name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
inf_sup_self | Mathlib.Order.Lattice | [
"Lattice",
"Lattice.toSemilatticeSup",
"le_sup_left._simp_2",
"congrArg",
"inf_of_le_left",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"SemilatticeInf.toMin",
"LE.le",
"Max.max",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"SemilatticeSup.toPartialOrder",
"... | true |
CategoryTheory.Preadditive.epi_of_cokernel_zero | Mathlib.CategoryTheory.Preadditive.Basic | [
"Eq.mpr",
"CategoryTheory.Limits.cokernel.desc",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.Limits.cokernel",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"id",
"CategoryTheory.... | true |
MonCat.ofHom_hom | Mathlib.Algebra.Category.MonCat.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"MonCat.Hom.hom",
"MonCat",
"MonCat.of",
"MonCat.ofHom",
"MonCat.instCategory",
"MonCat.carrier",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"MonCat.str",
"rfl"
] | true |
_private.Lean.Meta.WHNF.0.Lean.Meta.whnfCore.go._unsafe_rec | Lean.Meta.WHNF | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"_private.Lean.Meta.WHNF.0.Lean.Meta.reduceQuotRec",
"Lean.Meta.Config.iota",
"Lean.ConstantInfo.defnInfo",
"Lean.Meta.whnf",
"Lean.Meta.expandLet",
"Bool.not",
"Lean.Meta.recordUnfold",
"Lean.Meta.projectCore?",
"Lean.AxiomVal.toConstantVal",
"Lea... | false |
ZMod.ringEquivOfPrime | Mathlib.Data.ZMod.Basic | [
"Nontrivial",
"Nat.Prime",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"ZMod.commRing",
"Ring.toNonAssocRing",
"ZMod.ringEquivOfPrime._proof_1",
"AddGroupWithOne.toAddMonoidWithOne",
"Fintype.card",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocS... | true |
_private.Lean.Elab.PreDefinition.Eqns.0.Lean.Elab.Eqns.mkEqns.doRealize | Lean.Elab.PreDefinition.Eqns | [
"_private.Lean.Elab.PreDefinition.Eqns.0.Lean.Elab.Eqns.removeUnusedEqnHypotheses",
"Lean.ConstantVal.levelParams",
"ReaderT",
"Lean.Meta.tactic.hygienic",
"Lean.Meta.State",
"Lean.instMonadWithOptionsOfMonadFunctor",
"Lean.inferDefEqAttr",
"instMonadLiftT",
"Lean.Option.set",
"Lean.Expr",
"Lean... | true |
_private.Std.Data.ExtDTreeMap.Lemmas.0.Std.ExtDTreeMap.insertMany_list_eq_empty_iff._simp_1_1 | Std.Data.ExtDTreeMap.Lemmas | [
"Ordering",
"Std.ExtDTreeMap.instEmptyCollection",
"Std.TransCmp",
"Std.ExtDTreeMap.isEmpty",
"Std.ExtDTreeMap.isEmpty_iff",
"Bool.true",
"propext",
"Std.ExtDTreeMap",
"Bool",
"EmptyCollection.emptyCollection",
"Eq.symm",
"Eq"
] | false |
CategoryTheory.FreeBicategory.mk_associator_hom | Mathlib.CategoryTheory.Bicategory.Free | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.FreeBicategory.categoryStruct",
"CategoryTheory.FreeBicategory.Hom₂.associator",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.FreeBicategory.bicategory",
"CategoryTheory.FreeBicategory.quiver",
"CategoryTheory.Fre... | true |
Aesop.SearchM.State.mk._flat_ctor | Aesop.Search.SearchM | [
"Aesop.SearchM.State.mk",
"Aesop.Queue",
"Aesop.SearchM.State",
"Aesop.Iteration",
"Bool"
] | false |
WeierstrassCurve.Projective.dblZ_ne_zero_of_Y_ne' | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"WeierstrassCurve.Projective.negY",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"WeierstrassCurve.Projective.Equation",
"CommRing.toNonUnitalCommRing",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"sub_ne_zero",... | true |
_private.Mathlib.SetTheory.Ordinal.CantorNormalForm.0.Ordinal.CNF.eval_single_add'._simp_1_2 | Mathlib.SetTheory.Ordinal.CantorNormalForm | [
"instHAdd",
"HAdd.hAdd",
"IsLeftCancelAdd",
"propext",
"Eq",
"add_right_inj",
"Add"
] | false |
Lean.Meta.Grind.AC.MonadGetStruct.ctorIdx | Lean.Meta.Tactic.Grind.AC.Util | [
"Lean.Meta.Grind.AC.MonadGetStruct",
"Nat"
] | false |
_private.Mathlib.MeasureTheory.Measure.Haar.Basic.0.MeasureTheory.Measure.haar.index_union_eq._simp_1_2 | Mathlib.MeasureTheory.Measure.Haar.Basic | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Dyadic.blt.eq_3 | Init.Data.Dyadic.Basic | [
"instHMod",
"Dyadic.blt",
"Int",
"Int.instLTInt",
"HMod.hMod",
"instOfNat",
"LT.lt",
"Dyadic.zero",
"Bool",
"Int.instMod",
"Eq.refl",
"Int.decLt",
"Dyadic.ofOdd",
"OfNat.ofNat",
"Decidable.decide",
"Eq"
] | true |
max_zero_add_max_neg_zero_eq_abs_self | Mathlib.Algebra.Order.Group.Abs | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Lattice.toSemilatticeSup",
"abs",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Left.neg_nonpos_iff",
"SemilatticeInf.toPart... | true |
Polynomial.ofFn._proof_1 | Mathlib.Algebra.Polynomial.OfFn | [
"Finsupp.instFunLike",
"instDecidableNot",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"getElem?_neg",
"Pi.addCommMonoid",
"GetElem?.toGetElem",
"eq_false",
"AddMonoid.toAddSemigroup",
"Polynomial.ext",
"congrArg",
"Polynomial.coeff_ofFinsupp",
"AddMonoid.toAddZeroClass",
"List.ofF... | false |
Equiv.nonUnitalNonAssocRing._proof_3 | Mathlib.Algebra.Ring.TransferInstance | [
"NonUnitalNonAssocRing",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"HMul.hMul",
"Equiv",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"instHMul"
] | false |
GetElem.casesOn | Init.GetElem | [
"GetElem",
"GetElem.mk",
"GetElem.rec"
] | false |
Equiv.Perm.extendDomain_one | Mathlib.Algebra.Group.End | [
"Equiv.Perm.instOne",
"Equiv.Perm.extendDomain",
"Equiv",
"Subtype",
"Equiv.Perm",
"DecidablePred",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"Equiv.Perm.extendDomain_refl"
] | true |
TopCat.prodIsoProd_hom_snd | Mathlib.Topology.Category.TopCat.Limits.Products | [
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"TopCat.instCategory",
"CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso",
"CategoryTheory.Functor.category",
"instTopologicalSpaceProd",
"TopCat.prodIsoPro... | true |
Lean.Elab.Do.DoElemContKind.noConfusion | Lean.Elab.Do.Basic | [
"Lean.Elab.Do.DoElemContKind.noConfusionType",
"Lean.Elab.Do.DoElemContKind.ctorIdx",
"Lean.Elab.Do.DoElemContKind",
"noConfusionEnum",
"Nat",
"instDecidableEqNat",
"Eq"
] | false |
Lean.ScopedEnvExtension.StateStack.recOn | Lean.ScopedEnvExtension | [
"Lean.ScopedEnvExtension.StateStack",
"Lean.ScopedEnvExtension.State",
"Lean.ScopedEnvExtension.Entry",
"Lean.ScopedEnvExtension.StateStack.mk",
"Lean.ScopedEnvExtension.ScopedEntries",
"List",
"Lean.ScopedEnvExtension.StateStack.rec"
] | false |
_private.Mathlib.RingTheory.Multiplicity.0.Nat.finiteMultiplicity_iff.match_1_1 | Mathlib.RingTheory.Multiplicity | [
"Dvd.dvd",
"Nat.instMonoid",
"PartialOrder.toPreorder",
"semigroupDvd",
"Preorder.toLE",
"Ne",
"instOfNatNat",
"LE.le",
"Monoid.toPow",
"instHAdd",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"Monoid.toSemigroup",
"instAddNat",
"Nat.zero",
"instHPow",
"OfNat.ofNat",
"LinearOrder.toPartialOr... | false |
Mathlib.Tactic._aux_Mathlib_Tactic_SplitIfs___elabRules_Mathlib_Tactic_splitIfs_1 | Mathlib.Tactic.SplitIfs | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Lean.MessageData",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"_private.Mathlib.Tactic.SplitIfs.0.Mathlib.Tactic._aux_Mathlib_Tactic_SplitIfs___elabRules_Mathlib_Tactic_splitIfs_1.match_1",
"IO.mkRef",
"Lean.Elab.Tactic.expandLocation",
"Lean.Core.in... | false |
norm_le_norm_div_add | Mathlib.Analysis.Normed.Group.Basic | [
"Norm.norm",
"Real.instLE",
"Real",
"instHDiv",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"SeminormedGroup",
"SeminormedGroup.toGroup",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Eq.mp",
"HDiv.hDiv",
"LE.le",
"Real.instAdd",
"Group.toDivInvMo... | true |
NonemptyInterval.length_nonneg | Mathlib.Algebra.Order.Interval.Basic | [
"AddCommGroup.toAddCommMonoid",
"covariant_swap_add_of_covariant_add",
"PartialOrder.toPreorder",
"sub_nonneg_of_le",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"PartialOrder",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionComm... | true |
MeasureTheory.AnalyticSet.preimage | Mathlib.MeasureTheory.Constructions.Polish.Basic | [
"Set.ext",
"Eq.mpr",
"MeasureTheory.AnalyticSet.image_of_continuous",
"Continuous",
"Continuous.fst'",
"MeasureTheory.analyticSet_iff_exists_polishSpace_range",
"congrArg",
"Continuous.snd'",
"HEq.refl",
"Set.mem_image._simp_1",
"setOf",
"TopologicalSpace.IsCompletelyMetrizableSpace.prod",
"... | true |
_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_16 | Mathlib.Data.List.Cycle | [
"Iff.mpr",
"Lean.Grind.nestedProof",
"Membership.mem",
"List.length_pos_iff",
"_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14",
"instOfNatNat",
"List.cons",
"List",
"List.instMembership",
"Nat",
"LT.lt",
"instLTNat",
"OfNat.ofNat",
"Eq",
"List.... | false |
instMulActionSemiHomClassMulActionHom | Mathlib.GroupTheory.GroupAction.Hom | [
"SMul",
"MulActionSemiHomClass",
"instFunLikeMulActionHom",
"MulActionHom.map_smul'",
"MulActionHom",
"MulActionSemiHomClass.mk"
] | true |
ProbabilityTheory.Kernel.coe_mk | Mathlib.Probability.Kernel.Defs | [
"MeasureTheory.Measure.instMeasurableSpace",
"MeasureTheory.Measure",
"Measurable",
"ProbabilityTheory.Kernel.instFunLike",
"MeasurableSpace",
"ProbabilityTheory.Kernel.mk",
"Eq",
"DFunLike.coe",
"rfl",
"ProbabilityTheory.Kernel"
] | true |
_private.Mathlib.Data.Seq.Computation.0.Computation.LiftRel.symm.match_1_3 | Mathlib.Data.Seq.Computation | [
"Membership.mem",
"Exists",
"Computation",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"Computation.instMembership"
] | false |
CommGroupWithZero.instNormalizedGCDMonoid._proof_1 | Mathlib.Algebra.GCDMonoid.Basic | [
"CommMonoidWithZero.toCommMonoid",
"Units.val",
"GroupWithZero.toMonoidWithZero",
"of_eq_false",
"False",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"CommMonoid.toCommSemigroup",
"eq_false",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
"congrArg",
"Units.val... | false |
List.attach_reverse | Init.Data.List.Attach | [
"List.pmap_reverse._proof_1",
"Eq.mpr",
"List.map_pmap",
"congrArg",
"List.map",
"List.attach_cons.match_1",
"Membership.mem",
"List.reverse_pmap._proof_1",
"id",
"Subtype",
"List.pmap_congr_left",
"Subtype.mk",
"List.attach._proof_1",
"List.pmap",
"List",
"List.reverse_pmap",
"List.... | true |
AlgebraicGeometry.Scheme.Hom.normalizationDiagramMap._proof_1 | Mathlib.AlgebraicGeometry.Normalization | [
"Subalgebra.instSetLike",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"CommRingCat.hom_ext",
"CommRingCat.Hom.hom",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver... | false |
AlgebraicGeometry.Scheme.Cover.gluedCover._proof_4 | Mathlib.AlgebraicGeometry.Gluing | [
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"AlgebraicGeometry.Scheme.Cover.gluedCover.match_1",
"AlgebraicGeometry.Scheme.OpenCover",
"inferInstance",
"CategoryTheory.Limits.HasPullback",
"Prod.mk",
"CategoryTheory.PreZeroHypercover.X",
"Cat... | false |
Lean.Parser.Tactic.appendConfig | Init.Meta.Defs | [
"Lean.TSyntax",
"Array.instAppend",
"Lean.Parser.Tactic.getConfigItems",
"Lean.Syntax",
"Lean.TSyntaxArray",
"List.cons",
"instHAppendOfAppend",
"Lean.Parser.Tactic.mkOptConfig",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr4",
"HAppend.hAppend",
"List.nil"
] | true |
RightCancelSemigroup.toSemigroup | Mathlib.Algebra.Group.Defs | [
"Semigroup",
"RightCancelSemigroup"
] | true |
Subfield.extendScalars_self | Mathlib.FieldTheory.IntermediateField.Adjoin.Defs | [
"Eq.mpr",
"le_refl",
"Lattice.toSemilatticeSup",
"Subfield.toAlgebra",
"CompleteLattice.toLattice",
"congrArg",
"CommSemiring.toSemiring",
"IntermediateField",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RingHom",
"Membership.mem",
"Field.toDivisionRing",
"algebraMap",... | true |
MeasureTheory.diracProbaEquiv.congr_simp | Mathlib.MeasureTheory.Measure.DiracProba | [
"MeasureTheory.diracProba",
"Set.Elem",
"Equiv",
"MeasureTheory.ProbabilityMeasure",
"MeasureTheory.diracProbaEquiv",
"MeasurableSpace",
"TopologicalSpace",
"OpensMeasurableSpace",
"Eq.refl",
"Set.range",
"T0Space",
"Eq"
] | true |
HomologicalComplex.HomologySequence.snakeInput._proof_33 | Mathlib.Algebra.Homology.HomologySequence | [
"HomologicalComplex.HomologySequence.instEpiMap'ComposableArrows₃OfNatNat._proof_3",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"CategoryTheory.ComposableArrows.map'._proof_6",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"HomologicalComplex.HomologySequence.instEpiMap'ComposableArrow... | false |
Mathlib.Deriving.Fintype.«_aux_Mathlib_Tactic_DeriveFintype___macroRules_Mathlib_Deriving_Fintype_termDerive_fintype%__1» | Mathlib.Tactic.DeriveFintype | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",... | false |
_private.Lean.Elab.DocString.0.Lean.Doc.InternalState.mk.injEq | Lean.Elab.DocString | [
"Eq.propIntro",
"_private.Lean.Elab.DocString.0.Lean.Doc.InternalState.mk",
"String",
"Lean.Doc.InternalState",
"Lean.injEq_helper",
"Std.HashMap",
"instHashableString",
"instBEqOfDecidableEq",
"_private.Lean.Elab.DocString.0.Lean.Doc.Ref",
"And",
"instDecidableEqString",
"_private.Lean.Elab.D... | true |
CategoryTheory.Limits.ReflectsLimitsOfSize | Mathlib.CategoryTheory.Limits.Preserves.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.ReflectsLimitsOfSize.mk",
"CategoryTheory.Category"
] | true |
Matroid.Indep.exists_insert_of_not_maximal | Mathlib.Combinatorics.Matroid.Basic | [
"False",
"Iff.of_eq",
"congrArg",
"Matroid.IsBase.eq_of_subset_indep",
"Matroid.Indep.isBase_of_maximal",
"_private.Mathlib.Combinatorics.Matroid.Basic.0.Matroid.Indep.exists_insert_of_not_maximal._simp_1_5",
"Membership.mem",
"Exists",
"Matroid.IsBase",
"Eq.mp",
"Matroid.Indep",
"Insert.inser... | true |
LieModule.iSupIndep_genWeightSpace | Mathlib.Algebra.Lie.Weights.Basic | [
"LieHom",
"Module.End.instRing",
"Eq.mpr",
"Submodule",
"IsDomain",
"CommRing",
"iInf",
"LieModule.genWeightSpaceOf",
"iSupIndep",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"LieSubmodule.instInfSet",
"LieRing.IsNilpotent",
"Modu... | true |
Submodule.comapSubtypeEquivOfLe._proof_3 | Mathlib.Algebra.Module.Submodule.Map | [
"Submodule",
"Submodule.addCommMonoid",
"Membership.mem",
"Subtype",
"Submodule.module",
"AddCommMonoid",
"Submodule.comap",
"Submodule.setLike",
"Submodule.subtype",
"Semiring",
"Module",
"Subtype.val",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"SetLike.instMembership",
"Subtype.pr... | false |
Aesop.TreeM.Context.mk.noConfusion | Aesop.Tree.TreeM | [
"Aesop.TreeM.Context.noConfusion",
"id",
"Aesop.LocalRuleSet",
"Aesop.Iteration",
"Aesop.TreeM.Context.mk",
"Aesop.TreeM.Context",
"Eq"
] | false |
_private.Mathlib.NumberTheory.ModularForms.QExpansion.0.ModularFormClass.qExpansion_coeff_eq_intervalIntegral._simp_1_1 | Mathlib.NumberTheory.ModularForms.QExpansion | [
"Real",
"instHSMul",
"HMul.hMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"intervalIntegral",
"Real.measureSpace",
"AddZeroClass.toAddZero",
"Real.semiring",
"DistribSMul.toSMulZeroClass",
"ESe... | false |
CategoryTheory.ShortComplex.LeftHomologyMapData.compatibilityOfZerosOfIsColimitCokernelCofork._proof_3 | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData.f'",
"CategoryTheory.ShortComplex.LeftHomologyData.ofZeros_f'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.ShortComp... | false |
Std.IterM.DefaultConsumers.forIn'_eq_forIn'._unary | Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop | [
"Pure.pure",
"Eq.mpr",
"Std.IterM.DefaultConsumers.forIn'_eq_match_step.match_3",
"Std.IterStep",
"Std.IterStep.successor",
"Std.IterM.IsPlausibleIndirectOutput.indirect",
"congrArg",
"Std.Shrink",
"Std.IterM.DefaultConsumers.forIn'",
"Monad.toApplicative",
"invImage",
"Std.IteratorLoop.WithWF... | false |
_private.Mathlib.Probability.Kernel.IonescuTulcea.Maps.0.IicProdIoc_preimage._simp_1_2 | Mathlib.Probability.Kernel.IonescuTulcea.Maps | [
"Membership.mem",
"Set.mem_pi",
"propext",
"Set.pi",
"Eq",
"Set.instMembership",
"Set"
] | false |
FormalMultilinearSeries.applyComposition_ones | Mathlib.Analysis.Analytic.Composition | [
"Eq.mpr",
"FormalMultilinearSeries.congr",
"Fin.ext_iff",
"CommRing",
"_private.Mathlib.Analysis.Analytic.Composition.0.FormalMultilinearSeries.applyComposition_ones._proof_1_1",
"Composition.length",
"congrArg",
"CommSemiring.toSemiring",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul... | true |
_private.Mathlib.Analysis.Convex.Integral.0.Convex.integral_mem._simp_1_3 | Mathlib.Analysis.Convex.Integral | [
"MeasureTheory.SimpleFunc.mem_range",
"Finset",
"MeasureTheory.SimpleFunc",
"Membership.mem",
"MeasureTheory.SimpleFunc.instFunLike",
"MeasurableSpace",
"Finset.instSetLike",
"propext",
"Set.range",
"MeasureTheory.SimpleFunc.range",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"SetLike.inst... | false |
CategoryTheory.Bicategory.LeftLift.whiskering | Mathlib.CategoryTheory.Bicategory.Extension | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.Bicategory.LeftLift.homMk",
"CategoryTheory.Bicategory.LeftLift.lift",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory.LeftLift.whiskering._proof_4",
... | true |
Lean.Elab.Tactic.liftMetaTacticAux | Lean.Elab.Tactic.Basic | [
"Pure.pure",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"Lean.Elab.Tactic.getMainGoal",
"Lean.Meta.State",
"instMonadLiftT",
"Lean.Elab.Tactic.Context",
"Lean.MVarId",
"Lean.Meta.MetaM",
"IO.RealWorld",
"liftM",
"ReaderT.instMonadLift",
"Lean.Elab.Tactic.instMonadTacticM",
"Applicativ... | true |
Bool.recOn._@.Mathlib.Util.CompileInductive.3618634379._hygCtx._hyg.5 | Mathlib.Util.CompileInductive | [
"Bool.true",
"Bool.rec",
"Bool",
"Bool.false"
] | false |
Topology.IsInducing.isOpenMap | Mathlib.Topology.Maps.Basic | [
"Set.mem_range_self",
"Topology.IsInducing.map_nhds_of_mem",
"Eq.ge",
"Filter.map",
"PartialOrder.toPreorder",
"nhds",
"IsOpenMap",
"Topology.IsInducing",
"TopologicalSpace",
"IsOpen.mem_nhds",
"IsOpen",
"Set.range",
"IsOpenMap.of_nhds_le",
"Filter",
"Filter.instPartialOrder"
] | true |
CategoryTheory.CartesianMonoidalCategory.whiskerRight_toUnit_comp_leftUnitor_hom_assoc | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"CategoryTheory.SemiCartesianMonoidalCategory.snd",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.SemiCartesianMonoidalCat... | true |
CategoryTheory.Limits.ker._proof_5 | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.equalizer",
"CategoryTheory.Limits.ker._proof_1",
"CategoryTheory.Comma.left",
"CategoryTheory.Limits.... | false |
MeasureTheory.Measure.ext_of_generateFrom_of_iUnion | Mathlib.MeasureTheory.Measure.Restrict | [
"MeasureTheory.Measure",
"Set.univ",
"IsPiSystem",
"Membership.mem",
"Ne",
"MeasurableSpace.generateFrom",
"Set.countable_range",
"MeasurableSpace",
"Exists.casesOn",
"Nat",
"ENNReal",
"Eq.ndrec",
"instTopENNReal",
"MeasureTheory.Measure.ext_of_generateFrom_of_cover_subset",
"Set.range",... | true |
CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac_app | Mathlib.CategoryTheory.MorphismProperty.Factorization | [
"CategoryTheory.MorphismProperty.FunctorialFactorizationData",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.MorphismProperty.FunctorialFactorizationData.fac",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
... | true |
Submonoid.unitsTypeEquivIsUnitSubmonoid._proof_1 | Mathlib.Algebra.Group.Submonoid.Operations | [
"Monoid",
"Units.val",
"Monoid.toMulOneClass",
"Membership.mem",
"IsUnit.submonoid",
"Units",
"id",
"Subtype",
"Subtype.mk",
"Subtype.prop",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"IsUnit.unit",
"Eq.refl",
"Submonoid.instSetLike",
"Units.isUnit",
"Subtype.val",
"Eq",
"SetLike.ins... | false |
TrivSqZeroExt.kerIdeal._proof_2 | Mathlib.Algebra.TrivSqZeroExt.Ideal | [
"CommSemiring.toSemiring",
"IsScalarTower",
"IsScalarTower.left",
"AddCommMonoid",
"CommSemiring",
"Monoid.toSemigroup",
"Monoid.toMulAction",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.toAddMonoid",
"Module",
"MulAction.toSemigroupAction",
"MonoidWithZero.toMonoid... | false |
Std.HashSet.erase_emptyWithCapacity | Std.Data.HashSet.Lemmas | [
"Std.HashSet.erase",
"Std.HashSet",
"Std.HashMap.erase_emptyWithCapacity",
"_private.Std.Data.HashSet.Lemmas.0.Std.HashSet.ext",
"Unit",
"Nat",
"Hashable",
"Std.HashSet.emptyWithCapacity",
"BEq",
"Eq"
] | true |
Set.vadd_set_univ_pi | Mathlib.Algebra.Group.Pointwise.Set.Scalar | [
"Pi.instVAdd",
"Set.univ",
"Set.vaddSet",
"VAdd",
"Set.piMap_image_univ_pi",
"HVAdd.hVAdd",
"instHVAdd",
"Set.pi",
"VAdd.vadd",
"Eq",
"Set"
] | true |
HomologicalComplex.cyclesFunctor_map | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.cyclesFunctor",
"HomologicalComplex.homologyFunctor._proof_1",
"HomologicalComplex",
"ComplexShape",
"CategoryTheory.Functor.map",
"HomologicalCo... | true |
Nat.Partrec.Code.zero.elim | Mathlib.Computability.PartrecCode | [
"PULift.up",
"Nat.Partrec.Code",
"Nat",
"Nat.Partrec.Code.zero",
"Nat.Partrec.Code.ctorIdx",
"Eq.symm",
"Eq",
"Nat.Partrec.Code.ctorElim"
] | false |
AlgebraicTopology.NormalizedMooreComplex.objD._proof_1 | Mathlib.AlgebraicTopology.MooreComplex | [
"Finset.univ",
"Fin.succ",
"Finset",
"Membership.mem",
"instOfNatNat",
"Fin.fintype",
"instHAdd",
"Finset.instSetLike",
"HAdd.hAdd",
"Nat",
"of_eq_true",
"instAddNat",
"Finset.mem_univ._simp_1",
"OfNat.ofNat",
"Fin",
"SetLike.instMembership"
] | false |
ComplexShape.Embedding.not_boundaryGE_next' | Mathlib.Algebra.Homology.Embedding.Boundary | [
"Eq.mpr",
"ComplexShape.Embedding.BoundaryGE",
"congrArg",
"Classical.propDecidable",
"id",
"ComplexShape",
"dite",
"ComplexShape.next",
"ComplexShape.next_eq_self",
"Eq.ndrec",
"ComplexShape.Embedding",
"ComplexShape.Embedding.not_boundaryGE_next",
"Eq",
"ComplexShape.Embedding.IsRelIff",... | true |
_private.Batteries.Data.MLList.Basic.0.MLList.Spec.noConfusion | Batteries.Data.MLList.Basic | [
"_private.Batteries.Data.MLList.Basic.0.MLList.Spec.casesOn",
"HEq.refl",
"Unit",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Prod",
"Monad",
"_private.Batteries.Data.MLList.Basic.0.MLList.Spec",
"Eq",
"_private.Batteries.Data.MLList.Basic.0.MLList.Spec.noConfusionType",
"Option"
] | false |
Rat.cast_min | Mathlib.Data.Rat.Cast.Order | [
"Rat.instInf",
"DivisionRing.toRatCast",
"LinearOrder",
"Rat",
"Rat.linearOrder",
"IsStrictOrderedRing",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Rat.cast",
"SemilatticeInf.toMin",
"Field.toSemifield",
"Rat.cast_mono",
"Semifield.toDivisionSemir... | true |
Mathlib.Meta.FunProp.Config.mk | Mathlib.Tactic.FunProp.Types | [
"Mathlib.Meta.FunProp.Config.mk",
"Nat",
"Mathlib.Meta.FunProp.Config"
] | true |
ZMod.val_le | Mathlib.Data.ZMod.Basic | [
"Nat.instMulZeroClass",
"LT.lt.le",
"LE.le",
"instLENat",
"ZMod",
"Nat.instPreorder",
"Nat",
"NeZero",
"ZMod.val_lt",
"MulZeroClass.toZero",
"ZMod.val"
] | true |
_private.Lean.Data.KVMap.0.Lean.KVMap.insert.match_1 | Lean.Data.KVMap | [
"Lean.KVMap.mk",
"List",
"Lean.KVMap.casesOn",
"Lean.Name",
"Lean.DataValue",
"Prod",
"Lean.KVMap"
] | false |
HomologicalComplex.truncLE'ToRestriction_naturality | Mathlib.Algebra.Homology.Embedding.TruncLE | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"HomologicalComplex.truncLE'",
"HomologicalComplex.restrictionMap",
"HomologicalComplex.HasHomology",
"HomologicalC... | true |
_private.Mathlib.Order.Interval.Finset.Fin.0.Fin.finsetImage_val_Iio._simp_1_1 | Mathlib.Order.Interval.Finset.Fin | [
"Finset",
"Finset.coe_inj",
"SetLike.coe",
"Finset.instSetLike",
"propext",
"Eq.symm",
"Eq",
"Set"
] | false |
_private.Mathlib.RingTheory.Extension.Presentation.Submersive.0.Algebra.PreSubmersivePresentation.jacobian_reindex._simp_1_4 | Mathlib.RingTheory.Extension.Presentation.Submersive | [
"AlgHom",
"AlgHom.funLike",
"Algebra",
"Function.comp",
"CommSemiring",
"AlgHom.coe_comp",
"Semiring",
"AlgHom.comp",
"Eq.symm",
"Eq",
"DFunLike.coe"
] | false |
Lean.AttributeImpl.applicationTime._inherited_default | Lean.Attributes | [
"Lean.AttributeApplicationTime",
"id",
"Lean.AttributeApplicationTime.afterTypeChecking"
] | false |
ProbabilityTheory.setBernoulli._proof_1 | Mathlib.Probability.Distributions.SetBernoulli | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"NNReal.instCommSemiring",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"instDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"Algebra.id",
"DistribSMul.toSMulZeroClass",
"NNReal",
"AddCommM... | false |
instCoeSortProfiniteGrpType | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"ProfiniteGrp",
"TotallyDisconnectedSpace",
"TopCat.str",
"TopCat.carrier",
"ProfiniteGrp.toProfinite",
"CoeSort.mk",
"TopCat",
"CompHausLike.toTop",
"CoeSort"
] | true |
Topology.IsQuotientMap.trivializationOfSMulDisjoint._proof_9 | Mathlib.Topology.Covering.Quotient | [
"Iff.mpr",
"Eq.mpr",
"instHSMul",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Monoid.toMulOneClass",
"congrArg",
"mul_inv_eq_one",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Group.toDi... | false |
Order.krullDim_int | Mathlib.Order.KrullDimension | [
"Int.instAddCommGroup",
"Order.krullDim_of_noMaxOrder",
"WithBot",
"Int.instInhabited",
"instTopENat",
"Int.instLinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"WithBot.instTop",
"Int",
"Order.krullDim",
"instNonemptyOfInhabited",
"ENat",
"instLatticeInt",
"Line... | true |
MvPolynomial.support_rename_killCompl_subset | Mathlib.Algebra.MvPolynomial.Rename | [
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"MvPolynomial.killCompl",
"congrArg",
"CommSemiring.toSemiring",
"Function.Injective.injOn",
"MvPolynomial.support_killCompl",
"AlgHom",
"Finset",
"Finsupp.mapDomain",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"AddMonoidAlg... | true |
MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_left | Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym | [
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure.rnDeriv_add_of_mutuallySingular",
"MeasureTheory.Measure",
"MeasureTheory.instSFiniteOfSigmaFinite",
"congrArg",
"MeasureTheory.Measure.haveLebesgueDecomposition_add",
"MeasureTheory.SigmaFinite",
"Filter.Eve... | true |
AdicCompletion.instCommRingAdicCauchySequence | Mathlib.RingTheory.AdicCompletion.Algebra | [
"CommRing",
"Semiring.toModule",
"AdicCompletion.instCommRingAdicCauchySequence._proof_3",
"CommSemiring.toSemiring",
"Pi.commRing",
"AdicCompletion.instOneAdicCauchySequence",
"AdicCompletion.AdicCauchySequence.instSub",
"AdicCompletion.instCommRingAdicCauchySequence._proof_9",
"AdicCompletion.inst... | true |
CochainComplex.homOfDegreewiseSplit | Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit | [
"CochainComplex.cocycleOfDegreewiseSplit",
"HomologicalComplex.instCategory",
"CochainComplex.cocycleOfDegreewiseSplit._proof_10",
"CategoryTheory.CategoryStruct.toQuiver",
"CochainComplex.homOfDegreewiseSplit._proof_1",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.ShortComplex",
"A... | true |
_private.Mathlib.Tactic.NormNum.ModEq.0.Mathlib.Meta.NormNum.evalNatModEq.match_1 | Mathlib.Tactic.NormNum.ModEq | [
"Lean.Expr.sort",
"Lean.Level",
"Mathlib.Meta.NormNum.BoolResult",
"Qq.Quoted",
"Bool",
"Sigma.mk",
"Sigma.casesOn",
"Lean.Level.succ",
"Lean.Level.instOfNat",
"OfNat.ofNat",
"Sigma"
] | false |
upperSemicontinuous_biInf | Mathlib.Topology.Semicontinuity.Basic | [
"iInf",
"CompleteLattice.instOmegaCompletePartialOrder",
"CompletelyDistribLattice.toCompleteLattice",
"PartialOrder.toPreorder",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"upperSemicontinuous_iInf",
"UpperSemicontinuous",
"TopologicalSpace",
"CompleteLinearOrder.toCondition... | true |
_private.Std.Time.Time.HourMarker.0.Std.Time.HourMarker.toAbsolute._proof_1 | Std.Time.Time.HourMarker | [
"of_decide_eq_true",
"Int.decLe",
"id",
"Int",
"LE.le",
"Bool.true",
"instOfNat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable.decide",
"Eq",
"Int.instLEInt"
] | false |
Equiv.Perm.one_lt_of_mem_cycleType | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.Perm.cycleType",
"Membership.mem",
"Multiset",
"instOfNatNat",
"Multiset.instMembership",
"Equiv.Perm.two_le_of_mem_cycleType",
"Fintype",
"Equiv.Perm",
"Nat",
"LT.lt",
"instLTNat",
"OfNat.ofNat",
"DecidableEq"
] | true |
Nat.two_pow_pred_mul_two | Init.Data.Nat.Lemmas | [
"instPowNat",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"instSubNat",
"instMulNat",
"instOfNatNat",
"instNatPowNat",
"instHSub",
"Nat.sub_add_cancel",
"HPow.hPow",
"Nat",
"LT.lt",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"instHPow",
"instLTNat",
"OfNat.ofNat",
"Nat.succ",
... | true |
Lean.Meta.Config.ctxApprox._default | Lean.Meta.Basic | [
"id",
"Bool",
"Bool.false"
] | false |
_private.Mathlib.Algebra.Group.Defs.0.npowBinRec.go_spec._proof_1_6 | Mathlib.Algebra.Group.Defs | [
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"Lean.Grind.not_not",
"HMul.hMul",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Int.Linear.le_of_le_diseq",
"Nat.ToInt.natCast_ofNat",
"id",
"Lean.RArray",
"Int.instNegInt",
"Int.Linear.eq_le_subst_nonneg",
"Ne",
"instMu... | false |
AddGroupNormClass.toAddGroupSeminormClass | Mathlib.Algebra.Order.Hom.Basic | [
"outParam",
"AddGroupSeminormClass",
"PartialOrder",
"AddCommMonoid",
"AddGroup",
"AddGroupNormClass",
"FunLike"
] | true |
_private.Mathlib.Analysis.Convex.Deriv.0.bddBelow_slope_lt_of_mem_interior.match_1_1 | Mathlib.Analysis.Convex.Deriv | [
"Preorder.toLT",
"Semiring.toModule",
"AddGroupWithOne.toAddGroup",
"LinearOrder",
"PartialOrder.toPreorder",
"setOf",
"Membership.mem",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"addGroupIsAddTorsor",
"DivisionRing.toRing",
"slope",
"Field.toSemi... | false |
NonUnitalSubring.instSetLike | Mathlib.RingTheory.NonUnitalSubring.Defs | [
"SetLike",
"NonUnitalNonAssocRing",
"AddMonoid.toAddZeroClass",
"AddSubsemigroup.carrier",
"NonUnitalSubring",
"AddZeroClass.toAddZero",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"AddSubmonoid.toAddSubsemigroup",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"SetLike.mk",
"NonUnitalSub... | true |
Filter.Germ.instDivisionRing._proof_6 | Mathlib.Order.Filter.FilterProduct | [
"Nontrivial",
"Filter.Germ.instDivisionSemiring",
"DivisionRing.toDivisionSemiring",
"Filter.Germ",
"DivisionSemiring.toNontrivial",
"DivisionRing",
"Ultrafilter",
"Ultrafilter.toFilter"
] | false |
LinearMap.shortComplexKer._proof_1 | Mathlib.Algebra.Homology.ShortComplex.ModuleCat | [
"Submodule",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"LinearMap.ext",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"LinearMap.instFunLike",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Subtype",
"Sub... | false |
MulOpposite.instSemifield._proof_2 | Mathlib.Algebra.Field.Opposite | [
"Semiring.toOne",
"DivisionSemiring.zpow",
"MulOpposite",
"DivisionSemiring.zpow_zero'",
"Semifield",
"Int",
"Semifield.toDivisionSemiring",
"instOfNat",
"MulOpposite.instDivisionSemiring",
"DivisionSemiring.toSemiring",
"One.toOfNat1",
"OfNat.ofNat",
"Eq"
] | false |
StarMulEquiv.coe_trans | Mathlib.Algebra.Star.MonoidHom | [
"StarMulEquiv",
"Mul",
"Function.comp",
"StarMulEquiv.instEquivLike",
"Star",
"StarMulEquiv.trans",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
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