.Sigma.Basic | [
"Exists",
"_private.Mathlib.Data.Sigma.Basic.0.PSigma.exists.match_1_1",
"Iff",
"Iff.intro",
"Exists.intro",
"PSigma.mk",
"PSigma",
"_private.Mathlib.Data.Sigma.Basic.0.PSigma.exists.match_1_3"
] | true |
FractionalIdeal.dual_ne_zero | Mathlib.RingTheory.DedekindDomain.Different | [
"IsLocalization.IsInteger",
"AlgHom.toLinearMap",
"Eq.mpr",
"FractionalIdeal.dual",
"Submodule",
"Algebra.lmul",
"IsIntegralClosure",
"IsDomain",
"IsDedekindDomain.toIsDomain",
"IsIntegrallyClosed.isIntegral_iff",
"CommRing",
"instHSMul",
"IsDomain.to_noZeroDivisors",
"NonUnitalCommRing.to... | true |
Array.back?_flatMap | Init.Data.Array.Lemmas | [
"List.getLast?",
"Array.reverse",
"congrArg",
"List.reverse_toArray",
"List.back?_toArray",
"List.getLast?_flatMap",
"Array.flatMap",
"Array.casesOn",
"List.findSome?_toArray",
"Array.toList",
"List.toArray",
"Array",
"funext",
"List",
"Array.back?",
"Array.findSome?",
"List.findSome... | true |
intervalIntegral.FTCFilter.mk._flat_ctor | Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus | [
"Pure.pure",
"Set.Ioc",
"Real",
"Filter.smallSets",
"outParam",
"SProd.sprod",
"PartialOrder.toPreorder",
"intervalIntegral.FTCFilter.mk",
"PseudoMetricSpace.toUniformSpace",
"Preorder.toLE",
"nhds",
"Filter.TendstoIxxClass.mk",
"LE.le",
"Prod.fst",
"Filter.instPure",
"intervalIntegral... | false |
CategoryTheory.Oplax.OplaxTrans.StrongCore.mk | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Iso",
"CategoryTheory.Oplax.OplaxTrans.StrongCore.naturality_hom._autoParam",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"auto... | true |
AddMagmaCat.coe_of | Mathlib.Algebra.Category.Semigrp.Basic | [
"AddMagmaCat.of",
"AddMagmaCat.carrier",
"Eq",
"Add",
"rfl"
] | true |
CategoryTheory.LiftsToColimit.mk | Mathlib.CategoryTheory.Limits.Creates | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.LiftsToColimit.mk",
"CategoryTheory.LiftsToColimit",
"CategoryTheory.LiftableCocone.liftedCocone",
"CategoryTheory.LiftableCocone",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Data.Set.Image.0.Set.image_preimage_eq_range_inter._proof_1_1 | Mathlib.Data.Set.Image | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"Set.ext",
"of_eq_false",
"False",
"Set.mem_range",
"Lean.Grind.and_eq_of_eq_true_right",
"forall_not_of_not_exists",
"Lean.Grind.not_not",
"Lean.Grind.not_and",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Set.mem_inter_if... | false |
_private.Mathlib.Analysis.SpecialFunctions.Log.Base.0.Real.tendsto_logb_atTop_of_base_lt_one._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Log.Base | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
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