name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
TopologicalSpace.NonemptyCompacts.continuous_toCompacts | Mathlib.Topology.Sets.VietorisTopology | [
"Continuous",
"TopologicalSpace.NonemptyCompacts.toCompacts",
"TopologicalSpace.NonemptyCompacts",
"TopologicalSpace",
"TopologicalSpace.Compacts.topology",
"TopologicalSpace.NonemptyCompacts.topology",
"TopologicalSpace.NonemptyCompacts.isEmbedding_toCompacts",
"TopologicalSpace.Compacts",
"Topolog... | true |
Lean.DeclarationRange._sizeOf_inst | Lean.Data.DeclarationRange | [
"Lean.DeclarationRange",
"SizeOf.mk",
"Lean.DeclarationRange._sizeOf_1",
"SizeOf"
] | false |
Lean.Parser.Term.suffices.parenthesizer | Lean.Parser.Term | [
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.andthen.parenthesizer",
"Bool.true",
"Lean.PrettyPrinter.Parenthesizer.with... | true |
UInt64.toUInt8_toUInt16 | Init.Data.UInt.Lemmas | [
"instPowNat",
"UInt64.toUInt16",
"Dvd.dvd",
"UInt64.toNat_toUInt8",
"UInt8.toNat.inj",
"congrArg",
"UInt64",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"UInt64.toNat_toUInt16",
"UInt64.toNat",
"instNatPowNat",
"UInt64.toUInt8",
"Bool.true",
"HMod.hMod",
"UInt16.toUInt8",
"HPow.hPow... | true |
AddCommMonoid.primaryComponent.disjoint | Mathlib.GroupTheory.Torsion | [
"Iff.mpr",
"MulOne.toOne",
"Nat.Prime",
"AddSubmonoid.instCompleteLattice",
"Monoid.toMulOneClass",
"congrArg",
"Nat.unique_units",
"Nat.instMonoid",
"Nat.instIsCancelMulZero",
"AddCommMonoid.mem_primaryComponent_iff_addOrderOf",
"AddMonoid.addOrderOf_eq_one_iff",
"AddMonoid.toAddZeroClass",
... | true |
sectionOfRetractionKerToTensorAux_prop | Mathlib.RingTheory.Smooth.Kaehler | [
"Derivation",
"LinearMap.id",
"Eq.mpr",
"Submodule",
"RingHom.instRingHomClass",
"Submodule.addSubgroupClass",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"RingHomClass.toAddMonoidHomClass",
"Semiring.toModule",
"map_sub",
"CommRing.toNonUnitalCom... | true |
OneHom.withBotMap_apply | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"WithBot",
"One",
"OneHom.funLike",
"WithBot.one",
"OneHom.withBotMap",
"OneHom",
"Eq.refl",
"WithBot.map",
"Eq",
"DFunLike.coe"
] | true |
CategoryTheory.Limits.BinaryBicone.op._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.BinaryBicone.fst",
"CategoryTheory.Limits.BinaryBicone.inl_fst",
"CategoryTheory.Limits.HasZeroMorphisms",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"Categor... | false |
CategoryTheory.isFiltered_op_iff_isCofiltered | Mathlib.CategoryTheory.Filtered.Basic | [
"Opposite",
"CategoryTheory.IsCofiltered",
"inferInstance",
"CategoryTheory.isFiltered_op_of_isCofiltered",
"Iff",
"Iff.intro",
"CategoryTheory.Category.opposite",
"CategoryTheory.IsFiltered",
"CategoryTheory.isCofiltered_of_isFiltered_op",
"CategoryTheory.Category"
] | true |
IsRiemannianManifold.out | Mathlib.Geometry.Manifold.Riemannian.Basic | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real",
"NormedSpace",
"Real.denselyNormedField",
"instAddCommGroupTangentSpace",
"instIsTopologicalAddGroupTangentSpace",
"IsRiemannianManifold",
"SeminormedAddGroup.toContinuousENorm",
"Manifold.riemannianEDist",
"instModuleTangentSpace",
"PseudoE... | true |
Lean.Meta.Grind.Arith.Linear.instHashablePoly_lean | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Lean.Meta.Grind.Arith.Linear.instHashablePoly_lean.hash",
"Hashable.mk",
"Hashable",
"Lean.Grind.Linarith.Poly"
] | true |
_private.Mathlib.Data.Sum.Basic.0.Sum.LiftRel.exists_of_isLeft_left._proof_1_1 | Mathlib.Data.Sum.Basic | [
"Sum.isRight",
"of_eq_false",
"False",
"Lean.Grind.not_and",
"eq_false",
"Sum.isLeft_eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Sum.isRight_inr",
"False.elim",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"noConfusion_of_Nat",
"Exists",
"Lean.Grind.Bool.ne_of_eq_t... | false |
VonNeumannAlgebra.commutant_commutant | Mathlib.Analysis.VonNeumannAlgebra.Basic | [
"InnerProductSpace.toNormedSpace",
"CompleteSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Complex.instNormedField",
"VonNeumannAlgebra",
"PseudoMetricSpace.toUniformSpace",
"Mul",
"VonNeumannAlgebra.centralizer_centralizer",
"Complex.instRCLike",
"SetLike.coe_inj... | true |
Batteries.Tactic.DeclCache.recOn | Batteries.Util.Cache | [
"Batteries.Tactic.DeclCache.rec",
"Lean.Meta.MetaM",
"Batteries.Tactic.DeclCache.mk'",
"Batteries.Tactic.Cache",
"Lean.Name",
"Batteries.Tactic.DeclCache",
"Lean.ConstantInfo"
] | false |
Vector.extract_zipWith | Init.Data.Vector.Zip | [
"Vector.mk_zipWith_mk._proof_1",
"Vector",
"congrArg",
"Array.extract_zipWith",
"HSub.hSub",
"Vector.extract",
"Vector.casesOn",
"Eq.rec",
"instSubNat",
"instOfNatNat",
"Array.extract",
"Array",
"instHSub",
"Vector.mk",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Vecto... | true |
_private.Init.Data.Array.InsertIdx.0.Array.getElem_insertIdx._proof_1 | Init.Data.Array.InsertIdx | [
"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.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
... | false |
CategoryTheory.InjectiveResolution.kernelFork.eq_1 | Mathlib.CategoryTheory.Preadditive.Injective.Resolution | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.Limits.KernelFork.ofι",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CochainComplex.single₀",
"CategoryTheory.InjectiveResolution.ι",
"CategoryTheory.Limits.KernelFork",
"AddRightCancelSemigroup.toAddSemigrou... | true |
_private.Lean.Util.OccursCheck.0.Lean.occursCheck.visitMVar | Lean.Util.OccursCheck | [
"Inhabited.default",
"instInhabitedExceptTOfMonad",
"instInhabitedPUnit",
"Lean.MVarId",
"Lean.ExprSet",
"ExceptT",
"Unit",
"StateT.instMonad",
"StateT",
"Monad",
"Lean.MonadMCtx"
] | true |
Order.height_nat | Mathlib.Order.KrullDimension | [
"Iff.mpr",
"Preorder.toLT",
"instCompleteLinearOrderENat",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"ENat.instNatCast",
"congrArg",
"CommSemiring.toSemiring",
"instPreorderENat",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Order.height_le_coe_iff",
"Na... | true |
TensorProduct.finsuppScalarLeft._proof_3 | Mathlib.LinearAlgebra.DirectSum.Finsupp | [
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
_private.Init.Data.BitVec.Lemmas.0.BitVec.getMsbD_setWidth._proof_1_6 | Init.Data.BitVec.Lemmas | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.ev... | false |
CategoryTheory.AddMon.addMon | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.MonoidalCategory",
"CategoryTheory.AddMon.X",
"CategoryTheory.AddMonObj",
"CategoryTheory.AddMon",
"CategoryTheory.Category"
] | true |
CategoryTheory.Lax.OplaxTrans.vComp_naturality_comp | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax | [
"Mathlib.Tactic.Bicategory.evalWhiskerLeft_nil",
"Eq.mpr",
"CategoryTheory.Bicategory.whisker_exchange",
"Trans.trans",
"CategoryTheory.Lax.OplaxTrans.naturality",
"CategoryTheory.Lax.OplaxTrans",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Bicategory.whiske... | true |
_private.Init.Data.String.Substring.0.Substring.Raw.commonPrefix.loop._unary._proof_3 | Init.Data.String.Substring | [
"String.instLTRaw",
"Substring.Raw.str",
"Nat.sub_lt_sub_left",
"HSub.hSub",
"instSubNat",
"String.Pos.Raw",
"Substring.Raw",
"And",
"instHSub",
"Substring.Raw.stopPos",
"And.left",
"Nat",
"LT.lt",
"String.Pos.Raw.lt_next",
"instLTNat",
"String.Pos.Raw.next",
"String.Pos.Raw.byteIdx"... | false |
Maximal.mono | Mathlib.Order.Minimal | [
"Maximal.le_of_ge",
"Prop.le",
"LE.le",
"LE",
"Pi.hasLe",
"And.intro",
"Maximal"
] | true |
CategoryTheory.Cat.Hom₂.ext | Mathlib.CategoryTheory.Category.Cat | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.toCatHom",
"CategoryTheory.Cat.str",
"CategoryTheory.Cat.of",
"CategoryTheory.Cat.instQuiver",
"id",
"CategoryTheory.Cat.Hom.instQuiver",
"Ca... | true |
IsLocalRing.ResidueField.field._proof_15 | Mathlib.RingTheory.LocalRing.ResidueField.Defs | [
"CommRing",
"CommSemiring.toSemiring",
"IsLocalRing.maximalIdeal",
"IsLocalRing",
"CommRing.toCommSemiring",
"IsLocalRing.maximalIdeal.isMaximal",
"Ideal.IsMaximal"
] | false |
_private.Mathlib.Tactic.Linter.MinImports.0.Mathlib.Linter.MinImports.minImportsLinter.match_4 | Mathlib.Tactic.Linter.MinImports | [
"Lean.TSyntax",
"Prod.mk",
"Lean.Parser.ModuleParserState",
"List.cons",
"Lean.SyntaxNodeKind",
"Prod",
"Prod.casesOn",
"Lean.Name.mkStr4",
"Lean.MessageLog",
"List.nil"
] | false |
VectorBundleCore.mem_localTrivAt_baseSet | Mathlib.Topology.VectorBundle.Basic | [
"VectorBundleCore.localTrivAt",
"VectorBundleCore.Fiber",
"NormedSpace",
"VectorBundleCore.toTopologicalSpace",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"VectorBundleCore.toFiberBundleCore",
"TopologicalSpace",
"Bundle.TotalSpace.proj",
"SeminormedAddCommGroup.toPseudoMetricSpace",
... | true |
Interval.canLift | Mathlib.Order.Interval.Basic | [
"OrderBot.toBot",
"Ne",
"Bot.bot",
"Interval",
"LE",
"CanLift",
"Interval.coe",
"WithBot.canLift",
"instOrderBotInterval",
"instLEInterval",
"NonemptyInterval"
] | true |
_private.Init.Data.Range.Polymorphic.Fin.0.Fin.instLawfulUpwardEnumerableLE._proof_6 | Init.Data.Range.Polymorphic.Fin | [
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"Lean.Grind.not_and",
"Lean.Grind.CommRing.Expr.var",
"Int.Linear.Expr.eq... | false |
starLinearEquiv._proof_2 | Mathlib.Algebra.Star.Module | [
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"StarModule.star_smul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"StarAddMonoid.toInvolutiveStar",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
... | false |
CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mk._flat_ctor | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.mk",
"CategoryTheory.Category",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver"
] | false |
Std.ExtDTreeMap.instDecidableEqOfTransCmpOfLawfulEqCmpOfLawfulBEq | Std.Data.ExtDTreeMap.Basic | [
"decidable_of_iff",
"Std.ExtDTreeMap.instBEqOfLawfulEqCmpOfTransCmp",
"LawfulBEq",
"Ordering",
"instDecidableEqBool",
"Std.TransCmp",
"Bool.true",
"BEq.beq",
"Std.LawfulEqCmp",
"Std.ExtDTreeMap",
"Bool",
"Std.ExtDTreeMap.instDecidableEqOfTransCmpOfLawfulEqCmpOfLawfulBEq._proof_1",
"BEq",
"... | true |
iteratedDerivWithin_congr_right_of_isOpen | Mathlib.Analysis.Calculus.IteratedDeriv.Defs | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NormedSpace",
"congrArg",
"iteratedDerivWithin",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"id",
"Set.EqOn",
"Set.instInter",
"Inter.inter",
"And.right",
"And.left",
"Nat",
"SeminormedCommRing.toSeminormedRing",
"iteratedDer... | true |
AlgebraicGeometry.PresheafedSpace.GlueData.ι_isOpenEmbedding | Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing | [
"CategoryTheory.Limits.PreservesColimitsOfShape.preservesColimit",
"CategoryTheory.GlueData.diagram",
"Eq.mpr",
"CategoryTheory.Limits.MultispanShape.prod",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.hasLimitsOfShapeOfHasLimits",
"Opposite",
"CategoryTheory.Limits.W... | true |
LinearEquiv.isometryOfInner.congr_simp | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"InnerProductSpace.toNormedSpace",
"SeminormedAddCommGroup",
"Inner.inner",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"Eq.rec",
"LinearEquiv.isometryOfInner",
"Field.toSemifield",
"RCLike.toDenselyNormedField",
"RCLike",
"Semifield.toDivisionSemiring",
"S... | true |
norm_derivWithin_eq_norm_fderivWithin | Mathlib.Analysis.Calculus.Deriv.Basic | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"_private.Mathlib.Analysis.Calculus.D... | true |
PartialEquiv.prod_trans | Mathlib.Logic.Equiv.PartialEquiv | [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"PartialEquiv.prod",
"PartialEquiv",
"Set.mem_prod._simp_1",
"PartialEquiv.trans",
"Function.comp",
"Membership.mem",
"PartialEquiv.symm",
"id",
"Prod.mk",
"Set.instInter",
"Set.mem_preimage._simp_1",
"Prod.fst",
"Int... | true |
_private.Mathlib.Algebra.Lie.Free.0.«termLib.lift» | Mathlib.Algebra.Lie.Free | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
Lean.ExternEntry.adhoc.inj | Lean.Compiler.ExternAttr | [
"Lean.ExternEntry.adhoc.noConfusion",
"Lean.ExternEntry.adhoc",
"Lean.Name",
"Eq",
"Lean.ExternEntry"
] | true |
MvPowerSeries.WithPiTopology.instT0Space | Mathlib.RingTheory.MvPowerSeries.PiTopology | [
"Nat.instMulZeroClass",
"MvPowerSeries.WithPiTopology.instTopologicalSpace",
"MvPowerSeries",
"Pi.instT0Space",
"TopologicalSpace",
"Nat",
"T0Space",
"Finsupp",
"MulZeroClass.toZero"
] | true |
Int8.ofBitVec_uInt8ToBitVec | Init.Data.SInt.Lemmas | [
"Int8",
"Int8.ofBitVec",
"UInt8.toBitVec",
"UInt8.toInt8",
"UInt8",
"Eq",
"rfl"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.deleteVerts_adj._simp_1_1 | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"And",
"and_assoc",
"propext",
"Eq"
] | false |
OreLocalization.oreSetOfIsCancelMulZero | Mathlib.RingTheory.OreLocalization.OreSet | [
"HMul.hMul",
"OreLocalization.oreSetOfIsCancelMulZero._proof_1",
"MulZeroClass.toMul",
"OreLocalization.OreSet",
"Membership.mem",
"Subtype",
"IsCancelMulZero",
"MulZeroOneClass.toMulOneClass",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"OreLocalization.OreSet.mk",
"Submonoid.instSe... | true |
ChartedSpaceCore.mk.injEq | Mathlib.Geometry.Manifold.ChartedSpace | [
"Eq.propIntro",
"PartialEquiv",
"PartialEquiv.trans",
"Lean.injEq_helper",
"ChartedSpaceCore.mk",
"Membership.mem",
"PartialEquiv.symm",
"TopologicalSpace",
"And",
"ChartedSpaceCore.mk.inj",
"Eq.ndrec",
"PartialEquiv.source",
"Eq.refl",
"ContinuousOn",
"IsOpen",
"PartialEquiv.toFun",
... | true |
_private.Mathlib.Tactic.TermCongr.0.Mathlib.Tactic.TermCongr.CongrResult.eq.match_1 | Mathlib.Tactic.TermCongr | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Expr",
"Lean.Meta.MetaM",
"Option.none",
"Unit",
"Mathlib.Tactic.TermCongr.CongrType",
"Option"
] | false |
Matrix.smul_mat_empty | Mathlib.LinearAlgebra.Matrix.Notation | [
"instHSMul",
"instSMulOfMul",
"Function.hasSMul",
"instOfNatNat",
"Matrix.empty_eq",
"Distrib.toMul",
"Nat",
"Matrix.vecEmpty",
"NonUnitalNonAssocSemiring.toDistrib",
"HSMul.hSMul",
"NonUnitalNonAssocSemiring",
"OfNat.ofNat",
"Fin",
"Eq"
] | true |
_private.Mathlib.AlgebraicGeometry.Morphisms.Preimmersion.0.AlgebraicGeometry.IsPreimmersion.instIsStableUnderBaseChangeScheme._simp_2 | Mathlib.AlgebraicGeometry.Morphisms.Preimmersion | [
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap",
"CommRingCat.instCategory",
"AlgebraicGeometry.LocallyRingedSpace.Hom.toHom... | false |
Fin.foldrM_congr | Init.Data.Fin.Fold | [
"Fin.foldrM",
"Eq.rec",
"Fin.cast",
"Nat",
"Eq.refl",
"Eq.symm",
"Monad",
"Fin",
"Eq"
] | true |
Std.Tactic.BVDecide.BVExpr.bitblast.blastAdd.go_denote_eq | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Add | [
"Std.Sat.AIG.RefVec.get",
"Std.Sat.AIG.RefVecEntry.vec",
"BitVec",
"BitVec.getLsbD",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastAdd.go_denote_eq._unary",
"LE.le",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastAdd.go",
"instLENat",
"Std.Sat.AIG.Ref",
"BitVec.carry",
"Bool.xor",
"Std.Sat.AIG",
"Nat... | true |
AffineSubspace.topEquiv._proof_3 | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | [
"Submodule",
"Lattice.toSemilatticeSup",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"CompleteLattice.toLattice",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
... | false |
Finsupp.neLocus_eq_empty | Mathlib.Data.Finsupp.NeLocus | [
"Finsupp.instFunLike",
"instDecidableNot",
"False",
"Finsupp.ext",
"Finset.instUnion",
"Iff.of_eq",
"Classical.not_not",
"congrArg",
"Finset.filter_false",
"Finsupp.neLocus",
"Finset",
"Finsupp.support",
"Finset.eq_empty_iff_forall_notMem",
"Membership.mem",
"Finsupp.mem_neLocus",
"Eq.... | true |
Module.Invertible.finrank_eq_one | Mathlib.RingTheory.PicardGroup | [
"Nontrivial",
"Eq.mpr",
"Module.Invertible.free_iff_linearEquiv",
"Semiring.toModule",
"Cardinal.instOne",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"id",
"subsingleton_or_nontrivial",
"Nonempty.some",
"LinearEquiv.finrank_eq",
"instOfNatNat",
"AddCommMonoid",
"Or.casesOn",
"C... | true |
Aesop.nodeUnknownEmoji | Aesop.Tracing | [
"String"
] | true |
_private.Mathlib.Algebra.BigOperators.Fin.0.Fin.partialProd_contractNth._simp_1_4 | Mathlib.Algebra.BigOperators.Fin | [
"Fin.succ",
"instOfNatNat",
"LE.le",
"instLEFin",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instLTFin",
"propext",
"instAddNat",
"Fin.castSucc",
"OfNat.ofNat",
"Fin",
"Eq",
"Fin.castSucc_lt_succ_iff"
] | false |
GroupWithZero.toDivisionMonoid | Mathlib.Algebra.GroupWithZero.Basic | [
"GroupWithZero.toDivInvMonoid",
"GroupWithZero.toDivisionMonoid._proof_1",
"GroupWithZero",
"DivisionMonoid",
"GroupWithZero.toDivisionMonoid._proof_3",
"GroupWithZero.toDivisionMonoid._proof_2",
"DivisionMonoid.mk"
] | true |
EuclideanGeometry.left_ne_right_of_oangle_ne_zero | Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | [
"EuclideanGeometry.oangle",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.partialOrder",
"Real",
"Real.Angle",
"Module.Oriented",
"Real.instRCLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddCommGroup.toAddGroup",
"Fact",
"Real.semiring",
"Orientation.n... | true |
_private.Mathlib.Tactic.FunProp.Mor.0.Mathlib.Meta.FunProp.Mor.whnfPred.match_1 | Mathlib.Tactic.FunProp.Mor | [
"Option.ctorIdx",
"_private.Mathlib.Tactic.FunProp.Mor.0.Mathlib.Meta.FunProp.Mor.isCoeFunName._sparseCasesOn_1",
"Option.some",
"Lean.Expr",
"Mathlib.Meta.FunProp.Mor.App",
"Nat.hasNotBit",
"Mathlib.Meta.FunProp.Mor.App.casesOn",
"Mathlib.Meta.FunProp.Mor.App.mk",
"Option"
] | false |
Finset.card_smul_finset | Mathlib.Algebra.Group.Action.Pointwise.Finset | [
"instHSMul",
"Finset",
"Group",
"Finset.smulFinset",
"DivInvMonoid.toMonoid",
"Finset.card_image_of_injective",
"Group.toDivInvMonoid",
"Nat",
"MulAction",
"Monoid.toSemigroup",
"Finset.card",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq",
"MulAction.inje... | true |
Filter.pi_inf_principal_univ_pi_neBot | Mathlib.Order.Filter.Pi | [
"not_exists._simp_1",
"congrArg",
"Filter.NeBot",
"Set.univ",
"Exists",
"Ne",
"Bot.bot",
"Filter.instInf",
"Filter.pi_inf_principal_univ_pi_eq_bot._simp_1",
"iff_self",
"Iff",
"congr",
"True",
"of_eq_true",
"Filter.pi",
"Filter.principal",
"Set.pi",
"_private.Mathlib.Order.Filter.P... | true |
Matroid.ext_isBase | Mathlib.Combinatorics.Matroid.Basic | [
"Iff.mpr",
"Set.ext",
"LE.le.trans_eq",
"congrArg",
"Matroid.E",
"Membership.mem",
"Exists",
"Matroid.IsBase",
"Matroid.Indep",
"HasSubset.Subset",
"Matroid.IsBase.subset_ground",
"iff_self",
"funext",
"And",
"Iff",
"Set.instLE",
"Matroid.ext",
"congr",
"True",
"Iff.intro",
"... | true |
sup_compl_eq_top | Mathlib.Order.BooleanAlgebra.Basic | [
"BooleanAlgebra",
"Lattice.toSemilatticeSup",
"Compl.compl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"BooleanAlgebra.toCompl",
"SemilatticeInf.toPartialOrder",
"BooleanAlgebra.toBoundedOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"Max.max",
"BooleanAlgebra.toTop",
"top_uni... | true |
Submodule.restrictScalars_sup | Mathlib.Algebra.Module.Submodule.RestrictScalars | [
"Submodule",
"Lattice.toSemilatticeSup",
"Set.image_singleton",
"CompleteLattice.toLattice",
"congrArg",
"sSup_insert",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"Submodule.restrictScalars",
"SMul",
"Submodule.completeLattice",
"AddMonoid.toAddZeroClass",
"sSup_singleton",
"Submod... | true |
AbsoluteValue.comp | Mathlib.Topology.Algebra.Ring.Basic | [
"MulHom",
"AbsoluteValue.toMulHom",
"AbsoluteValue.comp._proof_2",
"RingHom",
"PartialOrder",
"MulHomClass.toMulHom",
"AbsoluteValue.comp._proof_4",
"MulHom.comp",
"AbsoluteValue.comp._proof_1",
"instDistribOfSemiring",
"AbsoluteValue.comp._proof_3",
"RingHom.instFunLike",
"Distrib.toMul",
... | true |
Module.subsingleton_of_localization_maximal | Mathlib.RingTheory.LocalProperties.Submodule | [
"Eq.mpr",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"IsLocalizedModule",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"id",
"subsingleton_iff_forall_eq",
"Ideal",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"propext",
"Ideal.IsMaximal"... | true |
ISize.toInt8 | Init.Data.SInt.Basic | [
"Int8",
"instOfNatNat",
"System.Platform.numBits",
"Nat",
"Int8.ofUInt8",
"ISize.toBitVec",
"BitVec.signExtend",
"OfNat.ofNat",
"UInt8.ofBitVec",
"ISize"
] | true |
_private.Init.Data.Range.Basic.0.Std.Legacy.Range.forIn'.loop._unary._proof_2 | Init.Data.Range.Basic | [
"Eq.mpr",
"Std.Legacy.Range.step",
"congrArg",
"Nat.add_sub_assoc",
"HSub.hSub",
"id",
"Nat.instMod",
"instHMod",
"Std.Legacy.Range.start",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HMod.hMod",
"instHSub",
"HAdd.hAdd",
"Nat",
"Std.Legacy.Range",
"instAddN... | false |
ENNReal.Tendsto.div_const | Mathlib.Topology.Instances.ENNReal.Lemmas | [
"ENNReal.Tendsto.mul_const",
"instHDiv",
"congrArg",
"ENNReal.inv_eq_top._simp_1",
"nhds",
"HDiv.hDiv",
"Ne",
"Inv.inv",
"Filter.Tendsto",
"True",
"ENNReal",
"ENNReal.instDivInvMonoid",
"DivInvMonoid.toDiv",
"eq_true",
"of_eq_true",
"Zero.toOfNat0",
"ENNReal.instInv",
"ENNReal.inst... | true |
AlgebraicGeometry.StructureSheaf.IsLocalization.to_stalk | Mathlib.AlgebraicGeometry.StructureSheaf | [
"CommRing",
"CommRingCat.carrier",
"PrimeSpectrum.isPrime",
"CommRingCat",
"AlgebraicGeometry.StructureSheaf.stalkAlgebra",
"CommRingCat.instCategory",
"TopCat.Presheaf.stalk",
"CommRingCat.instCommRingObjForgetRingHomCarrier",
"CommRing.toCommSemiring",
"IsLocalization.AtPrime",
"PrimeSpectrum"... | true |
ApproximatesLinearOn.inverse_continuousOn | Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | [
"Iff.mpr",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearEquiv.symm",
"PartialEquiv.right_inv'",
"Preorder.toLT",
"Continuous",
"PartialEquiv.map_target",
"NormedSpace",
"NormedAddCommGroup.toMetricSpace",
"AddCommGroup.toAddCommMonoid",
"PartialEquiv.target",
"SeminormedAddGroup.toN... | true |
CategoryTheory.Functor.OplaxMonoidal.δ_of_cartesianMonoidalCategory | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | [
"CategoryTheory.CartesianMonoidalCategory.prodComparison_snd",
"CategoryTheory.CartesianMonoidalCategory.prodComparison_fst",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Functor.OplaxMonoidal.δ_snd",
"Quiver.Hom",
"congrArg",
"CategoryTheory.SemiCartesianMonoida... | true |
_private.Lean.DocString.Parser.0.Lean.Doc.Parser.recoverHereWithKeeping | Lean.DocString.Parser | [
"Lean.Parser.RecoveryContext",
"Lean.Parser.ParserState.restore",
"Lean.Syntax",
"instOfNatNat",
"Lean.Parser.RecoveryContext.initialPos",
"Array.foldl",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Lean.Parser.RecoveryContext.initialSize",
"instAddNat",
"Lean.Parser.ParserContext",
"Lean.Par... | true |
Lean.Meta.Grind.CongrKey.mk._flat_ctor | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.CongrKey.mk",
"Lean.Meta.Grind.CongrKey",
"Lean.Expr",
"Lean.Meta.Grind.ENodeMap"
] | false |
CategoryTheory.GradedObject.hasMap_comp | Mathlib.CategoryTheory.GradedObject | [
"CategoryTheory.GradedObject.HasMap",
"CategoryTheory.GradedObject.isColimitCofanMapObjComp",
"CategoryTheory.GradedObject.mapObjFun",
"CategoryTheory.Discrete.functor",
"Set.Elem",
"Set.instSingletonSet",
"CategoryTheory.GradedObject.cofanMapObj",
"Nonempty.intro",
"CategoryTheory.Limits.HasColimit... | true |
NzsNum.not._unsafe_rec | Mathlib.Data.Num.Bitwise | [
"instDecidableNot",
"instDecidableEqBool",
"NzsNum.sign.match_1",
"Bool.true",
"NzsNum.msb",
"NzsNum.bit",
"Bool",
"NzsNum",
"NzsNum.not._unsafe_rec",
"Decidable.decide",
"Eq",
"Not"
] | false |
Algebra.Extension.Hom.mk.noConfusion | Mathlib.RingTheory.Extension.Basic | [
"Algebra.Extension.Hom.mk",
"CommRing",
"Algebra.Extension.commRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"HEq.refl",
"Algebra",
"RingHom",
"Algebra.toModule",
"Algebra.id",
"id",
"NonUnitalNonAss... | false |
Std.DTreeMap.Raw.isSome_minKey?_iff_isEmpty_eq_false | Std.Data.DTreeMap.Raw.Lemmas | [
"Ord.mk",
"Std.DTreeMap.Raw.minKey?",
"Ordering",
"Std.DTreeMap.Raw.isEmpty",
"Std.TransCmp",
"Bool.true",
"Iff",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Bool",
"Option.isSome",
"Std.DTreeMap.Internal.Impl.isSome_minKey?_iff_isEmpty_eq_false",
"Bool.false",
"Eq",
"Std.DTree... | true |
LieAlgebra.Orthogonal.typeBEquivSo'._proof_2 | Mathlib.Algebra.Lie.Classical | [
"LieAlgebra.Orthogonal.invertiblePD._proof_1",
"Set.ext",
"Units.val",
"Eq.mpr",
"Matrix.fromBlocks",
"Matrix.smul",
"Submodule",
"CommRing",
"instFintypeSum",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Matrix.submatrix",
"Semiring.toModule",
"instSMulOfMul",
"Equiv.i... | false |
TopCat.LocalPredicate.ctorIdx | Mathlib.Topology.Sheaves.LocalPredicate | [
"TopCat.carrier",
"Nat",
"TopCat",
"TopCat.LocalPredicate"
] | false |
Real.decidableLT | Mathlib.Data.Real.Basic | [
"Real",
"Decidable",
"Real.instLT",
"inferInstance",
"LinearOrder.toDecidableLT",
"LT.lt",
"Real.linearOrder"
] | true |
CategoryTheory.MonoOver.topLEPullbackSelf._proof_2 | Mathlib.CategoryTheory.Subobject.Lattice | [
"CategoryTheory.Over",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoOver.mk",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.instCategoryOver",
"CategoryTheory.Over.left",
"CategoryTheory.MonoOver.forget",
"CategoryTheory.... | false |
Lean.Meta.Grind.Arith.CommRing.RingM.Context.ctorIdx | Lean.Meta.Tactic.Grind.Arith.CommRing.RingM | [
"Lean.Meta.Grind.Arith.CommRing.RingM.Context",
"Nat"
] | false |
Lean.Meta.Grind.Arith.Cutsat.VarInfo.recOn | Lean.Meta.Tactic.Grind.Arith.Cutsat.ReorderVars | [
"Lean.Meta.Grind.Arith.Cutsat.VarInfo.rec",
"Lean.Meta.Grind.Arith.Cutsat.VarInfo.mk",
"Nat",
"Lean.Meta.Grind.Arith.Cutsat.VarInfo"
] | false |
div_le_comm₀ | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"div_le_iff₀",
"Preorder.toLT",
"instHDiv",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"CommMonoid.toCommSemigroup",
"MulZeroClass.toMul",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"... | true |
Lean.Meta.Sym.CongrInfo.congrTheorem.injEq | Lean.Meta.Sym.SymM | [
"Eq.propIntro",
"Lean.Meta.CongrTheorem",
"Lean.Meta.Sym.CongrInfo.congrTheorem.inj",
"Lean.Meta.Sym.CongrInfo.congrTheorem",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Lean.Meta.Sym.CongrInfo"
] | true |
Std.Tactic.BVDecide.LRAT.Internal.ReduceResult.ctorElimType | Std.Tactic.BVDecide.LRAT.Internal.Clause | [
"cond",
"Std.Tactic.BVDecide.LRAT.Internal.ReduceResult.reducedToNonunit",
"Std.Tactic.BVDecide.LRAT.Internal.ReduceResult.reducedToUnit",
"Nat.ble",
"PULift",
"Std.Tactic.BVDecide.LRAT.Internal.ReduceResult.encounteredBoth",
"Nat",
"Std.Tactic.BVDecide.LRAT.Internal.ReduceResult",
"Std.Tactic.BVDec... | false |
WeierstrassCurve.Projective.equation_some | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | [
"one_pow",
"MulOne.toOne",
"WeierstrassCurve.Projective.toAffine",
"CommRing",
"HMul.hMul",
"WeierstrassCurve.Projective.Equation",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Fin.instOfNat",... | true |
IsDenseInducing.toIsInducing | Mathlib.Topology.DenseEmbedding | [
"IsDenseInducing",
"Topology.IsInducing",
"TopologicalSpace"
] | true |
WithBot.WithTop.completeLinearOrder._proof_5 | Mathlib.Order.ConditionallyCompleteLattice.Basic | [
"WithBot.instBoundedOrder",
"WithBot",
"Lattice.toSemilatticeSup",
"Compl.compl",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"DistribLattice.toLattice",
"GeneralizedHeytingAlgebra.toHImp",
"BiheytingAlgebra.toHeytingAlgebra",
"Bot.bot",
"WithBot.linearOrder",
"Conditionall... | false |
MeasureTheory.Measure.IsComplete.casesOn | Mathlib.MeasureTheory.Measure.NullMeasurable | [
"MeasureTheory.Measure",
"MeasurableSet",
"MeasureTheory.Measure.IsComplete.rec",
"MeasureTheory.Measure.IsComplete",
"MeasurableSpace",
"MeasureTheory.Measure.IsComplete.mk",
"ENNReal",
"Zero.toOfNat0",
"ENNReal.instZero",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"MeasureTheory.Measure.instFunL... | false |
CochainComplex.HomComplex.Cochain.rightUnshift_rightShift | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift | [
"CategoryTheory.Category.assoc",
"HomologicalComplex.instCategory",
"CochainComplex.HomComplex.Cochain.rightShift",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CochainComplex.shiftFunctorObjXIso._proof_1",
"AddGroupWithOne.toAddMonoidWithOne"... | true |
_private.Init.Data.Array.Basic.0.Array.takeWhile.go._unary.eq_def | Init.Data.Array.Basic | [
"Eq.mpr",
"_private.Init.Data.Array.Basic.0.Array.takeWhile.go._unary",
"instSubsingletonDecidable",
"Array.push",
"congrArg",
"InvImage",
"HSub.hSub",
"Decidable",
"WellFounded.Nat.fix",
"WellFounded.Nat.fix_eq",
"Eq.rec",
"PSigma.casesOn",
"id",
"instDecidableEqBool",
"instSubNat",
"... | false |
_private.Mathlib.RingTheory.Regular.ProjectiveDimension.0.ModuleCat.projectiveDimension_quotient_eq_add_length_of_isWeaklyRegular._simp_1_3 | Mathlib.RingTheory.Regular.ProjectiveDimension | [
"Membership.mem",
"List.cons",
"List",
"List.instMembership",
"propext",
"Or",
"List.mem_cons",
"Eq"
] | false |
Matrix.instModuleForall | Mathlib.Data.Matrix.Action | [
"Pi.addCommMonoid",
"Matrix.instModuleForall._proof_5",
"Matrix.instModuleForall._proof_4",
"Matrix",
"Module.mk",
"DistribMulAction.mk",
"SMul.mk",
"SemigroupAction.mk",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Fintype",
"Matrix.instModuleForall._proof_2",
"NonAssocSemiring.toNonUnitalNo... | true |
Circle.instDistribMulAction | Mathlib.Analysis.Complex.Circle | [
"Circle.instMulAction",
"Circle.instDistribMulAction._proof_1",
"DistribMulAction.mk",
"DivInvMonoid.toMonoid",
"Circle.instDistribMulAction._proof_2",
"Group.toDivInvMonoid",
"Circle",
"AddMonoid",
"Semiring.toMonoid",
"DistribMulAction",
"Circle.instCommGroup",
"CommGroup.toGroup",
"Comple... | true |
Polynomial.Chebyshev.T_ne_zero | Mathlib.RingTheory.Polynomial.Chebyshev | [
"IsDomain",
"False",
"CommRing",
"WithBot",
"Polynomial.Chebyshev.T",
"congrArg",
"CommSemiring.toSemiring",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"Polynomial.Chebyshev.degree_T",
"AddMonoidWithOne.toNatCast",
"Ne",
"instOfNatNat",
"Bot.bot",
"Int",
"Poly... | true |
_private.Init.Data.Vector.Lemmas.0.Vector.contains_iff_exists_mem_beq._simp_1_1 | Init.Data.Vector.Lemmas | [
"Array.instMembership",
"Membership.mem",
"Exists",
"Array",
"Bool.true",
"And",
"BEq.beq",
"propext",
"Bool",
"BEq",
"Eq",
"Array.contains_iff_exists_mem_beq",
"Array.contains"
] | false |
Lean.Lsp.instToJsonPlainGoal | Lean.Data.Lsp.Extra | [
"Lean.Lsp.PlainGoal",
"Lean.ToJson.mk",
"Lean.ToJson",
"Lean.Lsp.instToJsonPlainGoal.toJson"
] | true |
CategoryTheory.Monad.monadicOfHasPreservesGSplitCoequalizersOfReflectsIsomorphisms._proof_2 | Mathlib.CategoryTheory.Monad.Monadicity | [
"CategoryTheory.Monad.ReflectsColimitOfIsSplitPair.mk",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Monad.ReflectsColimitOfIsSplitPair",
"CategoryTheory.Monad.PreservesColimitOfIsSplitPair",
"CategoryTheory.Functor.IsSplitPair",
"CategoryTheory.Mon... | false |
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