name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Meta.AC.PreContext.idem | Lean.Meta.Tactic.AC.Main | [
"Lean.Meta.AC.PreContext",
"Lean.Expr",
"Option"
] | true |
Lean.Elab.Tactic.BVDecide.Frontend.Diagnosis.ctorIdx | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide | [
"Lean.Elab.Tactic.BVDecide.Frontend.Diagnosis",
"Nat"
] | false |
Pi.Colex.instCompleteLinearOrderColexForall | Mathlib.Order.CompleteLattice.PiLex | [
"LinearOrder.toOrd",
"Pi.Colex.instCompleteLinearOrderColexForall._proof_6",
"BiheytingAlgebra",
"SemilatticeSup.mk",
"BiheytingAlgebra.toSDiff",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Pi.Colex.completeLattice",
"Colex",
"LinearOrder.toDecidableEq",
"Pi.Colex.instCompleteLinearOrderColexF... | true |
AddAction.orbitZMultiplesEquiv | Mathlib.Data.ZMod.QuotientGroup | [
"AddSubgroup.zmultiples_isAddCommutative",
"AddAction.orbit",
"AddAction.orbitEquivQuotientStabilizer",
"ZMod.commRing",
"AddMonoid.toAddSemigroup",
"CommSemiring.toSemiring",
"Equiv.trans",
"AddCommGroup.toAddCommMonoid",
"AddSubgroup.toAddGroup",
"Membership.mem",
"AddAction.instAddAction",
... | true |
_private.Lean.Elab.Tactic.Grind.Param.0.Lean.Elab.Tactic.parseModifier | Lean.Elab.Tactic.Grind.Param | [
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Core.instMonadRefCoreM",
"String",
"Lean.Core.instMonadEnvCoreM",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MessageData.instAppend",
"Lean.throwError",
"Lean.Syntax",
"Lean.instToMess... | true |
IsRegular.left | Mathlib.Algebra.Regular.Defs | [
"IsRegular",
"Mul",
"IsLeftRegular"
] | true |
CategoryTheory.InjectiveResolution.descHomotopyZeroSucc.congr_simp | Mathlib.CategoryTheory.Abelian.Injective.Resolution | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Categor... | true |
Lean.Meta.Tactic.TryThis.Suggestion.style?._default | Lean.Meta.TryThis | [
"Lean.Meta.Tactic.TryThis.SuggestionStyle",
"id",
"Option.none",
"Option"
] | false |
nonneg_of_mul_nonneg_left | Mathlib.Algebra.Order.Ring.Unbundled.Basic | [
"mul_neg_of_neg_of_pos",
"Preorder.toLT",
"HMul.hMul",
"MulZeroClass.toMul",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"le_of_not_gt",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"instDistribOfSemiring",
"MulPosStrictMono",
"Distrib.toMul",
"LT.... | true |
CliffordAlgebra.ofEven_ι | Mathlib.LinearAlgebra.CliffordAlgebra.EvenEquiv | [
"Subalgebra.instSetLike",
"CliffordAlgebra.EquivEven.Q'",
"AlgHom.toLinearMap",
"LinearMap.fst",
"Algebra.lmul",
"CliffordAlgebra.ι",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Algebra.algeb... | true |
Module.compHom.toLinearEquiv_apply | Mathlib.Algebra.Module.Equiv.Basic | [
"Semiring.toModule",
"RingEquiv.instEquivLike",
"RingEquiv.instRingEquivClass",
"Distrib.toAdd",
"instDistribOfSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Distrib.toMul",
"Module.compHom",
"RingHomClass.toRingHom",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"RingHomInvPair.ids"... | true |
Descriptive.Tree.drop | Mathlib.SetTheory.Descriptive.Tree | [
"Membership.mem",
"Subtype",
"Descriptive.tree",
"Subtype.mk",
"List",
"CompleteSublattice.instSetLike",
"List.drop",
"Nat",
"CompleteSublattice",
"CompleteBooleanAlgebra.toCompleteLattice",
"Descriptive.Tree.subAt",
"Subtype.val",
"Descriptive.instSetLikeSubtypeSetListMemCompleteSublatticeT... | true |
Std.ExtTreeMap.getD_empty | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtDTreeMap.Const.getD_empty",
"Ordering",
"Std.ExtTreeMap.getD",
"Std.TransCmp",
"Std.ExtTreeMap",
"EmptyCollection.emptyCollection",
"Std.ExtTreeMap.instEmptyCollection",
"Eq"
] | true |
TopCat.Presheaf.SheafConditionEqualizerProducts.w | Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | [
"CategoryTheory.Limits.limit.π",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.Opens.instPartialOrder",
"Cate... | true |
DifferentiableAt.mem_interior_convex_of_surjective_fderiv | Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | [
"ContinuousLinearMap.comp",
"Mathlib.Tactic.Push.not_forall_eq",
"Filter.instMembership",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Mathlib.Tactic.Push.not_exists._simp_1",
"Iff.mpr",
"IsModuleTopology.toContinuousSMul",
"sub_pos",
"AddGroup.toSubtractionMonoid",
"_private.Mathlib.Ge... | true |
Std.DTreeMap.Raw.Equiv.getKeyLTD_eq | Std.Data.DTreeMap.Raw.Lemmas | [
"Ord.mk",
"Ordering",
"Std.DTreeMap.Raw.Equiv",
"Std.TransCmp",
"Std.DTreeMap.Internal.Impl.Equiv.getKeyLTD_eq",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Raw.getKeyLTD",
"Std.DTreeMap.Raw.Equiv.inner",
"Eq",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Raw"
] | true |
Lean.quoteNameMk | Init.Meta.Defs | [
"Lean.quoteNameMk._f",
"Lean.Syntax.Term",
"Lean.Name.brecOn",
"Lean.Name"
] | true |
Lean.Meta.Simp.ConfigCtx.congrConsts._inherited_default | Init.MetaTypes | [
"id",
"Bool.true",
"Bool"
] | false |
IsSymmSndFDerivWithinAt._proof_4 | Mathlib.Analysis.Calculus.FDeriv.Symmetric | [
"AddMonoid.toAddSemigroup",
"ContinuousLinearMap.addCommGroup._proof_6",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"AddSemigroup.toAdd",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"NormedAddCommGroup.toAddCommGroup",
"SubNegMonoid.toAddMonoid",
"C... | false |
IsPrimitiveRoot.powerBasis.congr_simp | Mathlib.NumberTheory.Cyclotomic.Discriminant | [
"PowerBasis",
"IsDomain",
"Nat.instMulZeroClass",
"CommRing",
"CommSemiring.toSemiring",
"Algebra",
"Eq.rec",
"Set.instSingletonSet",
"IsCyclotomicExtension",
"Field.toSemifield",
"Field.toCommRing",
"CommRing.toCommSemiring",
"Nat",
"IsPrimitiveRoot.powerBasis",
"Eq.ndrec",
"Eq.refl",... | true |
ByteSlice.forIn.loop._sunfold | Batteries.Data.ByteSlice | [
"Pure.pure",
"ByteSlice",
"ByteSlice.forIn.loop.match_1",
"Monad.toApplicative",
"ByteSlice.forIn._proof_2",
"HSub.hSub",
"ByteSlice.forIn.loop.match_3",
"ByteSlice.size",
"instSubNat",
"ByteSlice.instGetElemNatUInt8LtSize",
"instOfNatNat",
"LE.le",
"instLENat",
"Applicative.toPure",
"Fo... | false |
Std.HashMap.mem_modify._simp_1 | Std.Data.HashMap.Lemmas | [
"Membership.mem",
"Std.HashMap",
"LawfulHashable",
"EquivBEq",
"propext",
"Hashable",
"BEq",
"Eq",
"Std.HashMap.instMembership",
"Std.HashMap.modify",
"Std.HashMap.mem_modify"
] | false |
AlgebraicGeometry.tilde.modulesSpecToSheafIso | Mathlib.AlgebraicGeometry.Modules.Tilde | [
"AlgebraicGeometry.tilde.modulesSpecToSheafIso._proof_4",
"AlgebraicGeometry.Spec",
"CategoryTheory.Functor",
"Lattice.toSemilatticeSup",
"CommRingCat.Hom.hom",
"Opposite",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"LinearE... | true |
circleIntegrable_sub_zpow_iff | Mathlib.MeasureTheory.Integral.CircleIntegral | [
"instInnerProductSpaceRealComplex",
"Iff.mpr",
"NormedCommRing.toNormedRing",
"_private.Mathlib.MeasureTheory.Integral.CircleIntegral.0.circleIntegrable_sub_zpow_iff._simp_1_1",
"_private.Mathlib.MeasureTheory.Integral.CircleIntegral.0.circleIntegrable_sub_zpow_iff._simp_1_3",
"AddGroup.toSubtractionMonoi... | true |
_private.Mathlib.Data.EReal.Inv.0.EReal.abs_mul._simp_1_1 | Mathlib.Data.EReal.Inv | [
"Real",
"HMul.hMul",
"EReal",
"Real.instMul",
"EReal.coe_mul",
"Eq.symm",
"Eq",
"Real.toEReal",
"EReal.instMul",
"instHMul"
] | false |
Ordinal.lt_opow_iff_log_lt' | Mathlib.SetTheory.Ordinal.Exponential | [
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Ne",
"Ordinal.one",
"Iff",
"HPow.hPow",
"Ordinal.log",
"LT.lt",
"Ordinal.zero",
"One.toOfNat1",
"Zero.toOfNat0",
"instHPow",
"OfNat.ofNat",
"Ordinal.instPow",
"lt_iff_lt_of_le_iff_le",
"... | true |
ModuleCat.normalEpi._proof_1 | Mathlib.Algebra.Category.ModuleCat.Abelian | [
"Submodule",
"RingHomSurjective.ids",
"Submodule.Quotient.addCommMonoid",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CategoryTheory.Limits.WalkingParallelPair",
"Submodule.Quotient.addCommGroup",
"LinearMap.ext",
"AddCommGroup.toAddCommMonoid",
... | false |
SSet.Subcomplex.PairingCore.ctorIdx | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | [
"SSet.Subcomplex.PairingCore",
"SSet",
"Nat",
"SSet.Subcomplex"
] | false |
_private.Mathlib.RepresentationTheory.Rep.Basic.0.Rep.mk | Mathlib.RepresentationTheory.Rep.Basic | [
"Monoid",
"Representation",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Rep",
"Semiring",
"Module",
"_private.Mathlib.RepresentationTheory.Rep.Basic.0.Rep.mk"
] | true |
_private.Mathlib.Algebra.Polynomial.Splits.0.Polynomial.«term_~ᵤ_» | Mathlib.Algebra.Polynomial.Splits | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.Name.anonymous",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
_private.Mathlib.MeasureTheory.Integral.IntervalIntegral.AbsolutelyContinuousFun.0.AbsolutelyContinuousOnInterval.dist_le_of_pairwiseDisjoint_hasSum._proof_1_5 | Mathlib.MeasureTheory.Integral.IntervalIntegral.AbsolutelyContinuousFun | [
"Real",
"instDecidableEqProd",
"Finset",
"Membership.mem",
"Set.Elem",
"Subtype",
"Nat",
"Finset.card",
"Prod",
"Real.decidableEq",
"Subtype.val",
"Eq",
"Set.instMembership",
"Finset.image",
"rfl",
"Set"
] | false |
Valuation.instCommGroupWithZeroSubtypeMemSubmonoidMrange._proof_5 | Mathlib.RingTheory.Valuation.Basic | [
"CommMonoidWithZero.toCommMonoid",
"Valuation.instCommGroupWithZeroSubtypeMemSubmonoidMrange._aux_1",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Semigroup.toMul",
"instHDiv",
"Valuation.instCommMonoidWithZeroSubtypeMemSubmonoidMrange",
"HMul.... | false |
Finsupp.DegLex.single_strictAnti | Mathlib.Data.Finsupp.MonomialOrder.DegLex | [
"Finsupp.instAddZeroClass",
"False",
"Nat.instMulZeroClass",
"Preorder.toLT",
"Equiv.instEquivLike",
"congrArg",
"and_self",
"Lex",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"ofDegLex",
"PartialOrder.toPreorder",
"Finsupp.instLTLex",
"SemilatticeInf.toPartialOrder",
"AddZeroClass.toAddZ... | true |
Lean.Grind.IntModule.toNatModule | Init.Grind.Module.Basic | [
"Lean.Grind.IntModule.nsmul",
"Lean.Grind.IntModule",
"Nat",
"Lean.Grind.IntModule.toAddCommGroup",
"Lean.Grind.NatModule",
"Lean.Grind.AddCommGroup.toAddCommMonoid",
"Lean.Grind.IntModule.toNatModule._proof_1",
"Lean.Grind.IntModule.toNatModule._proof_2",
"Lean.Grind.NatModule.mk"
] | true |
Mathlib.Tactic.BicategoryLike.Mor₂Iso.isStructural._sunfold | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"_private.Mathlib.Tactic.CategoryTheory.Coherence.Normalize.0.Mathlib.Tactic.BicategoryLike.Mor₂Iso.isStructural.match_1",
"Mathlib.Tactic.BicategoryLike.Mor₂Iso.isStructural",
"Mathlib.Tactic.BicategoryLike.Mor₂Iso",
"Mathlib.Tactic.BicategoryLike.CoherenceHom",
"Lean.Expr",
"Bool.and",
"Mathlib.Tactic... | false |
monoidHomOfForallMemZpowers._proof_3 | Mathlib.GroupTheory.SpecificGroups.Cyclic | [
"Iff.mpr",
"Eq.mpr",
"Dvd.dvd",
"zpow_add",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"DivInvMonoid.toZPow",
"Group",
"_private.Mathlib.GroupTheory.SpecificGroups.Cyclic.0.monoidHomOfForallMemZpowers._simp_1",
"Membership.mem",
"Exists",
"id",
"MulOne.toMul",
"DivInvMonoid.toMonoi... | false |
ListSlice.size_eq_length_toList | Init.Data.Slice.List.Lemmas | [
"Std.Slice.toList",
"Std.Iterators.Types.Take.instIterator",
"Std.Slice.Internal.ListSliceData",
"ListSlice.instToIterator",
"Std.Iterators.Types.ListIterator.instFinite",
"Std.Iterators.Types.ListIterator",
"Monad.toApplicative",
"Std.Iterators.Types.Take",
"Std.Slice.length_toList_eq_size",
"Std... | true |
CompactlySupportedContinuousMap.continuousMapEquiv._proof_3 | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"CompactlySupportedContinuousMap",
"ContinuousMap.mk",
"ContinuousMap",
"CompactlySupportedContinuousMap.instCompactlySupportedContinuousMapClass",
"toContinuousMap",
"CompactSpace",
"TopologicalSpace",
"CompactlySupportedContinuousMap.instFunLike",
"CompactlySupportedContinuousMapClass.toContinuous... | false |
List.ne_and_not_mem_of_not_mem_cons | Init.Data.List.Lemmas | [
"Membership.mem",
"Ne",
"List.not_mem_of_not_mem_cons",
"List.cons",
"List",
"And",
"List.instMembership",
"List.ne_of_not_mem_cons",
"And.intro",
"Not"
] | true |
_private.Mathlib.LinearAlgebra.Finsupp.Supported.0.Finsupp.lmapDomain_disjoint_ker._simp_1_3 | Mathlib.LinearAlgebra.Finsupp.Supported | [
"Submodule",
"Finsupp.module",
"Finsupp.mem_supported",
"Finset",
"AddMonoid.toAddZeroClass",
"Finsupp.supported",
"Finsupp.support",
"Membership.mem",
"AddZeroClass.toAddZero",
"HasSubset.Subset",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"AddZero.toZero",
"SetLike.coe",
"Finset.ins... | false |
Cardinal.mk_Ioi_real | Mathlib.Analysis.Real.Cardinality | [
"Eq.mpr",
"le_refl",
"Real.partialOrder",
"Real",
"Set.Ioi",
"Preorder.toLT",
"Cardinal.one_lt_aleph0",
"Cardinal.instOne",
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"HEq.refl",
"Real.instSub",
"Set.univ",
"PartialOrder.toPreorder",
"Nat.instAtLeastTwoHAddOfNat",
"HSub.hSub... | true |
Batteries.RBNode.All.balRight | Batteries.Data.RBMap.WF | [
"Iff.mpr",
"Batteries.RBNode",
"Batteries.RBNode.balLeft",
"Batteries.RBNode.balRight",
"Eq.rec",
"Batteries.RBNode.All.balLeft",
"Batteries.RBNode.reverse_balRight",
"Iff.mp",
"Batteries.RBNode.All.reverse",
"Batteries.RBNode.reverse",
"Batteries.RBNode.All",
"Eq.symm",
"Eq"
] | true |
ContinuousAlternatingMap.instSeminormedAddCommGroup._proof_3 | Mathlib.Analysis.Normed.Module.Alternating.Basic | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Real",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"SeminormedAddCommGroup.induced",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"ContinuousMultilinearMap.instAddMonoid",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZero... | false |
CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk_of_isPullback._proof_1 | Mathlib.CategoryTheory.Sites.MayerVietorisSquare | [
"CategoryTheory.Square.IsPullback.mk",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Presheaf.IsSheaf.amalgamateOfArrows",
"CategoryTheory.Square.f₂₄",
"Opposite",
"CategoryTheory.Mono",
"CategoryTheory.Limits.PullbackCone.condition",
"CategoryTheory.Category... | false |
MonoidWithZeroHom.instLinearOrderedCommGroupWithZeroMrange._proof_11 | Mathlib.RingTheory.Valuation.Archimedean | [
"CommMonoidWithZero.toCommMonoid",
"GroupWithZero.toMonoidWithZero",
"Semigroup.toMul",
"HMul.hMul",
"MonoidWithZeroHom.funLike",
"DivisionSemiring.toGroupWithZero",
"Membership.mem",
"MonoidWithZeroHom.monoidWithZeroHomClass",
"Subtype",
"CommGroupWithZero.zpow_succ'",
"Int",
"LinearOrderedCo... | false |
Set.compl_inv | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Inv",
"Compl.compl",
"Set.instCompl",
"Inv.inv",
"Set.inv",
"Set.preimage_compl",
"Eq",
"Set"
] | true |
CommRingCat.FilteredColimits.forget_preservesFilteredColimits | Mathlib.Algebra.Category.Ring.FilteredColimits | [
"CategoryTheory.Limits.PreservesFilteredColimits",
"CommRingCat.carrier",
"CommSemiring.toSemiring",
"CommRingCat",
"CommRingCat.instConcreteCategoryRingHomCarrier",
"RingCat.ring",
"RingHom",
"CommRingCat.instCategory",
"RingCat.FilteredColimits.forget_preservesFilteredColimits",
"RingCat.instCon... | true |
AlgebraicGeometry.coprodMk._proof_2 | Mathlib.AlgebraicGeometry.Limits | [
"CategoryTheory.Limits.PreservesColimitsOfShape.preservesColimit",
"AlgebraicGeometry.Scheme",
"TopCat.instCategory",
"AlgebraicGeometry.instPreservesColimitsOfShapeSchemeTopCatDiscreteForgetToTopOfSmall",
"UnivLE.small",
"AlgebraicGeometry.Scheme.forgetToTop",
"CategoryTheory.Limits.WalkingPair",
"Ca... | false |
CategoryTheory.AddGrpObj.neg_comp | Mathlib.CategoryTheory.Monoidal.Cartesian.Grp | [
"AddGroup.toSubtractionMonoid",
"CategoryTheory.Category.assoc",
"NegZeroClass.toNeg",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.IsAddMonHom",
"SubtractionMonoid.toSubNegZeroMonoid",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"Categ... | true |
Mathlib.Tactic.Monoidal.instMonadMor₁MonoidalM._sparseCasesOn_1 | Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Filter.lift'_bot | Mathlib.Order.Filter.Lift | [
"Eq.mpr",
"Filter.lift'_principal",
"congrArg",
"PartialOrder.toPreorder",
"Monotone",
"CompleteLattice.toConditionallyCompleteLattice",
"id",
"Bot.bot",
"Filter.lift'",
"Filter.principal_empty",
"Set.instEmptyCollection",
"CompleteBooleanAlgebra.toCompleteLattice",
"Filter.principal",
"Eq... | true |
mulMonoidHom._proof_2 | Mathlib.Algebra.Group.Prod | [
"mulMulHom",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"Prod.instMul",
"MulHom.map_mul'",
"CommMagma.toMul",
"MulHom.toFun",
"CommSemigroup.toCommMagma",
"Prod",
"Eq",
"CommMonoid",
"instHMul"
] | false |
CategoryTheory.Limits.IsColimit.descCoconeMorphism_eq_isInitial_to | Mathlib.CategoryTheory.Limits.ConeCategory | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.IsColimit",
"Equiv",
"CategoryTheory.Limits.IsInitial",
"CategoryTheory.Limits.Cocone.isColimitEquivIsInitial",
"CategoryTheory.Limits.IsI... | true |
MvPowerSeries.substAlgHom_X | Mathlib.RingTheory.MvPowerSeries.Substitution | [
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"MvPolynomial.aeval_X",
"MvPolynomial.aeval",
"MvPowerSeries.instCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"MvPolynomial.coe_X",
"MvPowerSeries.sub... | true |
Ring.uniformContinuousConstSMul_op | Mathlib.Topology.Algebra.UniformMulAction | [
"UniformSpace",
"Ring.toNonAssocRing",
"MulZeroClass.toMul",
"AddGroupWithOne.toAddGroup",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"AddGroupWithOne.toAddMonoidWithOne",
"AddZeroClass.toAddZero",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"DistribSMu... | true |
_private.Mathlib.GroupTheory.Complement.0.Subgroup.isComplement_subgroup_left_iff_existsUnique_quotientMk''._simp_1_4 | Mathlib.GroupTheory.Complement | [
"Quotient.eq''",
"Quotient.mk''",
"Setoid",
"Quotient",
"propext",
"Eq.symm",
"Eq",
"Setoid.r"
] | false |
IsUniformEmbedding.nonemptyCompacts_map | Mathlib.Topology.UniformSpace.Closeds | [
"UniformSpace",
"IsUniformEmbedding.injective",
"TopologicalSpace.NonemptyCompacts",
"IsUniformEmbedding",
"IsUniformEmbedding.toIsUniformInducing",
"IsUniformEmbedding.isUniformInducing",
"TopologicalSpace.NonemptyCompacts.uniformSpace",
"UniformContinuous.continuous",
"IsUniformEmbedding.mk",
"I... | true |
Path.mul_apply | Mathlib.Topology.Path | [
"Real",
"HMul.hMul",
"Mul",
"Set.Elem",
"Path.mul",
"TopologicalSpace",
"ContinuousMul",
"Path.instFunLike",
"Path",
"Eq.refl",
"Eq",
"DFunLike.coe",
"unitInterval",
"instHMul"
] | true |
CategoryTheory.SimplicialThickening.mk.noConfusion | Mathlib.AlgebraicTopology.SimplicialNerve | [
"CategoryTheory.SimplicialThickening",
"HEq.refl",
"LinearOrder",
"id",
"heq_of_eq",
"CategoryTheory.SimplicialThickening.noConfusion",
"Eq.refl",
"HEq",
"Eq",
"CategoryTheory.SimplicialThickening.mk"
] | false |
Array.getElem?_setIfInBounds_self_of_lt | Init.Data.Array.Lemmas | [
"GetElem?.toGetElem",
"congrArg",
"Option.some",
"Array.getElem_setIfInBounds_self",
"Array",
"GetElem.getElem",
"Array.instLawfulGetElemNatLtSize",
"Nat",
"getElem?_pos",
"LT.lt",
"True",
"eq_self",
"eq_true",
"of_eq_true",
"congrFun'",
"Array.setIfInBounds",
"Array.size_setIfInBoun... | true |
IsOfFinOrder.natCard_powers_le_orderOf | Mathlib.GroupTheory.OrderOfElement | [
"Set.fintypeImage._proof_1",
"Monoid",
"Eq.mpr",
"Fintype.card_ofFinset",
"Finset.coe_range",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Finset.Iio",
"Finset.card_range",
"Classical.propDecidable",
"Nat.instLocallyFiniteOrder",
"LocallyFiniteOrder.toLocallyFiniteOrderBot",
"Finset.coe_... | true |
AlgebraicGeometry.Scheme.Pullback.SpecTensorTo_SpecOfPoint | Mathlib.AlgebraicGeometry.PullbackCarrier | [
"AlgebraicGeometry.PresheafedSpace.Hom",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"AlgebraicGeometry.Scheme.Pullback.ofPointTensor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Ho... | true |
CategoryTheory.Pretriangulated.Opposite.instAdditiveOppositeShiftFunctorInt | Mathlib.CategoryTheory.Triangulated.Opposite.Basic | [
"Opposite",
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"_private.Mathlib.CategoryTheory.Triangulated.Opposite.Basic.0.CategoryTheory.Pretriangulated.Opposite.instAdditiveOppositeShiftFunctorInt._proof_1",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Opposite.instHas... | true |
ContinuousMultilinearMap.apply._proof_3 | Mathlib.Topology.Algebra.Module.Multilinear.Topology | [
"ContinuousMultilinearMap.compContinuousLinearMapL._proof_4",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"ContinuousMultilinearMap.addCommMonoid",
"ContinuousMultilinearMap.instModule",
"AddCommGroup.toAddGroup",
"ContinuousMultilinearM... | false |
CategoryTheory.StructuredArrow.faithful_map₂ | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Comma.faithful_map",
"CategoryTheory.Functor.id",
"CategoryTheory.Functor.Faithful.id",
"CategoryTheory.Discrete.natTrans",
"CategoryT... | true |
CategoryTheory.Functor.Final.colimitCoconeOfComp | Mathlib.CategoryTheory.Limits.Final | [
"CategoryTheory.Limits.ColimitCocone.cocone",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"Equiv.instEquivLike",
"CategoryTheory.Functor.Final.isColimitExtendCoconeEquiv",
"CategoryTheory.Functor.Final.extendCocone",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.IsColimit",
"Eq... | true |
RandGT | Mathlib.Control.Random | [
"ULift",
"StateT"
] | true |
Filter.EventuallyEq.fun_const_vadd | Mathlib.Order.Filter.Basic | [
"Filter.EventuallyEq",
"VAdd",
"id",
"HVAdd.hVAdd",
"instHVAdd",
"Filter.EventuallyEq.const_vadd",
"Filter"
] | true |
OrderIso.preimage_Ici | Mathlib.Order.Interval.Set.OrderIso | [
"Set.ext",
"Set.Ici",
"OrderIso.apply_symm_apply",
"congrArg",
"Preorder.toLE",
"Membership.mem",
"OrderIso",
"OrderIso.le_iff_le",
"LE.le",
"OrderIso.symm",
"iff_self",
"Iff",
"instFunLikeOrderIso",
"Set.preimage",
"congr",
"True",
"Set.mem_Ici",
"propext",
"of_eq_true",
"Eq.s... | true |
Lean.Elab.FixedParamPerms.fixedArePrefix | Lean.Elab.PreDefinition.FixedParams | [
"Array.instAppend",
"Option.instBEq",
"Lean.Elab.FixedParamPerms.perms",
"Array.all",
"Array.replicate",
"HSub.hSub",
"Lean.Elab.FixedParamPerms",
"Option.some",
"Array.instBEq",
"Array.map",
"instSubNat",
"instOfNatNat",
"instBEqOfDecidableEq",
"Array",
"Option.none",
"instHAppendOfAp... | true |
ByteArray.Iterator.mk | Init.Data.ByteArray.Basic | [
"ByteArray.Iterator",
"Nat",
"ByteArray.Iterator.mk",
"ByteArray"
] | true |
Lean.Server.Test.Runner.Client.InteractiveGoal.mk._flat_ctor | Lean.Server.Test.Runner | [
"String",
"Lean.Server.Test.Runner.Client.SubexprInfo",
"Lean.Server.Test.Runner.Client.InteractiveGoal",
"Lean.Server.Test.Runner.Client.InteractiveGoalCore.mk",
"Lean.Server.Test.Runner.Client.InteractiveGoal.mk",
"Lean.MVarId",
"Lean.Server.Test.Runner.Client.Hyp",
"Lean.Widget.TaggedText",
"Arra... | false |
CategoryTheory.Limits.HasColimit.exists_colimit | Mathlib.CategoryTheory.Limits.HasLimits | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasColimit",
"Nonempty",
"CategoryTheory.Limits.ColimitCocone",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Data.Nat.Fib.Zeckendorf.0.Nat.zeckendorf_sum_fib._simp_1_4 | Mathlib.Data.Nat.Fib.Zeckendorf | [
"List.Pairwise",
"List.IsChain",
"Trans",
"List",
"propext",
"List.isChain_iff_pairwise",
"Eq"
] | false |
Lean.Server.RequestHandlerCompleteness.noConfusion | Lean.Server.Requests | [
"Lean.Server.RequestHandlerCompleteness",
"Lean.Server.RequestHandlerCompleteness.noConfusionType",
"Lean.Server.RequestHandlerCompleteness.casesOn",
"String",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | false |
Lean.Meta.etaStruct? | Lean.Meta.Structure | [
"Std.Rco",
"Pure.pure",
"Unit.unit",
"Lean.ConstructorVal",
"Lean.ConstructorVal.induct",
"instForInOfForIn'",
"Lean.Expr.instBEq",
"Lean.Meta.State",
"Option.some",
"Std.PRange.instLawfulUpwardEnumerableLTNat",
"ForInStep.done",
"inferInstance",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Exp... | true |
Int.blt' | Init.Data.Int.Basic | [
"Nat.blt",
"Int",
"Bool.true",
"Nat",
"Bool",
"Bool.false",
"Int.rec"
] | true |
NonarchAddGroupNorm.apply_one | Mathlib.Analysis.Normed.Group.Seminorm | [
"AddGroup.toSubtractionMonoid",
"Real",
"Real.instZero",
"NonarchAddGroupNorm.instOneOfDecidableEq",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"Real.instOne",
"AddGroup",
"NonarchAddGroupNorm",
"One.toOfNat1",
"Zero.toOfNat0",
"NonarchAddGroupNorm.funLike",
"... | true |
AddGrpCat.hom_comp | Mathlib.Algebra.Category.Grp.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddGrpCat.instCategory",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddGrpCat",
"AddGrpCat.Hom.hom",
"AddGroup.toSubNegMonoid",
"AddGrpCat.carrier",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruc... | true |
AddSubgroup.toAddSubmonoid_le._simp_1 | Mathlib.Algebra.Group.Subgroup.Defs | [
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"AddSubmonoid",
"LE.le",
"AddSubgroup",
"AddGroup",
"AddGroup.toSubNegMonoid",
"propext",
"SubNegMonoid.toAddMonoid",
"AddSubgroup.toAddSubmonoid_le",
"Eq",
"AddSubgroup.toAddSubmonoid",... | false |
Lean.Compiler.LCNF.Phase | Lean.Compiler.LCNF.CompilerM | [
"Lean.Compiler.LCNF.Phase.base",
"Lean.Compiler.LCNF.Phase.impure",
"Lean.Compiler.LCNF.Phase.mono"
] | true |
CategoryTheory.Limits.Bicone._sizeOf_inst | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.Bicone._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"CategoryTheory.Limits.Bicone",
"CategoryTheory.Category"
] | false |
String.Pos.splits_append_rawEndPos | Init.Data.String.Lemmas.Splits | [
"String.Pos.Splits",
"String",
"String.Pos.Raw",
"String.Pos.Raw.IsValid.append_right",
"String.rawEndPos",
"instAppendString",
"instHAppendOfAppend",
"String.Pos.Raw.isValid_rawEndPos",
"String.pos",
"HAppend.hAppend",
"String.Pos.offset",
"rfl",
"String.Pos.Splits.mk"
] | true |
CategoryTheory.Limits.splitMonoOfIdempotentEqualizer | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.Limits.splitMonoOfIdempotentOfIsLimitFork",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.equalizer",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheor... | true |
PUnit.instMulAction | Mathlib.Algebra.Module.PUnit | [
"CommSemiring.toSemiring",
"SMul",
"PUnit.commRing",
"inferInstance",
"PUnit.instMulAction._proof_1",
"PUnit.instMulAction._proof_2",
"SemigroupAction.mk",
"CommRing.toCommSemiring",
"PUnit",
"MulAction",
"Semiring.toMonoid",
"Monoid.toSemigroup",
"PUnit.instSMul_mathlib",
"MulAction.mk"
] | true |
Sublattice.coe_inf._simp_1 | Mathlib.Order.Sublattice | [
"Sublattice",
"Lattice",
"Sublattice.coe_inf",
"Sublattice.instInfCoe",
"Membership.mem",
"Subtype",
"SemilatticeInf.toMin",
"Sublattice.instSetLike",
"Eq.symm",
"Subtype.val",
"Eq",
"SetLike.instMembership",
"Min.min",
"Lattice.toSemilatticeInf"
] | false |
Algebra.IsIntegral.isAlgebraic_iff_top | Mathlib.RingTheory.Algebraic.Integral | [
"Eq.mpr",
"CommRing",
"IsAlgebraic",
"congrArg",
"CommSemiring.toSemiring",
"Algebra.IsIntegral.isAlgebraic_iff",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"id",
"Algebra.IsIntegral",
"Algebra.IsAlgebraic",
"instDistribOfSemiring",
"FaithfulSMul",
"_private.Mathlib.RingTheory.Algebra... | true |
GaloisConnection.le_iff_le | Mathlib.Order.GaloisConnection.Defs | [
"Preorder.toLE",
"LE.le",
"Iff",
"Preorder",
"GaloisConnection"
] | true |
AddGroupNorm.ctorIdx | Mathlib.Analysis.Normed.Group.Seminorm | [
"AddGroup",
"Nat",
"AddGroupNorm"
] | false |
String.revFind_of_valid | Batteries.Data.String.Lemmas | [
"Bool.not",
"String.revFindAux_of_valid",
"congrArg",
"String.utf8Len_reverse",
"String",
"String.Legacy.revFind",
"List.tail?",
"String.utf8Len",
"String.utf8ByteSize",
"Eq.mp",
"String.ofList_toList",
"String.Pos.Raw",
"List.append_nil",
"instHAppendOfAppend",
"List",
"Option.map",
... | true |
_private.Mathlib.Computability.PartrecCode.0.Nat.Partrec.Code.evaln.match_1.eq_8 | Mathlib.Computability.PartrecCode | [
"Nat.Partrec.Code.rfind'",
"Nat.Partrec.Code.right",
"Nat.Partrec.Code",
"instOfNatNat",
"Nat.Partrec.Code.prec",
"Nat.Partrec.Code.succ",
"Nat.Partrec.Code.left",
"Nat.Partrec.Code.comp",
"Nat",
"Nat.Partrec.Code.zero",
"Eq.refl",
"Nat.Partrec.Code.pair",
"OfNat.ofNat",
"Nat.Partrec.Code.... | true |
CategoryTheory.SmallObject.restrictionLE | Mathlib.CategoryTheory.SmallObject.Iteration.Basic | [
"CategoryTheory.Functor",
"Preorder.toLT",
"Set.initialSegIicIicOfLE",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.comp",
"Preorder.toLE",
"Membership.mem",
"PartialOrder",
"Set.Elem",
"Preorder.smallCategory",
"LE.le",
"Monotone.functor",
"CategoryTheory.SmallObject.restrictionLE._pr... | true |
Monoid.Coprod.range_swap | Mathlib.GroupTheory.Coprod.Basic | [
"Iff.mpr",
"MonoidHom.range",
"MonoidHom.instFunLike",
"Monoid.Coprod.swap_surjective",
"MonoidHom",
"Monoid.toMulOneClass",
"Monoid.Coprod.swap",
"Group",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"MonoidHom.range_eq_top",
"MulOneClass.toMulOne",
"Subgroup.instTop",
"... | true |
CategoryTheory.eHomFunctor_map_app | Mathlib.CategoryTheory.Enriched.Ordinary.Basic | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.EnrichedOrdinaryCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.EnrichedOrdinaryCategory.toEnrichedCategory",
... | true |
Matrix.empty_eq | Mathlib.Data.Fin.VecNotation | [
"Pi.uniqueOfIsEmpty",
"instOfNatNat",
"Unique.instSubsingleton",
"Nat",
"Fin.isEmpty'",
"Matrix.vecEmpty",
"Subsingleton.elim",
"OfNat.ofNat",
"Fin",
"Eq"
] | true |
CategoryTheory.Dial.Hom.mk.sizeOf_spec | Mathlib.CategoryTheory.Dialectica.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.prod.fst",
"PartialOrder.toPreorder",
"instSizeOfDefault",
"Preorder.toLE",
"CategoryTheory.CategoryStruct.id",
"Preorder.smallCategory",
"instOfNatNat",
"CategoryTheory.Dial.Hom.mk",
"LE.le",
"CategoryTheory.Limits... | true |
Int.fib_two_mul | Mathlib.Data.Int.Fib.Basic | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"congrArg",
"Int.fib",
"Nat.instAtLeastTwoHAddOfNat",
"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_two_mul._proof_1_1",
"HSub.hSub",
"two_mul",
"id",
"Distrib.toAdd",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"Int",
... | true |
Topology._aux_Mathlib_Topology_Defs_Basic___macroRules_Topology_IsOpen_of_1 | Mathlib.Topology.Defs.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.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",... | false |
IsTensorProduct.map_injective_of_flat_left_right | Mathlib.RingTheory.Flat.Basic | [
"IsTensorProduct.map",
"Eq.mpr",
"IsTensorProduct.inductionOn",
"LinearEquiv.symm",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"CommSemiring.toSemiring",
"TensorProduct.map_injective_of_flat_flat'",
"EmbeddingLike.comp_injective._simp_1",
"TensorProduct.addCommMonoid",
"AddMo... | true |
_private.Init.Data.SInt.Lemmas.0.Int64.ofNat_add._simp_1_1 | Init.Data.SInt.Lemmas | [
"Int64.ofInt_eq_ofNat",
"Int64",
"Int",
"Nat.cast",
"Nat",
"instNatCastInt",
"Int64.ofNat",
"Int64.ofInt",
"Eq.symm",
"Eq"
] | false |
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