name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac._proof_4 | Mathlib.Algebra.Homology.ExactSequenceFour | [
"_private.Mathlib.Algebra.Homology.ExactSequenceFour.0.CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac._proof_3",
"instOfNatNat",
"LE.le",
"instLENat",
"autoParam",
"CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac._auto_1",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Decidable.byContradic... | false |
CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit.eq_1 | Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | [
"CategoryTheory.Limits.HasLimit.isoOfNatIso",
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.whiskeringLeftCompEvaluation",
"CategoryTheory.Limits.limitCompWhiskeringLeftIsoCompLimit._proof_4",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Functor.category",
"Cate... | true |
_private.Lean.Meta.Tactic.Grind.Arith.ModelUtil.0.Lean.Meta.Grind.Arith.pickUnusedValue.go | Lean.Meta.Tactic.Grind.Arith.ModelUtil | [
"Inhabited.default",
"Lean.Meta.Grind.Goal",
"Lean.Expr.instBEq",
"Rat",
"Std.HashSet",
"Int.instDecidableEq",
"Lean.Expr",
"Int",
"Std.HashMap",
"instBEqOfDecidableEq",
"Inhabited",
"Lean.Expr.instHashable",
"instHashableInt",
"Inhabited.mk"
] | true |
separableClosureOperator | Mathlib.FieldTheory.SeparableClosure | [
"IntermediateField.restrictScalars",
"IntermediateField.instPartialOrder",
"IntermediateField.isScalarTower_mid'",
"instSMulOfMul",
"IntermediateField",
"IntermediateField.toField",
"PartialOrder.toPreorder",
"ClosureOperator.mk'",
"Algebra",
"Membership.mem",
"separableClosure.algEquivOfAlgEqui... | true |
abs_mul_sign | Mathlib.Data.Sign.Basic | [
"AddGroup.toSubtractionMonoid",
"SignType.cast",
"NegZeroClass.toNeg",
"Preorder.toLT",
"HMul.hMul",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"SignType.instOne",
"abs",
"abs_of_neg",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"... | true |
PUnit.instAdd_mathlib.eq_1 | Mathlib.Algebra.Group.PUnit | [
"Add.mk",
"PUnit",
"Eq.refl",
"PUnit.unit",
"Eq",
"Add",
"PUnit.instAdd_mathlib"
] | true |
Equiv.image_symm_eq_preimage_of_finset | Mathlib.Data.Finset.Preimage | [
"Equiv.instEquivLike",
"Function.Injective.injOn",
"Finset",
"Equiv",
"SetLike.coe",
"Set.preimage",
"Finset.instSetLike",
"Finset.preimage",
"Equiv.injective",
"_private.Mathlib.Data.Finset.Preimage.0.Equiv.image_symm_eq_preimage_of_finset._proof_1_1",
"Equiv.symm",
"Eq",
"DFunLike.coe",
... | true |
TopologicalSpace.Opens.openPartialHomeomorphSubtypeCoe_target | Mathlib.Topology.OpenPartialHomeomorph.Basic | [
"Eq.mpr",
"congrArg",
"PartialEquiv.target",
"setOf",
"TopologicalSpace.Opens",
"Membership.mem",
"id",
"Subtype",
"TopologicalSpace.Opens.openPartialHomeomorphSubtypeCoe",
"TopologicalSpace.Opens.openPartialHomeomorphSubtypeCoe._proof_1",
"Subtype.range_coe_subtype",
"TopologicalSpace.Opens.i... | true |
String.Pos.Raw.isValid_ofList | Init.Data.String.Basic | [
"String.toList_ofList",
"Eq.mpr",
"_private.Init.Data.String.Basic.0.String.Pos.Raw.isValid_ofList._simp_1_1",
"congrArg",
"String",
"String.length_toList",
"String.utf8ByteSize",
"List.take_append_drop",
"Exists",
"Eq.mp",
"id",
"String.ofList_toList",
"String.Pos.Raw",
"And.casesOn",
"... | true |
MeasureTheory.lintegral_edist_lt_top | Mathlib.MeasureTheory.Function.L1Space.Integrable | [
"Iff.mpr",
"MeasureTheory.Integrable.aestronglyMeasurable",
"Eq.mpr",
"ENNReal.instAdd",
"lt_of_le_of_lt",
"MeasureTheory.Measure",
"Preorder.toLT",
"congrArg",
"NormedAddCommGroup.toMetricSpace",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Integrable",
"Mea... | true |
_private.Lean.Data.Name.0.Lean.Name.quickCmpImpl.unsafe_1 | Lean.Data.Name | [
"ptrEq",
"Bool",
"Lean.Name"
] | true |
_private.Lean.Meta.Tactic.Symm.0.Lean.Meta.Symm.initFn._sparseCasesOn_1._@.Lean.Meta.Tactic.Symm.3447505512._hygCtx._hyg.2 | Lean.Meta.Tactic.Symm | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
frattini_nongenerating | Mathlib.GroupTheory.Frattini | [
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"CompleteLattice.toBoundedOrder",
"Subgroup",
"frattini",
"Max.max",
"BoundedOrder.toOrderTop",
"Subgroup.instPartialOrder",
"Subgroup.in... | true |
Std.DHashMap.Raw.Const.getKeyD_modify | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw₀.Const.modify",
"congrArg",
"Std.DHashMap.Internal.Raw₀.Const.getKeyD_modify",
"Std.DHashMap.Raw",
"Membership.mem",
"Std.DHashMap.Raw.contains",
"... | true |
CategoryTheory.Limits.PreservesLimit₂.mk | Mathlib.CategoryTheory.Limits.Preserves.Bifunctor | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Functor.mapCone₂",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.PreservesLimit₂",
"CategoryTheory.Limits.PreservesLimit₂.mk",
"CategoryTheory.Functor.uncurry",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Functo... | true |
Lean.LOption.ctorIdx | Lean.Data.LOption | [
"Lean.LOption.casesOn",
"Nat",
"Lean.LOption"
] | false |
MeasureTheory.isMulLeftInvariant_smul_nnreal | Mathlib.MeasureTheory.Group.Measure | [
"ENNReal.ofNNReal",
"instHSMul",
"MeasureTheory.Measure",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"Mul",
"MeasureTheory.isMulLeftInvariant_smul",
"Algebra.id",
"NNReal",
"ENNReal.instCommSemiring",
"MeasureTheory.Measure.instMulAction",
"MeasurableSpace",
"ENNReal.instSMulNNRealOfM... | true |
CategoryTheory.Adjunction.natIsoOfRightAdjointNatIso | Mathlib.CategoryTheory.Adjunction.Opposites | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.coyoneda",
"CategoryTheory.Functor.category",
"CategoryTheory.Coyoneda.fullyFaithful",
"Equiv",
"CategoryTheory.Iso",
"CategoryTheory.Functor.whiskeringRight",
"CategoryTheory.Adjunction.lef... | true |
_private.Init.Data.Nat.Basic.0.Nat.zero_lt_of_ne_zero.match_1_1 | Init.Data.Nat.Basic | [
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.zero",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
AnalyticAt.rexp' | Mathlib.Analysis.SpecialFunctions.ExpDeriv | [
"Real",
"NormedSpace",
"AnalyticAt.rexp",
"Real.denselyNormedField",
"Real.normedAddCommGroup",
"Real.exp",
"AnalyticAt",
"NontriviallyNormedField.toNormedField",
"Real.normedField",
"DenselyNormedField.toNontriviallyNormedField",
"NormedField.toNormedSpace",
"NormedAddCommGroup.toSeminormedAd... | true |
List.Vector.mem_cons_self | Mathlib.Data.Vector.Mem | [
"Iff.mpr",
"List.Vector.get",
"List.Vector.get_cons_zero",
"List.Vector.mem_iff_get",
"List.Vector",
"Membership.mem",
"Exists",
"Fin.instOfNat",
"List",
"List.instMembership",
"Nat.instNeZeroSucc",
"Nat",
"Exists.intro",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Eq",
"List.Vector.toList"... | true |
_private.Std.Data.ExtHashMap.Basic.0.Std.ExtHashMap.instLawfulBEq.match_3 | Std.Data.ExtHashMap.Basic | [
"instLawfulHashableOfLawfulBEq",
"Std.ExtHashMap.instBEqOfEquivBEqOfLawfulHashable",
"LawfulBEq",
"Std.ExtHashMap",
"Bool.true",
"BEq.beq",
"Std.ExtHashMap.mk",
"Std.ExtDHashMap",
"Bool",
"Hashable",
"instEquivBEqOfLawfulBEq",
"BEq",
"Eq",
"Std.ExtHashMap.casesOn"
] | false |
RootPairing.chainBotCoeff.eq_1 | Mathlib.LinearAlgebra.RootSystem.Chain | [
"IsDomain",
"CommRing",
"instHSMul",
"instConditionallyCompleteLinearOrder",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Finite",
"PartialOrder.toPreorder",
"setOf",
"AddGroupWithOne.toAddMonoidWithOne",
"RootPairing.IsCrystallographic",
"Classical.propDecidable",
"AddCommGro... | true |
Bundle.Pretrivialization.preimage_symm_proj_baseSet | Mathlib.Topology.FiberBundle.Trivialization | [
"Iff.mpr",
"Eq.mpr",
"Bundle.Pretrivialization.mem_target",
"congrArg",
"PartialEquiv.target",
"Membership.mem",
"PartialEquiv.symm",
"id",
"HasSubset.Subset",
"Bundle.Pretrivialization.proj_symm_apply",
"Set.instInter",
"Set.inter_eq_right",
"Prod.fst",
"Inter.inter",
"Bundle.Pretrivial... | true |
NonnegSpectrumClass.rec | Mathlib.Algebra.Algebra.Spectrum.Quasispectrum | [
"NonnegSpectrumClass.mk",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"quasispectrum",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Preorder.toLE",
"Membership.mem",
"NonUnitalRing.toNonUnitalNonAssocRing",
"PartialOrder",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"LE.le",
... | false |
_private.Mathlib.Geometry.Manifold.LocalInvariantProperties.0.OpenPartialHomeomorph.isLocalStructomorphWithinAt_source_iff._simp_1_1 | Mathlib.Geometry.Manifold.LocalInvariantProperties | [
"Set.univ",
"Membership.mem",
"True",
"Set.mem_univ",
"eq_true",
"Eq",
"Set.instMembership",
"Set"
] | false |
Real.arccos_le_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse | [
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Real.partialOrder",
"Real.instLE",
"Real",
"Mathlib.Meta.NormNum.instAddMonoidWithOne",
"Mathlib.Tactic.Linarith.mul_... | true |
_private.Mathlib.Algebra.Order.CauSeq.Basic.0.CauSeq.mul_pos.match_1_3 | Mathlib.Algebra.Order.CauSeq.Basic | [
"AddGroupWithOne.toAddGroup",
"abs",
"LinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"Exists",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"GE.ge",
"DistribLattice.toLattice",
"DivisionRing.toRing",
"LE.le",
"Field.toSemifield",
"And",
"Se... | false |
UInt64.add_left_neg | Init.Data.UInt.Lemmas | [
"UInt64.instOfNat",
"instAddUInt64",
"UInt64",
"UInt64.toBitVec_inj",
"BitVec",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Iff.mp",
"BitVec.add_left_neg",
"OfNat.ofNat",
"Eq",
"Neg.neg",
"instNegUInt64",
"UInt64.toBitVec"
] | true |
Lean.Lsp.LeanClientCapabilities.noConfusionType | Lean.Data.Lsp.Capabilities | [
"Lean.Lsp.LeanClientCapabilities",
"Bool",
"Lean.Lsp.RpcWireFormat",
"Lean.Lsp.LeanClientCapabilities.casesOn",
"Eq",
"Option"
] | false |
sum_bernoulli' | Mathlib.NumberTheory.Bernoulli | [
"Rat.addCommMonoid",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"CharP.cast_eq_zero",
"Nat.cast_mul._simp_1",
"NormedCommRing.toNormedRing",
"Rat.instOfNat",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"Int.cast",
"Rat.instSub",
"Mathlib.Tact... | true |
_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_9 | Mathlib.Data.List.Chain | [
"Lean.Grind.nestedProof",
"congrArg",
"HEq.refl",
"cast",
"Membership.mem",
"Eq.rec",
"List.cons",
"List",
"List.instMembership",
"eq_of_heq",
"HEq",
"Eq",
"Lean.Grind.abstractFn",
"_private.Mathlib.Data.List.Chain.0.List.isChain_attachWith._proof_1_2",
"List.nil"
] | false |
Lean.MVarId.setFVarKind | Lean.MetavarContext | [
"Lean.MetavarContext",
"Lean.LocalDeclKind",
"Lean.MVarId",
"Lean.FVarId",
"Lean.MonadMCtx.modifyMCtx",
"Unit",
"Lean.MetavarContext.setFVarKind",
"Lean.MonadMCtx"
] | true |
Mathlib.Meta.FunProp.Mor.instInhabitedArg.default | Mathlib.Tactic.FunProp.Mor | [
"Inhabited.default",
"Mathlib.Meta.FunProp.Mor.Arg.mk",
"Lean.Expr",
"Lean.instInhabitedExpr",
"Mathlib.Meta.FunProp.Mor.Arg",
"instInhabitedOption",
"Option"
] | true |
NumberField.ComplexEmbedding.unmixedEmbeddingsOver | Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings | [
"setOf",
"Algebra",
"RingHom",
"Field.toSemifield",
"And",
"Semifield.toDivisionSemiring",
"NumberField.ComplexEmbedding.LiesOver",
"NumberField.ComplexEmbedding.IsUnmixed",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"Complex",
"Semiring.toNonAssocSemiring",
"Field",
"Compl... | true |
Fin.finsetImage_addNat_uIcc | Mathlib.Order.Interval.Finset.Fin | [
"congrArg",
"Finset",
"instDecidableEqFin",
"Fin.instLocallyFiniteOrder",
"Finset.coe_image",
"_private.Mathlib.Order.Interval.Finset.Fin.0.Fin.finsetImage_addNat_uIcc._simp_1_1",
"instHAdd",
"SetLike.coe",
"Finset.instSetLike",
"HAdd.hAdd",
"Nat",
"Fin.image_addNat_uIcc",
"congr",
"True",... | true |
IsSemisimpleModule.casesOn | Mathlib.RingTheory.SimpleModule.Basic | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"IsSemisimpleModule.rec",
"ComplementedLattice",
"IsSemisimpleModule",
"ConditionallyCompleteLattice.toLattice",
"Module",... | false |
Lean.Elab.Do.ControlStack.mkContinue | Lean.Elab.Do.Control | [
"Pure.pure",
"Lean.MetavarKind.natural",
"instMonadReaderOfReaderTOfMonad",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"Lean.Elab.Do.MonadInfo.mk",
"Lean.Elab.Do.MonadInfo.m",
"Lean.Meta.State",
"instMonadLiftT",
"MonadReader.read",
"ReaderT.instMonad",
"Lean.Elab.Do.ControlStack",
"Lea... | true |
_private.Mathlib.Algebra.Category.CoalgCat.Basic.0.CoalgCat.Hom.toCoalgHom_injective.match_1_1 | Mathlib.Algebra.Category.CoalgCat.Basic | [
"CoalgCat.toModuleCat",
"CommRing",
"Coalgebra.toCoalgebraStruct",
"CoalgCat",
"CoalgHom",
"AddCommGroup.toAddCommMonoid",
"CoalgCat.Hom.casesOn",
"CoalgCat.instCoalgebra",
"CommRing.toCommSemiring",
"ModuleCat.isAddCommGroup",
"CoalgCat.Hom.toCoalgHom'",
"CoalgCat.Hom.mk",
"ModuleCat.carrie... | false |
CategoryTheory.Functor.mapMonFunctor._proof_2 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.LaxMonoidalFunctor.Hom.hom",
"CategoryTheory.Functor.map",
"CategoryTheory.LaxMonoidalFunctor.toFunctor",
... | false |
Positive.instDistribSubtypeLtOfNat._proof_3 | Mathlib.Algebra.Order.Positive.Ring | [
"Preorder.toLT",
"AddMonoid.toAddSemigroup",
"instIsLeftCancelAddOfAddLeftReflectLE",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"PartialOrder",
"IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono",
"IsStrictOrderedRing.toIsOrderedCancelAddMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
... | false |
_private.Lean.Replay.0.Lean.Environment.Replay.State.rec | Lean.Replay | [
"Lean.NameSet",
"Lean.Kernel.Environment",
"_private.Lean.Replay.0.Lean.Environment.Replay.State",
"_private.Lean.Replay.0.Lean.Environment.Replay.State.mk"
] | false |
CategoryTheory.Limits.ker | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.ker._proof_5",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.Limits.ker._proof_1",
"CategoryTheory.Limits.kernel",
"CategoryTheory.Arrow.left",
"Categor... | true |
CategoryTheory.Idempotents.FunctorExtension₁.map._proof_2 | Mathlib.CategoryTheory.Idempotents.FunctorExtension | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Idempotents.Karoubi.Hom.f",
"CategoryTheory.Functor",
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Idempotents.FunctorExtension₁.map._proof_1",
"CategoryTheory.Id... | false |
Stream'.Seq.nil | Mathlib.Data.Seq.Defs | [
"Stream'.Seq",
"Subtype.mk",
"Stream'",
"Option.none",
"Stream'.Seq.nil._proof_1",
"Stream'.IsSeq",
"Stream'.const",
"Option"
] | true |
HahnSeries.instAdd | Mathlib.RingTheory.HahnSeries.Addition | [
"AddMonoid.toAddSemigroup",
"Add.mk",
"AddMonoid.toAddZeroClass",
"HahnSeries.instAdd._proof_1",
"AddZeroClass.toAddZero",
"PartialOrder",
"HahnSeries.mk",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"Pi.instAdd",
"HAdd.hAdd",
"AddMonoid",
"HahnSeries.coeff",
"HahnSeries",
"Add... | true |
NumberField.ComplexEmbedding.IsConj | Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings | [
"NumberField.ComplexEmbedding.conjugate",
"Algebra",
"RingHom",
"Field.toSemifield",
"RingHom.comp",
"Semifield.toDivisionSemiring",
"AlgEquiv",
"RingHomClass.toRingHom",
"NumberField.ComplexEmbedding.IsConj._proof_1",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"Complex",
"Se... | true |
Tactic.ComputeAsymptotics.Seq.FriendlyOperationClass.mk | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | [
"Stream'.Seq",
"Tactic.ComputeAsymptotics.Seq.FriendlyOperationClass.mk",
"Tactic.ComputeAsymptotics.Seq.FriendlyOperation",
"Tactic.ComputeAsymptotics.Seq.FriendlyOperationClass"
] | true |
Ordinal.right_eq_zero_of_add_eq_zero | Mathlib.SetTheory.Ordinal.Arithmetic | [
"Ordinal.add_eq_zero_iff",
"instHAdd",
"And",
"And.right",
"HAdd.hAdd",
"Ordinal.zero",
"Iff.mp",
"Ordinal.add",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Ordinal"
] | true |
NNReal.range_coe | Mathlib.Data.NNReal.Basic | [
"Real",
"Set.Ici",
"Real.instZero",
"_private.Mathlib.Data.Real.Basic.0.Real.le",
"NNReal",
"Subtype.range_coe",
"Zero.toOfNat0",
"Set.range",
"OfNat.ofNat",
"Eq",
"NNReal.toReal",
"Real.instPreorder",
"Set"
] | true |
_private.Mathlib.Algebra.Lie.Semisimple.Basic.0.LieAlgebra.IsSemisimple.finitelyAtomistic | Mathlib.Algebra.Lie.Semisimple.Basic | [
"LieAlgebra.toModule",
"CommRing",
"Lattice.toSemilatticeSup",
"LieAlgebra.IsSemisimple",
"LieRing.toAddCommGroup",
"Finset",
"PartialOrder.toPreorder",
"setOf",
"LieSubmodule.instPartialOrder",
"Preorder.toLE",
"Exists",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toB... | true |
Array.some_getElem_eq_getElem?_iff | Init.Data.Array.Lemmas | [
"congrArg",
"some_getElem_eq_getElem?_iff._simp_1",
"Option.some",
"Array",
"GetElem.getElem",
"iff_self",
"Iff",
"Array.instGetElemNatLtSize",
"Array.instLawfulGetElemNatLtSize",
"Nat",
"LT.lt",
"True",
"of_eq_true",
"Nat.decLt",
"congrFun'",
"instLTNat",
"GetElem?.getElem?",
"Eq"... | true |
CategoryTheory.AddGrp.mk | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.AddGrp",
"CategoryTheory.AddGrp.mk",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.AddGrpObj",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Data.ENat.Basic.0.ENat.top_ne_coe.match_1_1 | Mathlib.Data.ENat.Basic | [
"False",
"ENat.instNatCast",
"instTopENat",
"Option.ctorIdx",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Option.some",
"Eq.casesOn",
"Nat.cast",
"Option.none",
"Nat",
"ENat",
"Eq.refl",
"HEq",
"Top.top",
"Eq",
"Option"
] | false |
Std.Tactic.BVDecide.BVExpr.bitblast.blastRotateRight.go_get._proof_2 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.RotateRight | [
"HSub.hSub",
"Nat.instMod",
"instHMod",
"_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.RotateRight.0.Std.Tactic.BVDecide.BVExpr.bitblast.blastRotateRight.go_get._proof_1",
"instSubNat",
"instHAdd",
"HMod.hMod",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Decidable.byCont... | false |
TopCat.Presheaf.pushforwardToOfIso.eq_1 | Mathlib.Topology.Sheaves.Presheaf | [
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopCat.instCategory",
"TopCat.instCategoryPresheaf",
"TopCat.Presheaf.presheafEquivOfIso",
"TopCat.Presheaf",
"Equiv",
"CategoryTheory.Iso",
"CategoryTheory.Equivalence.functor",
"TopCat.Presheaf.pushforwardToOfIso",... | true |
Std.TransCmp.mk | Init.Data.Order.Ord | [
"Ordering",
"Std.OrientedCmp",
"Std.TransCmp",
"Bool.true",
"Bool",
"Std.TransCmp.mk",
"Ordering.isLE",
"Eq"
] | true |
CStarMatrix.instModule | Mathlib.Analysis.CStarAlgebra.CStarMatrix | [
"Module.mk",
"CStarMatrix.instModule._proof_1",
"AddCommMonoid",
"CStarMatrix",
"CStarMatrix.instDistribMulAction",
"Semiring.toMonoid",
"Semiring",
"Module.toDistribMulAction",
"AddCommMonoid.toAddMonoid",
"CStarMatrix.instModule._proof_2",
"CStarMatrix.instAddCommMonoid",
"Module"
] | true |
Bundle.Trivialization.prod._proof_1 | Mathlib.Topology.FiberBundle.Constructions | [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"Bundle.Trivialization.source_eq",
"SProd.sprod",
"OpenPartialHomeomorph.open_source",
"congrArg",
"HEq.refl",
"Set.mem_prod._simp_1",
"instTopologicalSpaceProd",
"FiberBundle.Prod.isInducing_diag",
"Membership.mem",
"Bundle.TotalSpace.mk",
"Eq.casesOn... | false |
CategoryTheory.MorphismProperty.IsStableUnderBaseChange.monomorphisms | Mathlib.CategoryTheory.MorphismProperty.Limits | [
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsPullback",
"CategoryTheory.MorphismProperty.monomorphisms",
"CategoryTheory.IsPullback.mono_snd_of_mono",
"inferInstance",
"CategoryTheory.MorphismProperty.IsStableUnderBaseChange",
"CategoryTheory.Morph... | true |
ne_of_ne_of_eq' | Mathlib.Tactic.Positivity.Core | [
"Eq.rec",
"Ne",
"Eq"
] | true |
UInt8.lt_of_lt_of_le | Init.Data.UInt.Lemmas | [
"Eq.mpr",
"_private.Init.Data.UInt.Lemmas.0.UInt8.lt_of_lt_of_le._simp_1_2",
"_private.Init.Data.UInt.Lemmas.0.UInt8.lt_of_lt_of_le._simp_1_1",
"id",
"instLTUInt8",
"LE.le",
"instLENat",
"implies_congr",
"Nat",
"LT.lt",
"instLTNat",
"UInt8.toNat",
"UInt8",
"Eq",
"Nat.lt_of_lt_of_le",
"... | true |
_private.Init.Data.Rat.Lemmas.0.Rat.le_iff_lt_or_eq._simp_1_1 | Init.Data.Rat.Lemmas | [
"Rat.num",
"HMul.hMul",
"Rat",
"Rat.den",
"Int",
"LE.le",
"Rat.instLE",
"Nat.cast",
"Int.instMul",
"propext",
"instNatCastInt",
"Eq",
"Rat.le_iff",
"Int.instLEInt",
"instHMul"
] | false |
Std.Do.ExceptConds.imp | Std.Do.PostCond | [
"Std.Do.PostShape.brecOn",
"Std.Do.PostShape",
"Std.Do.ExceptConds.imp._f",
"Std.Do.ExceptConds"
] | true |
T5Space | Mathlib.Topology.Separation.Regular | [
"TopologicalSpace",
"T5Space.mk"
] | true |
NumberField.InfinitePlace.embedding_of_isReal._proof_1 | Mathlib.NumberTheory.NumberField.InfinitePlace.Basic | [
"NumberField.ComplexEmbedding.IsReal",
"NumberField.InfinitePlace.isReal_iff",
"NumberField.InfinitePlace.embedding",
"NumberField.InfinitePlace.IsReal",
"Iff.mp",
"NumberField.InfinitePlace",
"Field"
] | false |
EMetric.tendsto_nhds | Mathlib.Topology.EMetricSpace.Defs | [
"Preorder.toLT",
"Filter.Eventually",
"PartialOrder.toPreorder",
"nhds",
"Metric.eball",
"PseudoEMetricSpace",
"GT.gt",
"Iff",
"PseudoEMetricSpace.toEDist",
"Filter.Tendsto",
"PseudoEMetricSpace.toUniformSpace",
"Metric.nhds_basis_eball",
"LT.lt",
"ENNReal",
"ENNReal.instPartialOrder",
... | true |
IsCompact.isClosed_image_restrict | Mathlib.Topology.IsClosedRestrict | [
"Eq.mpr",
"isCompact_iff_compactSpace",
"Pi.topologicalSpace",
"continuous_subtype_val",
"congrArg",
"Compl.compl",
"Homeomorph.isClosed_image",
"instTopologicalSpaceProd",
"Membership.mem",
"Set.Elem",
"id",
"Subtype",
"Set.instCompl",
"CompactSpace",
"Topology.image_snd_preimageImageRe... | true |
IsCompact.elim_directed_cover | Mathlib.Topology.Compactness.Compact | [
"Filter.instMembership",
"Set.Subset.refl",
"Set.Subset.trans",
"Directed",
"Nonempty.elim",
"nhdsWithin",
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"Set.instUnion",
"HasSubset.Subset.trans",
"Set.instIsTransSubset",
"HasSubset.Subset",
"_private.Mathlib.Topology.Compactness.Compact.0.... | true |
UpperSet.compl_map | Mathlib.Order.UpperLower.CompleteLattice | [
"LowerSet.map",
"UpperSet",
"OrderIso.bijective",
"Compl.compl",
"UpperSet.instSetLike",
"PartialOrder.toPreorder",
"Set.image_compl_eq",
"Preorder.toLE",
"OrderIso",
"UpperSet.map",
"SetLike.coe_injective",
"LowerSet.instPartialOrder",
"Set.instCompl",
"SetLike.coe",
"instFunLikeOrderIs... | true |
BooleanAlgebra.himp_eq._autoParam | Mathlib.Order.BooleanAlgebra.Defs | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
SimpleGraph.isClique_map_iff_of_nontrivial | Mathlib.Combinatorics.SimpleGraph.Clique | [
"Function.instEmbeddingLikeEmbedding",
"Set.mem_range_self",
"Eq.mpr",
"congrArg",
"SimpleGraph.Adj",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"HasSubset.Subset",
"Ne",
"Set.Nontrivial.exists_ne",
"EmbeddingLike.apply_eq_iff_eq",
"Function.Embedding",
"And.casesOn",
"SimpleGraph",
... | true |
CategoryTheory.Grothendieck.preEquivalence._simp_1 | Mathlib.CategoryTheory.Grothendieck | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Functor.map_comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Cate... | false |
List.bidirectionalRec.eq_2 | Mathlib.Data.List.Induction | [
"List.cons",
"instHAppendOfAppend",
"List",
"List.bidirectionalRec",
"Eq.refl",
"List.instAppend",
"Eq",
"HAppend.hAppend",
"List.nil"
] | true |
DihedralGroup.oddCommuteEquiv.match_7 | Mathlib.GroupTheory.SpecificGroups.Dihedral | [
"Sum.casesOn",
"Sum",
"Prod.mk",
"Sum.inl",
"ZMod",
"Sum.inr",
"Nat",
"Prod",
"Prod.casesOn"
] | false |
Finsupp.subset_mapRange_neLocus | Mathlib.Data.Finsupp.NeLocus | [
"Finsupp.instFunLike",
"Eq.mpr",
"Finsupp.neLocus",
"Finset",
"Membership.mem",
"id",
"HasSubset.Subset",
"Ne",
"congr_arg",
"Finset.instSetLike",
"implies_congr",
"Finsupp.mem_neLocus._simp_1",
"Finset.instHasSubset",
"Zero.toOfNat0",
"Finsupp.mapRange",
"OfNat.ofNat",
"Eq",
"DFun... | true |
CategoryTheory.ShortComplex.ShortExact.injective_f | Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory | [
"Eq.mpr",
"CategoryTheory.Mono",
"AddCommGrpCat.instCategory",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.Additive",
"AddMonoid.toAddZeroClass",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"AddCommGroup.toAddGroup",
"AddCommGrpCat.instConcrete... | true |
List.span.loop._sunfold | Init.Data.List.Basic | [
"List.reverseAux.match_1",
"List.filter.match_1",
"List.span.loop",
"Prod.mk",
"List.cons",
"List",
"Unit",
"List.reverse",
"Bool",
"Prod",
"List.nil"
] | false |
Units.instRepr.eq_1 | Mathlib.Algebra.Group.Units.Defs | [
"Monoid",
"Units.val",
"Function.comp",
"Units",
"Repr.mk",
"Nat",
"Std.Format",
"Eq.refl",
"Units.instRepr",
"Repr",
"Eq",
"Repr.reprPrec"
] | true |
Real.exists_int_int_abs_mul_sub_le | Mathlib.NumberTheory.DiophantineApproximation.Basic | [
"Int.instAddCommGroup",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Mathlib.Tactic.Push.not_exists._simp_1",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real.instIsOrderedRing",
"Int.ca... | true |
Complex.circleIntegral_sub_center_inv_smul_of_differentiable_on_off_countable | Mathlib.Analysis.Complex.CauchyIntegral | [
"NormedCommRing.toSeminormedCommRing",
"Set.diff_subset",
"Real",
"instHSMul",
"CompleteSpace",
"Semiring.toModule",
"Real.pi",
"Metric.closedBall_mem_nhds",
"HMul.hMul",
"NormedSpace",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Compl.compl",
"Dif... | true |
CochainComplex.Plus._proof_1 | Mathlib.Algebra.Homology.CochainComplexPlus | [
"IsRightCancelAdd",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Int",
"AddSemigroup.toAdd",
"Int.instAddGroup",
"AddRightCancelMonoid.toAddRightCancelSemigroup",
"AddGroup.toAddCancelMonoid",
"AddRightCancelSemigroup.toIsRightCancelAdd"
] | false |
Lean.Meta.Grind.PreInstance.mk.injEq | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.PreInstance",
"Eq.propIntro",
"Lean.Meta.Grind.PreInstance.mk.inj",
"Lean.injEq_helper",
"Lean.Expr",
"Array",
"And",
"Eq.ndrec",
"Eq.refl",
"Lean.Meta.Grind.PreInstance.mk",
"Eq"
] | true |
Multiset.sum_zero | Mathlib.Algebra.BigOperators.Group.Multiset.Defs | [
"Multiset.sum",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Multiset",
"AddCommMonoid",
"AddZero.toZero",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"OfNat.ofNat",
"Eq",
"rfl",
"Multiset.instZero"
] | true |
LinearMap.map_dfinsuppSumAddHom | Mathlib.LinearAlgebra.DFinsupp | [
"LinearMap.toAddMonoidHom",
"AddMonoidHom.map_dfinsuppSumAddHom",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"RingHom",
"AddZeroClass.toAddZero",
"DFinsupp.addZeroClass",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"AddZeroClass",
"Semiring",
"DFinsupp.sumAddHom",
"DFinsupp",... | true |
MeasureTheory.isSetAlgebra_generateSetAlgebra | Mathlib.MeasureTheory.SetAlgebra | [
"MeasureTheory.generateSetAlgebra.union",
"Membership.mem",
"MeasureTheory.IsSetAlgebra",
"MeasureTheory.generateSetAlgebra",
"MeasureTheory.generateSetAlgebra.compl",
"MeasureTheory.IsSetAlgebra.mk",
"Set.instMembership",
"MeasureTheory.generateSetAlgebra.empty",
"Set"
] | true |
Lean.Grind.CommRing.Expr.denoteSAsRing | Init.Grind.Ring.CommSemiringAdapter | [
"Lean.Grind.CommRing.Expr",
"Lean.Grind.CommRing.Expr.brecOn",
"Lean.Grind.Semiring",
"Lean.Grind.Ring.OfSemiring.Q",
"Lean.Grind.CommRing.Context",
"Lean.Grind.CommRing.Expr.denoteSAsRing._f"
] | true |
NonarchAddGroupNorm.coe_le_coe._simp_1 | Mathlib.Analysis.Normed.Group.Seminorm | [
"Real.instLE",
"Real",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"Pi.hasLe",
"AddGroup",
"NonarchAddGroupNorm",
"NonarchAddGroupNorm.coe_le_coe",
"propext",
"NonarchAddGroupNorm.instPartialOrder",
"NonarchAddGroupNorm.funLike",
"Eq",
"DFunLike.coe"
] | false |
Homeomorph.mulRight.congr_simp | Mathlib.Topology.Algebra.Group.Basic | [
"Monoid.toMulOneClass",
"Homeomorph.mulRight",
"Group",
"Eq.rec",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"TopologicalSpace",
"MulOneClass.toMulOne",
"Homeomorph",
"Eq.refl",
"SeparatelyContinuousMul",
"Eq"
] | true |
Lean.Parser.Command.whereStructInst.parenthesizer | Lean.Parser.Command | [
"Lean.Parser.optional.parenthesizer",
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.Parser.sepByIndent.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyPrinter.Parenthesi... | true |
OrderDual.gradeOrder._proof_2 | Mathlib.Order.Grade | [
"OrderDual.toDual",
"Preorder.toLT",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"CovBy",
"Equiv",
"CovBy.toDual",
"OrderDual.instLT",
"CovBy.grade",
"OrderDual",
"OrderDual.instPreorder",
"grade",
"DFunLike.coe",
"CovBy.ofDual",
"Preorder",
"GradeOrder",
"EquivLike.toFunLike"
] | false |
WeakSpace.instContinuousSMul | Mathlib.Topology.Algebra.Module.Spaces.WeakDual | [
"Semiring.toModule",
"instSMulOfMul",
"ContinuousSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"ContinuousLinearMap.addCommMonoid",
"AddZeroClass.toAddZero",
"instAddCommMonoidWeakSpace",
"Distrib.toAdd",
"DistribSMul.toSMulZeroClass",
"Continu... | true |
Std.Rci.HasRcoIntersection.casesOn | Init.Data.Range.Polymorphic.PRange | [
"Std.Rco",
"Std.Rci.HasRcoIntersection.mk",
"Std.Rci",
"Std.Rci.HasRcoIntersection.rec",
"Std.Rci.HasRcoIntersection"
] | false |
IsDenseInducing.closure_image_mem_nhds | Mathlib.Topology.DenseEmbedding | [
"Filter.instMembership",
"Trans.trans",
"IsDenseInducing.nhds_eq_comap",
"Filter.HasBasis.mem_iff",
"congrArg",
"Set.image_mono",
"Membership.mem",
"Exists",
"nhds",
"Eq.mp",
"closure_mono",
"DenseRange.subset_closure_image_preimage_of_isOpen",
"HasSubset.Subset",
"IsDenseInducing",
"Set... | true |
Con.mapOfSurjective | Mathlib.GroupTheory.Congruence.Hom | [
"Con.mk",
"Mul",
"MulHomClass",
"Setoid",
"Con.instLE",
"LE.le",
"Con.ker",
"Con.toSetoid",
"Con",
"Con.mapOfSurjective._proof_1",
"DFunLike.coe",
"Function.Surjective",
"Setoid.r",
"FunLike",
"Setoid.mapOfSurjective"
] | true |
Nat.le.intro | Init.Data.Nat.Basic | [
"Nat.le_add_right",
"Eq.rec",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq"
] | true |
Subgroup.IsSubnormal.eq_bot_or_top_of_isSimpleGroup | Mathlib.GroupTheory.IsSubnormal | [
"Group",
"Subgroup",
"IsSimpleGroup",
"Bot.bot",
"Subgroup.IsSubnormal",
"Subgroup.instTop",
"Subgroup.instBot",
"Or",
"Top.top",
"Eq",
"Subgroup.Normal.eq_bot_or_eq_top",
"Subgroup.IsSubnormal.normal_of_isSimpleGroup"
] | true |
_private.Mathlib.Data.Num.ZNum.0.ZNum.bit0_of_bit0.match_1_1 | Mathlib.Data.Num.ZNum | [
"Unit.unit",
"ZNum.pos",
"ZNum.zero",
"ZNum",
"Unit",
"ZNum.casesOn",
"PosNum",
"ZNum.neg"
] | false |
CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.map._proof_8 | Mathlib.AlgebraicTopology.ExtraDegeneracy | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Fin.succ",
"congrArg",
"CategoryTheory.SimplicialObject.Augmented.whiskering",
"CategoryTheory.SimplicialObject.const",
"CategoryTheory.Functor.category",
"CategoryTheory.SimplicialObject.Augmented.Extra... | false |
Filter.comap._proof_3 | Mathlib.Order.Filter.Defs | [
"Filter.instMembership",
"Filter.inter_mem",
"setOf",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"Set.inter_subset_inter",
"Set.instInter",
"Filter.comap.match_1",
"Inter.inter",
"And",
"Set.preimage",
"And.intro",
"Exists.intro",
"Set.instMembership",
"Filter",
"Set.instHasSubs... | false |
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