name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
PMF.toOuterMeasure_apply_fintype | Mathlib.Probability.ProbabilityMassFunction.Basic | [
"Finset.mem_univ",
"Finset.univ",
"ENNReal.instAddCommMonoid",
"PMF",
"Set.indicator",
"Finset",
"AddMonoid.toAddZeroClass",
"PMF.toOuterMeasure",
"PMF.instFunLike",
"Membership.mem",
"AddZeroClass.toAddZero",
"MeasureTheory.OuterMeasure",
"SummationFilter.instLeAtTopUnconditional",
"AddZe... | true |
Mathlib.Tactic.Abel.evalNeg | Mathlib.Tactic.Abel | [
"Mathlib.Tactic.Abel.NormalExpr.brecOn",
"Lean.Expr",
"Mathlib.Tactic.Abel.evalNeg._f",
"Prod",
"Mathlib.Tactic.Abel.M",
"Mathlib.Tactic.Abel.NormalExpr"
] | true |
ZMod.sq_add_sq | Mathlib.FieldTheory.Finite.Basic | [
"one_pow",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Polynomial.C",
"Polynomial.eval",
"instNeZeroNatHAdd_1",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"IsDomain.to_noZeroDivisors",
"Nat.Prime.eq_two_or_odd",
"Nat.Prime",
"Fintype.elems",
"LinearOrderedCommMonoidWithZero.toIsBotZer... | true |
CategoryTheory.FreeBicategory.id_def | Mathlib.CategoryTheory.Bicategory.Free | [
"CategoryTheory.FreeBicategory.categoryStruct",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.FreeBicategory.Hom.id",
"CategoryTheory.FreeBicategory",
"CategoryTheory.FreeBicategory.Hom",
"Quiver",
"Eq",
"rfl"
] | true |
CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_hom_inv' | Mathlib.CategoryTheory.Monoidal.Action.Basic | [
"Eq.mpr",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.MonoidalCategory.MonoidalLeftActi... | true |
_private.Mathlib.Tactic.WithoutCDot.0.Lean.Elab.Term.withoutCDotContents | Mathlib.Tactic.WithoutCDot | [
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.optional",
"instHAndThenOfAndThen",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.ppSpace",
"Unit",
"Nat",
"OfNat.ofNat",
"Lean.Parser.withoutForbidden",
"Lean.Parser.withoutPosition",
"Lean.Parser.instAndThenParser",
"Lean.Parse... | true |
_private.Mathlib.Analysis.Convex.Combination.0.convex_iff_sum_mem._simp_1_3 | Mathlib.Analysis.Convex.Combination | [
"Finset",
"Membership.mem",
"Insert.insert",
"Finset.mem_insert",
"Finset.instInsert",
"Finset.instSetLike",
"propext",
"Or",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | false |
convexHull_toCone_eq_sInf | Mathlib.Geometry.Convex.Cone.Basic | [
"IsGLB.sInf_eq",
"ConvexCone.instCompleteSemilatticeInf",
"ChainCompletePartialOrder.instOfCompleteLattice",
"ConvexCone.instPartialOrder",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"setOf",
"ConvexCone... | true |
top_unique | Mathlib.Order.BoundedOrder.Basic | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le.antisymm",
"PartialOrder",
"LE.le",
"OrderTop",
"OrderTop.toTop",
"le_top",
"Top.top",
"Eq"
] | true |
PSet.mem_def | Mathlib.SetTheory.ZFC.PSet | [
"PSet.instMembership",
"Iff.rfl",
"PSet.Func",
"Membership.mem",
"Exists",
"PSet",
"Iff",
"PSet.Type",
"PSet.Equiv"
] | true |
ProjectiveSpectrum.sup_vanishingIdeal_le | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology | [
"SetLike",
"Eq.mpr",
"Submodule",
"CommRing",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"HomogeneousIdeal._proof_1",
"AddMonoid.toAddSemigroup",
"instVAddOfAdd",
"ProjectiveSpectrum.mem_vanishingIdeal",
"congrArg",
"CommSemiring.toSemiring",
"Submodule.completeLattice",
"AddMonoid.t... | true |
instNonUnitalCommCStarAlgebraProd._proof_3 | Mathlib.Analysis.CStarAlgebra.Classes | [
"NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"instSMulOfMul",
"NonUnitalNonAssocRing.toMul",
"NonUnitalCommCStarAlgebra",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"NormedSpace.toModule",
"Complex.instNormedField",
"NormedField.toField"... | false |
Std.HashMap.getElem_congr | Std.Data.HashMap.Lemmas | [
"GetElem?.toGetElem",
"Membership.mem",
"Std.DHashMap.Const.get_congr",
"Std.HashMap",
"Std.HashMap.mem_congr",
"LawfulHashable",
"GetElem.getElem",
"Bool.true",
"BEq.beq",
"EquivBEq",
"Iff.mp",
"Bool",
"Hashable",
"Std.HashMap.instGetElem?Mem",
"Std.HashMap.inner",
"BEq",
"Eq",
"S... | true |
Complex.sqrt._proof_1 | Mathlib.Analysis.RCLike.Sqrt | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
Subgroup.mem_ofUnits_iff_exists_isUnit | Mathlib.Algebra.Group.Submonoid.Units | [
"Monoid",
"Monoid.toMulOneClass",
"IsUnit",
"Membership.mem",
"Exists",
"Units",
"Subgroup.mem_ofUnits_of_isUnit_of_unit_mem",
"Subgroup",
"Units.instGroup",
"_private.Mathlib.Algebra.Group.Submonoid.Units.0.Subgroup.mem_ofUnits_iff_exists_isUnit.match_1_1",
"Iff",
"Subgroup.unit_mem_of_mem_of... | true |
_private.Mathlib.Computability.TuringMachine.PostTuringMachine.0.Turing.TM1to0.trCfg.match_1.splitter | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Turing.Tape",
"Turing.TM1.Cfg",
"Turing.TM1.Cfg.mk",
"Inhabited",
"Turing.TM1to0.trCfg.match_1",
"Option"
] | true |
Num.bit0 | Mathlib.Data.Num.Basic | [
"castNum.match_1",
"PosNum.bit0",
"Num",
"Unit",
"instZeroNum",
"Num.pos",
"Zero.toOfNat0",
"PosNum",
"OfNat.ofNat"
] | true |
AddCommGroup.modEq_iff_intModEq._simp_1 | Mathlib.Data.Int.ModEq | [
"Int.instAddCommMonoid",
"AddCommGroup.ModEq",
"Int",
"Int.ModEq",
"propext",
"AddCommGroup.modEq_iff_intModEq",
"Eq"
] | false |
Polynomial.natDegree_map_lt' | Mathlib.Algebra.Polynomial.Eval.Degree | [
"Eq.mpr",
"congrArg",
"Polynomial.instDecidableEq",
"Classical.propDecidable",
"RingHom",
"id",
"Polynomial.leadingCoeff",
"instOfNatNat",
"Polynomial.natDegree_zero",
"Polynomial",
"dite",
"RingHom.instFunLike",
"Nat",
"LT.lt",
"Semiring",
"Zero.toOfNat0",
"Polynomial.map",
"instL... | true |
SSet.π₀Functor_map | Mathlib.AlgebraicTopology.SimplicialSet.PiZero | [
"SSet.π₀Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SSet.mapπ₀",
"CategoryTheory.Functor.category",
"TypeCat.ofHom",
"SSet",
"SSet.π₀",
"CategoryTheory.Functor.map",
"CategoryTheory.types",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"Eq.refl",... | true |
Std.Format.FlattenBehavior.ctorIdx | Init.Data.Format.Basic | [
"Nat",
"Std.Format.FlattenBehavior.casesOn",
"Std.Format.FlattenBehavior"
] | false |
Equiv.preorder | Mathlib.Order.Lattice | [
"Equiv.preorder._proof_1",
"Preorder.toLT",
"Equiv.instEquivLike",
"Equiv.le",
"Preorder.toLE",
"Equiv",
"Equiv.preorder._proof_2",
"LE",
"Equiv.lt",
"Function.Injective.preorder",
"DFunLike.coe",
"Preorder",
"EquivLike.toFunLike",
"LT"
] | true |
Polynomial.roots_eq_of_degree_le_card_of_ne_zero | Mathlib.Algebra.Polynomial.Roots | [
"Iff.mpr",
"WithBot.addMonoidWithOne",
"WithBot.instPreorder",
"Polynomial.eval",
"WithBot.zeroLEOneClass",
"IsDomain",
"WithBot.addLeftMono",
"CommRing",
"WithBot",
"Polynomial.roots",
"Nat.instIsOrderedAddMonoid",
"AddMonoid.toAddSemigroup",
"CommSemiring.toSemiring",
"Finset",
"Polyno... | true |
Std.Iterators.Types.Flatten.instIterator | Init.Data.Iterators.Combinators.Monadic.FlatMap | [
"Std.Iterators.Types.Flatten.IsPlausibleStep.innerYield",
"Pure.pure",
"Std.Shrink.deflate",
"Std.Iterator.mk",
"Std.Shrink",
"Monad.toApplicative",
"Std.Iterators.Types.Flatten.IsPlausibleStep.outerDone",
"Std.PlausibleIterStep",
"Option.some",
"Std.IterM.IsPlausibleStep",
"Std.IterStep.skip",
... | true |
SemilatticeInf.ext_inf | Mathlib.Order.Lattice | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"id",
"SemilatticeInf.toMin",
"LE.le",
"le_inf_iff",
"And",
"SemilatticeInf",
"Iff",
"propext",
"eq_of_forall_le_iff",
"Eq.symm",
"Eq",
"Min.min"
] | true |
List.Vector.sum_add_sum_eq_sum_zipWith | Mathlib.Data.Vector.Zip | [
"List.Vector.zipWith",
"AddMonoid.toAddZeroClass",
"List.sum",
"List.Vector",
"List.sum_add_sum_eq_sum_zipWith_of_length_eq",
"AddZeroClass.toAddZero",
"List.Vector.toList_length",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"Nat",
"AddZero.toAdd",
"AddCommMonoid.toAddMonoi... | true |
intervalIntegral.integral_same | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | [
"Set.Ioc",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"sub_self",
"intervalIntegral",
"AddCommGroup.toAddGroup",
"MeasureTheory.Measure.restrict",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Real.measurableSpace"... | true |
Std.TreeMap.Raw.Equiv.of_keysArray_unit_perm | Std.Data.TreeMap.Raw.Lemmas | [
"Iff.mpr",
"Ordering",
"Std.TreeMap.Raw.keysArray",
"Std.TreeMap.Raw.Equiv",
"Array.Perm",
"Std.TreeMap.Raw",
"Unit",
"Std.TreeMap.Raw.equiv_iff_keysArray_unit_perm"
] | true |
ONote.NFBelow.below.oadd' | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.NFBelow.below",
"Preorder.toLT",
"Ordinal.partialOrder",
"ONote.oadd",
"PartialOrder.toPreorder",
"ONote.NFBelow.below.oadd'",
"ONote.NFBelow",
"ONote.repr",
"LT.lt",
"ONote",
"ONote.NFBelow.oadd'",
"Ordinal",
"PNat"
] | true |
FreeRing.hom_ext_iff | Mathlib.RingTheory.FreeRing | [
"FreeRing.of",
"HEq.refl",
"instRingFreeRing",
"RingHom",
"FreeRing.hom_ext",
"Eq.casesOn",
"Iff",
"RingHom.instFunLike",
"Iff.intro",
"FreeRing",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Eq",
"DFunLike.coe",
"Ring"
] | true |
_private.Mathlib.Combinatorics.Matroid.Minor.Restrict.0.Matroid.restrictIndepMatroid._simp_7 | Mathlib.Combinatorics.Matroid.Minor.Restrict | [
"HasSubset.Subset",
"And",
"Set.instLE",
"maximal_subset_iff",
"propext",
"Maximal",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
Lean.Syntax.instForInTopDownOfMonad.loop._unsafe_rec | Lean.Syntax | [
"Pure.pure",
"Lean.Syntax.instForInTopDownOfMonad.loop._unsafe_rec",
"instForInOfForIn'",
"Monad.toApplicative",
"Lean.SourceInfo",
"Array.instMembership",
"Option.some",
"ForInStep.done",
"Lean.Syntax",
"inferInstance",
"Bool.and",
"instDecidableEqBool",
"Prod.mk",
"ForIn.forIn",
"instO... | false |
div_div_self | Mathlib.Algebra.GroupWithZero.Basic | [
"Eq.mpr",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"Monoid.toMulOneClass",
"congrArg",
"GroupWithZero",
"div_div_eq_mul_div",
"id",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"DivisionMonoid.toDivInvMonoid",
"MulOneClass.toMulO... | true |
RingSeminorm.exists_index_pow_le | Mathlib.Analysis.Normed.Unbundled.RingSeminorm | [
"Real.instIsOrderedRing",
"Real.instPow",
"Real.partialOrder",
"Real.instLE",
"Real",
"CommRing",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"RingSeminorm.ringSeminormClass",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"MulZeroClass.toMul",
"Nat.ble",
"Real.instZeroLEOne... | true |
_private.Mathlib.Topology.Category.Profinite.Nobeling.Span.0.Profinite.NobelingProof.GoodProducts.spanFin._simp_1_3 | Mathlib.Topology.Category.Profinite.Nobeling.Span | [
"Finsupp.mem_support_iff",
"Finsupp.instFunLike",
"Finset",
"Finsupp.support",
"Membership.mem",
"Ne",
"Finset.instSetLike",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"SetLike.instMembership",
"Finsupp",
"Zero"
] | false |
WittVector.wittPolyProdRemainder.congr_simp | Mathlib.RingTheory.WittVector.MulCoeff | [
"Nat.Prime",
"Fact",
"Eq.rec",
"instOfNatNat",
"Int",
"Nat",
"MvPolynomial",
"Eq.ndrec",
"Eq.refl",
"Prod",
"Int.instCommSemiring",
"OfNat.ofNat",
"Fin",
"Eq",
"WittVector.wittPolyProdRemainder"
] | true |
Lean.Expr.FindStep.noConfusionType | Lean.Util.FindExpr | [
"noConfusionTypeEnum",
"Lean.Expr.FindStep.ctorIdx",
"Nat",
"instDecidableEqNat",
"Lean.Expr.FindStep"
] | true |
Vector.length_iterM | Std.Data.Iterators.Lemmas.Producers.Monadic.Vector | [
"Pure.pure",
"Vector.iterM",
"Std.Iterators.Types.ArrayIterator",
"Vector",
"congrArg",
"Monad.toApplicative",
"Std.instLawfulIteratorLoopDefaultImplementation",
"Std.IterM.length",
"ULift",
"_private.Std.Data.Iterators.Lemmas.Producers.Monadic.Vector.0.Vector.length_iterM._simp_1_1",
"Vector.to... | true |
Lean.IRPhases.comptime.sizeOf_spec | Lean.Setup | [
"Lean.IRPhases.comptime",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.IRPhases",
"Lean.IRPhases._sizeOf_inst"
] | true |
Insert.recOn | Init.Core | [
"Insert",
"Insert.mk",
"Insert.rec"
] | false |
List.Vector.instFintype | Mathlib.Data.Fintype.Vector | [
"Equiv.instEquivLike",
"Finset.univ",
"Equiv.vectorEquivFin",
"List.Vector.instFintype._proof_1",
"instDecidableEqFin",
"Pi.instFintype",
"List.Vector",
"List.Vector.instFintype._proof_2",
"Finset.map",
"Function.Embedding.mk",
"Equiv",
"Fin.fintype",
"Fintype",
"Nat",
"Fintype.mk",
"E... | true |
Std.PRange.instLawfulUpwardEnumerableInt | Init.Data.Range.Polymorphic.Int | [
"Eq.mpr",
"congrArg",
"Std.PRange.LawfulUpwardEnumerable.mk",
"Std.PRange.instUpwardEnumerableInt",
"Std.PRange.UpwardEnumerable.LT",
"Option.some.injEq",
"Option.some",
"Exists",
"Int.instDecidableEq",
"Option.bind",
"id",
"Ne",
"instOfNatNat",
"Int",
"Std.PRange.UpwardEnumerable.succ?"... | true |
SimpleGraph.edgeFinset_eq_empty | Mathlib.Combinatorics.SimpleGraph.Finite | [
"Eq.mpr",
"SimpleGraph.edgeFinset_inj",
"congrArg",
"Finset",
"Iff.rfl",
"Set.Elem",
"id",
"Bot.bot",
"Finset.instEmptyCollection",
"SimpleGraph.edgeSet",
"SimpleGraph.edgeFinset",
"SimpleGraph",
"Iff",
"Fintype",
"SimpleGraph.edgeFinset_bot",
"propext",
"SimpleGraph.completeAtomicBo... | true |
ValuativeRel.veq_rfl | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"ValuativeRel.veq",
"CommRing",
"ValuativeRel.veq_refl",
"ValuativeRel"
] | true |
WeierstrassCurve.VariableChange.recOn | Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange | [
"CommRing",
"CommSemiring.toSemiring",
"WeierstrassCurve.VariableChange.mk",
"Units",
"WeierstrassCurve.VariableChange",
"CommRing.toCommSemiring",
"Semiring.toMonoid",
"WeierstrassCurve.VariableChange.rec"
] | false |
_private.Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection.0.ContMDiffAt.finsum_section_of_locallyFinite._simp_1_1 | Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | [
"ContMDiffWithinAt",
"NormedSpace",
"Set.univ",
"TopologicalSpace",
"ModelWithCorners",
"ENat",
"propext",
"ContMDiffAt",
"contMDiffWithinAt_univ",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"Eq.symm",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Eq",
"NormedA... | false |
SimpleGraph.instIsEmptyElemForallObjOppositeFinsetComponentComplFunctorEndOfFinite | Mathlib.Combinatorics.SimpleGraph.Ends.Properties | [
"_private.Mathlib.Combinatorics.SimpleGraph.Ends.Properties.0.SimpleGraph.instIsEmptyElemForallObjOppositeFinsetComponentComplFunctorEndOfFinite._simp_1",
"SimpleGraph.ComponentCompl.setLike",
"False",
"Opposite",
"SimpleGraph.ComponentCompl.disjoint_right",
"Finset.univ",
"Finset.coe_univ",
"congrArg... | true |
Lean.Meta.Grind.Arith.Cutsat.ToIntTermInfo.rec | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Meta.Grind.Arith.Cutsat.ToIntTermInfo",
"Lean.Expr",
"Lean.Meta.Grind.Arith.Cutsat.ToIntTermInfo.mk"
] | false |
_private.Mathlib.Algebra.Order.UpperLower.0.UpperSet.one_mul | Mathlib.Algebra.Order.UpperLower | [
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
"Set.iUnion₂_subset",
"instSMulOfMul",
"HMul.hMul",
"Set.Ici",
"UpperSet",
"IsOrderedMonoid",
"Monoid.toMulOneClass",
"congrArg",
"UpperSet.instSetLike",
"Set.smul",
"Preorder.toLE",
"Membership.mem",
"id",
"MulOne.toMul",
"DivInvMonoid.toMono... | true |
AddSubgroup.map_equiv_eq_comap_symm' | Mathlib.Algebra.Group.Subgroup.Map | [
"AddSubgroup.comap",
"AddMonoid.toAddZeroClass",
"AddEquiv.toAddMonoidHom",
"AddZeroClass.toAddZero",
"SetLike.coe_injective",
"AddSubgroup",
"AddGroup",
"Equiv.image_eq_preimage_symm",
"AddGroup.toSubNegMonoid",
"SetLike.coe",
"AddSubgroup.instSetLike",
"AddEquiv",
"AddZero.toAdd",
"SubNe... | true |
RingCon.correspondence._proof_4 | Mathlib.RingTheory.Congruence.Hom | [
"Eq.mpr",
"RingCon.instPartialOrder",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"RingCon.mapGen_apply_apply_of_surjective",
"Lattice.toSemilatticeSup",
"RingHomClass.toAddMonoidHomClass",
"RingCon.comap_bot",
"Set.Ici",
"RingCon.instFunLikeForallProp",
"CompleteLatti... | false |
BitVec.toNat_eq._simp_1 | Init.Data.BitVec.Lemmas | [
"BitVec",
"BitVec.toNat",
"Nat",
"propext",
"BitVec.toNat_eq",
"Eq"
] | false |
Lean.Elab.Tactic.ElabSimpArgResult.noConfusion | Lean.Elab.Tactic.Simp | [
"Lean.Elab.Tactic.ElabSimpArgResult.noConfusionType",
"Lean.FVarId",
"Array",
"Lean.Elab.Tactic.ElabSimpArgResult.casesOn",
"Bool.true",
"Lean.Elab.Tactic.ElabSimpArgResult",
"Lean.Meta.SimpExtension",
"Bool",
"Eq.ndrec",
"Bool.or",
"Lean.Name",
"Eq.refl",
"Option.isSome",
"Lean.Meta.SimpE... | false |
Std.DHashMap.Raw.Const.get?_insertMany_list_of_mem | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.Const.get?",
"List.Pairwise",
"congrArg",
"instForInOfForIn'",
"Std.DHashMap.Raw",
"Option.some",
"Membership.mem",
"inferInstance",
"id",
"Std.DHashMap.Internal.Raw₀.Const.wf_insertMany₀",
"Prod.mk",
"instOfNatNat",
"Std.DHash... | true |
_private.Mathlib.RingTheory.Polynomial.Cyclotomic.Eval.0.Polynomial.eval_one_cyclotomic_not_prime_pow._simp_1_5 | Mathlib.RingTheory.Polynomial.Cyclotomic.Eval | [
"Monoid",
"Dvd.dvd",
"semigroupDvd",
"True",
"Monoid.toSemigroup",
"eq_true",
"dvd_refl",
"Eq"
] | false |
IsMulIndecomposable.mem_or_inv_mem_closure_baseOf | Mathlib.Algebra.Group.Irreducible.Indecomposable | [
"Eq.mpr",
"lt_or_gt_of_ne",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"DivInvMonoid.toInv",
"IsOrderedMonoid.toIsOrderedCancelMonoid",
"Preorder.toLT",
"MonoidHom.instFunLike",
"InvOneClass.toOne",
"map_inv",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"and_... | true |
_private.Mathlib.Order.Interval.Finset.Fin.0.Fin.finsetImage_rev_Ico._simp_1_1 | Mathlib.Order.Interval.Finset.Fin | [
"Finset",
"Finset.coe_inj",
"SetLike.coe",
"Finset.instSetLike",
"propext",
"Eq.symm",
"Eq",
"Set"
] | false |
Filter.GenerateSets.brecOn | Mathlib.Order.Filter.Basic | [
"Membership.mem",
"Filter.GenerateSets.below",
"HasSubset.Subset",
"Filter.GenerateSets.below.univ",
"Filter.GenerateSets.below.inter",
"Filter.GenerateSets.below.superset",
"Filter.GenerateSets",
"Filter.GenerateSets.below.basic",
"Filter.GenerateSets.rec",
"Set.instMembership",
"Set.instHasSub... | true |
_private.Mathlib.Dynamics.PeriodicPts.Lemmas.0.Function.Injective.mem_periodicPts._proof_1_1 | Mathlib.Dynamics.PeriodicPts.Lemmas | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"Preorder.toLT",
"HMul.hMul",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Int.Linear.le_neg",
"Int.Linear.eq_norm",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"HSub.hSub",... | false |
Int16.toInt64_le._simp_1 | Init.Data.SInt.Lemmas | [
"Int16.toInt64_le",
"Int16",
"Int64",
"instLEInt16",
"LE.le",
"propext",
"Int16.toInt64",
"Eq",
"instLEInt64"
] | false |
LinearMap.finrank_genEigenspace_le | Mathlib.LinearAlgebra.Eigenspace.Zero | [
"Eq.mpr",
"Submodule",
"le_refl",
"ENat.instNatCast",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"PartialOrder.toPreorder",
"Membership.mem",
"Field.toDivisionRing",
"Field.instIsLocalRing",
"AddCommGroup",
"instPreorderENat",
"Subty... | true |
Graph.le_noEdge_iff | Mathlib.Combinatorics.Graph.Subgraph | [
"Graph.IsLink.edge_mem",
"Graph.IsSubgraph.mk",
"Eq.mpr",
"False",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"False.elim",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Eq.mp",
"id",
"Graph.IsSubgraph.edgeSet_mono",
"HasSubset.Subset",
"Graph",
"LE.le",
"Graph.n... | true |
Subgroup.subset_normalClosure | Mathlib.Algebra.Group.Subgroup.Basic | [
"Subgroup.conjugatesOfSet_subset_normalClosure",
"Set.Subset.trans",
"Subgroup.normalClosure",
"Group",
"Subgroup",
"HasSubset.Subset",
"SetLike.coe",
"Group.conjugatesOfSet",
"Group.subset_conjugatesOfSet",
"Subgroup.instSetLike",
"Set.instHasSubset",
"Set"
] | true |
Monotone.iSup | Mathlib.Order.CompleteLattice.Basic | [
"Eq.mpr",
"iSup",
"PartialOrder.toPreorder",
"Monotone",
"Membership.mem",
"Exists",
"id",
"Set.mem_range._simp_1",
"forall_exists_index._simp_1",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"forall_apply_eq_imp_iff._simp_1",
"implies_congr",
"Compl... | true |
CategoryTheory.Adjunction.counitSplitMonoOfRFull | Mathlib.CategoryTheory.Adjunction.FullyFaithful | [
"CategoryTheory.Functor.preimage",
"CategoryTheory.Adjunction.counitSplitMonoOfRFull._proof_1",
"CategoryTheory.Functor",
"CategoryTheory.SplitMono.mk",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.Functor.id",
"CategoryTheory.Adjunction.counit",
"CategoryTheory.A... | true |
SchwartzMap.instLaplacian._proof_3 | Mathlib.Analysis.Distribution.SchwartzSpace.Deriv | [
"InnerProductSpace.toNormedSpace",
"Real",
"NormedSpace",
"Real.instRCLike",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"LineDerivSMul",
"Real.semiring",
"SchwartzMap.instLineDerivSMul",
"SchwartzMap",
"smulCommClass_self",
"RCLike.toDenselyNormedField",
"SchwartzMap.instLineDer... | false |
Ordinal.typein_le_typein._simp_1 | Mathlib.SetTheory.Ordinal.Basic | [
"Ordinal.typein_le_typein",
"Preorder.toLT",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"PrincipalSeg.toRelEmbedding",
"Preorder.toLE",
"IsWellOrder",
"LE.le",
"RelEmbedding",
"LT.lt",
"propext",
"Eq",
"DFunLike.coe",
"Not",
"RelEmbedding.instFunLike",
"Ordinal.typein",
"Ordi... | false |
_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.BinOpKind.rightact | Lean.Elab.Extra | [
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.BinOpKind.rightact",
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.BinOpKind"
] | true |
Std.DTreeMap.Internal.Impl.Const.maxEntry.match_1.congr_eq_2 | Std.Data.DTreeMap.Internal.Model | [
"False",
"Std.DTreeMap.Internal.Impl.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"HEq.homo_ndrec",
"Std.DTreeMap.Internal.Impl.inner",
"Eq.casesOn",
"id",
"Bool.ctorIdx",
"Bool.true",
"heq_of_eq",
"Std.DTreeMap.Internal.Impl.leaf",
"Std.DTreeMap.Internal.Impl.isEmpty",
"Nat... | true |
Lean.Meta.LibrarySearch.DeclMod.casesOn | Lean.Meta.Tactic.LibrarySearch | [
"Lean.Meta.LibrarySearch.DeclMod.none",
"Lean.Meta.LibrarySearch.DeclMod.mp",
"Lean.Meta.LibrarySearch.DeclMod.rec",
"Lean.Meta.LibrarySearch.DeclMod.mpr",
"Lean.Meta.LibrarySearch.DeclMod"
] | false |
Batteries.BinomialHeap.Imp.Heap.WF.deleteMin | Batteries.Data.BinomialHeap.Basic | [
"Nat.zero_le",
"Batteries.BinomialHeap.Imp.Heap.deleteMin",
"Option.some.noConfusion",
"Batteries.BinomialHeap.Imp.FindMin.WF",
"Batteries.BinomialHeap.Imp.Heap.findMin",
"Batteries.BinomialHeap.Imp.Heap.WF",
"Option.ctorIdx",
"HEq.refl",
"False.elim",
"Batteries.BinomialHeap.Imp.FindMin.val",
"... | true |
LinearMap.smulRightₗ._proof_4 | Mathlib.Algebra.Module.LinearMap.End | [
"LinearMap.smulRightₗ._proof_1",
"instHSMul",
"Semiring.toModule",
"LinearMap.ext",
"CommSemiring.toNonUnitalCommSemiring",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearMap.instSMulCommClass",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"RingHom",
"SemigroupWith... | false |
CategoryTheory.ExactPairing.ofFullyFaithful._proof_2 | Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence | [
"CategoryTheory.Functor.preimage",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.map",
"CategoryTheory.ExactPairing",
"CategoryTheory.Functor.Monoidal.toOplaxMonoidal",
"CategoryTheory.Functo... | false |
Lean.Lsp.CodeActionOptions | Lean.Data.Lsp.CodeActions | [
"Lean.Lsp.CodeActionOptions.mk"
] | true |
AffineSubspace.direction_inf | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"Submodule",
"trans",
"Set.vsub",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"setOf",
"sInf_le_sInf",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"AddCommGroup",
"id",
"Set.in... | true |
MeasureTheory.measurableCylinders.finset._proof_1 | Mathlib.MeasureTheory.Constructions.Cylinders | [
"MeasurableSet",
"Finset",
"MeasureTheory.measurableCylinders",
"Membership.mem",
"Exists",
"Subtype",
"MeasureTheory.cylinder",
"MeasurableSpace",
"And",
"Finset.instSetLike",
"MeasurableSpace.pi",
"Iff.mp",
"Subtype.val",
"Eq",
"Set.instMembership",
"MeasureTheory.mem_measurableCylin... | false |
ULift.instOrderTop.eq_1 | Mathlib.Order.BoundedOrder.Basic | [
"ULift",
"ULift.instOrderTop",
"OrderTop",
"LE",
"ULift.instOrderTop._proof_2",
"ULift.instLE_mathlib",
"OrderTop.toTop",
"ULift.instTop",
"ULift.instOrderTop._proof_1",
"Eq.refl",
"OrderTop.lift",
"Eq",
"ULift.down"
] | true |
instDecidableEqLists'.decEq._f | Mathlib.SetTheory.Lists | [
"Decidable.isTrue",
"instDecidableEqLists'.decEq._proof_6",
"instDecidableEqLists'.decEq._proof_7",
"Decidable",
"Lists'.atom",
"instDecidableEqLists'.decEq._proof_4",
"instDecidableEqBool",
"instDecidableEqLists'.decEq._proof_3",
"instDecidableEqLists'.decEq.match_1",
"Lists'.cons'",
"dite",
... | false |
Aesop.TraceOption.traceClass | Aesop.Tracing | [
"Aesop.TraceOption",
"Lean.Name"
] | true |
CategoryTheory.ConcreteCategory.ext_iff | Mathlib.CategoryTheory.ConcreteCategory.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"HEq.refl",
"Eq.casesOn",
"CategoryTheory.ConcreteCategory.ext",
"CategoryTheory.ConcreteCategory",
"Iff",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"CategoryTheory.Category.toCategoryStruct",
"... | true |
CategoryTheory.CommSq.LiftStruct.opEquiv._proof_3 | Mathlib.CategoryTheory.CommSq | [
"Function.LeftInverse",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CommSq",
"Quiver.Hom.op",
"CategoryTheory.CommSq.LiftStruct.op",
"CategoryTheory.CommSq.LiftStruct",
"CategoryTheory.CommSq.LiftStruct.unop",
"CategoryTheory.CommSq.op",
"Opposite.op",
"... | false |
OrderIso.finTwoArrowIso | Mathlib.Order.Fin.Tuple | [
"RelIso.mk",
"Prod.instLE_mathlib",
"Preorder.toLE",
"OrderIso.finTwoArrowIso._proof_1",
"Equiv",
"OrderIso",
"instOfNatNat",
"LE.le",
"Pi.hasLe",
"Nat",
"OrderIso.piFinTwoIso",
"Prod",
"OfNat.ofNat",
"Fin",
"finTwoArrowEquiv",
"Preorder"
] | true |
List.drop | Init.Data.List.Basic | [
"List.drop._f",
"Nat.brecOn",
"List",
"Nat"
] | true |
Int.instCommutativeHMul | Init.Data.Int.Lemmas | [
"Std.Commutative",
"HMul.hMul",
"Int",
"Int.instMul",
"Int.mul_comm",
"Std.Commutative.mk",
"instHMul"
] | true |
MeasureTheory.Measure.snd_prod | Mathlib.MeasureTheory.Measure.Prod | [
"Set.instSProd",
"Eq.mpr",
"MulOne.toOne",
"MeasureTheory.Measure",
"HMul.hMul",
"MeasurableSet",
"SProd.sprod",
"congrArg",
"CommSemiring.toSemiring",
"Set.univ",
"Set.univ_prod",
"MeasureTheory.IsProbabilityMeasure.measure_univ",
"id",
"MulOne.toMul",
"MeasureTheory.Measure.prod_prod",... | true |
Array.getElem_scanl_zero._proof_1 | Batteries.Data.Array.Scan | [
"Nat.zero_lt_succ._simp_1",
"congrArg",
"Array.scanl",
"instOfNatNat",
"Array",
"instHAdd",
"Array.size_scanl",
"HAdd.hAdd",
"Nat",
"LT.lt",
"True",
"of_eq_true",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Array.size",
"Eq.trans"
] | false |
Manifold.IsImmersionAtOfComplement.instNormedAddCommGroupSmallComplement._proof_45 | Mathlib.Geometry.Manifold.Immersion | [
"NormedSpace",
"PartialOrder.toPreorder",
"Manifold.IsImmersionAtOfComplement",
"Preorder.toLE",
"Manifold.IsImmersionAtOfComplement.smallComplement",
"Manifold.IsImmersionAtOfComplement.instNormedAddCommGroupSmallComplement._proof_47",
"LE.le",
"TopologicalSpace",
"ModelWithCorners",
"Manifold.Is... | false |
List.compareLex._sunfold | Init.Data.Ord.Basic | [
"Ordering.gt",
"Ordering.swap.match_1",
"Ordering",
"Ordering.eq",
"List",
"Unit",
"Ordering.lt",
"List.compareLex",
"List.compareLex.match_1"
] | false |
_private.Mathlib.RingTheory.Etale.QuasiFinite.0.Algebra.exists_notMem_and_isIntegral_forall_mem_of_ne_of_liesOver._simp_1_2 | Mathlib.RingTheory.Etale.QuasiFinite | [
"HMul.hMul",
"Mul",
"MulHomClass",
"map_mul",
"Eq.symm",
"Eq",
"DFunLike.coe",
"FunLike",
"instHMul"
] | false |
CategoryTheory.Functor.LocallyCoverDense.rec | Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology | [
"CategoryTheory.Functor",
"Membership.mem",
"Set.Elem",
"CategoryTheory.Sieve",
"CategoryTheory.Functor.LocallyCoverDense.mk",
"CategoryTheory.Sieve.functorPushforward",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.Functor.LocallyCoverDense",
"Subtype.val",
"CategoryTheory.Sieve.functorP... | false |
Std.DHashMap.Raw.size_insertIfNew_le | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"congrArg",
"Std.DHashMap.Internal.Raw.insertIfNew_eq",
"Std.DHashMap.Raw",
"id",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"LE.le",
"instLENat",
"LawfulHashable",
"Subtype.mk",
"instHAdd",
"EquivBEq",
"HAdd.hAdd",
"Nat",
"Std.DHashMap.R... | true |
Matroid.closure_union_closure_right_eq | Mathlib.Combinatorics.Matroid.Closure | [
"Eq.mpr",
"congrArg",
"Set.instUnion",
"id",
"Matroid.closure_closure",
"Matroid.closure",
"Eq.refl",
"Union.union",
"Matroid.closure_closure_union_closure_eq_closure_union",
"Eq.symm",
"Eq",
"Matroid",
"Set"
] | true |
_private.Lean.Level.0.Lean.Level.substParams.go.match_3 | Lean.Level | [
"Unit.unit",
"Lean.Level.ctorIdx",
"Lean.Level.param",
"Nat.hasNotBit",
"Lean.Level.imax",
"Lean.Level",
"Unit",
"Lean.Level.zero",
"_private.Lean.Level.0.Lean.Level.substParams.go._sparseCasesOn_3",
"Lean.Name",
"Lean.Level.succ",
"Lean.Level.max"
] | false |
Finsupp.zipWith_neLocus_eq_right | Mathlib.Data.Finsupp.NeLocus | [
"Finsupp.instFunLike",
"Eq.mpr",
"congrArg",
"Finsupp.neLocus",
"Finset",
"Finset.ext",
"Membership.mem",
"id",
"Function.Injective.ne_iff",
"Ne",
"Iff",
"Finset.instSetLike",
"Finsupp.mem_neLocus._simp_1",
"congr",
"Finsupp.zipWith",
"Zero.toOfNat0",
"Function.Injective",
"OfNat.o... | true |
_private.Mathlib.Algebra.QuadraticAlgebra.Basic.0.QuadraticAlgebra.lift._simp_6 | Mathlib.Algebra.QuadraticAlgebra.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.toSMul",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Algebra.algebraMap_eq_smul_one",
"CommSemiring",
"AddMonoidWithOne.toOne",
"RingHom.instFunLike",
"Semi... | false |
LieAlgebra.IsKilling.coroot._proof_1 | Mathlib.Algebra.Lie.Weights.Killing | [
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddSubmonoidClass",
"Field.toCommRing",
"AddSubgroupClass.toAddSubmonoidClass",
"LieRing",
"AddGroup.toSubNegMonoid",
"LieSubalgebra",
"LieAlgebra",
"SubNegMonoid.toAddMonoid",
"Fie... | false |
TopCat.hasForgetToMeasCat._proof_2 | Mathlib.MeasureTheory.Category.MeasCat | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopCat.instCategory",
"ContinuousMap",
"MeasCat.instLargeCategory",
"Measurable",
"MeasCat.carrier",
"MeasCat",
"id",
"MeasCat.of",
"borel",
"Continuous.borel_measurable",
"TopCat.Hom.hom'",
"Subtype.mk",
"TopCat.str",
"TopCat.ca... | false |
Turing.TM2to1.Λ'.normal.noConfusion | Mathlib.Computability.TuringMachine.StackTuringMachine | [
"HEq.refl",
"id",
"Turing.TM2to1.Λ'",
"Turing.TM2to1.Λ'.noConfusion",
"heq_of_eq",
"Eq.refl",
"HEq",
"Eq",
"Turing.TM2to1.Λ'.normal"
] | false |
cfcL._proof_3 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"instSMulOfMul",
"CommSemiring.toSemiring",
"IsTopologicalSemiring",
"SeparatelyContinuousMul.to_continuousSMul",
"PseudoMetricSpace.toUniformSpace",
"ContinuousConstSMul",
"instDistribOfSemiring",
"CommSemiring",
"IsSemitopologicalSemiring.toSeparatelyContinuousMul",
"MetricSpace",
"Distrib.toM... | false |
AlgebraicGeometry.Scheme.Cover.instCategoryI₀Pullback₁._proof_8 | Mathlib.AlgebraicGeometry.Cover.Directed | [
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.Category.comp_id._autoParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.Scheme.isJointlySurjectivePreserving",
"CategoryTheory.CategoryStruct.id",
"Al... | false |
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