name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Finset.HasAntidiagonal.mk._flat_ctor | Mathlib.Algebra.Order.Antidiag.Prod | [
"Finset.HasAntidiagonal",
"AddMonoid.toAddSemigroup",
"Finset",
"Membership.mem",
"Prod.fst",
"instHAdd",
"AddSemigroup.toAdd",
"Iff",
"Finset.instSetLike",
"HAdd.hAdd",
"AddMonoid",
"Finset.HasAntidiagonal.mk",
"Prod",
"Eq",
"Prod.snd",
"SetLike.instMembership"
] | false |
ZeroAtInftyContinuousMap | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"TopologicalSpace",
"ZeroAtInftyContinuousMap.mk",
"Zero"
] | true |
Lean.logNamedErrorAt | Lean.Log | [
"Lean.MessageData",
"Lean.MonadLog",
"Lean.AddMessageContext",
"Lean.Syntax",
"Unit",
"Lean.MessageData.tagWithErrorName",
"Lean.MessageSeverity.error",
"Lean.Name",
"Monad",
"Bool.false",
"Lean.MonadOptions",
"Lean.logAt"
] | true |
Nat.cast_npow | Mathlib.Algebra.Group.NatPowAssoc | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Nat.recAux",
"HMul.hMul",
"Monoid.toMulOneClass",
"Pow",
"congrArg",
"Nat.instMonoid",
"Nat.instMulOneClass",
"Monoid.PowAssoc",
"npow_one",
"id",
"MulOne.toMul",
"npow_zero",
"AddMonoidWithOne.toNatCast",
"instMul... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.CNF.0.Std.Tactic.BVDecide.LRAT.Internal.Clause.limplies_iff_mem._simp_1_2 | Std.Tactic.BVDecide.LRAT.Internal.CNF | [
"Exists",
"Prod.mk",
"propext",
"Prod",
"Prod.exists",
"Eq"
] | false |
Std.ExtDTreeMap.minEntry._proof_3 | Std.Data.ExtDTreeMap.Basic | [
"Iff.mpr",
"Std.ExtDTreeMap.mk",
"Std.ExtDTreeMap.isEmpty_eq_false_iff",
"Std.DTreeMap",
"Std.DTreeMap.Equiv.minEntry_eq",
"Std.DTreeMap.minEntry",
"Ordering",
"Eq.rec",
"Ne",
"Std.ExtDTreeMap.instEmptyCollection",
"Std.TransCmp",
"Std.ExtDTreeMap.isEmpty",
"Std.ExtDTreeMap.minEntry._proof_2... | false |
_private.Mathlib.GroupTheory.FreeGroup.Basic.0.FreeGroup.instGroup.match_10 | Mathlib.GroupTheory.FreeGroup.Basic | [
"Prod.mk",
"Bool",
"Prod",
"Prod.casesOn"
] | false |
Fin.isValue | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Fin | [
"Pure.pure",
"Unit.unit",
"Lean.Meta.getNatValue?",
"Lean.Expr.isApp",
"ReaderT",
"Lean.Meta.State",
"Lean.Expr.cleanupAnnotations",
"instMonadLiftT",
"Lean.Meta.Simp.MethodsRef",
"ReaderT.instMonad",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"liftM",
"_pri... | true |
CategoryTheory.Pseudofunctor.ObjectProperty.IsClosedUnderMapObj | Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty | [
"CategoryTheory.Cat",
"CategoryTheory.Bicategory",
"CategoryTheory.Pseudofunctor",
"CategoryTheory.Pseudofunctor.ObjectProperty.IsClosedUnderMapObj.mk",
"CategoryTheory.Pseudofunctor.ObjectProperty",
"CategoryTheory.Cat.bicategory"
] | true |
WeakDual.instAddCommGroup._proof_10 | Mathlib.Topology.Algebra.Module.Spaces.WeakDual | [
"CommRing",
"Semiring.toModule",
"instSMulOfMul",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Neg.mk",
"ContinuousLinearMap.addCommGroup._proof_4",
"WeakDual.instAddCommGroup._aux_6",
"WeakDual.instAddCommGroup._aux_1",
"AddCommGroup",
"Int",
"Co... | false |
Std.Time.Number.mk.injEq | Std.Time.Format.Basic | [
"Eq.propIntro",
"Std.Time.Number.mk.inj",
"Nat",
"Std.Time.Number",
"Eq.ndrec",
"Eq.refl",
"Std.Time.Number.mk",
"Eq"
] | true |
AlgebraicGeometry.pullback_of_geometrically' | Mathlib.AlgebraicGeometry.Geometrically.Basic | [
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"Field.toCommRing",
"AlgebraicGeometry.geometrically",
"CategoryTheory.IsPullback.flip",
"CategoryTheory.Limits.pull... | true |
CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.homotopyEquiv._proof_1 | Mathlib.AlgebraicTopology.ExtraDegeneracy | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"instNeZeroNatHAdd_1",
"MulOne.toOne",
"SubtractionMonoid.toInvolutiveNeg",
"neg_smul",
"ChainComplex",
"HomologicalComplex.instCategory",
"instHSMul",
"CategoryTheory.Comma.right",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",... | false |
MeasureTheory.Measure.measurePreserving_zsmul | Mathlib.MeasureTheory.Measure.Haar.Unique | [
"MeasureTheory.MeasurePreserving",
"continuous_zsmul",
"instHSMul",
"MeasureTheory.Measure",
"Set.univ",
"AddCommGroup.toAddGroup",
"BorelSpace",
"AddCommGroup",
"Ne",
"Int",
"zsmulAddGroupHom",
"CompactSpace",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.Measure.IsAddHaarMeasur... | true |
PartialEquiv.single._proof_2 | Mathlib.Logic.Equiv.PartialEquiv | [
"Function.const_apply",
"Eq.mpr",
"Set.eq_of_mem_singleton",
"congrArg",
"Membership.mem",
"Set.instSingletonSet",
"id",
"Function.const",
"Eq.refl",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.Algebra.Star.CHSH.0.CHSH_id._proof_1_2 | Mathlib.Algebra.Star.CHSH | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
SimpleGraph.Subgraph.incidenceSet_subset | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"SimpleGraph.Subgraph",
"Membership.mem",
"HasSubset.Subset",
"SimpleGraph",
"And.left",
"Sym2.instSetLike",
"SimpleGraph.Subgraph.edgeSet",
"Set.instMembership",
"Sym2",
"SetLike.instMembership",
"Set.instHasSubset",
"SimpleGraph.Subgraph.incidenceSet",
"Set"
] | true |
_private.Init.Data.String.Lemmas.Pattern.Char.0.String.Slice.Pattern.Model.Char.revMatchesAt_iff_revMatchesAt_beq._simp_1_2 | Init.Data.String.Lemmas.Pattern.Char | [
"String.Slice",
"instBEqOfDecidableEq",
"BEq.beq",
"String.Slice.Pattern.Model.CharPred.instPatternModelForallCharBool",
"String.Slice.Pattern.Model.Char.instPatternModelChar",
"String.Slice.Pattern.Model.Char.isLongestRevMatchAt_iff_isLongestRevMatchAt_beq",
"propext",
"Bool",
"String.Slice.Pos",
... | false |
Condensed.instAB4StarCondensedMod | Mathlib.Condensed.AB | [
"ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier",
"CategoryTheory.Functor.op",
"CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions",
"CondensedMod",
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasLimitsOfShapeOfHasLimi... | true |
CategoryTheory.AddModObj.ext | Mathlib.CategoryTheory.Monoidal.Mod | [
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft",
"CategoryTheory.AddModObj",
"CategoryTheory.AddModObj.vadd",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso",
"CategoryTheory.AddModObj.mk",
"Cate... | true |
Polynomial.prod_max_one_norm_roots_le_mahlerMeasure_of_one_le_leadingCoeff | Mathlib.Analysis.Polynomial.MahlerMeasure | [
"Real.instIsOrderedRing",
"Norm.norm",
"Eq.mpr",
"Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots",
"MulOne.toOne",
"Real.partialOrder",
"Real.instLE",
"Real",
"Polynomial.roots",
"Polynomial.one_le_prod_max_one_norm_roots",
"HMul.hMul",
"Complex.commRing",
"Multiset.map",
"Real.in... | true |
CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.ShortComplex.opcycles",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.op_comp",
"CategoryTheory.Limits.HasZeroMorphisms",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Q... | true |
Aesop.GoalStats._sizeOf_inst | Aesop.Stats.Basic | [
"Aesop.GoalStats",
"Aesop.GoalStats._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
Convex.nhdsWithin_diff_eq_nhdsLT | Mathlib.Analysis.Convex.Topology | [
"Eq.mpr",
"OrderTopology",
"Set.Ioi",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"congrArg",
"Compl.compl",
"Convex.nhdsWithin_inter_Iio_eq_nhdsLT",
"LinearOrder",
"Filter.instCompleteLatticeFilter",
"nhdsWith... | true |
Perfection.lift.congr_simp | Mathlib.RingTheory.Perfection | [
"PerfectRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.Prime",
"Perfection",
"CommSemiring.toSemiring",
"RingHom",
"Fact",
"Equiv",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Monoid.toPow",
"CommSemiring",
"Nat",
"Semiring.toMonoid",
"Eq.refl",
"CharP",
"Perfection.instCommSem... | true |
MonoidAlgebra.ofCoeff_eq_zero | Mathlib.Algebra.MonoidAlgebra.Defs | [
"MonoidAlgebra.addCommMonoid",
"MonoidAlgebra.ofCoeff",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"Iff",
"MonoidAlgebra.ofCoeff_inj",
"MonoidAlgebra",
"Semiring",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"Finsupp.instZero",
"OfNat.ofNat",
"Eq",
"Finsupp... | true |
MeasureTheory.ProgMeasurable.neg | Mathlib.Probability.Process.Adapted | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"MeasureTheory.IsStronglyProgressive",
"MeasureTheory.Filtration",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"ContinuousNeg",
"MeasurableSpace",
"MeasureTheory.IsStronglyProgressive.neg",
"TopologicalSpace",
"... | true |
_private.Mathlib.Algebra.Lie.Extension.0.LieAlgebra.Extension.twoCocycleAux._proof_9 | Mathlib.Algebra.Lie.Extension | [
"LieHom",
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"Eq.mpr",
"Subtype.mk.congr_simp",
"Function.LeftInverse",
"CommRing",
"LieAlgebra.Extension",
"map_sub",
"LieAlgebra.Extension.proj",
"SemilinearMapClass.distribMulActionSemiHomClass",
"AddMonoid.toAddSemigroup",
"LieRing.toAddCom... | false |
Std.Sat.CNF.add | Std.Sat.CNF.Basic | [
"Std.Sat.CNF",
"Array.push",
"Std.Sat.CNF.mk",
"Std.Sat.CNF.Clause",
"Std.Sat.CNF.clauses"
] | true |
uniformEquicontinuous_iff_uniformContinuous | Mathlib.Topology.UniformSpace.Equicontinuity | [
"Filter.instMembership",
"UniformContinuous",
"UniformSpace",
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"Filter.Eventually",
"Function.swap",
"UniformFun.hasBasis_uniformity",
"Iff.rfl",
"uniformity",
"Function.comp",
"Membership.mem",
"id",
"Equiv",
"UniformFun.uniformSpace",
"Un... | true |
Std.Net.SocketAddressV6 | Std.Net.Addr | [
"Std.Net.SocketAddressV6.mk"
] | true |
Complex.sqrt | Mathlib.Analysis.RCLike.Sqrt | [
"Complex.instPow",
"Complex.sqrt._proof_1",
"Complex.instNatCast",
"Inv.inv",
"HPow.hPow",
"instHPow",
"Complex",
"OfNat.ofNat",
"instOfNatAtLeastTwo",
"Complex.instInv"
] | true |
Subgroup.leftTransversals.diff.eq_1 | Mathlib.GroupTheory.Transfer | [
"MonoidHom.instFunLike",
"Equiv.instEquivLike",
"HMul.hMul",
"Finset.univ",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"Subgroup.FiniteIndex",
"Subgroup.leftTransversals.diff",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",... | true |
List.zipRight'_cons_cons | Mathlib.Data.List.Map2 | [
"Option.some",
"Prod.mk",
"Prod.fst",
"List.cons",
"List",
"List.zipRight'",
"Prod",
"Eq",
"Prod.snd",
"rfl",
"Option"
] | true |
CategoryTheory.MorphismProperty.Under.Hom.mk_hom | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty.Under",
"CategoryTheory.MorphismProperty",
"CategoryTheory.instCategoryUnder",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.IsMultiplicative.instTop",
"CategoryThe... | true |
Array.insertIdx_comm._proof_2 | Init.Data.Array.InsertIdx | [
"_private.Init.Data.Array.InsertIdx.0.Array.insertIdx_comm._proof_1",
"LE.le",
"instLENat",
"Array",
"Nat",
"Decidable.byContradiction",
"Array.size",
"Not",
"Nat.decLe"
] | false |
Tactic.NormNum.nat_sqrt_helper | Mathlib.Tactic.NormNum.NatSqrt | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.le_of_ble_eq_true",
"HMul.hMul",
"pow_two",
"Nat.ble",
"Monoid.toMulOneClass",
"congrArg",
"Nat.instMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"two_mul",
"Eq.mp",
"id",
"MulOne.toMul",
"Distrib.toAdd",
"AddMonoidWithOne.toNatCast",... | true |
Set.decidableInter | Mathlib.Data.Set.Basic | [
"Set.decidableInter._aux_1",
"Decidable",
"Membership.mem",
"Set.instInter",
"Inter.inter",
"Set.instMembership",
"Set"
] | true |
ModuleCat.carrier | Mathlib.Algebra.Category.ModuleCat.Basic | [
"ModuleCat",
"Ring"
] | true |
MulOpposite.instField._proof_9 | Mathlib.Algebra.Field.Opposite | [
"Semigroup.toMul",
"HMul.hMul",
"MulOpposite",
"Field.toDivisionRing",
"MulOpposite.instDivisionRing",
"NNRat",
"DivisionRing.toRing",
"DivisionRing.nnqsmul",
"DivisionRing.nnqsmul_def",
"Semiring.toMonoid",
"Monoid.toSemigroup",
"NNRat.cast",
"Ring.toSemiring",
"Eq",
"Field",
"Divisio... | false |
Std.DHashMap.modify.congr_simp | Std.Data.DHashMap.Lemmas | [
"LawfulBEq",
"Eq.rec",
"Std.DHashMap.modify",
"Eq.refl",
"Hashable",
"BEq",
"Eq",
"Std.DHashMap"
] | true |
TrivialLieModule.instAddCommGroup._proof_21 | Mathlib.Algebra.Lie.Abelian | [
"TrivialLieModule",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Int",
"Nat.cast",
"autoParam",
"TrivialLieModule.instAddCommGroup._aux_17",
"AddGroup.toSubNegMonoid",
"Nat",
"SubNegMonoid.zsmul_neg'",
"TrivialLieModule.instAddCommGroup._aux_12",
"instNatCastInt",
"Int.negSucc",
"Nat.succ",... | false |
derivWithin_neg | Mathlib.Analysis.Calculus.Deriv.Add | [
"NormedCommRing.toNormedRing",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"hasDerivWithinAt_neg",
"AddGroupWithOne.toAddMonoidWithOne",
"PseudoMetricSpace.toUniformSpace",
"UniqueDiffWithinAt",
"NormedField.toField",
"HasDerivWithinAt.d... | true |
IsExtreme.left_mem_of_mem_openSegment | Mathlib.Analysis.Convex.Extreme | [
"SMul",
"IsExtreme",
"Membership.mem",
"PartialOrder",
"AddCommMonoid",
"Semiring",
"openSegment",
"Set.instMembership",
"Set"
] | true |
List.Vector.getElem_def._proof_1 | Mathlib.Data.Vector.Defs | [
"Eq.mpr",
"congrArg",
"List.Vector",
"id",
"List.Vector.toList_length",
"Nat",
"LT.lt",
"instLTNat",
"Eq",
"List.length",
"List.Vector.toList"
] | false |
collinear_iff_exists_forall_eq_smul_vadd | Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional | [
"Eq.mpr",
"False",
"Collinear",
"instHSMul",
"AddMonoid.toAddSemigroup",
"Set.mem_empty_iff_false._simp_1",
"AddGroupWithOne.toAddGroup",
"vadd_vadd",
"congrArg",
"collinear_iff_of_mem",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"exists_const._simp_1",
"AddMonoid.to... | true |
Lean.Linter.Coe.linter.deprecatedCoercions | Lean.Linter.Coe | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
_private.Lean.Data.Lsp.Diagnostics.0.Lean.Lsp.instBEqPublishDiagnosticsParams.beq.match_1 | Lean.Data.Lsp.Diagnostics | [
"Int",
"Array",
"Lean.Lsp.DocumentUri",
"Lean.Lsp.PublishDiagnosticsParams.mk",
"Lean.Lsp.Diagnostic",
"Lean.Lsp.PublishDiagnosticsParams.casesOn",
"Lean.Lsp.PublishDiagnosticsParams",
"Option"
] | false |
GradedRingHom.coe_mul._simp_1 | Mathlib.RingTheory.GradedAlgebra.RingHom | [
"SetLike",
"HMul.hMul",
"GradedRingHom",
"Function.comp",
"GradedRingHom.instFunLike",
"GradedRingHom.instMul",
"Semiring",
"GradedRingHom.coe_mul",
"Eq.symm",
"Eq",
"DFunLike.coe",
"instHMul"
] | false |
Lean.Lsp.ClientCapabilities.lean? | Lean.Data.Lsp.Capabilities | [
"Lean.Lsp.LeanClientCapabilities",
"Lean.Lsp.ClientCapabilities",
"Option"
] | true |
IntermediateField.finrank_fixedField_eq_card | Mathlib.FieldTheory.Galois.Basic | [
"Subgroup.instFiniteSubtypeMem",
"FixedPoints.finrank_eq_card",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Fintype.ofFinite",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Finite.algHom",
"congrArg",
"IntermediateField",
"Inte... | true |
CategoryTheory.instMonoidalFunctorFunctorCongrLeft._proof_8 | Mathlib.CategoryTheory.Monoidal.FunctorCategory | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Equivalence.congrLeft",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.instMonoidalFunctorFunctorCongrLeft._aux_1",
"CategoryTheory.Functor.CoreMonoidal.left_unitality",
"CategoryTheory.Functor.catego... | false |
DividedPowers.OfInvertibleFactorial.dpow_comp | Mathlib.RingTheory.DividedPowers.RatAlgebra | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semigroup.toMul",
"Semiring.toModule",
"HMul.hMul",
"Ideal.pow_eq_zero_of_mem",
"IsScalarTower.right",
"DividedPowers.OfInvertibleFactorial.dpow_mem",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
"CommSemiring.toNonUnitalCommSemiring",
"co... | true |
_private.Mathlib.Order.Filter.Ultrafilter.Defs.0.Ultrafilter.bind._simp_2 | Mathlib.Order.Filter.Ultrafilter.Defs | [
"Compl.compl",
"Membership.mem",
"Set.instCompl",
"propext",
"Ultrafilter.compl_mem_iff_notMem",
"Ultrafilter.instMembershipSet",
"Ultrafilter",
"Eq.symm",
"Eq",
"Not",
"Set"
] | false |
Matrix.blockDiag'_blockDiagonal' | Mathlib.Data.Matrix.Block | [
"Matrix",
"Matrix.blockDiagonal'_apply_eq",
"Matrix.blockDiag'",
"funext",
"Matrix.blockDiagonal'",
"Eq",
"Matrix.ext",
"DecidableEq",
"Zero"
] | true |
PresheafOfModules.forgetToPresheafModuleCatObjMap._proof_1 | Mathlib.Algebra.Category.ModuleCat.Presheaf | [
"PresheafOfModules.map",
"PresheafOfModules.forgetToPresheafModuleCatObjObj",
"CategoryTheory.Functor",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"Linear... | false |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula.0.WeierstrassCurve.Projective.dblU_smul._simp_1_6 | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"GroupWithZero.toMonoidWithZero",
"False",
"GroupWithZero.toDivInvMonoid",
"eq_false",
"GroupWithZero",
"DivInvMonoid.toZPow",
"Ne",
"Int",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Zero.toOfNat0",
"zpow_ne_zero",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq... | false |
_private.Mathlib.Tactic.ReduceModChar.0.Tactic.ReduceModChar._aux_Mathlib_Tactic_ReduceModChar___elabRules_Tactic_ReduceModChar_reduce_mod_char!_1.unsafe_impl_2 | Mathlib.Tactic.ReduceModChar | [
"Lean.TSyntax",
"Classical.ofNonempty",
"instNonemptyOfMonad",
"instInhabitedPUnit",
"Lean.Elab.Tactic.instMonadTacticM",
"List.cons",
"Unit",
"instNonemptyOfInhabited",
"Pi.instNonempty",
"Lean.SyntaxNodeKind",
"Lean.Elab.Tactic.TacticM",
"Lean.Name.mkStr4",
"List.nil",
"Option"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.TensorProduct.0.TensorProduct.inner_definite | Mathlib.Analysis.InnerProductSpace.TensorProduct | [
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Finsupp.instFunLike",
"Real.instIsOrderedRing",
"Set.singleton_subset_iff",
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Submodule",
"RingHomSurjective.ids",
"False",
"Submodule.module._proof_1",
"Real.partialOrder... | true |
Num.pos.inj | Mathlib.Data.Num.Basic | [
"Num",
"Num.pos",
"PosNum",
"Eq",
"Num.pos.noConfusion"
] | true |
Complex.norm_cpow_eq_rpow_re_of_pos | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Iff.mpr",
"Norm.norm",
"Eq.mpr",
"Real.instPow",
"Real",
"instHDiv",
"InvOneClass.toOne",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"MulZeroClass.toMul",
"Real.instZero",
"congrArg",
"Complex.im",
"DivInvOneMonoid.toDivInvMonoid",
"Real.instD... | true |
DiffContOnCl.circleAverage_smul_div | Mathlib.Analysis.Complex.MeanValue | [
"instInnerProductSpaceRealComplex",
"Iff.mpr",
"DiffContOnCl",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"False",
"Real.instLE",
"Real",
"instHSMul",
"instHDiv",
"CompleteSpace",
"SeminormedAddCommGroup",
"Real.lattice",
"Complex.instNormedAddCom... | true |
_private.Mathlib.NumberTheory.ArithmeticFunction.Misc.0.ArithmeticFunction.sum_Ioc_mul_eq_sum_sum._proof_1_8 | Mathlib.NumberTheory.ArithmeticFunction.Misc | [
"Lean.RArray.leaf",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Preorder.toLT",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Nat.not_le_eq",
"Lean.Grind.Nat.lt_eq",
"Preorder.toLE",
"Eq.mp",
"Nat.ToInt.natCast_ofNat",
"Nat.Linear.ExprCnstr... | false |
CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesEIso_inv_τ₁ | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.ShortComplex.toCycles_comp_homologyπ",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesE",
"CategoryTheory.ShortComplex.homologyπ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.cokernel... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Equiv.constToList_eq._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
Lean.InductiveVal.mk._flat_ctor | Lean.Declaration | [
"Lean.InductiveVal.mk",
"Lean.Expr",
"Lean.ConstantVal.mk",
"List",
"Nat",
"Bool",
"Lean.Name",
"Lean.InductiveVal"
] | false |
MulAction.fixedPoints_of_subsingleton | Mathlib.GroupTheory.GroupAction.Basic | [
"Eq.mpr",
"instHSMul",
"Set.univ",
"Group",
"Membership.mem",
"id",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"Set.eq_univ_of_forall",
"MulAction",
"Monoid.toSemigroup",
"Subsingleton",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.fixedPoints",
"_private.Mathlib.GroupTheo... | true |
Std.DTreeMap.Internal.Impl.getKey?_eq_some | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Std.TransOrd",
"Option.some",
"Membership.mem",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.getKey?",
"Std.DTreeMap.Internal.Impl.getKey?_eq_some_of_contains",
"Eq",
"Std.LawfulEqOrd",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd",
"Opt... | true |
LieModule.Weight.toLinear_apply | Mathlib.Algebra.Lie.Weights.Linear | [
"LieAlgebra.toModule",
"CommRing",
"LieModule.Weight.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieRing.IsNilpotent",
"LinearMap.instFunL... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_10 | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | [
"Lean.RArray.leaf",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Eq.rec",
"Lean.RArray.branch",
"id",
"instOfNatNat",
"SimpleGraph.Dart",
"LE.le",
"instLENat",
"SimpleGraph",
"Bool.true",
"SimpleGraph.Walk.darts",
"List",
"instHAdd",
"Nat.Linear.Expr.eq_of_toNormPoly_eq",
"HAdd.h... | false |
Std.Time.instHSubOffsetOffset_10 | Std.Time.Date.Basic | [
"Rat.instOfNat",
"instHDiv",
"Rat",
"HDiv.hDiv",
"Std.Time.Day.Offset",
"Std.Time.Internal.UnitVal.sub",
"Std.Time.Day.Offset.toMilliseconds",
"Std.Time.Millisecond.Offset",
"HSub.mk",
"OfNat.ofNat",
"Rat.instDiv",
"HSub"
] | true |
Std.ExtDHashMap.Const.mem_unitOfList._simp_1 | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"List.contains",
"Membership.mem",
"LawfulHashable",
"Bool.true",
"List",
"Unit",
"EquivBEq",
"Std.ExtDHashMap.Const.unitOfList",
"propext",
"Std.ExtDHashMap",
"Bool",
"Std.ExtDHashMap.Const.mem_unitOfList",
"Hashable",
"BEq",
... | false |
Mathlib.Tactic.Linarith.SimplexAlgorithm.Tableau.casesOn | Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Datatypes | [
"Mathlib.Tactic.Linarith.SimplexAlgorithm.Tableau",
"Mathlib.Tactic.Linarith.SimplexAlgorithm.Tableau.mk",
"Mathlib.Tactic.Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm",
"Array",
"Nat",
"Mathlib.Tactic.Linarith.SimplexAlgorithm.Tableau.rec",
"Array.size"
] | false |
MeasureTheory.Measure.InnerRegularCompactLTTop | Mathlib.MeasureTheory.Measure.Regular | [
"MeasureTheory.Measure",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.Measure.InnerRegularCompactLTTop.mk"
] | true |
AddOreLocalization.oreSub.eq_1 | Mathlib.GroupTheory.OreLocalization.Basic | [
"AddOreLocalization.oreEqv",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Subtype",
"Prod.mk",
"AddSubmonoid",
"AddOreLocalization",
"AddOreLocalization.oreSub",
"AddAction",
"Quotient.mk'",
"AddOreLocalization.AddOreSet",
"AddMonoid",
"Eq.refl",
"Prod",
"AddSubmonoid.instSetLike",
"... | true |
CategoryTheory.RelCat.Hom.ofRel.noConfusion | Mathlib.CategoryTheory.Category.RelCat | [
"CategoryTheory.RelCat.Hom.ofRel",
"SetRel",
"CategoryTheory.RelCat.Hom",
"id",
"CategoryTheory.RelCat.Hom.noConfusion",
"CategoryTheory.RelCat",
"heq_of_eq",
"Eq.refl",
"HEq",
"Eq"
] | false |
instDistribPNat._proof_2 | Mathlib.Data.PNat.Basic | [
"HMul.hMul",
"Positive.instDistribSubtypeLtOfNat._proof_2",
"instMulPNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Nat.instPartialOrder",
"Nat.instSemiring",
"Nat.instIsStrictOrderedRing",
"Eq",
"instAddPNat",
"instHMul",
"PNat"
] | false |
CategoryTheory.Abelian.SpectralObject.cyclesMap._proof_9 | Mathlib.Algebra.Homology.SpectralObject.Cycles | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.cyclesMap._proof_7",
"CategoryTheory.Abelian.SpectralObject.cyclesMap._proof_2",
"CategoryTheory.ComposableArrows.app'",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Composab... | false |
CategoryTheory.Limits.sigmaComparison_map_desc_assoc | Mathlib.CategoryTheory.Limits.Shapes.Products | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Eq.mp",
"CategoryTheory.Limits.sigmaComparison",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Limits.HasCoproduct",
"CategoryTheory.Functor.map",
"Cate... | true |
Lean.Meta.Rewrites.RwDirection.forward.sizeOf_spec | Lean.Meta.Tactic.Rewrites | [
"Lean.Meta.Rewrites.RwDirection",
"Lean.Meta.Rewrites.RwDirection._sizeOf_inst",
"Lean.Meta.Rewrites.RwDirection.forward",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Algebra.Polynomial.Homogenize.0.Polynomial.homogenize_finsetProd._simp_1_1 | Mathlib.Algebra.Polynomial.Homogenize | [
"Finset.cons",
"Finset",
"Membership.mem",
"And",
"Finset.instSetLike",
"Finset.forall_mem_cons",
"propext",
"Eq",
"Not",
"SetLike.instMembership"
] | false |
Lean.Meta.SimpAll.State.ctorIdx | Lean.Meta.Tactic.Simp.SimpAll | [
"Nat",
"Lean.Meta.SimpAll.State"
] | false |
Vector.contains_empty | Init.Data.Vector.Lemmas | [
"List.contains_toArray",
"congrArg",
"List.contains",
"Vector.contains",
"instOfNatNat",
"List.toArray",
"Vector.contains_mk",
"Vector.mk",
"Nat",
"True",
"eq_self",
"Bool",
"of_eq_true",
"congrFun'",
"OfNat.ofNat",
"Bool.false",
"BEq",
"Eq",
"Array.size",
"rfl",
"Eq.trans",
... | true |
AlgebraicGeometry.etale_iff | Mathlib.AlgebraicGeometry.Morphisms.Etale | [
"AlgebraicGeometry.Etale.casesOn",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"CommRingCat.Hom.hom",
"Opposite",
"RingHom.Etale",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Qui... | true |
ContextFreeGrammar.derives_reverse | Mathlib.Computability.ContextFreeGrammar | [
"ContextFreeGrammar",
"Eq.mpr",
"Symbol",
"congrArg",
"ContextFreeGrammar.reverse",
"HEq.refl",
"ContextFreeGrammar.Derives.reverse",
"ContextFreeGrammar.reverse_reverse",
"ContextFreeGrammar.Derives",
"Eq.casesOn",
"List",
"heq_of_eq",
"Iff",
"List.reverse_reverse",
"HEq.casesOn",
"Tr... | true |
Lean.Meta.Grind.SplitCandidateAnchors.mk.inj | Lean.Meta.Tactic.Grind.Split | [
"Lean.Meta.Grind.SplitCandidateWithAnchor",
"Lean.Meta.Grind.SplitCandidateAnchors.mk",
"Lean.Meta.Grind.SplitCandidateAnchors",
"Array",
"And",
"Nat",
"And.intro",
"Eq",
"Lean.Meta.Grind.SplitCandidateAnchors.mk.noConfusion"
] | true |
CochainComplex.cm5b.p._proof_1 | Mathlib.Algebra.Homology.Factorizations.CM5b | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"CategoryTheory.Abelian",
"CochainComplex.instHasHomotopyCofiberOfHasBinaryBiproductXHAddOfNat",
"Categor... | false |
HahnSeries.cardSuppLTSubring._proof_5 | Mathlib.RingTheory.HahnSeries.Cardinal | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Cardinal",
"AddGroupWithOne.toAddGroup",
"AddMonoid.toAddZeroClass",
"HahnSeries.cardSuppLTAddSubgroup",
"AddSubsemigroup.carrier",
"Membership.mem",
"Fact",
"AddZeroClass.toAddZero",
"PartialOrder",
"AddSubmonoid.toAddSubsemigroup",
"Su... | false |
Finset.biUnion_filter_eq_of_maps_to | Mathlib.Data.Finset.Union | [
"Finset",
"Membership.mem",
"Finset.biUnion",
"_private.Mathlib.Data.Finset.Union.0.Finset.biUnion_filter_eq_of_maps_to._proof_1_1",
"Finset.instSetLike",
"Finset.filter",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | true |
AntisymmRel.le_congr | Mathlib.Order.Antisymmetrization | [
"AntisymmRel.trans_le",
"LE.le.trans_antisymmRel",
"Preorder.toLE",
"LE.le",
"Iff",
"Iff.intro",
"AntisymmRel",
"AntisymmRel.symm",
"Preorder"
] | true |
_private.Mathlib.Topology.ContinuousMap.Bounded.Normed.0.zpowRec.match_1.eq_2 | Mathlib.Topology.ContinuousMap.Bounded.Normed | [
"zpowRec.match_1",
"Int.ofNat",
"Int",
"Nat",
"Eq.refl",
"Int.negSucc",
"Eq"
] | true |
Aesop.Goal.instHashable | Aesop.Tree.Data | [
"Aesop.Goal.id",
"Aesop.Goal",
"Aesop.GoalId",
"Aesop.GoalId.instHashable",
"Hashable.mk",
"Hashable.hash",
"Hashable"
] | true |
String.isEmpty_iff._simp_1 | Init.Data.String.Lemmas.IsEmpty | [
"String.isEmpty_iff",
"String",
"String.isEmpty",
"Bool.true",
"propext",
"Bool",
"Eq"
] | false |
Aesop.SlotIndex.casesOn | Aesop.Forward.SlotIndex | [
"Aesop.SlotIndex",
"Nat",
"Aesop.SlotIndex.mk",
"Aesop.SlotIndex.rec"
] | false |
MvPFunctor.WPath.child.injEq | Mathlib.Data.PFunctor.Multivariate.W | [
"MvPFunctor",
"PFunctor.A",
"Eq.propIntro",
"PFunctor.B",
"Lean.injEq_helper",
"HEq.homo_ndrec",
"PFunctor.W",
"instOfNatNat",
"MvPFunctor.WPath.child.inj",
"MvPFunctor.A",
"WType.mk",
"instHAdd",
"And",
"HAdd.hAdd",
"MvPFunctor.WPath",
"Nat",
"Eq.ndrec",
"MvPFunctor.last",
"inst... | true |
le_smul_of_one_le_left | Mathlib.Algebra.Order.Module.Defs | [
"Monoid",
"MulOne.toOne",
"instHSMul",
"smul_le_smul_of_nonneg_right",
"Monoid.toMulOneClass",
"congrArg",
"Preorder.toLE",
"SMulPosMono",
"Eq.mp",
"LE.le",
"one_smul",
"MulOneClass.toMulOne",
"MulAction",
"Monoid.toSemigroup",
"One.toOfNat1",
"Zero.toOfNat0",
"HSMul.hSMul",
"Semig... | true |
MvPolynomial.coeff_rename_embDomain | Mathlib.Algebra.MvPolynomial.Rename | [
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"Finsupp.mapDomain",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"Algebra.id... | true |
le_of_not_gt | Mathlib.Order.Defs.LinearOrder | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"le_or_gt",
"LT.lt",
"Or.resolve_right",
"LinearOrder.toPartialOrder",
"Not"
] | true |
tensorKaehlerQuotKerSqEquiv._proof_1 | Mathlib.RingTheory.Smooth.Kaehler | [
"Derivation",
"Ideal.Quotient.isScalarTower",
"Derivation.liftKaehlerDifferential",
"LinearMap.id",
"Ideal.Quotient.commSemiring",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"IsScalarTower.to_smulCommClass'",
"Ideal.Algebra.kerSquareLift",
"Derivation.ext",
"LinearEqu... | false |
Lean.Grind.CommRing.SimpResult.k₂ | Lean.Meta.Tactic.Grind.Arith.CommRing.Poly | [
"Int",
"Lean.Grind.CommRing.SimpResult"
] | true |
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