name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ModuleCon.instAddZeroClassQuotient._proof_2 | Mathlib.Algebra.Module.Congruence.Defs | [
"SMul",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
"ModuleCon.instZeroQuotient",
"AddZero.toAdd",
"Zero.toOfNat0",
"AddCon.addZeroClass._proof_2",
"ModuleCon.instAddQuotient",
"OfNat.ofNat",
"AddZero.mk",
"Eq",
"ModuleCon.toAddCon",
"ModuleCon"... | false |
instBooleanAlgebraSubtypeProdAndEqHMulFstSndOfNatHAdd._proof_12 | Mathlib.Algebra.Order.Ring.Idempotent | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"HMul.hMul",
"CommSemiring.toSemiring",
"MulOne.toMul",
"Subtype",
"Distrib.toAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Prod.fst",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"instMulZeroOneClassOfSemiring",
"Co... | false |
Mathlib.Tactic.Sat.Clause.mk.noConfusion | Mathlib.Tactic.Sat.FromLRAT | [
"Lean.Expr",
"id",
"Int",
"Mathlib.Tactic.Sat.Clause.noConfusion",
"Array",
"Mathlib.Tactic.Sat.Clause.mk",
"Eq",
"Mathlib.Tactic.Sat.Clause"
] | false |
instDifferentialAlgebra | Mathlib.RingTheory.Derivation.DifferentialRing | [
"Derivation",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"RingHom",
"Algebra.id",
"Differential",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Int",
"Derivation.in... | true |
Matrix.conjTranspose_circulant | Mathlib.LinearAlgebra.Matrix.Circulant | [
"Pi.instStarForall",
"NegZeroClass.toNeg",
"neg_sub",
"congrArg",
"Matrix",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"instHSub",
"SubtractionMonoid",
"Star",
"True",
"eq_self",
"of_... | true |
_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.UniformOnFun.isUniformInducing_pi_restrict._simp_1_1 | Mathlib.Topology.UniformSpace.UniformConvergenceTopology | [
"UniformSpace",
"isUniformInducing_iff_uniformSpace",
"IsUniformInducing",
"propext",
"UniformSpace.comap",
"Eq"
] | false |
BoxIntegral.Prepartition.eq_of_boxes_subset_iUnion_superset | Mathlib.Analysis.BoxIntegral.Partition.Basic | [
"Iff.mpr",
"Exists.choose_spec",
"Real",
"le_rfl",
"BoxIntegral.Prepartition.eq_of_mem_of_mem",
"BoxIntegral.Prepartition",
"BoxIntegral.Box.toSet",
"Finset",
"PartialOrder.toPreorder",
"Membership.mem",
"Eq.le",
"HasSubset.Subset",
"LE.le",
"Set.instInter",
"BoxIntegral.Prepartition.box... | true |
AlgebraicGeometry.Scheme.Cover.trans_map | Mathlib.AlgebraicGeometry.Cover.Directed | [
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreZeroHypercover.I₀",
"AlgebraicGeometry.Scheme.Cover",
"CategoryTheory.CategoryStruct.c... | true |
_private.Mathlib.RingTheory.Localization.Ideal.0.IsLocalization.map_eq_top_of_not_subset._simp_1_1 | Mathlib.RingTheory.Localization.Ideal | [
"Set.not_subset_iff_exists_mem_notMem",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"And",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.instHasSubset",
"Set"
] | false |
DFinsupp.extendWith_single_zero | Mathlib.Data.DFinsupp.Defs | [
"DFinsupp.single_eq_same",
"Eq.mpr",
"DFinsupp.ext",
"Option.instDecidableEq",
"congrArg",
"Decidable.eq_or_ne",
"DFinsupp.single",
"Option.casesOn",
"DFinsupp.extendWith_some",
"Option.some",
"Function.Injective.ne",
"DFinsupp.instDFunLike",
"id",
"DFinsupp.single_eq_of_ne",
"Ne",
"Ne... | true |
Int.sub_mul | Init.Data.Int.Lemmas | [
"HMul.hMul",
"congrArg",
"HSub.hSub",
"Int.instNegInt",
"Int",
"Int.instMul",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"True",
"eq_self",
"of_eq_true",
"Int.instAdd",
"Int.instSub",
"congrFun'",
"Int.neg_mul",
"Int.add_mul",
"Eq",
"Neg.neg",
"Eq.trans",
"instHMul"
] | true |
Ideal.IsAugmentation | Mathlib.RingTheory.Ideal.IsAugmentation | [
"Submodule",
"Semiring.toModule",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"Submodule.restrictScalars",
"Submodule.completeLattice",
"Algebra",
"Algebra.toSMul",
"CompleteLattice.toBoundedOrder",
"Algebra.toModule",
"Submodule.instPartialOrder",
"Ideal",
"Submodule.one",
"CommSemi... | true |
Lean.Meta.Grind.AttrKind.infer.sizeOf_spec | Lean.Meta.Tactic.Grind.Attr | [
"instOfNatNat",
"Lean.Meta.Grind.AttrKind",
"Lean.Meta.Grind.AttrKind._sizeOf_inst",
"Nat",
"Lean.Meta.Grind.AttrKind.infer",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
Std.DTreeMap.Internal.RooSliceData.noConfusion | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"HEq.refl",
"Std.DTreeMap.Internal.RooSliceData",
"Std.DTreeMap.Internal.RooSliceData.noConfusionType",
"Std.DTreeMap.Internal.RooSliceData.casesOn",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.Roo"
] | false |
_private.Mathlib.MeasureTheory.Function.JacobianOneDim.0.MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAt._simp_1_4 | Mathlib.MeasureTheory.Function.JacobianOneDim | [
"Membership.mem",
"SDiff.sdiff",
"And",
"Set.mem_diff",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.instSDiff",
"Set"
] | false |
_private.Mathlib.CategoryTheory.RepresentedBy.0.CategoryTheory.Functor.IsRepresentedBy.iff_of_isoObj._simp_1_3 | Mathlib.CategoryTheory.RepresentedBy | [
"CategoryTheory.op_comp",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"Quiver.Hom.op",
"Opposite.op",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.CategoryStruct",
"Eq.symm",
"Eq"
] | false |
Finset.union_subset_right | Mathlib.Data.Finset.Lattice.Basic | [
"Finset.instUnion",
"Finset.Subset.trans",
"Finset",
"HasSubset.Subset",
"Finset.instHasSubset",
"Union.union",
"Finset.subset_union_right",
"DecidableEq"
] | true |
_private.Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory.0.MeasureTheory.SimpleFunc.exists_le_lowerSemicontinuous_lintegral_ge._simp_1_5 | Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | [
"Preorder.toLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Ne",
"lt_top_iff_ne_top",
"OrderTop",
"OrderTop.toTop",
"LT.lt",
"propext",
"Top.top",
"Eq"
] | false |
_private.Mathlib.Analysis.Normed.Operator.BanachSteinhaus.0.banach_steinhaus_iSup_nnnorm._simp_1_2 | Mathlib.Analysis.Normed.Operator.BanachSteinhaus | [
"Set.range_comp",
"Function.comp",
"Set.image",
"Set.range",
"Eq.symm",
"Eq",
"Set"
] | false |
Algebra.FormallySmooth.iff_injective_cotangentComplexBaseChange | Mathlib.RingTheory.Smooth.Local | [
"Derivation",
"Module.FaithfullyFlat.instOfNontrivialOfFree",
"Eq.mpr",
"TensorProduct.AlgebraTensorModule.cancelBaseChange",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"LinearMap.baseChange",
"Module.FaithfullyFlat.lTensor_injective_iff_injective",
"LinearEquiv.symm",
... | true |
WithAbs.instIsSeparable_1 | Mathlib.Analysis.Normed.Field.WithAbs | [
"WithAbs",
"WithAbs.instRing",
"AlgEquiv.symm",
"Algebra",
"Field.toDivisionRing",
"PartialOrder",
"DivisionRing.toRing",
"Field.toSemifield",
"Field.toCommRing",
"Algebra.IsSeparable",
"WithAbs.instAlgebra",
"CommRing.toCommSemiring",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSe... | true |
Valuation.map_sub_lt | Mathlib.RingTheory.Valuation.Basic | [
"Eq.mpr",
"NegZeroClass.toNeg",
"Preorder.toLT",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"sub_eq_add_neg",
"HSub.hSub",
"LinearOrderedCommMonoidWithZero.toLinearOrder",
"SemilatticeInf.toPartialOrder",
"AddZeroClass.toAddZero",
"Distri... | true |
PosNum.minFac.eq_3 | Mathlib.Data.Num.Prime | [
"castPosNum",
"Nat.instOne",
"PosNum.bit1",
"PosNum.minFac",
"instOnePosNum",
"PosNum.minFacAux",
"Nat",
"One.toOfNat1",
"instAddNat",
"Eq.refl",
"PosNum",
"OfNat.ofNat",
"Eq"
] | true |
Matrix.submatrix_id_id | Mathlib.LinearAlgebra.Matrix.Defs | [
"Matrix.submatrix",
"Matrix",
"id",
"Eq",
"Matrix.ext",
"rfl"
] | true |
Turing.ToPartrec.instDecidableEqCode.decEq | Mathlib.Computability.TuringMachine.Config | [
"Turing.ToPartrec.Code.brecOn",
"Turing.ToPartrec.instDecidableEqCode.decEq._f",
"Decidable",
"Eq",
"Turing.ToPartrec.Code"
] | true |
Mathlib.Tactic.Abel.NormalExpr.zero.sizeOf_spec | Mathlib.Tactic.Abel | [
"Mathlib.Tactic.Abel.NormalExpr.zero",
"Lean.Expr",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Mathlib.Tactic.Abel.NormalExpr._sizeOf_inst",
"OfNat.ofNat",
"Eq",
"Mathlib.Tactic.Abel.NormalExpr",
"Lean.Expr._sizeOf_inst"
] | true |
CategoryTheory.PreGaloisCategory.endMulEquivAutGalois_pi | Mathlib.CategoryTheory.Galois.Prorepresentability | [
"CategoryTheory.GaloisCategory.toPreGaloisCategory",
"CategoryTheory.PreGaloisCategory.PointedGaloisObject.pt",
"CategoryTheory.Functor",
"MulEquiv.instEquivLike",
"MonoidHom.instFunLike",
"CategoryTheory.PreGaloisCategory.AutGalois.π",
"MonoidHom",
"Monoid.toMulOneClass",
"CategoryTheory.ConcreteCa... | true |
IsDedekindDomain.HeightOneSpectrum.noConfusionType | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"CommRing",
"Semiring.toModule",
"IsDedekindDomain.HeightOneSpectrum.casesOn",
"CommSemiring.toSemiring",
"IsDedekindDomain.HeightOneSpectrum",
"Ne",
"Bot.bot",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Submodule.instBot",
"CommRing.toCommSemiring",
"NonAssocSemiring.toNonUnitalNo... | false |
CategoryTheory.Adjunction.lim_preservesLimits | Mathlib.CategoryTheory.Adjunction.Limits | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.lim",
"CategoryTheory.Adjunction.rightAdjoint_preservesLimits",
"CategoryTheory.Limits.constLimAdj",
"CategoryTheory.Functor.const",
"CategoryTheory.Limits.PreservesLimits",
... | true |
SheafOfModules.freeFunctor | Mathlib.Algebra.Category.ModuleCat.Sheaf.Free | [
"SheafOfModules.freeFunctor._proof_1",
"CategoryTheory.Functor",
"AddCommGrpCat.instCategory",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"RingCat.ring",
"AddCommGroup.toAddGroup",
"RingHom",
"AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier",
"AddZeroClass.toAddZero",
"... | true |
Std.LawfulBEqCmp.compare_beq_eq_beq | Init.Data.Order.Ord | [
"Std.LawfulBEqCmp.compare_eq_iff_beq",
"Eq.mpr",
"instDecidableEqOrdering",
"instLawfulBEq",
"congrArg",
"Iff.rfl",
"beq_iff_eq",
"Ordering",
"Bool.eq_iff_iff",
"Ordering.eq",
"id",
"instBEqOfDecidableEq",
"Bool.true",
"BEq.beq",
"Iff",
"Std.LawfulBEqCmp",
"propext",
"Bool",
"BEq... | true |
Int.pos_of_neg_neg | Init.Data.Int.Order | [
"Eq.mpr",
"congrArg",
"id",
"Int.instNegInt",
"Int",
"Int.neg_zero",
"Int.instLTInt",
"Int.lt_of_neg_lt_neg",
"instOfNat",
"LT.lt",
"OfNat.ofNat",
"Eq",
"Neg.neg"
] | true |
OrderEmbedding.ltEmbedding_apply | Mathlib.Order.Hom.Basic | [
"Preorder.toLT",
"Preorder.toLE",
"RelEmbedding",
"OrderEmbedding.ltEmbedding",
"LT.lt",
"OrderEmbedding",
"Eq",
"DFunLike.coe",
"instFunLikeOrderEmbedding",
"RelEmbedding.instFunLike",
"rfl",
"Preorder"
] | true |
Std.DHashMap.Internal.Raw₀.Const.get_filterMap | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.Internal.List.getValue_filterMap",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Std.Internal.List.containsKey_of_perm",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw₀.contains_of_contains_filterMap",
"Std.Internal.List.getValue_of_perm",
"Std.DHashMap.... | true |
_private.Mathlib.Topology.Inseparable.0.inseparable_iff_forall_isClosed._simp_1_3 | Mathlib.Topology.Inseparable | [
"And",
"propext",
"Eq.symm",
"Eq",
"forall_and"
] | false |
Complex.tendsto_exp_nhds_zero_iff | Mathlib.Analysis.SpecialFunctions.Exp | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"congrArg",
"Iff.rfl",
"Complex.instNormedField",
"Complex.comap_exp_nhds_zero",
"PseudoMetricSpace.toUniformSpace",
"Complex.instZero",
"Function.comp",
"nhds",
"id",
"_private.Mathlib.Analysis.SpecialFunctions.Exp.0.Complex.tendsto_e... | true |
CommGrpCat | Mathlib.Algebra.Category.Grp.Basic | [
"CommGrpCat.mk"
] | true |
Lean.Language.SnapshotTask.ReportingRange.some.injEq | Lean.Language.Basic | [
"Lean.Syntax.Range",
"Lean.Language.SnapshotTask.ReportingRange.some.inj",
"Lean.Language.SnapshotTask.ReportingRange.some",
"Eq.propIntro",
"Lean.Language.SnapshotTask.ReportingRange",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.RingTheory.Algebraic.Integral.0.IsAlgebraic.of_mul.match_1_1 | Mathlib.RingTheory.Algebraic.Integral | [
"Subalgebra.instSetLike",
"CommRing",
"HMul.hMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.adjoin",
"RingHom",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"Ne",
"instDistribOfSemiring",
"And.casesOn",
"And",
"CommRing.toCommSemiring",
"RingHom.ins... | false |
_private.Mathlib.Data.List.Lattice.0.List.bagInter_sublist_left._proof_1_5 | Mathlib.Data.List.Lattice | [
"False",
"eq_false",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"Eq.mp",
"id",
"instBEqOfDecidableEq",
"List.cons",
"List",
"True",
"eq_true",
"List.Sublist",
"Eq.refl",
"Eq.symm",
"List.Sublist.cons",
"Not",
"Eq.trans",
"List.bagInter",
"True.intro",
"D... | false |
Polynomial.not_dvd_of_degree_lt | Mathlib.Algebra.Polynomial.Degree.Domain | [
"WithBot.instPreorder",
"WithBot",
"Preorder.toLT",
"Dvd.dvd",
"semigroupDvd",
"SemigroupWithZero.toSemigroup",
"id",
"Ne",
"Polynomial.degree",
"NonUnitalSemiring.toSemigroupWithZero",
"Polynomial",
"instDistribOfSemiring",
"NoZeroDivisors",
"Distrib.toMul",
"Nat.instPreorder",
"Polyn... | true |
CategoryTheory.MonoOver.isColimitCoconeOfHasStrongEpiMonoFactorisation | Mathlib.CategoryTheory.Subobject.MonoOver | [
"CategoryTheory.Limits.MonoFactorisation.I",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.MonoOver.liftStructOfHasStrongEpiMonoFactorisation",
"CategoryTheory.Functor.category",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Limits.IsColimit.mk",
... | true |
PrespectralSpace.exists_isCompact_and_isOpen_between | Mathlib.Topology.Spectral.Prespectral | [
"Filter.instMembership",
"Iff.mpr",
"subset_refl._simp_1",
"Set.union_subset_union",
"congrArg",
"and_self",
"nhdsWithin",
"subset_trans",
"setOf",
"Set.Finite",
"Membership.mem",
"Exists",
"Set.instUnion",
"PrespectralSpace",
"Set.instIsTransSubset",
"Set.inter_subset_left",
"Set.in... | true |
AddEquiv.map_add' | Mathlib.Algebra.Group.Equiv.Defs | [
"Equiv.toFun",
"instHAdd",
"HAdd.hAdd",
"AddEquiv",
"AddEquiv.toEquiv",
"Eq",
"Add"
] | true |
ConcaveOn.le_slope_of_hasDerivAt | Mathlib.Analysis.Convex.Deriv | [
"NormedCommRing.toSeminormedCommRing",
"HasDerivAt.hasDerivWithinAt",
"Real.partialOrder",
"Real.instLE",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"IsTopologicalRing.toIsTopologicalSemiring",
"Real.denselyNormedField",
"IsTopologicalSemiring.... | true |
AddGroupTopology.instBoundedOrder | Mathlib.Topology.Algebra.Group.GroupTopology | [
"AddGroupTopology.instBoundedOrder._proof_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddGroupTopology.instPartialOrder",
"OrderTop.mk",
"AddGroupTopology.instBot",
"AddGroupTopology",
"AddGroup",
"AddGroupTopology.instTop",
"OrderBot.mk",
"BoundedOrder.mk",
"BoundedOrder",
"AddGroupTop... | true |
isRegular_op | Mathlib.Algebra.Regular.Opposite | [
"congrArg",
"isRightRegular_op._simp_2",
"MulOpposite",
"_private.Mathlib.Algebra.Regular.Opposite.0.isRegular_op._simp_1_1",
"IsRegular",
"Mul",
"isLeftRegular_op._simp_2",
"_private.Mathlib.Algebra.Regular.Opposite.0.isRegular_op._simp_1_2",
"iff_self",
"IsLeftRegular",
"IsRightRegular",
"An... | true |
_private.Mathlib.Topology.MetricSpace.HausdorffDimension.0.intrinsicInterior.eq_1 | Mathlib.Topology.MetricSpace.HausdorffDimension | [
"AddCommGroup.toAddCommMonoid",
"intrinsicInterior",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"Subtype",
"AffineSubspace.instSetLike",
"TopologicalSpace",
"affineSpan",
"Set.preimage",
"interior",
"AddTorsor",
"Eq.refl",
"Set.image",
"instTopologicalSpaceSubtype",
"... | true |
CategoryTheory.AddMon.mkIso.eq_1 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.AddMon.instCategory",
"CategoryTheory.Iso",
"CategoryTheory.AddMonObj.add",
"CategoryTheory.AddMonObj.zero",
"CategoryTheory.AddMon.addMon",
"CategoryTheory.AddMon.X",
"CategoryTheory.Monoida... | true |
CompactlySupportedContinuousMap.comp | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"CompactlySupportedContinuousMap",
"ContinuousMap",
"CompactlySupportedContinuousMap.continuousMapEquiv._proof_5",
"CompactlySupportedContinuousMap.comp._proof_2",
"ContinuousMap.comp",
"toContinuousMap",
"TopologicalSpace",
"CompactlySupportedContinuousMap.instFunLike",
"CocompactMap.instFunLike",
... | true |
Aesop.ForwardInstantiationStats.rec | Aesop.Stats.Basic | [
"Aesop.ForwardInstantiationStats",
"Nat",
"Aesop.ForwardInstantiationStats.mk"
] | false |
mabs_eq_inv_self | Mathlib.Algebra.Order.Group.Abs | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"IsOrderedMonoid",
"congrArg",
"LinearOrder",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid"... | true |
HomologicalComplex₂.instHasTotalIntObjUpCompShiftFunctor₁ShiftFunctor₂ | Mathlib.Algebra.Homology.TotalComplexShift | [
"Int.instAddCommGroup",
"HomologicalComplex.instCategory",
"ComplexShape.instTotalComplexShape",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"Int.instLinearOrder",
"ComplexShape.instTensorSignsIntUp",
"PartialOrder.toPreorder",
"instIsRightCancelAddOfAddRightReflectLE",
"AddGroupWithOne.toAddMonoidW... | true |
CategoryTheory.Functor.IsDenseSubsite.sheafifyOfIsEquivalenceCompIso | Mathlib.CategoryTheory.Sites.DenseSubsite.Basic | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.rightUnitor",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Functor.associator",
"CategoryTheory.Iso",
"CategoryTheory.presheafToSheaf",
"Ca... | true |
Lean.Elab.Tactic.BVDecide.Frontend.UnsatProver.Result.mk | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide | [
"Lean.Elab.Tactic.BVDecide.Frontend.UnsatProver.Result.mk",
"Lean.Elab.Tactic.BVDecide.Frontend.UnsatProver.Result",
"Lean.Expr",
"Lean.Elab.Tactic.BVDecide.Frontend.LratCert"
] | true |
CategoryTheory.Enriched.FunctorCategory.functorEnrichedOrdinaryCategory._proof_2 | Mathlib.CategoryTheory.Enriched.FunctorCategory | [
"CategoryTheory.Functor",
"CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_comp",
"CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom",
"Equiv.instEquivLike",
"CategoryTheory.EnrichedOrdinaryCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalC... | false |
Lean.Grind.ConfigInteractive.instances._inherited_default | Init.Grind.Config | [
"id",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | false |
CategoryTheory.«_aux_Mathlib_CategoryTheory_Monoidal_Rigid_Basic___macroRules_CategoryTheory_termᘁ__1» | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | [
"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.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr3",... | false |
AddSubgroup.quotientEquivProdOfLE'_symm_apply | Mathlib.GroupTheory.Coset.Basic | [
"Equiv.instEquivLike",
"AddSubgroup.quotientEquivProdOfLE'",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"AddSubgroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"QuotientAddGroup.mk",
"Equiv",
"Subtype",
"LE.le",
"Pr... | true |
Sym.append_inj_left | Mathlib.Data.Sym.Basic | [
"PartialOrder.toPreorder",
"instIsRightCancelAddOfAddRightReflectLE",
"Multiset.instAddCancelCommMonoid",
"Preorder.toLE",
"Multiset",
"Subtype",
"add_left_inj",
"Sym.append",
"Subtype.ext_iff",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Nat",
"AddCancelCommMonoid.toAddCommMonoid",
"Sym",
"Iff.t... | true |
_private.Std.Sync.Channel.0.Std.CloseableChannel.Unbounded.send | Std.Sync.Channel | [
"Pure.pure",
"Unit.unit",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Unbounded",
"Task",
"Except.ok",
"Monad.toApplicative",
"Except.error",
"Task.pure",
"instDecidableEqBool",
"Applicative.toPure",
"Std.CloseableChannel.Error",
"Std.CloseableChannel.Error.closed",
"_private.Std.Sync.... | true |
Std.Time.instTransOrdPlainDate | Std.Time.Date.PlainDate | [
"Std.Time.instOrdPlainDate",
"Std.Time.PlainDate",
"Std.TransOrd",
"_private.Std.Time.Date.PlainDate.0.Std.Time.instTransOrdPlainDate._proof_1"
] | true |
Std.DTreeMap.Raw.mem_of_get_eq | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.instMembership",
"Membership.mem",
"Ordering",
"Std.LawfulEqCmp",
"Std.DTreeMap.Raw.get",
"Eq",
"Std.DTreeMap.Raw"
] | true |
AlgEquiv.restrictNormal_apply | Mathlib.FieldTheory.Normal.Defs | [
"IntermediateField.isScalarTower_mid'",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"IntermediateField",
"IntermediateField.toField",
"Algebra",
"Normal",
"Membership.mem",
"Algebra.toModule",
"Algebra.id",
"Subtype",
"NonUnitalNonAssocRi... | true |
Function.not_lt_argminOn | Mathlib.Order.WellFounded | [
"InvImage",
"WellFoundedLT",
"Membership.mem",
"wellFounded_lt",
"LT.lt",
"Exists.intro",
"WellFounded.not_lt_min",
"InvImage.wf",
"Function.argminOn",
"Set.instMembership",
"Not",
"LT",
"Set"
] | true |
MulAction.equivSubgroupOrbitsSetoidComap._proof_3 | Mathlib.GroupTheory.GroupAction.Quotient | [
"Eq.mpr",
"_private.Mathlib.GroupTheory.GroupAction.Quotient.0.MulAction.equivSubgroupOrbitsSetoidComap._simp_1",
"_private.Mathlib.GroupTheory.GroupAction.Quotient.0.MulAction.equivSubgroupOrbitsSetoidComap._simp_2",
"congrArg",
"MulAction.orbitRel.Quotient.orbit",
"Group",
"Quotient.mk''",
"Membersh... | false |
CategoryTheory.Pseudofunctor.StrongTrans.associator_inv_as_app | Mathlib.CategoryTheory.Bicategory.FunctorBicategory.Pseudo | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pseudofunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Pseudofunctor.StrongTrans.Hom.as",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.Ps... | true |
Rep.barComplex.d_single | Mathlib.RepresentationTheory.Homological.Resolution | [
"Finsupp.instAddZeroClass",
"NegZeroClass.toNeg",
"Rep.V",
"Finsupp.distribMulAction",
"LinearEquiv.symm",
"CommRing",
"instHSMul",
"Representation",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"InvOneClass.toOne",
"LinearMap.comp.congr_simp... | true |
CategoryTheory.MonoidalCoherence.tensor_right_iso | Mathlib.Tactic.CategoryTheory.MonoidalComp | [
"CategoryTheory.MonoidalCoherence.iso",
"CategoryTheory.MonoidalCategory.whiskerLeftIso",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCoherence",
"CategoryTheory.Iso",
"CategoryTheory.MonoidalCoherence.tensor_right",
"CategoryTheory.M... | true |
mabs.eq_1 | Mathlib.Algebra.Order.Group.Unbundled.Abs | [
"Lattice",
"Lattice.toSemilatticeSup",
"DivInvOneMonoid.toInvOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"SemilatticeSup.toMax",
"Inv.inv",
"Max.max",
"Eq.refl",
"InvOneClass.toInv",
"Eq",
"mabs"
] | true |
Lean.Lsp.OpenNamespace.rec | Lean.Data.Lsp.Internal | [
"Lean.Lsp.OpenNamespace.allExcept",
"Array",
"Lean.Lsp.OpenNamespace.renamed",
"Lean.Name",
"Lean.Lsp.OpenNamespace"
] | false |
tendstoLocallyUniformlyOn_iff_forall_tendsto | Mathlib.Topology.UniformSpace.LocallyUniformConvergence | [
"Filter.instMembership",
"_private.Mathlib.Topology.UniformSpace.LocallyUniformConvergence.0.tendstoLocallyUniformlyOn_iff_forall_tendsto._simp_1_3",
"UniformSpace",
"Eq.mpr",
"TendstoLocallyUniformlyOn",
"SProd.sprod",
"congrArg",
"Filter.map",
"nhdsWithin",
"Filter.Eventually",
"uniformity",
... | true |
_private.Init.Data.UInt.Bitwise.0.UInt16.shiftLeft_add_of_toNat_lt._proof_1_3 | Init.Data.UInt.Bitwise | [
"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 |
CompletePartialOrder | Mathlib.Order.CompletePartialOrder | [
"CompletePartialOrder.mk"
] | true |
InfClosed.image | Mathlib.Order.SupClosed | [
"Eq.mpr",
"congrArg",
"Membership.mem",
"id",
"SemilatticeInf.toMin",
"And.casesOn",
"InfHomClass.map_inf",
"And",
"SemilatticeInf",
"Exists.casesOn",
"InfHomClass",
"Set.mem_image_of_mem",
"Eq.ndrec",
"Set.image",
"InfClosed",
"Eq.symm",
"Eq",
"Set.instMembership",
"DFunLike.coe... | true |
InnerProductSpace.rankOne_one_right_eq_toSpanSingleton | Mathlib.Analysis.InnerProductSpace.LinearMap | [
"ContinuousLinearMap.ext_ring",
"NormedCommRing.toNormedRing",
"one_pow",
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"MulOne.toOne",
"Real",
"instHSMul",
"SeminormedAddCommGroup",... | true |
CategoryTheory.CanonicallyOverClass.casesOn | Mathlib.CategoryTheory.Comma.Over.OverClass | [
"CategoryTheory.CanonicallyOverClass.mk",
"CategoryTheory.CanonicallyOverClass.rec",
"CategoryTheory.OverClass",
"CategoryTheory.CanonicallyOverClass",
"CategoryTheory.Category"
] | false |
Filter.diff_mem_inf_principal_compl | Mathlib.Order.Filter.Basic | [
"Filter.instMembership",
"False",
"Filter.mem_principal_self",
"Filter.inter_mem_inf",
"Compl.compl",
"Membership.mem",
"Filter.instInf",
"Set.instCompl",
"SDiff.sdiff",
"Filter.principal",
"Set.instMembership",
"Filter",
"Min.min",
"Set.instSDiff",
"Set"
] | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._auto_112 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
ENNReal.log_le_log_iff._simp_1 | Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog | [
"ENNReal.log_le_log_iff",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"ENNReal.log",
"LE.le",
"ENNReal.instLE",
"ENNReal",
"propext",
"instPartialOrderEReal",
"Eq"
] | false |
_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.instEmitToStringOfToString | Lean.Compiler.LCNF.EmitC | [
"Pure.pure",
"String",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.State",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.EmitM",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.EmitToString.mk",
"IO.RealWorld",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.EmitToS... | true |
Mathlib.Tactic.MkIff.compactRelation._unsafe_rec | Mathlib.Tactic.MkIffOfInductiveProp | [
"bne",
"_private.Mathlib.Tactic.MkIffOfInductiveProp.0.Mathlib.Tactic.MkIff.compactRelation.match_7",
"Lean.Expr.instBEq",
"List.map",
"Option.some",
"Function.comp",
"Mathlib.Tactic.MkIff.compactRelation._unsafe_rec",
"Lean.Expr",
"id",
"Prod.mk",
"Lean.Expr.replaceFVar",
"List.cons",
"Opti... | false |
AlgCat.limitSemiring._aux_43 | Mathlib.Algebra.Category.AlgCat.Limits | [
"Subalgebra.instSetLike",
"AlgCat.instAlgebraObjForgetAlgHomCarrier",
"Int.cast",
"CategoryTheory.Functor",
"CommRing",
"CategoryTheory.Limits.Types.Small.limitCone",
"Equiv.addGroupWithOne",
"AlgCat.instCategory",
"AlgHom",
"AlgCat.instConcreteCategoryAlgHomCarrier",
"AlgHom.funLike",
"AlgCat... | false |
CategoryTheory.instFinalDiscreteOfIsConnected | Mathlib.CategoryTheory.Limits.Final.Connected | [
"Eq.mpr",
"CategoryTheory.Functor",
"congrArg",
"Unique",
"id",
"CategoryTheory.discreteCategory",
"propext",
"CategoryTheory.IsConnected",
"CategoryTheory.isConnected_iff_final_of_unique",
"Eq.symm",
"Eq",
"CategoryTheory.Functor.Final",
"CategoryTheory.Category",
"CategoryTheory.Discrete... | true |
lt_or_antisymmRel_or_gt_or_incompRel | Mathlib.Order.Comparable | [
"Iff.mpr",
"Eq.mpr",
"instDecidableNot",
"_private.Mathlib.Order.Comparable.0.lt_or_antisymmRel_or_gt_or_incompRel._simp_1_1",
"Preorder.toLT",
"congrArg",
"False.elim",
"Classical.propDecidable",
"Preorder.toLE",
"id",
"LE.le",
"Or.casesOn",
"IncompRel",
"And",
"Decidable.of_not_not",
... | true |
Float.toRatParts' | Batteries.Lean.Float | [
"instShiftRightUInt64",
"UInt8.instOfNat",
"Float.toRatParts'.match_1",
"UInt64",
"Float",
"Int.instDecidableEq",
"instDecidableEqBool",
"Int.instNegInt",
"Prod.mk",
"UInt8.toUInt64",
"Int",
"UInt64.toNat",
"instBEqOfDecidableEq",
"instHShiftRightOfShiftRight",
"Nat.cast",
"Int.instLTI... | true |
OrderAddMonoidIso.mk.injEq | Mathlib.Algebra.Order.Hom.Monoid | [
"OrderAddMonoidIso.mk.inj",
"OrderAddMonoidIso",
"Eq.propIntro",
"Preorder.toLE",
"Equiv.toFun",
"LE.le",
"Iff",
"Eq.ndrec",
"AddEquiv",
"Eq.refl",
"AddEquiv.toEquiv",
"Eq",
"OrderAddMonoidIso.mk",
"Add",
"Preorder"
] | true |
Bundle.Trivial.trivialization.isLinear | Mathlib.Topology.VectorBundle.Constructions | [
"Bundle.Trivialization.toFun'",
"instHSMul",
"NormedSpace",
"Bundle.Trivialization.IsLinear.mk",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Bundle.Trivial.trivialization",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"Membership.... | true |
Lean.Elab.Do.DoElemCont.recOn | Lean.Elab.Do.Basic | [
"Lean.Elab.Do.DoElemContKind",
"Lean.Expr",
"Lean.Elab.Do.DoElemCont",
"Lean.Elab.Do.DoElabM",
"Lean.Elab.Do.DoElemCont.rec",
"Lean.Name",
"Lean.Elab.Do.DoElemCont.mk"
] | false |
Monoid.CoprodI.Word.mem_rcons_iff | Mathlib.GroupTheory.CoprodI | [
"Monoid",
"Eq.mpr",
"MulOne.toOne",
"dite_congr",
"Monoid.toMulOneClass",
"congrArg",
"Monoid.CoprodI.Word.toList",
"Membership.mem",
"Exists",
"Eq.rec",
"id",
"Monoid.CoprodI.Word.cons._proof_2",
"Monoid.CoprodI.Word",
"Ne",
"dite",
"List.cons",
"Monoid.CoprodI.Word.mk",
"List",
... | true |
Function.Exact.linearEquivOfSurjective_apply | Mathlib.Algebra.Exact | [
"Function.Exact",
"Submodule",
"RingHomSurjective.ids",
"Submodule.Quotient.addCommMonoid",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"Submodule.hasQuotient",
"LinearMap.range",
"AddCommGroup",
"Function.Exact.linearEquivOfSurjective._proof_1",
"SubtractionMonoid.toSubNegZeroMonoi... | true |
Finset.mem_of_max | Mathlib.Data.Finset.Max | [
"WithBot.some",
"WithBot",
"LinearOrder.toDecidableEq",
"Option.ctorIdx",
"HEq.refl",
"Finset",
"LinearOrder",
"False.elim",
"noConfusion_of_Nat",
"Option.some",
"_private.Mathlib.Data.Finset.Max.0.Finset.mem_of_max._proof_1_1",
"Membership.mem",
"Eq.casesOn",
"Finset.induction_on",
"Fin... | true |
UInt64.add_sub_cancel | Init.Data.UInt.Lemmas | [
"instAddUInt64",
"UInt64",
"HSub.hSub",
"UInt64.toBitVec_inj",
"BitVec",
"instOfNatNat",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"instSubUInt64",
"BitVec.add_sub_cancel",
"Iff.mp",
"OfNat.ofNat",
"Eq",
"UInt64.toBitVec"
] | true |
Filter.lift'_mono | Mathlib.Order.Filter.Lift | [
"Iff.mpr",
"Filter.principal_mono",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Function.comp",
"HasSubset.Subset",
"LE.le",
"Pi.hasLe",
"Filter.lift'",
"Set.instLE",
"Filter.principal",
"Filter",
"Filter.lift_mono",
"Set.instHasSubset",
"Filter.instPartialOrder",
"Set"
] | true |
Std.TreeSet.all | Std.Data.TreeSet.Basic | [
"Std.TreeSet",
"Ordering",
"Std.TreeSet.inner",
"Unit",
"Std.TreeMap.all",
"Bool"
] | true |
CategoryTheory.Functor.congruence_homRel | Mathlib.CategoryTheory.Quotient | [
"CategoryTheory.HomRel.IsStableUnderPrecomp.mk",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Congruence",
"CategoryTheory.Congruence.mk",
"Eq.mp",
"id",
"CategoryTheory.HomRel.IsStableUnderPostcomp.mk",
"CategoryTheory.Functor.map... | true |
Algebra.PreSubmersivePresentation.ofHasCoeffs_algebra_algebraMap_apply | Mathlib.RingTheory.Extension.Presentation.Core | [
"Algebra.Presentation.relationOfHasCoeffs",
"Algebra.Presentation.HasCoeffs",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.algebraMap",
"AddMonoidAlgebra.commRing",
"CommSemiring.toSemiring",
"Algebra.Presentation.ModelOfHasCoeffs",
"Ideal.Quotient.mk",
"IsScalarTowe... | true |
CategoryTheory.Limits.pushoutCoconeOfRightIso_inl | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso | [
"CategoryTheory.Limits.pushoutCoconeOfRightIso",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.PushoutCocone.inl",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.Li... | true |
Subsemigroup.comap_sup_map_of_injective | Mathlib.Algebra.Group.Subsemigroup.Operations | [
"MulHom",
"Lattice.toSemilatticeSup",
"Subsemigroup.map",
"CompleteLattice.toLattice",
"Subsemigroup.comap",
"Mul",
"SemilatticeSup.toMax",
"Subsemigroup.gciMapComap",
"Subsemigroup.instCompleteLattice",
"Max.max",
"Subsemigroup",
"GaloisCoinsertion.u_sup_l",
"MulHom.funLike",
"Function.In... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.get?_inter_of_contains_eq_false_right._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
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