name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Int.lcm_dvd | Init.Data.Int.Gcd | [
"Int.lcm",
"Dvd.dvd",
"Int.ofNat_dvd",
"Int",
"Nat.cast",
"Int.instDvd",
"Nat.instDvd",
"Nat",
"Iff.mp",
"instNatCastInt",
"Int.coe_lcm_dvd"
] | true |
CategoryTheory.Iso.mk.inj | Mathlib.CategoryTheory.Iso | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso.inv_hom_id._autoParam",
"CategoryTheory.Iso.mk.noConfusion",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.Iso.mk",
"autoParam",
"And",
"And.intro",
"CategoryTheory.CategoryStruct.comp",
"eq... | true |
_private.Mathlib.Analysis.Normed.Lp.PiLp.0.PiLp.lipschitzWith_ofLp_aux | Mathlib.Analysis.Normed.Lp.PiLp | [
"WithLp",
"Eq.mpr",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"LipschitzWith",
"Finset.univ",
"_private.Mathlib.Analysis.Normed.Lp.PiLp.0.PiLp.lipschitzWith_ofLp_aux._simp_1_2",
"Finset",
"LipschitzWith.of_edist_le",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Fact",
... | true |
Std.DTreeMap.ofList_equiv_foldl | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.insert",
"Ordering",
"id",
"Sigma.fst",
"List.foldl",
"Std.DTreeMap.insertMany_list_equiv_foldl",
"List",
"Std.DTreeMap.Equiv",
"Std.DTreeMap.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Std.DTreeMap.ofList",
"Sigma.snd",
"Sigma"
] | true |
RingCon.instNonAssocSemiringQuotient._proof_3 | Mathlib.RingTheory.Congruence.Defs | [
"AddMonoidWithOne.natCast_zero._autoParam",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingCon.toCon",
"instHSMul",
"AddMonoidWithOne.natCast_zero",
"RingCon.instNatCastQuotient",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"AddMonoid.toNSMul",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Q... | false |
Finset.sup_image₂_right | Mathlib.Data.Finset.NAry | [
"Eq.mpr",
"Finset.sup_product_right",
"SProd.sprod",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Function.comp",
"id",
"Prod.mk",
"Finset.instSProd",
"Finset.sup_image",
"Finset.sup",
"Eq.refl",
"congrFun'",
"SemilatticeSup.toPartialOrder",
"Funct... | true |
Function.locallyFinsuppWithin.le_def | Mathlib.Topology.LocallyFinsupp | [
"Function.locallyFinsuppWithin.instFunLike",
"LE.le",
"LE",
"Pi.hasLe",
"TopologicalSpace",
"Iff",
"Iff.intro",
"Function.locallyFinsuppWithin.instLE",
"Function.locallyFinsuppWithin",
"DFunLike.coe",
"Zero",
"Set"
] | true |
CategoryTheory.exactPairingUnit._proof_1 | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.MonoidalCategory.whiskerLeftIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"Ca... | false |
ZNum.zneg_neg | Mathlib.Data.Num.ZNum | [
"ZNum.pos",
"ZNum",
"ZNum.instNeg",
"PosNum",
"ZNum.neg",
"Eq",
"Neg.neg",
"rfl"
] | true |
UInt8.add_mul | Init.Data.UInt.Lemmas | [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"id",
"instAddUInt8",
"UInt8.mul_add",
"instHAdd",
"HAdd.hAdd",
"instMulUInt8",
"Eq.refl",
"UInt8",
"Eq",
"UInt8.mul_comm",
"instHMul"
] | true |
NonUnitalAlgHom.mk.injEq | Mathlib.Algebra.Algebra.NonUnitalHom | [
"DistribMulActionHom.toMulActionHom",
"Monoid",
"NonUnitalAlgHom.mk",
"MonoidHom.instFunLike",
"HMul.hMul",
"MonoidHom",
"Eq.propIntro",
"Monoid.toMulOneClass",
"DistribMulActionHom",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZ... | true |
LeanSearchClient.SearchServer.query | LeanSearchClient.Syntax | [
"String",
"Lean.Meta.MetaM",
"LeanSearchClient.SearchServer",
"Array",
"Nat",
"LeanSearchClient.SearchResult"
] | true |
Action.leftRegularTensorIso_inv_hom | Mathlib.CategoryTheory.Action.Monoidal | [
"MonoidHom.instFunLike",
"Action.trivial",
"DivInvOneMonoid.toInvOneClass",
"Action.leftRegularTensorIso",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CategoryTheory.ConcreteCategory.hom",
"Action.... | true |
ModuleCat.monoidalClosedHomEquiv._proof_2 | Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CategoryTheory.Functor",
"CommRing",
"Semiring.toModule",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"TensorProduct.add... | false |
_private.Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots.0.IsPrimitiveRoot.eq_pow_of_pow_eq_one._simp_1_2 | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"Monoid",
"Units.val",
"Units.ext_iff",
"Units",
"propext",
"Eq.symm",
"Eq"
] | false |
Lean.Meta.RefinedDiscrTree.ModuleDiscrTreeRef.casesOn | Mathlib.Lean.Meta.RefinedDiscrTree.Initialize | [
"Lean.Meta.RefinedDiscrTree",
"Lean.Meta.RefinedDiscrTree.ModuleDiscrTreeRef",
"Lean.Meta.RefinedDiscrTree.ModuleDiscrTreeRef.mk",
"Lean.Meta.RefinedDiscrTree.ModuleDiscrTreeRef.rec",
"IO.Ref"
] | false |
String.Slice.Pattern.ToBackwardSearcher.DefaultBackwardSearcher.instIteratorIdSearchStepOfBackwardPattern.match_1 | Init.Data.String.Pattern.Basic | [
"Unit.unit",
"Std.IterStep",
"String.Slice.Pattern.SearchStep",
"String.Slice",
"Std.IterStep.skip",
"String.Slice.Pattern.SearchStep.rejected",
"Id",
"Unit",
"Std.IterStep.yield",
"String.Slice.Pattern.SearchStep.casesOn",
"String.Slice.Pattern.SearchStep.matched",
"Std.IterStep.done",
"Std... | false |
_private.Mathlib.CategoryTheory.Sites.Sieves.0.CategoryTheory.Presieve.ofArrows_of_unique.match_1_1 | Mathlib.CategoryTheory.Sites.Sieves | [
"Unit.unit",
"Inhabited.default",
"CategoryTheory.Presieve.singleton.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"Unique",
"Unit",
"CategoryTheory.Presieve.singleton.casesOn",
"CategoryTheory.Presieve.singleton",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Ca... | false |
MvQPF.wrepr.eq_1 | Mathlib.Data.QPF.Multivariate.Constructions.Fix | [
"MvPFunctor.Obj",
"MvQPF.recF",
"Function.comp",
"TypeVec.append1",
"instOfNatNat",
"MvPFunctor.wMk'",
"instHAdd",
"HAdd.hAdd",
"Nat",
"MvQPF.repr",
"instAddNat",
"Eq.refl",
"MvQPF",
"MvQPF.P",
"OfNat.ofNat",
"MvPFunctor.W",
"Eq",
"MvQPF.wrepr",
"TypeVec"
] | true |
Lean.Meta.Grind.CongrTheoremCacheKey.mk | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.CongrTheoremCacheKey.mk",
"Lean.Meta.Grind.CongrTheoremCacheKey",
"Lean.Expr",
"Nat"
] | true |
Sym2.toFinset_ne_empty._simp_1 | Mathlib.Data.Sym.Sym2 | [
"False",
"eq_false",
"Finset",
"Sym2.toFinset",
"Finset.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Sym2.toFinset_ne_empty",
"Eq",
"Sym2",
"DecidableEq"
] | false |
analyticOn_cexp | Mathlib.Analysis.SpecialFunctions.ExpDeriv | [
"AnalyticOn",
"Complex.instNormedAddCommGroup",
"Set.univ",
"Complex.instDenselyNormedField",
"analyticOnNhd_cexp",
"AnalyticOnNhd.analyticOn",
"Complex.exp",
"NontriviallyNormedField.toNormedField",
"DenselyNormedField.toNontriviallyNormedField",
"NormedField.toNormedSpace",
"Complex"
] | true |
AlgebraicGeometry.SpecMapRestrictBasicOpenIso._proof_7 | Mathlib.AlgebraicGeometry.AffineScheme | [
"Eq.mpr",
"AlgebraicGeometry.IsAffineOpen.isoSpec",
"CategoryTheory.Category.assoc",
"AlgEquiv.instEquivLike",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.morphismRestrict_ι_assoc",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme.homOfLE",
"AlgebraicGe... | false |
IntermediateField.LinearDisjoint.congr_simp | Mathlib.FieldTheory.LinearDisjoint | [
"IntermediateField",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"Eq.rec",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Eq.refl",
"Semifield.toCommSemiring",
"IntermediateField.LinearDisjoint",
"Eq",
"Field"
] | true |
Lean.Meta.Closure.Context._sizeOf_inst | Lean.Meta.Closure | [
"Lean.Meta.Closure.Context",
"SizeOf.mk",
"SizeOf",
"Lean.Meta.Closure.Context._sizeOf_1"
] | false |
_private.Mathlib.Algebra.Module.Torsion.PrimaryComponent.0.Ideal.primaryComponent_torsionBySet_of_isCoprime._simp_1_4 | Mathlib.Algebra.Module.Torsion.PrimaryComponent | [
"Subtype.forall",
"Subtype",
"Subtype.mk",
"propext",
"Eq"
] | false |
MeasureTheory.Measure.pi_caratheodory | Mathlib.MeasureTheory.Constructions.Pi | [
"ENNReal.instCanonicallyOrderedAdd",
"Finset.mem_univ",
"Eq.mpr",
"ENNReal.instAdd",
"Set.diff_subset",
"MeasureTheory.OuterMeasure.boundedBy_caratheodory",
"MeasureTheory.Measure",
"MeasurableSpace.instLE",
"MeasureTheory.OuterMeasure.caratheodory",
"MeasurableSpace.comap",
"MeasurableSet",
"... | true |
_private.Mathlib.GroupTheory.Congruence.Defs.0.Con.sSup_eq_conGen.match_1_1 | Mathlib.GroupTheory.Congruence.Defs | [
"Mul",
"Membership.mem",
"Exists",
"And",
"Exists.casesOn",
"Exists.intro",
"Con",
"Con.instFunLikeForallProp",
"Set.instMembership",
"DFunLike.coe",
"Set"
] | false |
BooleanSubalgebra.coe_comap._simp_1 | Mathlib.Order.BooleanSubalgebra | [
"BooleanAlgebra",
"BooleanSubalgebra",
"BoundedLatticeHom.instFunLike",
"BooleanAlgebra.toBoundedOrder",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"SetLike.coe",
"Set.preimage",
"BoundedLatticeHom",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",
"BooleanSubal... | false |
_private.Std.Time.Date.Unit.Weekday.0.Std.Time.instReprWeekday.repr.match_1.splitter | Std.Time.Date.Unit.Weekday | [
"Std.Time.Weekday.thursday",
"Std.Time.Weekday.friday",
"Std.Time.Weekday.tuesday",
"Std.Time.Weekday.saturday",
"Unit",
"_private.Std.Time.Date.Unit.Weekday.0.Std.Time.instReprWeekday.repr.match_1",
"Std.Time.Weekday.wednesday",
"Std.Time.Weekday.monday",
"Std.Time.Weekday.sunday",
"Std.Time.Week... | true |
Aesop.GoalWithMVars.mk.sizeOf_spec | Aesop.Script.GoalWithMVars | [
"Lean.instBEqMVarId",
"Std.HashSet",
"Lean.MVarId",
"instOfNatNat",
"Std.HashSet._sizeOf_inst",
"Lean.MVarId._sizeOf_inst",
"instHAdd",
"Aesop.GoalWithMVars",
"HAdd.hAdd",
"Lean.instHashableMVarId",
"Nat",
"Aesop.GoalWithMVars.mk",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Aesop.GoalW... | true |
continuous_mabs | Mathlib.Topology.Algebra.Order.Group | [
"OrderTopology",
"Continuous",
"DivInvOneMonoid.toInvOneClass",
"IsOrderedMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id",
"CommGroup",
"OrderTopology.to_orderCl... | true |
Lean.Meta.Simp.mkCast | Batteries.Lean.Meta.Simp | [
"Lean.Meta.Simp.Result.getProof",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.Simp.Result",
"Lean.Meta.mkAppM",
"List.toArray",
"List.cons",
"Lean.Meta.instMonadMetaM",
"Monad.toBind",
"Bind.bind",
"Lean.Name.mkStr1",
"List.nil"
] | true |
FintypeCat.Skeleton.incl._proof_2 | Mathlib.CategoryTheory.FintypeCat | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finite",
"FintypeCat",
"ULift",
"id",
"FintypeCat.Skeleton.instSmallCategory",
"Finite.of_fintype",
"Fin.fintype",
"instFiniteULift",
"CategoryTheory.types",
"CategoryTheory.CategoryStruct.comp",
"FintypeCat.Skeleton.len",
"Eq.refl",... | false |
CategoryTheory.Precoverage.ZeroHypercover.singleton.congr_simp | Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap | [
"CategoryTheory.Precoverage",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"Membership.mem",
"Eq.rec",
"CategoryTheory.Precoverage.ZeroHypercover",
"CategoryTheory.Precoverage.ZeroHypercover.singleton",
"CategoryTheory.Presieve.singleton",
"CategoryTheory.Prec... | true |
riemannianMetricVectorSpace._proof_1 | Mathlib.Geometry.Manifold.Riemannian.Basic | [
"InnerProductSpace.toNormedSpace",
"Real",
"instAddMonoidWithOneENat",
"chartedSpaceSelf",
"instContMDiffAddSelf",
"ContMDiffAdd.toIsManifold",
"ENat.instNatCast",
"Real.denselyNormedField",
"Real.instRCLike",
"AddCommGroup.toAddCommMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"PseudoMetricSpace.to... | false |
ArchimedeanClass.instLinearOrderedAddCommMonoidWithTop._proof_1 | Mathlib.Algebra.Order.Ring.Archimedean | [
"Eq.mpr",
"CommRing",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"MulZeroClass.toMul",
"congrArg",
"CommSemiring.toSemiring",
"LinearOrder",
"ArchimedeanClass.instLinearOrder",
"MulZeroClass.zero_mul",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"ArchimedeanClass.ind",
"Preorder.toLE",... | false |
ContinuousMap.HomotopyEquiv.piCongrRight._proof_2 | Mathlib.Topology.Homotopy.Equiv | [
"Pi.topologicalSpace",
"ContinuousMap.HomotopyEquiv.right_inv",
"ContinuousMap.HomotopyEquiv.invFun",
"ContinuousMap.piMap",
"ContinuousMap.comp",
"TopologicalSpace",
"ContinuousMap.id",
"ContinuousMap.HomotopyEquiv.toFun",
"ContinuousMap.HomotopyEquiv",
"ContinuousMap.Homotopic",
"ContinuousMap... | false |
Int.add_le_add_left | Init.Data.Int.Order | [
"Eq.mpr",
"congrArg",
"_private.Init.Data.Int.Order.0.Int.add_le_add_left.match_1_1",
"Int.add_assoc",
"Int.le.intro",
"Exists",
"id",
"Int.le.dest",
"Int",
"LE.le",
"Nat.cast",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Int.instAdd",
"Eq.refl",
"instNatCastInt",
"Eq",
"Int.instLEInt"
] | true |
Lean.Meta.Grind.SavedState.grind | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.State",
"Lean.Meta.Grind.SavedState"
] | true |
ENNReal.holderConjugate_coe_iff | Mathlib.Data.Real.ConjExponents | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"ENNReal.holderTriple_coe_iff",
"ENNReal.ofNNReal",
"NeZero.charZero_one",
"NNReal",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"NNReal.instZero",
"NNReal.instPartialOrder",
"Iff",
"IsStrictOrderedRing.toCharZero",
"ENNReal.HolderConjugate",
"NNReal.i... | true |
AlgHom.restrictNormalAux._proof_10 | Mathlib.FieldTheory.Normal.Defs | [
"Subalgebra.instSetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"IsScalarTower.toAlgHom",
"Algebra",
"Normal",
"Algebra.toSMul",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
... | false |
Set.image_const_mul_uIcc | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"congrArg",
"LinearOrder",
"IsStrictOrderedRing",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"DistribLattice.toLattice",
"... | true |
Plausible.Injective.testable | Mathlib.Testing.Plausible.Functions | [
"Plausible.Testable",
"Plausible.NamedBinder",
"Function.Injective",
"Eq"
] | true |
CategoryTheory.Arrow.homMk.congr_simp | Mathlib.CategoryTheory.Comma.Arrow | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Eq.rec",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"CategoryTheory.CategoryStruct.comp",
"Eq.ndrec",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Arrow",
"CategoryTheory.instQuiverArrow",
"Eq",
... | true |
Simplicial.«_aux_Mathlib_AlgebraicTopology_SimplicialObject_Basic___delab_app_Simplicial_term__⦋_⦌_1» | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Mathlib.Notation3.MatchState.empty",
"Mathlib.Notation3.withHeadRefIfTagAppFns",
"Mathlib.Notation3.matchApp",
"Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM",
"Lean.SourceInfo",
"Lean.PrettyPrinter.Delaborator.Context",
"Lean.Meta.Stat... | false |
Matrix.isHermitian_add_transpose_self | Mathlib.LinearAlgebra.Matrix.Hermitian | [
"Matrix.add",
"IsSelfAdjoint.add_star_self",
"Matrix",
"Matrix.addCommMonoid",
"StarAddMonoid.toInvolutiveStar",
"AddCommMonoid",
"instHAdd",
"HAdd.hAdd",
"Matrix.instStarAddMonoid",
"StarAddMonoid",
"Matrix.IsHermitian",
"InvolutiveStar.toStar",
"AddCommMonoid.toAddMonoid",
"AddCommSemigr... | true |
Mathlib.Tactic.introv | Mathlib.Tactic.Basic | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.const",
"Lean.binderIdent",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1"
] | true |
AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot_symm_mk_mk | Mathlib.RingTheory.AdjoinRoot | [
"Ideal.quotEquivOfEq",
"Eq.mpr",
"Polynomial.C",
"CommRing",
"AdjoinRoot",
"AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot._proof_1",
"congrArg",
"CommSemiring.toSemiring",
"AdjoinRoot.quotAdjoinRootEquivQuotPolynomialQuot._proof_3",
"Ideal.Quotient.mk",
"RingEquiv.instEquivLike",
"Ideal.quo... | true |
hasSum_iff_tendsto_nat_of_nonneg | Mathlib.Topology.Algebra.InfiniteSum.ENNReal | [
"NNReal.instTopologicalSpace",
"_private.Mathlib.Topology.Algebra.InfiniteSum.ENNReal.0.hasSum_iff_tendsto_nat_of_nonneg._simp_1_1",
"Eq.mpr",
"Real.instLE",
"Real",
"NNReal.canLift",
"_private.Mathlib.Topology.Algebra.InfiniteSum.ENNReal.0.hasSum_iff_tendsto_nat_of_nonneg._simp_1_2",
"Real.instZero",... | true |
BoxIntegral.IntegrationParams.exists_memBaseSet_le_iUnion_eq | Mathlib.Analysis.BoxIntegral.Partition.Filter | [
"Real",
"Set.Ioi",
"BoxIntegral.Prepartition.compl_congr",
"BoxIntegral.Prepartition",
"Real.instZero",
"BoxIntegral.IntegrationParams.MemBaseSet.mk",
"BoxIntegral.Box.toSet",
"PartialOrder.toPreorder",
"BoxIntegral.TaggedPrepartition.IsSubordinate",
"Preorder.toLE",
"BoxIntegral.Prepartition.co... | true |
Lean.Level.hasMVarEx | Lean.Level | [
"Lean.Level",
"Lean.Level.hasMVar",
"Bool"
] | true |
List.maxOn_cons_cons | Init.Data.List.MinMaxOn | [
"List.minOn_cons_cons._proof_1",
"minOn",
"Eq.mpr",
"maxOn_eq_minOn",
"congrArg",
"List.maxOn.congr_simp",
"List.maxOn_eq_minOn",
"maxOn",
"id",
"Ne",
"List.minOn",
"LE",
"List.cons",
"List",
"DecidableLE",
"List.minOn_cons_cons",
"congr",
"Eq.ndrec",
"Eq.refl",
"List.maxOn",
... | true |
Mathlib.Explode.instInhabitedEntries.default | Mathlib.Tactic.Explode.Datatypes | [
"Inhabited.default",
"Lean.Expr.instBEq",
"Mathlib.Explode.Entries",
"Lean.Expr",
"Mathlib.Explode.Entry",
"Lean.ExprMap",
"Mathlib.Explode.Entries.mk",
"List",
"Lean.Expr.instHashable",
"instInhabitedList",
"Std.HashMap.instInhabited"
] | true |
_private.Mathlib.Probability.Kernel.IonescuTulcea.Traj.0.ProbabilityTheory.Kernel.trajContent_tendsto_zero._proof_1_3 | Mathlib.Probability.Kernel.IonescuTulcea.Traj | [
"False",
"congrArg",
"Finset",
"Classical.byContradiction",
"Nat.instLocallyFiniteOrder",
"Membership.mem",
"LocallyFiniteOrder.toLocallyFiniteOrderBot",
"Subtype",
"False.casesOn",
"instOfNatNat",
"instHAdd",
"Finset.instSetLike",
"HAdd.hAdd",
"Nat.instPreorder",
"Nat",
"True",
"eq_... | false |
TwoP.casesOn | Mathlib.CategoryTheory.Category.TwoP | [
"TwoP.mk",
"TwoP",
"TwoPointing",
"TwoP.rec"
] | false |
Mathlib.Tactic.CheckCompositions.checkCompositionsTac | Mathlib.Tactic.CategoryTheory.CheckCompositions | [
"ReaderT",
"Lean.Meta.State",
"instMonadLiftT",
"Lean.Elab.Tactic.Context",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"liftM",
"ReaderT.instMonadLift",
"Lean.Elab.Tactic.instMonadTacticM",
"Lean.Elab.Tactic.getMainTarget",
"Unit",
"Lean.Core.CoreM",
"StateRefT'",
"Lean.Elab.Term.Co... | true |
Nucleus.instMin._proof_3 | Mathlib.Order.Nucleus | [
"Nucleus",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeInf.toMin",
"LE.le",
"le_inf",
"Nucleus.instFunLike",
"SemilatticeInf",
"DFunLike.coe",
"Min.min",
"Nucleus.le_apply"
] | false |
_private.Mathlib.Algebra.Homology.Factorizations.CM5a.0.CochainComplex.Plus.modelCategoryQuillen.cm5a_cof.CofFibFactorizationQuasiIsoLE.sequence | Mathlib.Algebra.Homology.Factorizations.CM5a | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"_private.Mathlib.Algebra.Homology.Factorizations.CM5a.0.CochainComplex.Plus.modelCategoryQuillen.cm5a_cof.CofFibFactorizationQuasiIsoLE.sequence._f",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
... | true |
CategoryTheory.StructuredArrow.mapIso_inverse_obj_right | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.Iso",
"CategoryTheory.Comma",
"CategoryTheory.commaCategory",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.StructuredArrow.mapIso",
"Eq.refl",
"CategoryTheory.instCategoryStructuredArrow",
"CategoryTheory.Func... | true |
_private.Mathlib.ModelTheory.Algebra.Field.IsAlgClosed.0.FirstOrder.Field.finite_ACF_prime_not_realize_of_ACF_zero_realize._simp_1_3 | Mathlib.ModelTheory.Algebra.Field.IsAlgClosed | [
"FirstOrder.Language.BoundedFormula.realize_not",
"FirstOrder.Language.BoundedFormula.not",
"FirstOrder.Language.BoundedFormula.Realize",
"FirstOrder.Language.Structure",
"Nat",
"propext",
"FirstOrder.Language",
"FirstOrder.Language.BoundedFormula",
"Fin",
"Eq",
"Not"
] | false |
Algebra.Presentation.HasCoeffs.mk | Mathlib.RingTheory.Extension.Presentation.Core | [
"Algebra.Presentation.HasCoeffs",
"CommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra.Presentation.coeffs",
"Algebra",
"RingHom",
"Algebra.toSMul",
"HasSubset.Subset",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"Algebra.Presentation.HasCoeffs.mk",
... | true |
Lean.Grind.AC.Seq.sort | Init.Grind.AC | [
"Lean.Grind.AC.Seq.sort'",
"Lean.Grind.AC.Seq.erase0.match_1",
"Lean.Grind.AC.Seq.var",
"Lean.Grind.AC.Var",
"Lean.Grind.AC.Seq"
] | true |
_private.Mathlib.RingTheory.Noetherian.OfPrime.0.IsNoetherianRing.of_prime._simp_1_2 | Mathlib.RingTheory.Noetherian.OfPrime | [
"SetLike",
"Membership.mem",
"SetLike.coe",
"SetLike.mem_coe",
"propext",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
SimpleGraph.Walk.append_copy_copy | Mathlib.Combinatorics.SimpleGraph.Walk.Operations | [
"SimpleGraph.Walk",
"Eq.rec",
"SimpleGraph",
"SimpleGraph.Walk.copy",
"Eq.refl",
"Eq.symm",
"Eq",
"SimpleGraph.Walk.append"
] | true |
Lean.Compiler.LCNF.JoinPointContextExtender.ExtendState.fvarMap | Lean.Compiler.LCNF.JoinPoints | [
"Lean.instBEqFVarId",
"Lean.FVarId",
"Std.HashMap",
"Lean.Compiler.LCNF.Purity.pure",
"Lean.instHashableFVarId",
"Lean.Compiler.LCNF.Param",
"Lean.Compiler.LCNF.JoinPointContextExtender.ExtendState"
] | true |
CompactExhaustion.shiftr._proof_1 | Mathlib.Topology.Compactness.SigmaCompact | [
"CompactExhaustion.isCompact",
"TopologicalSpace",
"Nat",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"CompactExhaustion",
"CompactExhaustion.instFunLikeNatSet",
"DFunLike.coe",
"Nat.casesOn",
"IsCompact",
"isCompact_empty",
"Set"
] | false |
Fin.finsetImage_castAdd_Iic | Mathlib.Order.Interval.Finset.Fin | [
"Fin.castAdd",
"Finset",
"PartialOrder.toPreorder",
"instDecidableEqFin",
"Nat.le_add_right",
"instHAdd",
"Fin.instPartialOrder",
"HAdd.hAdd",
"Nat",
"Finset.Iic",
"instAddNat",
"Fin.finsetImage_castLE_Iic",
"Fin.instLocallyFiniteOrderBot",
"Fin",
"Eq",
"Finset.image"
] | true |
RatFunc.liftOn | Mathlib.FieldTheory.RatFunc.Defs | [
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"Membership.mem",
"nonZeroDivisors",
"Polynomial",
"MulZeroOneClass.toMulOneClass",
"CommRing.toCommSemiring",
"RatFunc",
"MonoidWithZero.toMulZeroOneClass",
"Polynomial.semiring",
"Polynomial.instMul",
"Submonoid.instSetLike",
"Eq",
"S... | true |
FiniteGrp.instConcreteCategoryMonoidHomCarrierToGrp._aux_3 | Mathlib.Algebra.Category.Grp.FiniteGrp | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"GrpCat",
"MonoidHom.instFunLike",
"FiniteGrp",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"GrpCat.str",
"Monoid.toMulOneClass",
"CategoryTheory.InducedCategory.homMk",
"FiniteGrp.toGrp",
"DivInvMonoid.toMonoid",
"Group... | false |
TensorProduct.instSmall | Mathlib.LinearAlgebra.TensorProduct.Map | [
"LinearEquiv.symm",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"Shrink.instAddCommMonoid",
"Equiv",
"Small.mk",
"TensorProduct.congr",
"Nonempty.intro",
"AddCommMonoid",
"CommSemiring",
"RingHomInvPair.ids",
"LinearEquiv.toEquiv",
"Exists.intro",
"Shrink.linearEquiv",
"Non... | true |
Subgroup.quotientEquivProdOfLE'._proof_6 | Mathlib.GroupTheory.Coset.Basic | [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"QuotientGroup.mk",
"Group",
"Group.toDivisionMonoid",
"Quotient.mk''",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"QuotientGroup.leftRel",
"MulOne.toMul",
"QuotientGroup.instHasQuotientSubgroup",
"DivInvMonoid.... | false |
Asymptotics.IsBigOWith.sub | Mathlib.Analysis.Asymptotics.Defs | [
"Eq.mpr",
"NegZeroClass.toNeg",
"Real",
"SeminormedAddCommGroup",
"Asymptotics.IsBigOWith",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"Norm",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.... | true |
Std.DTreeMap.Internal.Impl.rotateR.eq_2 | Std.Data.DTreeMap.Internal.Balancing | [
"Std.DTreeMap.Internal.Impl.doubleR",
"HMul.hMul",
"Std.DTreeMap.Internal.Impl.singleR",
"Std.DTreeMap.Internal.Impl.rotateR",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"instMulNat",
"Nat",
"LT.lt",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"Eq",
"Std.DTreeMap.Inter... | true |
ProbabilityTheory.beta_eq_betaIntegralReal | Mathlib.Probability.Distributions.Beta | [
"Eq.mpr",
"Real",
"instHDiv",
"HMul.hMul",
"Real.instZero",
"congrArg",
"Real.instDivInvMonoid",
"Complex.ofReal_div._simp_1",
"Real.instLT",
"Complex.instDivInvMonoid",
"Complex.instMul",
"Complex.ofReal_add",
"Complex.Gamma",
"id",
"HDiv.hDiv",
"Complex.ofReal",
"Real.instAdd",
"... | true |
PowerSeries.rescale._proof_1 | Mathlib.RingTheory.PowerSeries.Basic | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Semiring.toModule",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"mul_boole",
"id",
"PowerSeries.coeff",
"PowerSeries.coeff_mk",
"NonAssocSemiring.toMulZeroOneClass... | false |
_private.Lean.Elab.DocString.0.Lean.Doc.fixupInline.match_1 | Lean.Elab.DocString | [
"_private.Lean.Elab.DocString.0.Lean.Doc.Ref.mk",
"Option.ctorIdx",
"String",
"_private.Lean.Elab.DocString.0.Lean.Doc.Ref.casesOn",
"_private.Lean.Elab.DocString.0.Lean.Doc.getModState._sparseCasesOn_1",
"Option.some",
"Lean.Syntax",
"namedPattern",
"Nat.hasNotBit",
"_private.Lean.Elab.DocString.... | false |
CategoryTheory.Arrow.hom.congr_left | Mathlib.CategoryTheory.Comma.Arrow | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Arrow.left",
"id",
"Eq.refl",
"CategoryTheory.Arrow.Hom.left",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Arrow",
"CategoryTheory.instQuiverArrow",
"Eq",
"CategoryTheory.Category"
] | true |
finsuppTensorFinsuppRid | Mathlib.LinearAlgebra.DirectSum.Finsupp | [
"Semiring.toModule",
"Finsupp.module",
"TensorProduct.rid",
"CommSemiring.toSemiring",
"finsuppTensorFinsuppRid._proof_2",
"TensorProduct.addCommMonoid",
"finsuppTensorFinsupp",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Algebra.id",
"Finsupp.lcongr",
"AddCommMonoid",
"Finsupp.in... | true |
Nat.not_dvd_of_pos_of_lt | Init.Data.Nat.Lemmas | [
"Iff.mpr",
"False",
"Dvd.dvd",
"HMul.hMul",
"Nat.le_mul_of_pos_right",
"Nat.not_lt",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Or.casesOn",
"GT.gt",
"Exists.casesOn",
"Nat.instDvd",
"Nat",
"Nat.lt_irrefl",
"LT.lt",
"Eq.ndrec",
"Or",
"instLTNat",
"OfNat.ofNat",
"E... | true |
CategoryTheory.Pseudofunctor.DescentData'.comm | Mathlib.CategoryTheory.Sites.Descent.DescentDataPrime | [
"CategoryTheory.Pseudofunctor.DescentData'.pullHom_pullHom'",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Pseudofunctor.DescentData'.pullHom'",
"Opposite",
"CategoryTheory.Pseudofunctor.DescentData'.pullHom_pullHom'._proof_12",
"CategoryTheory.Pseudofunctor.DescentData'.comm._auto_3",
"... | true |
_private.Std.Time.Date.Unit.Year.0.Std.Time.Year.instTransOrdOffset._proof_1 | Std.Time.Date.Unit.Year | [
"Std.TransOrd",
"Int.instTransOrd",
"Std.Time.Year.Offset",
"Std.Time.Year.instOrdOffset"
] | false |
instDecidableEqFreeMagma.decEq | Mathlib.Algebra.Free | [
"FreeMagma.brecOn",
"instDecidableEqFreeMagma.decEq._f",
"Decidable",
"Eq",
"FreeMagma",
"DecidableEq"
] | true |
CategoryTheory.IndParallelPairPresentation.F₂ | Mathlib.CategoryTheory.Limits.Indization.ParallelPair | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.IndParallelPairPresentation.ℐ",
"CategoryTheory.IndParallelPairPresentation",
"CategoryTheory.types",
"CategoryTheory.IndParallelPairPresentation.I",
"Ca... | true |
Lean.Grind.AC.instBEqExpr | Init.Grind.AC | [
"Lean.Grind.AC.Expr",
"BEq.mk",
"Lean.Grind.AC.instBEqExpr.beq",
"BEq"
] | true |
Finset.card_mono | Mathlib.Data.Finset.Card | [
"Finset",
"Finset.card_le_card",
"PartialOrder.toPreorder",
"Monotone",
"Finset.partialOrder",
"Nat.instPreorder",
"Nat",
"Finset.card"
] | true |
Std.Time.HourMarker.rec | Std.Time.Time.HourMarker | [
"Std.Time.HourMarker.pm",
"Std.Time.HourMarker",
"Std.Time.HourMarker.am"
] | false |
MonotoneOn.inv | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"Iff.mpr",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Preorder.toLE",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"MulLeftMono",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"MulRightMono",
"LE.le",
"Group.toDivInvMonoid",
"inv_le_i... | true |
CategoryTheory.MorphismProperty.Under.mapPushoutAdj._proof_9 | Mathlib.CategoryTheory.MorphismProperty.OverAdjunction | [
"CategoryTheory.MorphismProperty.Under",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Comma.right",
"CategoryTheory.MorphismProperty.Over.map._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismP... | false |
_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod.LFunction_one_sub._simp_1_5 | Mathlib.NumberTheory.LSeries.ZMod | [
"imp_self",
"True",
"propext",
"Eq"
] | false |
Int.tdiv_add_tmod | Init.Data.Int.DivMod.Lemmas | [
"Int.tmod",
"HMul.hMul",
"Int",
"Int.mul_tdiv_add_tmod",
"Int.instMul",
"Int.tdiv",
"instHAdd",
"HAdd.hAdd",
"Int.instAdd",
"Eq",
"instHMul"
] | true |
«termΣ'_,_» | Init.NotationExtra | [
"Lean.explicitBinders",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
Lean.LocalContext.modifyLocalDecls | Lean.LocalContext | [
"Lean.instBEqFVarId",
"Lean.LocalContext.mk",
"Lean.FVarIdMap",
"Option.some",
"Lean.LocalDecl.index",
"Lean.FVarId",
"instOfNatNat",
"Lean.PersistentArray",
"Lean.PersistentArray.foldl",
"Lean.PersistentHashMap.insert",
"Lean.PersistentHashMap",
"Lean.instHashableFVarId",
"Lean.LocalDecl.fv... | true |
Fintype.card_fin_two | Mathlib.Data.Fintype.Parity | [
"Fact",
"Fintype.card",
"instOfNatNat",
"Fin.fintype",
"Fact.mk",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Even",
"Exists.intro",
"instAddNat",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
_private.Init.Data.Array.InsertIdx.0.Array.getElem_insertIdx_of_gt._proof_1_1 | Init.Data.Array.InsertIdx | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"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",
"Lean.Omega.LinearC... | false |
_private.Batteries.Data.String.Lemmas.0.String.Pos.Raw.get?.match_1.eq_1 | Batteries.Data.String.Lemmas | [
"String",
"String.Pos.Raw",
"String.Pos.Raw.get?.match_1",
"Eq.refl",
"Eq"
] | true |
CochainComplex.instHasShiftInt._proof_1 | Mathlib.Algebra.Homology.HomotopyCategory.Shift | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Int",
"Int.instAddMonoid",
"AddZero.toZero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"rfl"
] | false |
HVertexOperator.compHahnSeries_add | Mathlib.Algebra.Vertex.HVertexOperator | [
"HahnModule.instBaseModule",
"Eq.mpr",
"Pi.Function.module",
"CommRing",
"HVertexOperator",
"Pi.addCommMonoid",
"HVertexOperator.compHahnSeries._proof_1",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup... | true |
MeasurableEquiv.eq_image_iff_symm_image_eq | Mathlib.MeasureTheory.MeasurableSpace.Embedding | [
"MeasurableEquiv.instEquivLike",
"Eq.mpr",
"MeasurableEquiv.toEquiv",
"Equiv.instEquivLike",
"congrArg",
"MeasurableEquiv.coe_toEquiv",
"Iff.rfl",
"MeasurableEquiv.symm",
"id",
"Equiv",
"MeasurableSpace",
"Iff",
"propext",
"Equiv.eq_image_iff_symm_image_eq",
"MeasurableEquiv.coe_toEquiv_... | true |
Subsemiring.pointwise_smul_le_pointwise_smul_iff₀ | Mathlib.Algebra.Ring.Subsemiring.Pointwise | [
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Subsemiring.instSetLike",
"Set.smul_set_subset_smul_set_iff₀",
"PartialOrder.toPreorder",
"GroupWithZero",
"Preorder.toLE",
"Subsemiring.instPartialOrder",
"Ne",
"AddCommMonoidWithOne.toAddMonoidWithOne",
... | true |
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