name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Array.findSomeM?._sparseCasesOn_1.else_eq | Init.Data.List.ToArray | [
"Option.ctorIdx",
"Option.casesOn",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"instOfNatNat",
"Bool.true",
"Nat.land",
"Option.none",
"absurd",
"Nat",
"Bool",
"Eq.ndrec",
"Array.findSomeM?._sparseCasesOn_1",
"Nat.eq_of_beq_eq_true",
"Eq.refl",
"OfNat.ofNat",
"Eq.symm",
"E... | false |
_private.Init.Data.List.Nat.TakeDrop.0.List.lt_length_drop._simp_1_1 | Init.Data.List.Nat.TakeDrop | [
"Nat.add_lt_add_iff_left",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"propext",
"instAddNat",
"instLTNat",
"Eq"
] | false |
Nat.lcm_lcm_self_right_right | Init.Data.Nat.Lcm | [
"Nat.lcm",
"Eq.mpr",
"Nat.lcm_comm",
"congrArg",
"id",
"Nat.lcm_lcm_self_right_left",
"Nat",
"Eq.refl",
"Eq"
] | true |
AddMonoidHom.continuous_of_isBounded_nhds_zero | Mathlib.Analysis.Normed.Module.Basic | [
"Filter.instMembership",
"norm_smul_le",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real.instIsOrderedRing",
"Norm.norm",
"Metric.isBounded_iff_subset_ball",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"... | true |
Std.DTreeMap.Const.isEmpty_insertMany_list | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"instForInOfForIn'",
"Std.DTreeMap.isEmpty",
"Ord.mk",
"Ordering",
"inferInstance",
"Bool.and",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Id",
"Std.DTreeMap.Const.insertMany",
"Membership",
"List",
"List.instMembership",
"List.isEmpty",
"Std.DTreeMap.wf",
"Bool",
"Id.i... | true |
PartialEquiv.refl_prod_refl | Mathlib.Logic.Equiv.PartialEquiv | [
"Set.ext",
"congrArg",
"PartialEquiv.prod",
"PartialEquiv",
"Set.mem_univ._simp_1",
"Set.univ",
"Membership.mem",
"PartialEquiv.symm",
"Prod.mk",
"Set.univ_prod_univ",
"Prod.fst",
"iff_self",
"PartialEquiv.ext",
"Iff",
"Prod.ext",
"PartialEquiv.prod_symm",
"congr",
"True",
"eq_se... | true |
prod_mk_prod | Mathlib.Algebra.BigOperators.Pi | [
"False",
"Finset.prod_insert",
"HMul.hMul",
"eq_false",
"Monoid.toMulOneClass",
"congrArg",
"and_self",
"Finset",
"Membership.mem",
"MulOne.toMul",
"Insert.insert",
"Prod.mk",
"Finset.induction_on",
"Finset.instEmptyCollection",
"Prod.fst",
"Finset.instInsert",
"Finset.prod",
"MulO... | true |
CategoryTheory.MorphismProperty.IsStableUnderFiniteCoproducts.rec | Mathlib.CategoryTheory.MorphismProperty.Limits | [
"CategoryTheory.MorphismProperty",
"Finite",
"CategoryTheory.MorphismProperty.IsStableUnderFiniteCoproducts",
"CategoryTheory.MorphismProperty.IsStableUnderCoproductsOfShape",
"CategoryTheory.MorphismProperty.IsStableUnderFiniteCoproducts.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.... | false |
_private.Mathlib.Algebra.Lie.Nilpotent.0.LieModule.derivedSeries_le_lowerCentralSeries._simp_1_1 | Mathlib.Algebra.Lie.Nilpotent | [
"LE.le",
"OrderTop",
"LE",
"OrderTop.toTop",
"le_top",
"True",
"eq_true",
"Top.top",
"Eq"
] | false |
FiniteGaloisIntermediateField.instMax._proof_3 | Mathlib.FieldTheory.Galois.GaloisClosure | [
"FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField",
"Lattice.toSemilatticeSup",
"instSMulOfMul",
"FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax",
"FiniteGaloisIntermediateField.instMax._proof_1",
"IntermediateField",
"IntermediateField.toField",
"Algebra... | false |
Int16.le_antisymm | Init.Data.SInt.Lemmas | [
"Iff.mpr",
"Int16.le_antisymm_iff",
"Int16",
"Eq.mp",
"instLEInt16",
"LE.le",
"And",
"Eq",
"and_imp._simp_1"
] | true |
Batteries.RBNode.EMem.eq_1 | Batteries.Data.RBMap.Lemmas | [
"Batteries.RBNode",
"Batteries.RBNode.Any",
"Batteries.RBNode.EMem",
"Eq.refl",
"Eq"
] | true |
ProfiniteAddGrp.Hom.ext | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"ProfiniteAddGrp.Hom",
"_private.Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic.0.ProfiniteAddGrp.Hom.ext.match_1",
"HEq.refl",
"ContinuousAddMonoidHom",
"ProfiniteAddGrp.Hom.hom'",
"_private.Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic.0.ProfiniteAddGrp.Hom.mk",
"Eq.casesOn",
"Profinite... | true |
_private.Mathlib.Data.Stream.Init.0.Stream'.even_interleave.match_1_1 | Mathlib.Data.Stream.Init | [
"Stream'.interleave",
"Exists",
"Stream'.even",
"Stream'",
"Exists.casesOn",
"Exists.intro",
"Eq"
] | false |
CategoryTheory.OverPresheafAux.OverArrows.map₂.congr_simp | Mathlib.CategoryTheory.Comma.Presheaf.Basic | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.OverPresheafAux.OverArrows.map₂",
"CategoryTheory.yoneda",
"Eq.rec",
"CategoryTheory.Functor.map",
"CategoryTheory.OverPresheafAux.OverArrows",
"Catego... | true |
Types.subobjectEquivSet | Mathlib.CategoryTheory.Subobject.Types | [
"CategoryTheory.Over",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Types.monoOverEquivalenceSet",
"OrderIso",
"BiheytingAlgebra.toCoheytingAlgebra",
"CategoryTheory.instCategoryOver",
"CategoryTheory.instPartialOrderSubobject",
"BooleanAlgebra.toBiheytingAlgebra",... | true |
Algebra.basicOpen_subset_etaleLocus_iff_etale | Mathlib.RingTheory.Etale.Locus | [
"Eq.mpr",
"CommRing",
"PrimeSpectrum.basicOpen",
"Algebra.Etale.mk",
"OreLocalization.instAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"instFinitePresentationAway",
"Algebra.FormallyEtale",
"Algebra.etaleLocus",
"Algebra.Etale.formallyEtale",
"Localization.Away",
"Algebra",
"Topologica... | true |
_private.Init.Data.String.Lemmas.Pattern.Char.0.String.Slice.Pattern.Model.Char.revMatchAt?_eq._simp_1_2 | Init.Data.String.Lemmas.Pattern.Char | [
"String.Slice.Pos.prev",
"String.Slice",
"Exists",
"Ne",
"String.Slice.startPos",
"String.Slice.Pattern.Model.Char.instPatternModelChar",
"propext",
"String.Slice.Pattern.Model.Char.isLongestRevMatchAt_iff._proof_1",
"String.Slice.Pos.get",
"String.Slice.Pos",
"Char",
"String.Slice.Pattern.Mod... | false |
groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"Rep.V",
"CommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Module.End.instSemiring",
"LinearMap.inst... | true |
TopCat.pullbackIsoProdSubtype | Mathlib.Topology.Category.TopCat.Limits.Pullbacks | [
"CategoryTheory.Limits.hasFiniteLimits_of_hasLimits",
"CategoryTheory.Limits.pullback",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopCat.pullbackCone",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"ContinuousMap",
"CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso"... | true |
Finset.range_val | Mathlib.Data.Finset.Range | [
"Multiset",
"Finset.val",
"Finset.range",
"Nat",
"Multiset.range",
"Eq",
"rfl"
] | true |
SaturatedAddSubmonoid.rec | Mathlib.Algebra.Group.Submonoid.Saturation | [
"SaturatedAddSubmonoid.mk",
"AddSubmonoid",
"AddZeroClass",
"AddSubmonoid.AddSaturated",
"SaturatedAddSubmonoid"
] | false |
IsLeftCancelVAdd.mk | Mathlib.Algebra.Group.Action.Defs | [
"IsLeftCancelVAdd.mk",
"VAdd",
"HVAdd.hVAdd",
"instHVAdd",
"Eq",
"IsLeftCancelVAdd"
] | true |
AlgebraicIndependent.transcendental_adjoin_iff | Mathlib.RingTheory.AlgebraicIndependent.Transcendental | [
"Subalgebra.instSetLike",
"Nontrivial",
"Eq.mpr",
"CommRing",
"AlgebraicIndependent",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Set.disjoint_singleton_right",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"CommSemiring.toSemiring",
"HEq.refl",
"AlgebraicIndependent.a... | true |
instLocallyConvexSpaceRealOfPolynormableSpace | Mathlib.Analysis.LocallyConvex.WithSeminorms | [
"NormedCommRing.toSeminormedCommRing",
"WithSeminorms.toLocallyConvexSpace",
"Real.partialOrder",
"Real",
"Continuous",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedField.toFiel... | true |
Finset.le_inf_of_directed_le | Mathlib.Data.Finset.Lattice.Fold | [
"Eq.mpr",
"False",
"id.eq_1",
"Finset.mem_insert_self",
"eq_false",
"and_true",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"Preorder.toLE",
"DirectedOn",
"Membership.mem",
"Exists",
"forall_prop_of_false",
"SemilatticeInf.toPartialOrder",
"id",
"Ins... | true |
Turing.PartrecToTM2.contSupp.match_1 | Mathlib.Computability.TuringMachine.ToPartrec | [
"Unit.unit",
"Turing.PartrecToTM2.Cont'",
"Turing.PartrecToTM2.Cont'.cons₂",
"Turing.PartrecToTM2.Cont'.comp",
"Unit",
"Turing.PartrecToTM2.Cont'.casesOn",
"Turing.PartrecToTM2.Cont'.halt",
"Turing.PartrecToTM2.Cont'.fix",
"Turing.PartrecToTM2.Cont'.cons₁",
"Turing.ToPartrec.Code"
] | false |
Lean.Server.ServerRequestResponse.success.sizeOf_spec | Lean.Server.Requests | [
"Lean.Server.ServerRequestResponse._sizeOf_inst",
"instOfNatNat",
"Lean.Server.ServerRequestResponse",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"SizeOf",
"OfNat.ofNat",
"Eq",
"Lean.Server.ServerRequestResponse.success"
] | true |
OrderAddMonoidHom.snd.eq_1 | Mathlib.Algebra.Order.Monoid.Lex | [
"OrderAddMonoidHom.mk",
"Prod.instAddZeroClass",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"PartialOrder",
"AddMonoidHom.snd",
"AddMonoid",
"Prod.instPreorder",
"Eq.refl",
"OrderAddMonoidHom.snd",
"Prod",
"OrderAddMonoidHom",
"Eq",
"OrderAddMonoidHom.snd._proof_1",
"Preorder... | true |
_private.Mathlib.RingTheory.Finiteness.Nilpotent.0.Matrix.isNilpotent_iff_forall_row._simp_1_1 | Mathlib.RingTheory.Finiteness.Nilpotent | [
"CommSemiring.toSemiring",
"Matrix",
"Monoid.toPow",
"CommSemiring",
"Fintype",
"HPow.hPow",
"Matrix.transpose_pow",
"Matrix.transpose",
"Nat",
"Semiring.toMonoid",
"instHPow",
"Matrix.semiring",
"Eq.symm",
"Eq",
"DecidableEq"
] | false |
Fin.succAbove_ne_last_last | Mathlib.Data.Fin.SuccPred | [
"Iff.mpr",
"Fin.succAbove",
"Eq.mpr",
"Fin.succ",
"congrArg",
"Fin.lt_last_iff_ne_last",
"Eq.rec",
"id",
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Fin.last",
"LT.lt",
"instLTFin",
"instAddNat",
"Eq.refl",
"Fin.succAbove_of_lt_succ",
"Fin.succ_last",
"OfNat.ofNat"... | true |
_private.Mathlib.Tactic.Linarith.Preprocessing.0.Mathlib.Tactic.Linarith.filterComparisons.match_1 | Mathlib.Tactic.Linarith.Preprocessing | [
"Unit.unit",
"Mathlib.Ineq",
"Mathlib.Ineq.lt",
"Mathlib.Ineq.casesOn",
"Unit",
"Mathlib.Ineq.eq",
"Mathlib.Ineq.le"
] | false |
_private.Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage.0.Dynamics.dynEntourage_comp_subset._simp_1_3 | Mathlib.Dynamics.TopologicalEntropy.DynamicalEntourage | [
"Set.iInter",
"Membership.mem",
"Set.mem_iInter",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Lean.Data.Json.Basic.0.Lean.Json.hash' | Lean.Data.Json.Basic | [
"Inhabited.default",
"Lean.Json",
"UInt64",
"instInhabitedUInt64"
] | true |
RingQuot.instOne | Mathlib.Algebra.RingQuot | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"One",
"One.mk",
"RingQuot.Rel",
"RingQuot",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"RingQuot.mk",
"Semiring",
"One.toOfNat1",
"OfNat.ofNat",
"Semiring.toNonAssocSemiring",
"Quot.mk"
] | true |
_private.Mathlib.Probability.Kernel.Disintegration.CondCDF.0.ProbabilityTheory.setLIntegral_preCDF_fst._simp_1_1 | Mathlib.Probability.Kernel.Disintegration.CondCDF | [
"propext",
"Nonempty",
"forall_const",
"Eq"
] | false |
CommRingCat.instIsLocalHomCarrierPtWalkingParallelPairEqualizerForkRingHomHomι | Mathlib.Algebra.Category.Ring.Constructions | [
"Units.val",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"CommRingCat.Hom.hom",
"HMul.hMul",
"CommRingCat.carrier",
"Subring.instSetLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"Monoid.toMulOneClass",
"co... | true |
_private.Batteries.Data.List.Basic.0.List.takeWhile₂TR.go.match_1.splitter | Batteries.Data.List.Basic | [
"_private.Batteries.Data.List.Basic.0.List.takeWhile₂TR.go.match_1.splitter._sparseCasesOn_2",
"False",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.cons",
"Bool.true",
"Nat.land",
"List",
"absurd",
"Nat",
"Bool",
"Eq.ndrec",
"Nat.eq_of_beq_eq_true",
"Eq.refl",
"HEq",
"Of... | true |
Finset.lcm_def | Mathlib.Algebra.GCDMonoid.Finset | [
"Multiset.map",
"Finset",
"NormalizedGCDMonoid",
"Finset.val",
"CommMonoidWithZero",
"Finset.lcm",
"Multiset.lcm",
"Eq",
"rfl"
] | true |
_private.Lean.Meta.Tactic.FunInd.0.Lean.Tactic.FunInd.withLetDecls.go._unary | Lean.Meta.Tactic.FunInd | [
"Lean.LocalDeclKind.default",
"Array.push",
"instMonadControlTOfPure",
"Lean.Meta.State",
"InvImage",
"HSub.hSub",
"WellFounded.Nat.fix",
"Lean.Expr",
"Lean.Meta.MetaM",
"PSigma.casesOn",
"IO.RealWorld",
"instSubNat",
"instOfNatNat",
"Applicative.toPure",
"dite",
"Array",
"GetElem.ge... | false |
binomialSeries_radius_eq_one | Mathlib.Analysis.Analytic.Binomial | [
"_private.Mathlib.Analysis.Analytic.Binomial.0.binomialSeries_radius_eq_one._proof_1_2",
"NormedCommRing.toNormedRing",
"IsSemitopologicalRing.toIsTopologicalAddGroup",
"binomialSeries_eq_ordinaryHypergeometricSeries",
"Int.cast",
"Eq.mpr",
"NegZeroClass.toNeg",
"Int.cast_natCast",
"False",
"Algeb... | true |
CategoryTheory.yonedaCommRingObj_map_apply | Mathlib.CategoryTheory.Monoidal.Cartesian.Ring | [
"CategoryTheory.yonedaCommRingObj",
"Opposite",
"CommRingCat.carrier",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"CommRingCat.instConcreteCategoryRingHomCarrier",
"Quiver.Hom.unop",
... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_69 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.instEquivLike",
"_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_68",
"Lean.Grind.Nat.lt_eq",
"Equiv",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"List.cons",
"List.idxOfNth",
"GetElem.getElem",
"List.getElem_filte... | false |
Bool.completeLinearOrder._proof_4 | Mathlib.Data.Fintype.Order | [
"BiheytingAlgebra",
"Lattice.toSemilatticeSup",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"inferInstance",
"GeneralizedHeytingAlgebra.toHImp",
"BiheytingAlgebra.toHeytingAlgebra",
"CompleteDistribLattice.toBiheytingAlgebra",
"SemilatticeInf.toMi... | false |
ULift.seminormedCommRing._proof_10 | Mathlib.Analysis.Normed.Ring.Basic | [
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"SeminormedCommRing",
"NonUnitalNonAssocRing.toMul",
"NonUnitalNonAssocRing.toAddCommGroup",
"ULift",
"AddCommGroup.toAddGroup",
"ULift.nonUnitalSeminormedRing",
"NonUnitalRing.toNonUnitalNonAssocRing",
"instHAdd",
"AddSemigroup.toAdd",
"AddGroup.toSubN... | false |
Lean.Meta.InfoCacheKey.expr | Lean.Meta.Basic | [
"Lean.Meta.InfoCacheKey",
"Lean.Expr"
] | true |
ProbabilityTheory.cauchyPDFReal | Mathlib.Probability.Distributions.Cauchy | [
"Real",
"Real.pi",
"HMul.hMul",
"Real.instInv",
"Real.instSub",
"HSub.hSub",
"NNReal",
"instOfNatNat",
"Monoid.toPow",
"Real.instAdd",
"Real.instMonoid",
"instHAdd",
"instHSub",
"Inv.inv",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"Real.instMul",
"instHPow",
"OfNat.ofNat",
"NNReal.toR... | true |
Choose.choose_modEq_choose_mod_mul_choose_div_nat | Mathlib.Data.Nat.Choose.Lucas | [
"Nat.cast_mul._simp_1",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.Prime",
"Nat.choose",
"instHDiv",
"HMul.hMul",
"congrArg",
"Int.natCast_modEq_iff",
"cast",
"Fact",
"Int.natCast_modEq_iff._simp_1",
"id",
"HDiv.hDiv",
"Nat.instMod",
"instHMod",
"AddMonoidWithOne.toNat... | true |
_private.Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity.0.MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul'._simp_1_1 | Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity | [
"ENNReal.rpow_mul",
"Real",
"HMul.hMul",
"ENNReal.instPowReal",
"HPow.hPow",
"Real.instMul",
"ENNReal",
"instHPow",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Algebra.norm_one_add_smul | Mathlib.RingTheory.NormTrace | [
"Eq.mpr",
"Polynomial.C",
"Polynomial.eval",
"Matrix.smul",
"Polynomial.instOne",
"Algebra.norm_eq_matrix_det",
"CommRing",
"instHSMul",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Matrix.add",
"Semiring.toModule",
"instSMulOfMul",
"SemilinearMapClass.toMulAc... | true |
_private.Mathlib.NumberTheory.SmoothNumbers.0.Nat.smoothNumbersUpTo_subset_image._simp_1_1 | Mathlib.NumberTheory.SmoothNumbers | [
"Finset",
"Membership.mem",
"Finset.mem_range",
"Finset.range",
"Finset.instSetLike",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Eq",
"SetLike.instMembership"
] | false |
RootPairing.pairing_smul_root_eq | Mathlib.LinearAlgebra.RootSystem.Defs | [
"RootPairing.pairing",
"CommRing",
"instHSMul",
"Equiv.instEquivLike",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"_private.Mathlib.LinearAlgebra.RootSystem.Defs.0.RootPairing.pairing_smul_root_eq._simp_1_1",
"AddMonoid.toAddZeroClass",... | true |
ContDiffWithinAt.comp_contMDiffWithinAt | Mathlib.Geometry.Manifold.ContMDiff.NormedSpace | [
"ContDiffWithinAt.contMDiffWithinAt",
"chartedSpaceSelf",
"ContMDiffWithinAt",
"NormedSpace",
"PseudoMetricSpace.toUniformSpace",
"Function.comp",
"HasSubset.Subset",
"TopologicalSpace",
"ModelWithCorners",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Set.preimage",
"ENat",
"NontriviallyNo... | true |
List.prefix_nil | Init.Data.List.Sublist | [
"Eq.rec",
"List.sublist_nil",
"List",
"Iff",
"List.IsPrefix",
"List.prefix_rfl",
"Iff.intro",
"Iff.mp",
"List.Sublist",
"List.IsPrefix.sublist",
"Eq",
"List.nil"
] | true |
ChartedSpaceCore.open_target | Mathlib.Geometry.Manifold.ChartedSpace | [
"Set.Subset.antisymm",
"congrArg",
"PartialEquiv.target",
"PartialEquiv",
"PartialEquiv.trans",
"Membership.mem",
"PartialEquiv.symm",
"Eq.mp",
"Set.inter_subset_left",
"PartialEquiv.target_subset_preimage_source",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"Set.preimage",
"And.... | true |
Lean.Compiler.compiler.traceUnnormalized | Lean.Compiler.Options | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
CircularOrder.recOn | Mathlib.Order.Circular | [
"CircularPartialOrder.toCircularPreorder",
"CircularPreorder.toBtw",
"CircularOrder.rec",
"CircularPartialOrder",
"Btw.btw",
"Or",
"CircularOrder.mk",
"CircularOrder"
] | false |
CategoryTheory.ObjectProperty.whiskerLeft_def | Mathlib.CategoryTheory.Monoidal.Subcategory | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.ObjectProperty.instMonoidalCategoryStru... | true |
Std.Internal.List.getEntry?_filter_containsKey_of_containsKey_eq_false_left | Std.Data.Internal.List.Associative | [
"Iff.mpr",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Decidable.casesOn",
"congrArg",
"Decidable",
"id",
"instDecidableEqBool",
"Sigma.fst",
"if_pos",
"Bool.true",
"Std.Internal.List.getEntry?_eq_none",
"Option.none",
"List",
"Std.Internal.List.containsKey",
"EquivBEq",
"Std.Intern... | true |
CategoryTheory.Triangulated.TStructure.instIsLEObjTruncGT | Mathlib.CategoryTheory.Triangulated.TStructure.TruncLEGT | [
"CategoryTheory.Triangulated.TStructure.truncGT",
"CategoryTheory.Triangulated.TStructure.truncGE",
"CategoryTheory.Triangulated.TStructure.IsLE",
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"inferInstance",
"CategoryTheory.IsTriangulated",
"id",
"Int",
"Int.instAddMonoid",
... | true |
_private.Mathlib.Order.Filter.AtTopBot.BigOperators.0.Function.Injective.map_atTop_finsetProd_eq._simp_1_1 | Mathlib.Order.Filter.AtTopBot.BigOperators | [
"Finset.instUnion",
"Finset",
"Membership.mem",
"Finset.instSetLike",
"propext",
"Finset.mem_union",
"Or",
"Union.union",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | false |
IntermediateField.gi._proof_2 | Mathlib.FieldTheory.IntermediateField.Adjoin.Defs | [
"IntermediateField.instPartialOrder",
"le_rfl",
"ChainCompletePartialOrder.instOfCompleteLattice",
"IntermediateField",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"LE.le",
"ChainCompletePartialOrder.toPartialOrder",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"SetLike.coe"... | false |
_private.Lean.Meta.Tactic.Grind.EMatchAction.0.Lean.Meta.Grind.Action.CollectState.visited | Lean.Meta.Tactic.Grind.EMatchAction | [
"Std.HashSet",
"Lean.Meta.Sym.instHashableExprPtr",
"_private.Lean.Meta.Tactic.Grind.EMatchAction.0.Lean.Meta.Grind.Action.CollectState",
"Lean.Meta.Sym.ExprPtr",
"Lean.Meta.Sym.instBEqExprPtr"
] | true |
NumberField.of_tower | Mathlib.NumberTheory.NumberField.Basic | [
"instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors",
"NumberField.instFiniteDimensional",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"Module.Finite.left",
"IsPrincipalIdealRing.isDedekindDomain",
"Algebra",
"DivisionSemiring.toGroupWithZero",
"Algebra.toSMul",
"Field.toDivisionRing",
"Field.... | true |
exists_lt_of_lt_csSup' | Mathlib.Order.ConditionallyCompleteLattice.Basic | [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Eq.mpr",
"csSup_le'",
"Mathlib.Tactic.Push.not_and_eq",
"Preorder.toLT",
"ConditionallyCompleteLinearOrderBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"id",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyC... | true |
Ordnode.splitMin_eq | Mathlib.Data.Ordmap.Invariants | [
"Ordnode.eraseMin",
"Ordnode",
"Ordnode.splitMin'",
"Prod.mk",
"Ordnode.node",
"Ordnode.splitMin_eq._f",
"Nat",
"Ordnode.brecOn",
"Ordnode.findMin'",
"Prod",
"Eq"
] | true |
ContinuousMap.setOfIdeal_open | Mathlib.Topology.ContinuousMap.Ideals | [
"Eq.mpr",
"Semiring.toModule",
"congrArg",
"IsTopologicalSemiring",
"Set.iInter",
"Compl.compl",
"ContinuousMap",
"continuous_const",
"setOf",
"Membership.mem",
"ContinuousMap.instContinuousMapClass",
"id",
"ContinuousMap.instSemiringOfIsTopologicalSemiring",
"Ideal",
"Set.instCompl",
... | true |
Lean.Compiler.LCNF.LambdaLifting.State.mk.noConfusion | Lean.Compiler.LCNF.LambdaLifting | [
"Lean.Compiler.LCNF.LambdaLifting.State.noConfusion",
"Lean.Compiler.LCNF.LambdaLifting.State",
"Lean.Compiler.LCNF.Decl",
"id",
"Lean.Compiler.LCNF.Purity.pure",
"Array",
"Nat",
"Lean.Compiler.LCNF.LambdaLifting.State.mk",
"Eq"
] | false |
Ultrafilter.mem_pure._simp_1 | Mathlib.Order.Filter.Ultrafilter.Defs | [
"Pure.pure",
"Ultrafilter.mem_pure",
"Membership.mem",
"Ultrafilter.instPure",
"propext",
"Ultrafilter.instMembershipSet",
"Ultrafilter",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Std.Data.DHashMap.Internal.RawLemmas.0.Std.DHashMap.Internal.Raw₀.Const.find?_toArray_eq_none_iff_contains_eq_false._simp_1_2 | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.Const.toList",
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Raw",
"List.find?",
"instOfNatNat",
"LawfulHashable",
"Prod.fst",
"Std.DHashMap.Internal.Raw₀.Const.find?_toList_eq_none_iff_contains_eq_false",
"Option.none",
"BEq.beq",
"EquivBEq",
... | false |
εNFA.toNFA_evalFrom_match | Mathlib.Computability.EpsilonNFA | [
"εNFA.toNFA",
"NFA.evalFrom",
"List",
"εNFA.evalFrom",
"Eq",
"εNFA",
"rfl",
"εNFA.εClosure",
"Set"
] | true |
CategoryTheory.Adjunction.counit | Mathlib.CategoryTheory.Adjunction.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Adjunction",
"CategoryTheory.Category"
] | true |
CategoryTheory.exactPairingUnit | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | [
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.exactPairingUnit._proof_2",
"CategoryTheory.ExactPairing",
"CategoryTheory.ExactPairing.mk",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.MonoidalCategoryStruct.tensorUnit",
"C... | true |
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Cpop.0.Std.Tactic.BVDecide.BVExpr.bitblast.denote_blastCpopLayer.go._proof_1_2 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Cpop | [
"Lean.Omega.LinearCombo.coordinate_eval_6",
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"instHDiv",
"HMul.hMul",
"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",
"L... | false |
Std.DTreeMap.Raw.get?_inter_of_not_mem_left | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.get?",
"Std.DTreeMap.Raw.instMembership",
"congrArg",
"Ord.mk",
"Membership.mem",
"Ordering",
"Eq.mp",
"id",
"Std.DTreeMap.Raw.contains_eq_false_iff_not_mem",
"Std.TransCmp",
"Inter.inter",
"Std.DTreeMap.Raw.instInter",
"Option.none",
"Std.DTreeMap.Raw.WF.out",
"Std.Law... | true |
AlgebraicGeometry.QuasiCompact | Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Category.toCategoryStruct",
"AlgebraicGeometry.Scheme.instCategory",
"AlgebraicGeometry.QuasiCompact.mk"
] | true |
segment_translate_image | Mathlib.Analysis.Convex.Segment | [
"segment_translate_preimage",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"AddRightMono",
"Eq.rec",
"AddZeroClass.toAddZero",
"PartialOrder",
"AddCommGroup",
"Distrib.toAd... | true |
_private.Mathlib.FieldTheory.Minpoly.ConjRootClass.0.ConjRootClass.instFintypeElemCarrierOfNormalOfDecidableEqOfAlgEquiv._simp_2 | Mathlib.FieldTheory.Minpoly.ConjRootClass | [
"Algebra",
"Field.toDivisionRing",
"IsConjRoot",
"DivisionRing.toRing",
"ConjRootClass",
"Field.toSemifield",
"Field.toCommRing",
"Semifield.toDivisionSemiring",
"propext",
"DivisionSemiring.toSemiring",
"ConjRootClass.mk",
"Semifield.toCommSemiring",
"Eq.symm",
"Eq",
"Field",
"ConjRoo... | false |
Prod.mk_left_inj | Mathlib.Data.Prod.Basic | [
"Function.Injective.eq_iff",
"Prod.mk",
"Prod.mk_left_injective",
"Iff",
"Prod",
"Eq"
] | true |
Algebra.adjoin_nonUnitalSubalgebra_eq_span | Mathlib.RingTheory.Adjoin.Basic | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"MulOne.toOne",
"Algebra.to_smulCommClass",
"Lattice.toSemilatticeSup",
"NonUnitalSubalgebra",
"IsScalarTower.right",
"congrArg",
"CommSemiring.toSemiring",
"Submodule.completeLattice",
"NonUnitalSubalgebra.toSubmodule",
"Part... | true |
AddSubgroup.opEquiv | Mathlib.Algebra.Group.Subgroup.MulOpposite | [
"AddSubgroup.unop",
"RelIso.mk",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"Equiv.mk",
"AddSubgroup.op_le_op_iff",
"AddOpposite",
"OrderIso",
"LE.le",
"AddSubgroup.op_unop",
"AddSubgroup",
"AddSubgroup.op",
"AddGroup",
"AddOpposite.instAddGroup",
"AddS... | true |
Graph.mem_loopSet | Mathlib.Combinatorics.Graph.Basic | [
"Graph.IsLoopAt",
"Iff.rfl",
"Membership.mem",
"Graph",
"Iff",
"Graph.loopSet",
"Set.instMembership",
"Set"
] | true |
analyticOrderAt_neg | Mathlib.Analysis.Analytic.Order | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"SubtractionMonoid.toInvolutiveNeg",
"instHSMul",
"Pi.instNeg",
"NormedRing.toRing",
"Equiv.instEquivLike",
"NormedSpace",
"ENat.instNatCast",
"P... | true |
Lean.Elab.HoverableInfoPrio.size | Lean.Server.InfoUtils | [
"Lean.Elab.HoverableInfoPrio",
"Nat"
] | true |
Lean.Parser.Term.let._regBuiltin.Lean.Parser.Term.let_1 | Lean.Parser.Term | [
"Lean.Parser.Term.let",
"IO",
"Unit",
"Lean.Parser.addBuiltinLeadingParser",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | false |
SmoothBumpCovering.apply_ind | Mathlib.Geometry.Manifold.PartitionOfUnity | [
"SmoothBumpCovering",
"Real",
"NormedSpace",
"SmoothBumpCovering.c",
"Real.denselyNormedField",
"Filter.EventuallyEq.eq_of_nhds",
"NormedSpace.toModule",
"Membership.mem",
"SmoothBumpCovering.eventuallyEq_one",
"Real.instOne",
"SmoothBumpFunction.toFun",
"TopologicalSpace",
"ModelWithCorners... | true |
Mathlib.Tactic.DeprecateTo.renameTheorem | Mathlib.Tactic.DeprecateTo | [
"Pure.pure",
"cond",
"Lean.mkNullNode",
"Lean.TSyntax",
"Inhabited.default",
"Lean.Unhygienic.run",
"Lean.mkNode",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.identKind",
"Lean.Unhygienic",
"Lean.SourceInfo",
"Lean.Syntax.isOfKind",
"Lean.instInhabitedTSyntax",
"Lean.Syntax.atom",
"Lean.TSyn... | true |
AlgebraicGeometry.Scheme.IdealSheafData.mk.inj | Mathlib.AlgebraicGeometry.IdealSheaf.Basic | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"CommRingCat.Hom.hom",
"Semiring.toModule",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"TopologicalSpace.Opens.instPartialOr... | true |
Unitary.linearIsometryEquiv_coe_apply | Mathlib.Analysis.InnerProductSpace.Adjoint | [
"InnerProductSpace.toNormedSpace",
"MulEquiv.instEquivLike",
"LinearIsometryEquiv.instGroup",
"CompleteSpace",
"ContinuousLinearMap.semiring",
"Submonoid.mul",
"Unitary.coe_linearIsometryEquiv_apply",
"Monoid.toMulOneClass",
"AddCommGroup.toAddCommMonoid",
"unitary",
"NormedSpace.toModule",
"P... | true |
MeasureTheory.charFun_map_smul | Mathlib.MeasureTheory.Measure.CharacteristicFunction.Basic | [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Continuous.comp_aestronglyMeasurable",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddCommGroup",
"NormedSpace.to... | true |
SSet.S.subcomplex | Mathlib.AlgebraicTopology.SimplicialSet.Simplices | [
"SSet.S.simplex",
"SSet.S",
"SSet.Subcomplex.ofSimplex",
"SSet",
"SSet.S.dim",
"SSet.Subcomplex"
] | true |
Lean.Elab.OptionInfo.noConfusion | Lean.Elab.InfoTree.Types | [
"Lean.Elab.OptionInfo.casesOn",
"Lean.Elab.OptionInfo",
"Lean.Syntax",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq",
"Lean.Elab.OptionInfo.noConfusionType"
] | false |
LowerSet.instMulAction._proof_1 | Mathlib.Algebra.Order.UpperLower | [
"Preorder.toLE",
"SetLike.coe_injective",
"SetLike.coe",
"Function.Injective",
"LowerSet",
"Preorder",
"Set",
"LowerSet.instSetLike"
] | false |
Cardinal.continuum_le_lift._simp_1 | Mathlib.SetTheory.Cardinal.Continuum | [
"Cardinal",
"Cardinal.lift",
"LE.le",
"Cardinal.instLE",
"Cardinal.continuum",
"Cardinal.continuum_le_lift",
"propext",
"Eq"
] | false |
_private.Mathlib.Algebra.Homology.Embedding.Connect.0.CochainComplex.ConnectData.d.match_1.eq_4 | Mathlib.Algebra.Homology.Embedding.Connect | [
"Int.ofNat",
"instOfNatNat",
"Int",
"Unit",
"CochainComplex.ConnectData.d.match_1",
"Nat",
"Eq.refl",
"Int.negSucc",
"OfNat.ofNat",
"Eq"
] | true |
IsUnit.mul | Mathlib.Algebra.Group.Units.Defs | [
"Monoid",
"Units.val",
"HMul.hMul",
"Monoid.toMulOneClass",
"IsUnit",
"Units",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Exists.casesOn",
"Exists.intro",
"Eq.ndrec",
"Units.instMul",
"Eq",
"rfl",
"instHMul"
] | true |
AddHom.prod_map_comap_prod' | Mathlib.Algebra.Group.Subsemigroup.Operations | [
"AddSubsemigroup.instSetLike",
"Prod.instAdd",
"AddHom",
"AddSubsemigroup.comap",
"AddHom.funLike",
"SetLike.coe_injective",
"Set.preimage_prod_map_prod",
"AddHom.prodMap",
"SetLike.coe",
"AddSubsemigroup",
"AddSubsemigroup.prod",
"Prod",
"Eq",
"DFunLike.coe",
"Add"
] | true |
Lean.Lsp.CompletionItem.getFileSource! | Lean.Server.FileSource | [
"Lean.Json.getArrVal?",
"Lean.Json",
"instMonadExceptOfExcept",
"Lean.instFromJsonString",
"instMonadExceptOfMonadExceptOf",
"String",
"MonadExcept.throw",
"panicWithPosWithDecl",
"Lean.FromJson.fromJson?",
"Lean.Json.getObjValAs?",
"instOfNatNat",
"ToString.toString",
"Except.instMonad",
... | true |
ProbabilityTheory.IndepFun.eq_1 | Mathlib.Probability.Independence.Basic | [
"Unit.unit",
"MeasureTheory.Measure",
"MeasureTheory.Measure.dirac",
"ProbabilityTheory.Kernel.IndepFun",
"MeasurableSpace",
"Unit",
"PUnit.instMeasurableSpace",
"Eq.refl",
"ProbabilityTheory.IndepFun",
"ProbabilityTheory.Kernel.const",
"Eq"
] | true |
Finset.unop_sum | Mathlib.Algebra.BigOperators.Group.Finset.Defs | [
"AddEquivClass.instAddMonoidHomClass",
"Finset",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"MulOpposite.opAddEquiv",
"map_sum",
"AddCommMonoid",
"MulOpposite.instAddCommMonoid",
"MulOpposite.instAdd",
"AddEquiv.instAddEquivClass",
"AddEquiv",
"MulOpposite.unop",
"AddCommMonoid.toAddMonoid",... | true |
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