name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Expr.lam._impl | Lean.Expr | [
"Lean.Expr",
"Lean.Expr.Data",
"Lean.Expr._impl",
"Lean.Name",
"Lean.Expr.lam._impl",
"Lean.BinderInfo"
] | false |
MulEquiv.monoidHomCongrLeft_apply | Mathlib.Algebra.Group.Equiv.Basic | [
"MulEquiv.instEquivLike",
"MonoidHom",
"Monoid.toMulOneClass",
"MulEquiv.instMulEquivClass",
"MulOne.toMul",
"MonoidHomClass.toMonoidHom",
"MonoidHom.comp",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"MulEquivClass.instMonoidHomClass",
"MulEquiv",
"Eq.refl",
"MonoidHom.mul",
"MulOneCla... | true |
CategoryTheory.Limits.pushoutIsPushoutOfEpiComp._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Mono | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.pushout.condition",
"id",
"congr",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Limits.pushout",
"CategoryTheory.Cat... | false |
_private.Init.Data.Vector.Attach.0.Vector.pmap_eq_map_attach._simp_1_1 | Init.Data.Vector.Attach | [
"Vector",
"Vector.eq_mk",
"Array",
"Vector.mk",
"Nat",
"propext",
"Eq",
"Array.size",
"Vector.toArray"
] | false |
CategoryTheory.Endofunctor.Coalgebra.Hom.ext | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"_private.Mathlib.CategoryTheory.Endofunctor.Algebra.0.CategoryTheory.Endofunctor.Coalgebra.Hom.ext.match_1",
"CategoryTheory.Endofunctor.Coalgebra.str",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"Eq.casesOn",
"CategoryTheory.Endofunctor.Coalgebra.Ho... | true |
CategoryTheory.Functor.whiskerLeft_comp | Mathlib.CategoryTheory.Whiskering | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.whiskerLeft",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"rfl",
"CategoryTheory... | true |
_private.Mathlib.Combinatorics.Matroid.Circuit.0.Matroid.fundCircuit_eq_of_mem._simp_1_1 | Mathlib.Combinatorics.Matroid.Circuit | [
"Std.Antisymm",
"HasSubset.Subset",
"Std.Refl",
"And",
"subset_antisymm_iff",
"propext",
"HasSubset",
"Eq"
] | false |
PiTensorProduct.liftEquiv._proof_1 | Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm | [
"PiTensorProduct.instModule",
"NormedCommRing.toNormedRing",
"Norm.norm",
"PiTensorProduct.instSeminormedAddCommGroup",
"LinearMap.mkContinuous.congr_simp",
"Real.instLE",
"Real",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"HMul.hMul",
"NormedSpace",
"congrArg",
"MultilinearMap.instAdd",... | false |
_private.Lean.Server.Completion.CompletionCollectors.0.Lean.Server.Completion.State.mk.inj | Lean.Server.Completion.CompletionCollectors | [
"_private.Lean.Server.Completion.CompletionCollectors.0.Lean.Server.Completion.State",
"_private.Lean.Server.Completion.CompletionCollectors.0.Lean.Server.Completion.State.mk",
"Array",
"_private.Lean.Server.Completion.CompletionCollectors.0.Lean.Server.Completion.State.mk.noConfusion",
"Lean.Lsp.Resolvable... | true |
_private.Init.GrindInstances.Ring.UInt.0.Lean.Grind.instIsCharPUSizeHPowNatOfNatNumBits._simp_1 | Init.GrindInstances.Ring.UInt | [
"instPowNat",
"USize.ofNat_eq_iff_mod_eq_toNat",
"USize.ofNat",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"instNatPowNat",
"System.Platform.numBits",
"HMod.hMod",
"HPow.hPow",
"USize.toNat",
"Nat",
"propext",
"instHPow",
"OfNat.ofNat",
"Eq",
"USize"
] | false |
Topology.IsInducing.image_vietoris | Mathlib.Topology.Sets.VietorisTopology | [
"Set.ext",
"Set.image_image",
"Eq.mpr",
"Topology.IsInducing.isOpen_iff",
"_private.Mathlib.Topology.Sets.VietorisTopology.0.Topology.IsInducing.image_vietoris._simp_1_3",
"congrArg",
"TopologicalSpace.vietoris",
"setOf",
"Set.powerset",
"Membership.mem",
"Set.instUnion",
"id",
"HasSubset.Su... | true |
MeasureTheory.integrable_norm_pow_of_le | Mathlib.MeasureTheory.Function.L1Space.Integrable | [
"Real.instIsOrderedRing",
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.instPow",
"Real.partialOrder",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"Real.instRCLike",
"Real.instZeroLEOneClass",
"congrArg",
"Nat.cast_nonneg... | true |
le_inv_of_neg | Mathlib.Algebra.Order.Field.Basic | [
"Iff.mpr",
"Eq.mpr",
"Preorder.toLT",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"inv_le_inv_of_neg",
"congrArg",
"inv_lt_zero'",
"Iff.rfl",
"InvolutiveInv.toInv",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"DivisionMonoid.toDivInvOneMon... | true |
_private.Lean.Meta.IndPredBelow.0.Lean.Meta.IndPredBelow.Context.mk | Lean.Meta.IndPredBelow | [
"Lean.FVarIdMap",
"Lean.Expr",
"Array",
"List",
"Nat",
"Bool",
"_private.Lean.Meta.IndPredBelow.0.Lean.Meta.IndPredBelow.Context.mk",
"Lean.Name",
"_private.Lean.Meta.IndPredBelow.0.Lean.Meta.IndPredBelow.Context"
] | true |
ContinuousLinearEquiv.instIsManifoldtransContinuousLinearEquiv | Mathlib.Geometry.Manifold.Diffeomorph | [
"subset_refl._simp_1",
"ContDiff.comp_contDiffOn",
"Set.range_comp",
"ContinuousLinearEquiv.symm",
"ContinuousLinearEquiv.toDiffeomorph._proof_1",
"NormedSpace",
"ContDiff.contDiffOn",
"ContDiffOn.comp",
"contDiffGroupoid",
"congrArg",
"ContinuousLinearEquiv.toLinearEquiv",
"AddCommGroup.toAdd... | true |
_private.Lean.Meta.IndPredBelow.0.Lean.Meta.IndPredBelow.toImplicit._proof_2 | Lean.Meta.IndPredBelow | [
"Lean.RArray.leaf",
"invImage",
"Nat.Linear.ExprCnstr.eq_true_of_isValid",
"Lean.RArray.branch",
"namedPattern",
"Lean.Expr",
"id",
"Lean.BinderInfo._sizeOf_inst",
"instOfNatNat",
"LE.le",
"sizeOfWFRel",
"instLENat",
"Nat.Linear.Expr.num",
"Lean.Expr.forallE",
"Bool.true",
"instHAdd",
... | false |
Lean.Meta.Cases.Context.rec | Lean.Meta.Tactic.Cases | [
"Lean.Meta.Cases.Context",
"Lean.Meta.Cases.Context.mk",
"Lean.Expr",
"Array",
"Nat",
"Lean.LocalDecl",
"Lean.InductiveVal"
] | false |
Std.Stream.take | Batteries.Data.Stream | [
"Std.Stream.take._f",
"Nat.brecOn",
"List",
"Nat",
"Prod",
"Std.Stream"
] | true |
Matrix.of_mem_specialOrthogonalGroup_fin_two_iff._simp_1 | Mathlib.LinearAlgebra.UnitaryGroup | [
"NegZeroClass.toNeg",
"CommRing",
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"Matrix",
"Matrix.of",
"instDecidableEqFin",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"Equiv",
"Distrib.toAdd",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatNat",
"SubNegZeroMonoid.toNeg... | false |
sub_mem_pNilradical_iff_pow_expChar_pow_eq | Mathlib.FieldTheory.IsPerfectClosure | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"CommRing",
"Semiring.toModule",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"_private.Mathlib.FieldTheory.IsPerfectClosure.0.sub_mem_pNilradical_iff_pow_expChar_pow_eq._simp_1_1",
"AddGroupWithOne.toAddMonoidWith... | true |
_private.Lean.DocString.Types.0.Lean.Doc.instOrdBlock.ord.match_1 | Lean.DocString.Types | [
"Lean.Doc.Block.blockquote",
"String",
"Lean.Doc.Block",
"Lean.Doc.Block.concat",
"Lean.Doc.Block.casesOn",
"Nat.hasNotBit",
"Lean.Doc.DescItem",
"Int",
"Lean.Doc.Block.dl",
"Lean.Doc.Block.ul",
"Array",
"Lean.Doc.Block.ol",
"Lean.Doc.Block.code",
"Lean.Doc.Block.para",
"Lean.Doc.Block.c... | false |
CategoryTheory.SimplicialObject.Augmented.whiskering_obj | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.SimplicialObject.Augmented.whiskering",
"CategoryTheory.Functor.category",
"CategoryTheory.SimplicialObject.Augmented.whiskeringObj",
"Eq.refl",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category",
"CategoryTheory.SimplicialObject.Augmented",
"Ca... | true |
_private.Init.Data.List.Pairwise.0.List.pairwise_append_comm._simp_1_2 | Init.Data.List.Pairwise | [
"and_left_comm",
"And",
"propext",
"Eq"
] | false |
_private.Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno.0.OrderedFinpartition.extend.match_1.eq_2 | Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | [
"Option.some",
"OrderedFinpartition",
"Option.none",
"Unit",
"Nat",
"Eq.refl",
"OrderedFinpartition.extend.match_1",
"Fin",
"Eq",
"OrderedFinpartition.length",
"Option"
] | true |
String.Slice.endsWith_slice_iff._simp_1 | Init.Data.String.Lemmas.Pattern.TakeDrop.String | [
"String.Slice.Pattern.BackwardSliceSearcher.instBackwardPattern",
"String.Slice",
"String.Slice.endsWith_slice_iff",
"Bool.true",
"String.Slice.copy",
"String.toList",
"propext",
"List.IsSuffix",
"Bool",
"Char",
"String.Slice.endsWith",
"Eq"
] | false |
ChainClosure.casesOn | Mathlib.Order.CompleteLattice.Chain | [
"ChainClosure.rec",
"Set.sUnion",
"Membership.mem",
"SuccChain",
"ChainClosure.union",
"ChainClosure",
"Set.instMembership",
"ChainClosure.succ",
"Set"
] | false |
_private.Init.Data.Vector.Algebra.0.Vector.add_zero._proof_1_2 | Init.Data.Vector.Algebra | [
"False",
"Vector.getElem_add",
"Vector.instZero",
"Lean.Grind.nestedProof",
"eq_false",
"Vector",
"congrArg",
"Vector.instGetElemNatLt",
"Classical.byContradiction",
"Lean.Grind.Nat.lt_eq",
"Exists",
"Eq.mp",
"id",
"Vector.ext",
"Lean.Grind.forall_imp_eq_or",
"instOfNatNat",
"LE.le",... | false |
UnitAddTorus.hasSum_prod_mFourierCoeff | Mathlib.Analysis.Fourier.AddCircleMulti | [
"instInnerProductSpaceRealComplex",
"LinearIsometryEquiv.instEquivLike",
"HasSum.congr_fun",
"NormedCommRing.toNormedRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.to... | true |
_private.Mathlib.Tactic.Abel.0.Mathlib.Tactic.Abel.eval.match_1 | Mathlib.Tactic.Abel | [
"of_decide_eq_true",
"String",
"_private.Mathlib.Tactic.Abel.0.Mathlib.Tactic.Abel.eval._sparseCasesOn_2",
"Lean.Expr.const",
"Array.getLit",
"Lean.Expr",
"id",
"Nat.hasNotBit",
"Prod.mk",
"instOfNatNat",
"Lean.Level",
"Lean.Literal",
"Lean.Name.ctorIdx",
"dite",
"Lean.Name.str",
"List... | false |
MeasureTheory.OuterMeasure.noConfusionType | Mathlib.MeasureTheory.OuterMeasure.Defs | [
"Function.onFun",
"ENNReal.instAddCommMonoid",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Disjoint",
"CompleteLattice.toConditionallyCompleteLattice",
"MeasureTheory.OuterMeasure",
"HasSubset.Subset",
"LE.le",
"tsum",
"Nat",
"ENNReal.instLE",
"Pairwise",
"ENNReal",
"CompleteDistri... | false |
CategoryTheory.SimplicialObject.cechNerve_obj | Mathlib.AlgebraicTopology.CechNerve | [
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"instOfNatNat",
"CategoryTheory.instCategoryArrow",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SimplexCategory",
"instAddNat",
"CategoryTheory.Category.opposite",
"CategoryTheory.Limits.HasWidePullb... | true |
Set.setOf_or | Mathlib.Data.Set.Basic | [
"setOf",
"Set.instUnion",
"Or",
"Union.union",
"Eq",
"rfl",
"Set"
] | true |
_private.Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar.0.MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_aux._simp_1_4 | Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | [
"not_le",
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"LT.lt",
"propext",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
_private.Mathlib.CategoryTheory.Sites.DenseSubsite.Basic.0.CategoryTheory.Functor.IsCoverDense.Types.pushforwardFamily_compatible._simp_1_2 | Mathlib.CategoryTheory.Sites.DenseSubsite.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.map_comp_apply",
"CategoryTheory.Functor.map",
"CategoryTheory.ConcreteCategory",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategory... | false |
Unitization.addEquiv._proof_1 | Mathlib.Algebra.Algebra.Unitization | [
"Unitization.equiv",
"Equiv.toFun",
"Unitization.instAdd",
"instHAdd",
"HAdd.hAdd",
"Unitization",
"Prod",
"Eq",
"Add",
"rfl"
] | false |
NumberField.mixedEmbedding.convexBodySum_volume | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | [
"instWeaklyLocallyCompactSpaceOfLocallyCompactSpace",
"instInnerProductSpaceRealComplex",
"Iff.mpr",
"IsModuleTopology.toContinuousSMul",
"NormedCommRing.toNormedRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real.instIsOrderedRing",
"Norm.norm",
"Eq.mpr",
"Pi.Function.module... | true |
ModuleCat.MonoidalCategory.braiding_hom_apply | Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric | [
"CommRing",
"ModuleCat",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"ModuleCat.instConcreteCategoryLinearMapIdCarrier",
"LinearMap",
"ModuleCat.monoidalCategory",
"ModuleCat.MonoidalCategory.instBraidedCategory",
"CommRing.toCommSemiring",
"Mo... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Arith.Cutsat.SupportedTermKind.toNat.elim | Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr | [
"PULift.up",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Arith.Cutsat.SupportedTermKind.toNat",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Arith.Cutsat.SupportedTermKind.ctorIdx",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.A... | false |
Std.Time.Month.instLEQuarter | Std.Time.Date.Unit.Month | [
"Std.Time.Month.Quarter",
"LE",
"LE.mk",
"Std.Time.Month.instLEQuarter._aux_1"
] | true |
Topology.ContinuousMapGeneratedBy.id_apply | Mathlib.Topology.Convenient.ContinuousMapGeneratedBy | [
"id",
"TopologicalSpace",
"Eq.refl",
"Topology.ContinuousMapGeneratedBy",
"Topology.ContinuousMapGeneratedBy.id",
"Eq",
"DFunLike.coe",
"Topology.instFunLikeContinuousMapGeneratedBy"
] | true |
WeierstrassCurve.Jacobian.addX_of_Z_eq_zero_left | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"Mathlib.Tactic.Ring.Common.mul_congr",
"HMul.hMul",
"Mathlib.Tactic.Ring.Common.const_pos",
"Nat.rawCast",
"Mathlib.Tactic.Ring.Common.single_pow",
"... | true |
ProfiniteGrp.limitConeIsLimit._proof_3 | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"ProfiniteGrp.group",
"ProfiniteGrp.topologicalGroup",
"ProfiniteGrp",
"CategoryTheory.SmallCategory",
"TotallyDisconnectedSpace",
"TopCat.str",
"TopCat.carrier",
"IsTopologicalGroup",
"ProfiniteGrp.toProfinite",
"TopCat",
"CompHausLike... | false |
_private.Mathlib.NumberTheory.Multiplicity.0.odd_sq_dvd_geom_sum₂_sub._simp_1_10 | Mathlib.NumberTheory.Multiplicity | [
"IsRightCancelAdd",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"AddMonoid",
"add_eq_right",
"propext",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
mul_lt_of_lt_one_right | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"MulOne.toOne",
"Preorder.toLT",
"HMul.hMul",
"congrArg",
"mul_lt_mul_of_pos_left",
"Eq.mp",
"MulOne.toMul",
"MulOneClass.toMulOne",
"LT.lt",
"PosMulStrictMono",
"One.toOfNat1",
"Zero.toOfNat0",
"mul_one",
"MulOneClass",
"OfNat.ofNat",
"Preorder",
"instHMul",
"Zero"
] | true |
_private.Std.Data.Iterators.Lemmas.Producers.Monadic.List.0.Std.Types.ListIterator.stepAsHetT_iterM._simp_1_5 | Std.Data.Iterators.Lemmas.Producers.Monadic.List | [
"Std.IterM.internalState",
"propext",
"Std.IterM",
"Std.IterM.ext_iff",
"Eq"
] | false |
Lean.Server.Watchdog.RequestQueueMap._sizeOf_inst | Lean.Server.Watchdog | [
"SizeOf.mk",
"Lean.Server.Watchdog.RequestQueueMap._sizeOf_1",
"SizeOf",
"Lean.Server.Watchdog.RequestQueueMap"
] | false |
CategoryTheory.SingleFunctors.functor | Mathlib.CategoryTheory.Shift.SingleFunctors | [
"CategoryTheory.Functor",
"AddMonoid",
"CategoryTheory.SingleFunctors",
"CategoryTheory.HasShift",
"CategoryTheory.Category"
] | true |
linearOrderOfCompares._proof_7 | Mathlib.Order.Compare | [
"Preorder.toLT",
"Ordering",
"Ordering.eq",
"Iff",
"Ordering.Compares",
"Eq",
"Ordering.Compares.eq_eq",
"Preorder"
] | false |
TopologicalGroup.IsSES.pushforward._proof_1 | Mathlib.MeasureTheory.Measure.Haar.Extension | [
"AddMonoid.toAddSemigroup",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"IsTopologicalAddGroup.toContinuousAdd",
"AddSemigroup.toAdd",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"NormedAddCommGroup.toAddCommGroup",
"SubNegMonoid.toAddMonoid",
"Conti... | false |
CategoryTheory.nerve.ext_of_isThin_iff | Mathlib.AlgebraicTopology.SimplicialSet.Nerve | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"HEq.refl",
"PartialOrder.toPreorder",
"Eq.casesOn",
"Preorder.smallCategory",
"instOfNatNat",
"CategoryTheory.nerve.ext_of_isThin",
"instHAdd",
"Iff",
"Fin.instPartialOrder",
"HAdd.hAdd",
"Quiver.IsThin",
"Nat",
"Iff.intro",
"Categ... | true |
Filter.add_pure | Mathlib.Order.Filter.Pointwise | [
"Pure.pure",
"Filter.instAdd",
"Filter.map",
"Filter.instPure",
"instHAdd",
"HAdd.hAdd",
"Filter.map₂_pure_right",
"Eq",
"Filter",
"Add"
] | true |
Function.Injective.addCommGroupWithOne._proof_2 | Mathlib.Algebra.Ring.InjSurj | [
"Int.cast",
"NegZeroClass.toNeg",
"instHSMul",
"Function.Injective.addGroupWithOne",
"AddMonoidWithOne.natCast_zero",
"AddCommGroupWithOne",
"One",
"AddCommMonoidWithOne.toAddCommMonoid",
"AddGroupWithOne.toAddGroup",
"SMul",
"AddMonoid.toZero",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hS... | false |
WithOne.map₂_coe_right | Mathlib.Algebra.Group.WithOne.Map | [
"WithOne",
"WithOne.map₂",
"WithOne.map",
"WithOne.coe",
"Eq.ndrec",
"One.toOfNat1",
"WithOne.recOneCoe",
"Eq.refl",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"WithOne.instOne"
] | true |
_private.Mathlib.NumberTheory.RamificationInertia.Inertia.0.Ideal._aux_Mathlib_NumberTheory_RamificationInertia_Inertia___macroRules__private_Mathlib_NumberTheory_RamificationInertia_Inertia_0_Ideal_termF_1 | Mathlib.NumberTheory.RamificationInertia.Inertia | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr... | false |
UInt32.le_iff_toNat_le_toNat | Batteries.Data.UInt | [
"UInt32.toNat",
"Iff.rfl",
"LE.le",
"instLENat",
"Iff",
"Nat",
"instLEUInt32",
"UInt32"
] | true |
Lean.Lsp.DocumentHighlight.mk.injEq | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.DocumentHighlightKind",
"Lean.Lsp.DocumentHighlight.mk.inj",
"Eq.propIntro",
"Lean.Lsp.DocumentHighlight.mk",
"Lean.injEq_helper",
"Lean.Lsp.DocumentHighlight",
"And",
"Eq.ndrec",
"Eq.refl",
"Lean.Lsp.Range",
"Eq",
"Option"
] | true |
SubmonoidClass.coe_pow | Mathlib.Algebra.Group.Submonoid.Defs | [
"SetLike",
"Monoid",
"Monoid.toMulOneClass",
"SubmonoidClass.instPow",
"Membership.mem",
"Subtype",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"instHPow",
"SubmonoidClass",
"Subtype.val",
"Eq",
"SetLike.instMembership",
"rfl"
] | true |
Lean.instNonemptyDynlib | Lean.LoadDynlib | [
"_private.Lean.LoadDynlib.0.Lean.DynlibImpl",
"Nonempty",
"Lean.Dynlib",
"Subtype.property"
] | true |
Lean.Meta.Grind.Entry.rec | Lean.Meta.Tactic.Grind.Extension | [
"Lean.Meta.Grind.Entry.funCC",
"Lean.Meta.Grind.InjectiveTheorem",
"Lean.Meta.Grind.Entry.ext",
"Lean.Meta.Grind.Entry.ematch",
"Lean.Meta.Grind.EMatchTheorem",
"Lean.Meta.Grind.Entry.inj",
"Lean.Meta.Grind.Entry",
"Bool",
"Lean.Name",
"Lean.Meta.Grind.Entry.cases"
] | false |
JacobsonNoether.exist_pow_eq_zero_of_le | Mathlib.FieldTheory.JacobsonNoether | [
"LieHom",
"Subring.mem_center_iff",
"LieAlgebra.toModule",
"Module.End.instRing",
"sub_pow_expChar_pow_of_commute",
"LinearMap.pow_mulRight",
"Eq.mpr",
"JacobsonNoether.exists_pow_mem_center_of_inseparable'",
"Algebra.to_smulCommClass",
"Module.End.instMonoid",
"instSMulOfMul",
"HMul.hMul",
... | true |
_private.Mathlib.Order.CompleteLattice.Finset.0.Set.iUnion_finset_eq_set._simp_1_1 | Mathlib.Order.CompleteLattice.Finset | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Finsupp.linearCombination.eq_1 | Mathlib.LinearAlgebra.Finsupp.LinearCombination | [
"LinearMap.id",
"Pi.Function.module",
"Semiring.toModule",
"Pi.addCommMonoid",
"Finsupp.module",
"Finsupp.linearCombination._proof_2",
"Finsupp.linearCombination._proof_1",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"Finsupp.instAd... | true |
Ergodic.mem_extremePoints_measure_univ_eq | Mathlib.Dynamics.Ergodic.Extreme | [
"mem_extremePoints_iff_left",
"MeasureTheory.MeasurePreserving",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Ergodic",
"instHSMul",
"MeasureTheory.Measure",
"Preorder.toLT",
"instSMulOfMul",
"IsScalarTower.right",
"Set.extremePoints",
"congrArg",
"CommSemiring.toSemiring",
"Measu... | true |
BitVec.toNat_toInt_of_sle | Init.Data.BitVec.Lemmas | [
"BitVec.toNat_toInt_of_msb",
"BitVec",
"instOfNatNat",
"BitVec.toNat",
"BitVec.ofNat",
"Bool.true",
"Nat",
"BitVec.zero_sle_iff_msb_eq_false",
"Iff.mp",
"Bool",
"BitVec.toInt",
"Int.toNat",
"BitVec.msb",
"OfNat.ofNat",
"Bool.false",
"Eq",
"BitVec.sle"
] | true |
QuotientAddGroup.quotientKerEquivOfSurjective.eq_1 | Mathlib.GroupTheory.QuotientGroup.Basic | [
"AddMonoidHom.normal_ker",
"AddMonoid.toAddZeroClass",
"QuotientAddGroup.quotientKerEquivOfSurjective._proof_2",
"QuotientAddGroup.Quotient.addGroup",
"AddZeroClass.toAddZero",
"AddSubgroup",
"QuotientAddGroup.quotientKerEquivOfRightInverse",
"HasQuotient.Quotient",
"AddGroup",
"AddGroup.toSubNegM... | true |
IntermediateField.comap | Mathlib.FieldTheory.IntermediateField.Basic | [
"IntermediateField.mk",
"IntermediateField.comap._proof_2",
"IntermediateField",
"AlgHom",
"Algebra",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Subalgebra.comap",
"Semifield.toCommSemiring",
"Subalgebra",
"Field",
"IntermediateField.toSubalgebra"
] | true |
CliffordAlgebra.reverseOp.eq_1 | Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation | [
"CliffordAlgebra.ι",
"CommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"HMul.hMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"AlgHom",
"MulOpposite.opLinearEquiv",
"instAlgebraCliffordAlgebra",
"MulOpposite.instAlgebra",
"Mul... | true |
Matrix.toBilin'Aux.eq_1 | Mathlib.LinearAlgebra.Matrix.BilinearForm | [
"Pi.Function.module",
"Semiring.toModule",
"Pi.addCommMonoid",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"Matrix",
"Matrix.toBilin'Aux._proof_1",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Matrix.toLinearMap₂'Aux",
"Fintype",
"NonAssocSemiring.toNonUnitalNonAssocSemi... | true |
Std.DTreeMap.Internal.Unit.RooSliceData.mk.sizeOf_spec | Std.Data.DTreeMap.Internal.Zipper | [
"Std.Roo._sizeOf_inst",
"Std.DTreeMap.Internal.Unit.RooSliceData",
"Ord",
"instOfNatNat",
"Std.DTreeMap.Internal.Unit.RooSliceData._sizeOf_inst",
"instHAdd",
"Unit",
"Std.DTreeMap.Internal.Impl._sizeOf_inst",
"HAdd.hAdd",
"Std.DTreeMap.Internal.Unit.RooSliceData.mk",
"Nat",
"SizeOf.sizeOf",
... | true |
Polynomial.reflect_reflect | Mathlib.Algebra.Polynomial.Reverse | [
"Polynomial.revAt",
"Polynomial.ext",
"congrArg",
"Polynomial.coeff_reflect",
"Polynomial",
"Polynomial.coeff",
"Function.Embedding",
"Nat",
"True",
"Polynomial.reflect",
"eq_self",
"of_eq_true",
"Semiring",
"congrFun'",
"Function.instFunLikeEmbedding",
"Polynomial.revAt_invol",
"Eq"... | true |
MeasureTheory.cylinder_empty | Mathlib.MeasureTheory.Constructions.Cylinders | [
"Eq.mpr",
"congrArg",
"Finset",
"Finset.restrict",
"Membership.mem",
"id",
"Subtype",
"Set.preimage_empty",
"MeasureTheory.cylinder",
"Set.preimage",
"Finset.instSetLike",
"Set.instEmptyCollection",
"Eq.refl",
"EmptyCollection.emptyCollection",
"Subtype.val",
"Eq",
"MeasureTheory.cyl... | true |
_private.Init.Data.List.Lemmas.0.List.mem_iff_get.match_1_1 | Init.Data.List.Lemmas | [
"List.get",
"Exists",
"List",
"Exists.casesOn",
"Exists.intro",
"Fin",
"Eq",
"List.length"
] | false |
Polynomial.degreeLTEquiv._proof_3 | Mathlib.RingTheory.Polynomial.Basic | [
"Iff.mpr",
"WithBot.addMonoidWithOne",
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.degreeLT",
"WithBot.zeroLEOneClass",
"Submodule",
"WithBot.addLeftMono",
"lt_of_le_of_lt",
"Function.LeftInverse",
"WithBot.some",
"WithBot",
"Preorder.toLT",
"Nat.instIsOrderedAddMonoid",
"WithBot.instL... | false |
LinearMap.BilinForm.span_singleton_sup_orthogonal_eq_top | Mathlib.LinearAlgebra.BilinearForm.Orthogonal | [
"Submodule",
"Lattice.toSemilatticeSup",
"LinearMap.BilinForm",
"LinearMap.span_singleton_sup_orthogonal_eq_top",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"AddCommGroup",
"Set.instSingletonSet",
"Submod... | true |
AddMonoidAlgebra.liftMagma | Mathlib.Algebra.MonoidAlgebra.Basic | [
"MulHom",
"DistribMulActionHom.mk",
"AddMonoidAlgebra.liftMagma._proof_2",
"NonUnitalAlgHom.mk",
"instHSMul",
"AddMonoidAlgebra.liftMagma._proof_3",
"MonoidHom.instFunLike",
"Semiring.toModule",
"instSMulOfMul",
"Equiv.instEquivLike",
"MonoidAlgebra.distribMulAction",
"AddMonoidAlgebra.liftMag... | true |
CategoryTheory.ihom.«term_⟶[_]_» | Mathlib.CategoryTheory.Monoidal.Closed.Basic | [
"Lean.Name.mkStr3",
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
Std.DTreeMap.Internal.Impl.containsThenInsertIfNew! | Std.Data.DTreeMap.Internal.Operations | [
"Ord",
"Std.DTreeMap.Internal.Impl.insert!",
"instDecidableEqBool",
"Prod.mk",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"Bool",
"Prod",
"Bool.false",
"Eq",
"Std.DTreeMap.Internal.Impl",
"ite"
] | true |
Std.DHashMap.Internal.Raw.buckets_empty | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.instEmptyCollection",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.AssocList.nil",
"instOfNatNat",
"Array",
"GetElem.getElem",
"Array.instGetElemNatLtSize",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Std.DHashMap.Internal.AssocList",
"instLTNat",
"Std.DHashMap.Internal.Raw.... | true |
AlgebraicClosure.instCommRing._proof_7 | Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure | [
"Nat.instMulZeroClass",
"Semiring.toModule",
"AddMonoidAlgebra.commRing",
"Add.mk",
"AlgebraicClosure.instCommRing._proof_3",
"AlgebraicClosure.instCommRing._aux_1",
"AddSemigroup.mk",
"Field.toSemifield",
"Field.toCommRing",
"Finsupp.instAddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"HA... | false |
_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_4 | Mathlib.Data.List.Basic | [
"Lean.Grind.nestedProof",
"_private.Mathlib.Data.List.Basic.0.List.eq_cons_of_length_one._proof_1_1",
"Fin.isLt",
"Fin.mk",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"List.length"
] | false |
WithBot.coe_injective | Mathlib.Order.WithBot | [
"WithBot.some",
"WithBot",
"Option.some_injective",
"Function.Injective"
] | true |
Lean.Nat.mkInstHPow | Lean.Expr | [
"Lean.Expr",
"Lean.Nat.mkInstPow",
"Lean.Level",
"Lean.mkConst",
"List.cons",
"Lean.Level.zero",
"Lean.mkApp3",
"Lean.Nat.mkType",
"Lean.Name.mkStr1",
"List.nil"
] | true |
Lean.Lsp.instFileSourceRpcKeepAliveParams | Lean.Server.FileSource | [
"Lean.Lsp.FileSource.mk",
"Lean.Lsp.RpcKeepAliveParams.uri",
"Lean.Lsp.FileSource",
"Lean.Lsp.RpcKeepAliveParams"
] | true |
CategoryTheory.RegularEpi.w | Mathlib.CategoryTheory.Limits.Shapes.RegularMono | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.RegularEpi.left",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.RegularEpi.right",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.RegularEpi.W",
"CategoryTheory.RegularEpi",
"CategoryTheory.Category"... | true |
Lean.KeyedDeclsAttribute.OLeanEntry.noConfusionType | Lean.KeyedDeclsAttribute | [
"Lean.KeyedDeclsAttribute.OLeanEntry.casesOn",
"Lean.Name",
"Lean.KeyedDeclsAttribute.OLeanEntry",
"Eq",
"Lean.KeyedDeclsAttribute.Key"
] | false |
Lean.Meta.withExistingLocalDecls | Lean.Meta.Basic | [
"Lean.Meta.MetaM",
"_private.Lean.Meta.Basic.0.Lean.Meta.withExistingLocalDeclsImp",
"List",
"Lean.Meta.mapMetaM",
"MonadControlT",
"Lean.LocalDecl",
"Monad"
] | true |
CategoryTheory.SingleObj.mapHom._proof_6 | Mathlib.CategoryTheory.SingleObj | [
"Monoid",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SingleObj.star",
"CategoryTheory.Functor.map",
"CategoryTheory.SingleObj",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Functor.map_comp",
"CategoryTheory.Category.toCategoryStruct"... | false |
ThreeAPFree | Mathlib.Combinatorics.Additive.AP.Three.Defs | [
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"instHAdd",
"HAdd.hAdd",
"AddMonoid",
"AddZero.toAdd",
"Eq",
"Set.instMembership",
"Set"
] | true |
SimpleGraph.Walk.toDeleteEdge._proof_1 | Mathlib.Combinatorics.SimpleGraph.Walk.Maps | [
"False",
"eq_false",
"congrArg",
"Mathlib.Tactic.Contrapose.contrapose₃",
"SimpleGraph.Walk",
"Membership.mem",
"Set.instSingletonSet",
"SimpleGraph",
"List",
"List.instMembership",
"True",
"of_eq_true",
"implies_true",
"Singleton.singleton",
"not_false_eq_true",
"Eq",
"Set.instMembe... | false |
AddAction.IsPreprimitive.mk._flat_ctor | Mathlib.GroupTheory.GroupAction.Primitive | [
"AddAction.IsPreprimitive.mk",
"AddAction.IsTrivialBlock",
"Exists",
"VAdd",
"AddAction.IsPreprimitive",
"HVAdd.hVAdd",
"instHVAdd",
"Eq",
"AddAction.IsPretransitive.mk",
"AddAction.IsBlock",
"Set"
] | false |
_private.Mathlib.Tactic.Linter.UnusedTactic.0.Mathlib.Linter.UnusedTactic.eraseUsedTactics.match_4 | Mathlib.Tactic.Linter.UnusedTactic | [
"Lean.Elab.InfoTree.casesOn",
"Lean.Elab.InfoTree",
"Lean.MVarId",
"Lean.Elab.PartialContextInfo",
"Lean.Elab.InfoTree.context",
"Lean.PersistentArray",
"Lean.Elab.InfoTree.node",
"Lean.Elab.InfoTree.hole",
"Lean.Elab.Info"
] | false |
Multiset.mem_ndunion | Mathlib.Data.Multiset.FinsetOps | [
"instLawfulBEq",
"List.mem_union_iff",
"Membership.mem",
"Multiset",
"instBEqOfDecidableEq",
"Quot.induction_on₂",
"Multiset.instMembership",
"List",
"Iff",
"Or",
"List.isSetoid",
"Multiset.ndunion",
"Setoid.r",
"DecidableEq"
] | true |
List.getElem?_set_self | Init.Data.List.Lemmas | [
"GetElem?.toGetElem",
"congrArg",
"List.instGetElem?NatLtLength",
"Option.some",
"List.set",
"List.getElem_set_self",
"GetElem.getElem",
"List",
"Nat",
"getElem?_pos",
"LT.lt",
"True",
"eq_self",
"eq_true",
"of_eq_true",
"congrFun'",
"instLTNat",
"GetElem?.getElem?",
"Eq",
"Lis... | true |
CategoryTheory.Limits.kerIsKernel | Mathlib.CategoryTheory.Limits.FunctorCategory.Shapes.Kernels | [
"CategoryTheory.Limits.evaluationJointlyReflectsLimits",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Fork.ofι",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Limits.kerIsKernel._proof_1",
"Quiver.Hom",
... | true |
ZFSet.IsOrdinal.mem_trichotomous | Mathlib.SetTheory.ZFC.Ordinal | [
"Eq.mpr",
"congrArg",
"ZFSet",
"Membership.mem",
"ZFSet.IsOrdinal",
"id",
"HasSubset.Subset",
"eq_comm",
"ZFSet.IsOrdinal.mem_or_subset",
"propext",
"ZFSet.instHasSubset",
"Or",
"ZFSet.IsOrdinal.subset_iff_eq_or_mem",
"Eq.symm",
"Eq",
"ZFSet.instSetLike",
"SetLike.instMembership"
] | true |
_private.Mathlib.Combinatorics.Matroid.Basic.0.Matroid.exists_isBasis_union_inter_isBasis.match_1_1 | Mathlib.Combinatorics.Matroid.Basic | [
"Exists",
"Exists.casesOn",
"Exists.intro",
"Matroid.IsBasis",
"Matroid",
"Set"
] | false |
_private.Mathlib.LinearAlgebra.Finsupp.Span.0.Finsupp.lsingle_range_le_ker_lapply._simp_1_1 | Mathlib.LinearAlgebra.Finsupp.Span | [
"eq_top_iff",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"LE.le",
"OrderTop",
"OrderTop.toTop",
"propext",
"Top.top",
"Eq"
] | false |
Std.TreeMap.filter_equiv_self_iff | Std.Data.TreeMap.Lemmas | [
"Iff.mpr",
"Std.TreeMap.Equiv",
"GetElem?.toGetElem",
"Std.DTreeMap",
"Std.TreeMap.Equiv.inner",
"Std.TreeMap.getKey",
"Std.TreeMap.filter",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"GetElem.getElem",
"Std.DTreeMap.instMembership",
"Bool.true",
"Iff",
"Std.DTr... | true |
_private.Mathlib.Control.Bitraversable.Instances.0.Sum.bitraverse.match_1.eq_1 | Mathlib.Control.Bitraversable.Instances | [
"Sum.bitraverse.match_1",
"Sum",
"Sum.inl",
"Sum.inr",
"Eq.refl",
"Eq"
] | true |
Std.DTreeMap.Internal.Const.instSliceableImplRioSlice | Std.Data.DTreeMap.Internal.Zipper | [
"Std.DTreeMap.Internal.Const.RioSliceData.mk",
"Ord",
"Std.DTreeMap.Internal.Const.RioSlice",
"Std.Rio.Sliceable.mk",
"Std.Rio",
"Std.Slice.mk",
"Std.DTreeMap.Internal.Const.RioSliceData",
"Std.Rio.Sliceable",
"Std.DTreeMap.Internal.Impl"
] | true |
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