name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Topology.Homotopy.HSpaces.0.HSpace.prod._simp_2 | Mathlib.Topology.Homotopy.HSpaces | [
"Prod.mk_inj",
"Prod.mk",
"And",
"propext",
"Prod",
"Eq"
] | false |
Topology.isEmbedding_sigmoid | Mathlib.Analysis.SpecialFunctions.Sigmoid | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"Set.Icc.instZero",
"Real.instZero",
"PartialOrder.toPreorder",
"Subtype.instLinearOrder",
"PseudoMetricSpace.toUniformSpace",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Eq.rec",
"Real.semirin... | true |
ContinuousOrderHom.instContinuousOrderHomClass | Mathlib.Topology.Order.Hom.Basic | [
"ContinuousOrderHom",
"ContinuousOrderHom.continuous_toFun",
"TopologicalSpace",
"ContinuousMapClass.mk",
"ContinuousOrderHom.toOrderHom",
"ContinuousOrderHomClass",
"ContinuousOrderHom.instFunLike",
"ContinuousOrderHomClass.mk",
"Preorder",
"OrderHom.monotone'"
] | true |
differentiableAt_natCast | Mathlib.Analysis.Calculus.FDeriv.Const | [
"AddCommGroup.toAddCommMonoid",
"DifferentiableAt",
"NormedField.toField",
"Pi.instNatCast",
"AddCommGroup",
"NatCast",
"Nat.cast",
"Field.toSemifield",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"Nat",
"differentiableAt_const",
"DivisionSemiring.toSemiring",
"NontriviallyNormedFi... | true |
_private.Mathlib.Analysis.Calculus.FDeriv.Partial.0.hasStrictFDerivAt_uncurry_coprod.match_1_1 | Mathlib.Analysis.Calculus.FDeriv.Partial | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Std.DTreeMap.Internal.Impl.Const.maxEntry.match_1 | Std.Data.DTreeMap.Internal.Queries | [
"False",
"Std.DTreeMap.Internal.Impl.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"namedPattern",
"Std.DTreeMap.Internal.Impl.inner",
"Eq.casesOn",
"Bool.ctorIdx",
"Bool.true",
"Std.DTreeMap.Internal.Impl.leaf",
"Std.DTreeMap.Internal.Impl.isEmpty",
"Nat",
"Bool",
"Eq.refl",... | false |
intervalIntegral.integral_finset_sum | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | [
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"IntervalIntegrable",
"AddCommGroup.toAddCommMonoid",
"Finset",
"PseudoMetricSpace.toUniformSpace",
"intervalIntegral",
"Membership.mem",
"NormedAddGroup.toENormedAddMonoid",
"intervalIntegral.integral_finsetSum",
"Real.measurableSpace",
"Semin... | true |
ContinuousAffineEquiv.prodAssoc_toAffineEquiv | Mathlib.Topology.Algebra.ContinuousAffineEquiv | [
"AffineEquiv.prodAssoc",
"AddCommGroup.toAddCommMonoid",
"instTopologicalSpaceProd",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"TopologicalSpace",
"Prod.instAddTorsor",
"AddTorsor",
"Eq.refl",
"ContinuousAffineEquiv.toAffineEquiv",
"Module",
"Prod",
"Prod.instModule",
"AffineEquiv",
"Ri... | true |
CommGrpCat.coyoneda.eq_1 | Mathlib.Algebra.Category.Grp.Yoneda | [
"CommGrpCat.coyoneda._proof_3",
"CommGrpCat.coyoneda._proof_1",
"MonoidHom.instCommGroup",
"CategoryTheory.Functor",
"MonoidHom.instFunLike",
"Opposite",
"CommGrpCat.coyoneda",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CommGrpCat.coyoneda._pr... | true |
StrictAnti.wellFoundedLT | Mathlib.Order.Monotone.Basic | [
"instIsWellFoundedInvImage",
"Preorder.toLT",
"InvImage",
"WellFoundedLT",
"WellFoundedGT",
"GT.gt",
"StrictAnti",
"LT.lt",
"Preorder",
"Subrelation.isWellFounded",
"StrictAnti.imp"
] | true |
Filter.tendsto_atTop_mono' | Mathlib.Order.Filter.AtTopBot.Tendsto | [
"Iff.mpr",
"Filter.Eventually",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Filter.mp_mem",
"id",
"LE.le",
"Filter.tendsto_atTop",
"Filter.atTop",
"Filter.Tendsto",
"Iff.mp",
"Filter.EventuallyLE",
"Set.instMembership",
"Filter",
"Filter.univ_mem'",
"Preorder",
"le_trans",
"Set"... | true |
segment_eq_image' | Mathlib.Analysis.Convex.Segment | [
"Eq.mpr",
"instHSMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"sub_smul",
"Preorder.toLE",
"AddCommGrou... | true |
Bool.le_true._simp_1 | Init.Data.Bool | [
"Bool.le_true",
"LE.le",
"Bool.true",
"Bool.instLE",
"True",
"eq_true",
"Bool",
"Eq"
] | false |
Finset.prod_filter | Mathlib.Algebra.BigOperators.Group.Finset.Basic | [
"Eq.mpr",
"MulOne.toOne",
"Trans.trans",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Membership.mem",
"Finset.filter_subset",
"Eq.mp",
"id",
"Finset.prod_congr",
"Finset.prod_subset",
"if_pos",
"Finset.prod",
"instTransEq",
"MulOneClass.toMulOne",
"And",
"And.right",
"Finset.i... | true |
_private.Lean.Elab.DeclModifiers.0.Lean.Elab.Modifiers.isNoncomputable.match_1 | Lean.Elab.DeclModifiers | [
"Unit.unit",
"Lean.Elab.ComputeKind",
"Lean.Elab.ComputeKind.ctorIdx",
"Nat.hasNotBit",
"Lean.Elab.ComputeKind.noncomputable",
"Unit",
"_private.Lean.Elab.DeclModifiers.0.Lean.Elab.Modifiers.isNoncomputable._sparseCasesOn_1"
] | false |
Multiset.zero_disjoint | Mathlib.Data.Multiset.UnionInter | [
"Disjoint",
"disjoint_bot_left",
"Multiset",
"Multiset.instOrderBot",
"Zero.toOfNat0",
"OfNat.ofNat",
"Multiset.instPartialOrder",
"Multiset.instZero"
] | true |
CategoryTheory.CommGrpObj | Mathlib.CategoryTheory.Monoidal.Cartesian.CommGrp_ | [
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.BraidedCategory",
"CategoryTheory.CommGrpObj.mk",
"CategoryTheory.Category",
"CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory"
] | true |
_private.Lean.Elab.Tactic.Grind.BuiltinTactic.0.Lean.Elab.Tactic.Grind.evalFail._regBuiltin._private.Lean.Elab.Tactic.Grind.BuiltinTactic.0.Lean.Elab.Tactic.Grind.evalFail_1 | Lean.Elab.Tactic.Grind.BuiltinTactic | [
"Lean.Name.mkStr5",
"IO",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.str",
"Lean.Name.anonymous",
"Unit",
"Lean.Elab.Tactic.Grind.GrindTactic",
"Nat",
"_private.Lean.Elab.Tactic.Grind.BuiltinTactic.0.Lean.Elab.Tactic.Grind.evalFail",
"OfNat.ofNat",
"Lean.Elab.Tactic.Grind.grindTacElabAttribut... | false |
Fin.univ_image_get | Mathlib.Data.Fintype.Basic | [
"List.ofFn_get",
"Finset.univ",
"congrArg",
"Finset",
"List.get",
"List.ofFn",
"List.toFinset",
"Fin.fintype",
"List",
"Fin.univ_image_def",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Fin",
"Eq",
"List.length",
"Finset.image",
"Eq.trans",
"DecidableEq"
] | true |
Std.DTreeMap.instUnion | Std.Data.DTreeMap.Basic | [
"Std.DTreeMap",
"Union",
"Ordering",
"Std.DTreeMap.union",
"Union.mk"
] | true |
Polynomial.UniversalCoprimeFactorizationRing.isCoprime_factor₁_factor₂ | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"IsUnit.mul_iff",
"Polynomial.MonicDegreeEq.monic",
"Nontrivial",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"Polynomial.UniversalCoprimeFactorizationRing",
"Polynomial.instOne",
"CommRing",
"HMul.hMul",
"Polynomial.MonicDegreeEq",
... | true |
ComplexShape.notMem_range_embeddingUpIntLE_iff | Mathlib.Algebra.Homology.Embedding.Basic | [
"ComplexShape.embeddingUpIntLE",
"Nat.instOne",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.instAddCancelCommMonoid",
"id",
"Ne",
"Int",
"Int.instLTInt",
"AddMonoidWithOne.toOne",
"Iff",
"instHSub",
"_private.Mathlib.Algebra.Homology.Em... | true |
PMF.filter_apply_eq_zero_iff | Mathlib.Probability.ProbabilityMassFunction.Constructions | [
"Eq.mpr",
"congrArg",
"PMF",
"Set.mem_inter_iff",
"Iff.rfl",
"PMF.instFunLike",
"Membership.mem",
"Exists",
"PMF.support",
"id",
"Set.instInter",
"PMF.filter",
"PMF.support_filter",
"Inter.inter",
"PMF.apply_eq_zero_iff",
"And",
"Iff",
"not_and_or",
"ENNReal",
"propext",
"Zer... | true |
CliffordAlgebra.EvenHom._sizeOf_1 | Mathlib.LinearAlgebra.CliffordAlgebra.Even | [
"CommRing",
"instHSMul",
"Semiring.toModule",
"HMul.hMul",
"CliffordAlgebra.EvenHom",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"CliffordAlgebra.EvenHom.rec",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"QuadraticForm",
"LinearMap.instFunLike",
"Algebra",
"RingHom",
"Al... | false |
Finsupp.lcoeFun._proof_1 | Mathlib.LinearAlgebra.Finsupp.Pi | [
"Finsupp.instFunLike",
"Pi.addCommMonoid",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"AddZero.toZero",
"funext",
"instHAdd",
"HAdd.hAdd",
"eq_self",
"of_eq_true",
"AddZero.toAdd",
"AddCommMonoid.toAddMonoid",
"AddCommSemigroup.toA... | false |
_private.Mathlib.Order.Heyting.Hom.0.OrderIsoClass.toHeytingHomClass._simp_1 | Mathlib.Order.Heyting.Hom | [
"map_inv_le_iff",
"LE.le",
"LE",
"OrderIsoClass",
"EquivLike",
"propext",
"EquivLike.inv",
"Eq.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
CategoryTheory.PreGaloisCategory.instPreservesColimitsOfShapeActionFintypeCatAutFunctorSingleObjFunctorToActionOfFinite | Mathlib.CategoryTheory.Galois.Action | [
"CategoryTheory.GaloisCategory.toPreGaloisCategory",
"CategoryTheory.Functor",
"_private.Mathlib.CategoryTheory.Galois.Action.0.CategoryTheory.PreGaloisCategory.instPreservesColimitsOfShapeActionFintypeCatAutFunctorSingleObjFunctorToActionOfFinite._proof_1",
"Finite",
"FintypeCat",
"CategoryTheory.Functor... | true |
CStarMatrix.toCLM_apply_single_apply | Mathlib.Analysis.CStarAlgebra.CStarMatrix | [
"Pi.uniformSpace",
"Pi.Function.module",
"CStarMatrix.instModule",
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"Equiv.instEquivLike",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Complex.commRing",
"congrArg",
"DistribMulAct... | true |
_private.Lean.MetavarContext.0.Lean.DependsOn.dep.visit | Lean.MetavarContext | [
"Lean.DependsOn.State",
"Inhabited.default",
"instInhabitedOfMonad",
"instInhabitedBool",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Id",
"_private.Lean.MetavarContext.0.Lean.DependsOn.M",
"Bool",
"Id.instMonad",
"StateT.instMonad"
] | true |
ULift.instLinearOrder._proof_2 | Mathlib.Order.Lattice | [
"Preorder.toLT",
"ULift.instLT_mathlib",
"LinearOrder",
"PartialOrder.toPreorder",
"ULift",
"ULift.down_lt",
"Iff",
"LT.lt",
"LinearOrder.toPartialOrder",
"ULift.down"
] | false |
Metric.closedBall_subset_closedBall | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Real.instLE",
"Real",
"HasSubset.Subset",
"LE.le",
"PseudoMetricSpace",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Metric.closedBall",
"Real.instPreorder",
"Set.instHasSubset",
"le_trans",
"Set"
] | true |
Array.extract_size_left | Init.Data.Array.Extract | [
"Eq.mpr",
"id",
"LE.le",
"instLENat",
"Array.extract",
"List.toArray",
"Array",
"_private.Init.Data.Array.Extract.0.Array.extract_size_left._proof_1_1",
"Nat",
"Decidable.byContradiction",
"Eq",
"Array.size",
"Not",
"Nat.decLe",
"Min.min",
"instMinNat",
"List.nil",
"Array.extract_e... | true |
LinearEquiv.curry._proof_2 | Mathlib.Algebra.Module.Equiv.Basic | [
"Pi.Function.module",
"instHSMul",
"Pi.addCommMonoid",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"Equiv.toFun",
"AddCommMonoid",
"AddZero.toZero",
"Semiring.toMonoid",
"Semiring",
"Equiv.curry",
"HSMul.hSMul",
"... | false |
_private.Mathlib.Topology.Algebra.Valued.LocallyCompact.0.Valued.integer.mem_iff._simp_1_2 | Mathlib.Topology.Algebra.Valued.LocallyCompact | [
"Real.instLE",
"Real",
"PartialOrder.toPreorder",
"Preorder.toLE",
"NNReal",
"LE.le",
"NNReal.instPartialOrder",
"propext",
"Eq.symm",
"Eq",
"NNReal.toReal",
"NNReal.coe_le_coe"
] | false |
DirichletCharacter.LFunction_ne_zero_of_one_le_re | Mathlib.NumberTheory.LSeries.Nonvanishing | [
"LE.le.eq_or_lt",
"Nat.instMulZeroClass",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
"ZMod.commRing",
"DirichletCharacter.LFunction_eq_LSeries",
"MulChar.hasOne",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Complex.instZero",
"DirichletCharacter.LFunct... | true |
_private.Lean.Environment.0.Lean.ImportedModule.mk.injEq | Lean.Environment | [
"_private.Lean.Environment.0.Lean.ImportedModule.mk.inj",
"Lean.EffectiveImport",
"Eq.propIntro",
"Lean.CompactedRegion",
"Lean.injEq_helper",
"_private.Lean.Environment.0.Lean.ImportedModule.mk",
"Array",
"And",
"Bool",
"Eq.ndrec",
"Eq.refl",
"_private.Lean.Environment.0.Lean.ImportedModule",... | true |
Std.Rxo.Iterator.mk.sizeOf_spec | Init.Data.Range.Polymorphic.RangeIterator | [
"Std.Rxo.Iterator._sizeOf_inst",
"Option._sizeOf_inst",
"Std.Rxo.Iterator.mk",
"instOfNatNat",
"Std.Rxo.Iterator",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"SizeOf",
"OfNat.ofNat",
"Eq",
"Option"
] | true |
_private.Std.Internal.Http.Data.Body.Full.0.Std.Http.Body.Full.mk.injEq | Std.Internal.Http.Data.Body.Full | [
"_private.Std.Internal.Http.Data.Body.Full.0.Std.Http.Body.Full.mk",
"Eq.propIntro",
"Std.Mutex",
"Eq.ndrec",
"Eq.refl",
"ByteArray",
"Std.Http.Body.Full",
"Eq",
"_private.Std.Internal.Http.Data.Body.Full.0.Std.Http.Body.Full.mk.inj",
"Option"
] | true |
normalClosure_of_stabilizer_eq_top | Mathlib.GroupTheory.GroupAction.Jordan | [
"SubMulAction.mulAction",
"Nontrivial",
"SubMulAction.instSetLike",
"Eq.mpr",
"False",
"Subgroup.le_normalClosure",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"instHSMul",
"Preorder.toLT",
"inv_smul_eq_iff",
"instCompleteLinearOrderENat",
"Nat.instIsOrderedAddMonoid",
"instSMulOfMul",
"ins... | true |
_private.Aesop.Util.Tactic.Ext.0.Aesop.straightLineExt.go._sparseCasesOn_5 | Aesop.Util.Tactic.Ext | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.Integrals.Basic.0.integral_cos_sq._simp_1_3 | Mathlib.Analysis.SpecialFunctions.Integrals.Basic | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
Subgroup.exists_smul_eq | Mathlib.GroupTheory.SchurZassenhaus | [
"Quotient.sound'",
"Iff.mpr",
"Eq.mpr",
"Nat.Coprime",
"MulOne.toOne",
"Equiv.apply_symm_apply",
"MulAction.right_quotientAction'",
"DivInvMonoid.toInv",
"instHSMul",
"InvOneClass.toOne",
"inv_eq_one",
"Equiv.instEquivLike",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneM... | true |
Relation.SymmGen | Mathlib.Logic.Relation | [
"Or"
] | true |
_private.Lean.Meta.Tactic.FunInd.0.Lean.Tactic.FunInd.deriveInductionStructural.match_24 | Lean.Meta.Tactic.FunInd | [
"Lean.Expr",
"Prod.mk",
"Array",
"Nat",
"Bool",
"Prod",
"Prod.casesOn"
] | false |
Std.ExtTreeSet.getD_inter_of_not_mem_left | Std.Data.ExtTreeSet.Lemmas | [
"Membership.mem",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Inter.inter",
"Unit",
"Std.ExtTreeSet.instMembershipOfTransCmp",
"Std.ExtTreeSet.getD",
"Std.ExtTreeSet",
"Eq",
"Std.ExtTreeSet.instInterOfTransCmp",
"Std.ExtTreeMap.getKeyD_inter_of_not_mem_left",
"Not"
] | true |
Field.Emb.Cardinal.strictMono_leastExt | Mathlib.FieldTheory.CardinalEmb | [
"LE.le.eq_or_lt",
"False",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"StrictMono",
"CommRing.toNonUnitalCommRing",
"IntermediateField.adjoin.mono",
"Cardinal",
"lowerBounds",
"IntermediateField",
"Field.Emb.Cardinal.isLeast_leastExt",
"Set.image_mono",
"PartialOrder.t... | true |
RelEmbedding._sizeOf_1 | Mathlib.Order.RelIso.Basic | [
"instOfNatNat",
"Function.Embedding._sizeOf_inst",
"Function.Embedding",
"instHAdd",
"RelEmbedding",
"Iff",
"RelEmbedding.rec",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"SizeOf",
"Function.instFunLikeEmbedding",
"OfNat.ofNat",
"DFunLike.coe"
] | false |
Configuration.ProjectivePlane.ctorIdx | Mathlib.Combinatorics.Configuration | [
"Membership",
"Nat",
"Configuration.ProjectivePlane"
] | false |
_private.Mathlib.Computability.Primrec.Basic.0.Primrec.nat_div._simp_1_1 | Mathlib.Computability.Primrec.Basic | [
"eq_comm",
"propext",
"Eq"
] | false |
CategoryTheory.sum.inlCompAssociator_hom_app | Mathlib.CategoryTheory.Sums.Associator | [
"CategoryTheory.Functor",
"CategoryTheory.sum",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"Sum",
"CategoryTheory.Sum.inr_",
"CategoryTheory.Functor.sum'",
"CategoryTheory.Sum.inl_"... | true |
Lean.Compiler.LCNF.SpecState.specInfo | Lean.Compiler.LCNF.SpecInfo | [
"Lean.Compiler.LCNF.SpecState",
"Lean.PHashMap",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.Compiler.LCNF.SpecEntry",
"Lean.instHashableName"
] | true |
Std.Internal.IO.Process.totalMemory | Std.Internal.Async.Process | [
"UInt64",
"Std.Internal.UV.System.totalMemory",
"IO"
] | true |
Aesop.RuleBuilderInput._sizeOf_1 | Aesop.Builder.Basic | [
"Lean.TSyntax._sizeOf_inst",
"Aesop.RuleBuilderOptions._sizeOf_inst",
"Aesop.RuleBuilderOptions",
"instOfNatNat",
"Lean.Syntax.Term",
"List.cons",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Aesop.PhaseSpec",
"Aesop.PhaseSpec._sizeOf_inst",
"Aesop.RuleBuilderInput.rec",... | false |
Int8.le_of_lt | Init.Data.SInt.Lemmas | [
"Eq.mpr",
"Int8",
"_private.Init.Data.SInt.Lemmas.0.Int8.le_of_lt._simp_1_1",
"_private.Init.Data.SInt.Lemmas.0.Int8.le_of_lt._simp_1_2",
"Int8.toInt",
"id",
"Int",
"LE.le",
"Int.instLTInt",
"implies_congr",
"LT.lt",
"instLEInt8",
"instLTInt8",
"Eq",
"Int.le_of_lt",
"Int.instLEInt"
] | true |
CategoryTheory.Endofunctor.algebraPreadditive_homGroup_nsmul_f | Mathlib.CategoryTheory.Preadditive.EndoFunctor | [
"CategoryTheory.Functor",
"instHSMul",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"AddMonoid.toNSMul",
"AddCommGroup.toAddGroup",
"CategoryTheory.Endofunctor.Algebra.a",
"CategoryTheory.Preadditive",
"AddGroup.... | true |
IndexedPartition.piecewise_apply | Mathlib.Data.Setoid.Partition | [
"IndexedPartition",
"IndexedPartition.piecewise",
"IndexedPartition.index",
"Eq",
"rfl",
"Set"
] | true |
_private.Mathlib.Geometry.Manifold.VectorField.LieBracket.0.VectorField.mlieBracketWithin_smul_left._abel_1_1 | Mathlib.Geometry.Manifold.VectorField.LieBracket | [
"NormedCommRing.toNormedRing",
"Mathlib.Tactic.Abel.const_add_termg",
"Mathlib.Tactic.Abel.term_atomg",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"NormedRing.toRing",
"chartedSpaceSelf",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoi... | false |
fourier_coe_apply' | Mathlib.Analysis.Fourier.AddCircle | [
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"instHDiv",
"Real.pi",
"HMul.hMul",
"congrArg",
"ContinuousMap",
"AddCommMagma.to_isCommutative",
"Nat.instAtLeastTwoHAddOfNat",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"SeminormedRin... | true |
_private.Mathlib.Data.Finset.Sum.0.Finset.disjSum_eq_empty._simp_1_1 | Mathlib.Data.Finset.Sum | [
"Finset",
"Membership.mem",
"Finset.ext_iff",
"Iff",
"Finset.instSetLike",
"propext",
"Eq",
"SetLike.instMembership"
] | false |
OrderType.card_zero | Mathlib.Order.Types.Arithmetic | [
"Cardinal.mk_eq_zero",
"Cardinal",
"congrArg",
"OrderType.card_type",
"OrderType.type_of_isEmpty",
"OrderType.type",
"Cardinal.mk",
"Eq.mp",
"PEmpty",
"instLinearOrderPEmpty",
"OrderType.card",
"congr",
"Zero.toOfNat0",
"PEmpty.instIsEmpty",
"OrderType",
"OrderType.instZero",
"OfNat.... | true |
bUnion_mem_nhdsSet | Mathlib.Topology.NhdsSet | [
"Filter.instMembership",
"Iff.mpr",
"Set.subset_iUnion₂",
"Membership.mem",
"nhds",
"mem_nhdsSet_iff_forall",
"TopologicalSpace",
"nhdsSet",
"Set.instMembership",
"Set.iUnion",
"Filter",
"Filter.mem_of_superset",
"Set"
] | true |
Filter.Germ.instSemiring._proof_11 | Mathlib.Order.Filter.Germ.Basic | [
"AddMonoid.toAddSemigroup",
"NonAssocSemiring.toOne",
"instOfNatNat",
"Filter.Germ.instNonAssocSemiring",
"NatCast.natCast",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Filter.Germ",
"Nat",
"Semi... | false |
three'_nsmul | Mathlib.Algebra.Group.Defs | [
"Eq.mpr",
"instHSMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"AddZeroClass.toAddZero",
"id",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"AddMonoid",
"instAddNat",
"AddZero.toAdd",
"Eq.refl",
"HSMul.hSMul",
"OfNat.ofNat",
"Eq",
"succ_nsmul",
"two_nsmu... | true |
CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_snd_app | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.snd",
"CategoryTheory.Functor",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.CategoricalPullback.CatCo... | true |
Con.gi.eq_1 | Mathlib.GroupTheory.Congruence.Defs | [
"Pi.preorder",
"Con.gi",
"PartialOrder.toPreorder",
"GaloisInsertion.mk",
"Con.gi._proof_1",
"Preorder.toLE",
"Mul",
"conGen",
"LE.le",
"Con.gi._proof_3",
"Con.gi._proof_2",
"GaloisInsertion",
"Eq.refl",
"Con",
"Prop.partialOrder",
"Eq",
"Con.instFunLikeForallProp",
"DFunLike.coe",... | true |
Cardinal.beth_natCast_le_lift._simp_1 | Mathlib.SetTheory.Cardinal.Aleph | [
"Cardinal",
"Cardinal.lift",
"AddMonoidWithOne.toNatCast",
"LE.le",
"Nat.cast",
"Cardinal.instLE",
"Ordinal.addMonoidWithOne",
"Cardinal.beth_natCast_le_lift",
"Nat",
"propext",
"Eq",
"Cardinal.beth",
"Ordinal"
] | false |
_private.Mathlib.Analysis.Normed.Unbundled.SmoothingSeminorm.0.μ_bddAbove | Mathlib.Analysis.Normed.Unbundled.SmoothingSeminorm | [
"div_le_one_of_le₀",
"Iff.mpr",
"Real.instIsOrderedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",
"Real.instPow",
"Real.partialOrder",
"Real.instLE",
"Real",
"CommRing",
"DivInvMonoid.toInv",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing"... | true |
_private.Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic.0.InnerProductGeometry.cos_angle_mul_norm_mul_norm._simp_1_1 | Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic | [
"or_imp",
"And",
"propext",
"Or",
"Eq"
] | false |
AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal._proof_3 | Mathlib.AlgebraicGeometry.IdealSheaf.Basic | [
"Eq.mpr",
"AlgebraicGeometry.Scheme.mem_zeroLocus_iff._simp_1",
"SetLike.mem_coe._simp_1",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"TopologicalSpace.Closeds.isClosed",
"Semiring.toModule",
"Opposite",
"Topology.IsOp... | false |
_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS._sunfold | Mathlib.Data.Fin.Tuple.Reflection | [
"Pure.pure",
"_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.mkProdEqQ.makeRHS",
"Lean.Meta.State",
"Lean.Expr.const",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Expr.sort",
"Lean.Level",
"Applicative.toPure",
"List.cons",
"Lean.instToExprNat",
"Lean.Name.anonymous",
"Lean.... | false |
List.partition.loop.eq_2 | Init.Data.List.Lemmas | [
"List.filter.match_1",
"Prod.mk",
"List.cons",
"List",
"Unit",
"Bool",
"Eq.refl",
"Prod",
"List.partition.loop",
"Eq"
] | true |
Polynomial.hilbertPoly_mul_one_sub_succ | Mathlib.RingTheory.Polynomial.HilbertPoly | [
"Units.val",
"Eq.mpr",
"Polynomial.eval",
"Polynomial.instOne",
"Semigroup.toMul",
"Semiring.toModule",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"PowerSeries.invOneSubPow",
"Polynomial.coe_one",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"mul_assoc",
"AddGro... | true |
Mathlib.Tactic.Bicategory.Mor₂OfExpr | Mathlib.Tactic.CategoryTheory.Bicategory.Datatypes | [
"Inhabited.default",
"Mathlib.Tactic.BicategoryLike.Mor₂",
"instInhabitedOfMonad",
"Mathlib.Tactic.Bicategory.Context",
"Lean.Expr",
"Lean.Meta.MetaM",
"Mathlib.Tactic.BicategoryLike.State",
"Lean.Meta.instMonadMetaM",
"Mathlib.Tactic.Bicategory.BicategoryM",
"StateT.instMonad",
"StateT",
"ins... | true |
Computation.Mem | Mathlib.Data.Seq.Computation | [
"Option.some",
"Membership.mem",
"instOfNatNat",
"Computation",
"Stream'",
"instHAdd",
"Stream'.instMembership",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Subtype.val",
"Eq",
"Option"
] | true |
GroupLike.val_inj._simp_1 | Mathlib.RingTheory.Coalgebra.GroupLike | [
"Coalgebra",
"CommSemiring.toSemiring",
"AddCommMonoid",
"CommSemiring",
"GroupLike",
"GroupLike.val_inj",
"propext",
"GroupLike.val",
"Module",
"Eq"
] | false |
Lean.Meta.mkSizeOfFns | Lean.Meta.SizeOf | [
"Pure.pure",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.NameMap",
"Std.Rio.instForIn'InferInstanceMembershipOfLawfulUpwardEnumerableOfLawfulUpwardEnumerableLTOfLawfulUpwardEnumerableLeast?OfMonadOfFiniteIteratorId",
"Array.push",
"instForInOfForIn'",
"Std.PRange.instLawfulUpwa... | true |
skewAdjointLieSubalgebra | Mathlib.Algebra.Lie.SkewAdjoint | [
"Module.End.instRing",
"LinearMap.BilinForm.isSkewAdjoint_bracket",
"Submodule",
"CommRing",
"Semiring.toModule",
"instSMulOfMul",
"LieRing.toAddCommGroup",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"LinearMap.module",
"IsScalarTower.le... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.forM_eq_forM_toArray._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.toList",
"List.toArray",
"Array",
"Eq.symm",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.toArray",
"Sigma",
"Std.DTreeMap.Internal.Impl.toArray_toList"
] | false |
forall_gt_imp_ne_iff_le | Mathlib.Order.Basic | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ne",
"LE.le",
"LT.lt.trans_le'",
"LT.lt.ne'",
"Iff",
"LT.lt",
"Iff.intro",
"le_of_forall_gt_imp_ne",
"LinearOrder.toPartialOrder"
] | true |
ContinuousLinearMapWOT._sizeOf_inst | Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | [
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMapWOT",
"RingHom",
"AddCommGroup",
"TopologicalSpace",
"ContinuousLinearMapWOT._sizeOf_1",
"SizeOf.mk",
"Semiring",
"SizeOf",
"Module",
"Semiring.toNonAssocSemiring"
] | false |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec.0.BitVec.instDecidableEqLiteral.decEq._proof_1 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec | [
"BitVec",
"BitVec.Literal.mk",
"Nat",
"Eq",
"rfl",
"BitVec.Literal"
] | false |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.List.getValue?_filter_containsKey._simp_1_2 | Std.Data.Internal.List.Associative | [
"Option.none",
"Option.map",
"Option.map_eq_none_iff",
"propext",
"Eq",
"Option"
] | false |
Lean.Meta.Grind.AC.MonadGetStruct.noConfusion | Lean.Meta.Tactic.Grind.AC.Util | [
"Lean.Meta.Grind.AC.MonadGetStruct.casesOn",
"HEq.refl",
"Lean.Meta.Grind.AC.MonadGetStruct",
"Lean.Meta.Grind.AC.MonadGetStruct.noConfusionType",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Lean.Meta.Grind.AC.Struct",
"Eq"
] | false |
BitVec.reduceGetMsb | Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec | [
"BitVec.getMsbD",
"BitVec.reduceGetBit",
"Nat",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2"
] | true |
MulOpposite.isCancelMulZero_iff | Mathlib.Algebra.GroupWithZero.Opposite | [
"Function.Injective.isCancelMulZero",
"HMul.hMul",
"MulOpposite.op_injective",
"MulOpposite.instIsCancelMulZero",
"MulOpposite",
"Mul",
"Function.comp",
"inferInstance",
"IsCancelMulZero",
"MulOpposite.instZero",
"Iff",
"Function.Injective.comp",
"Iff.intro",
"Zero.toOfNat0",
"OfNat.ofNa... | true |
Submodule.mem_sSup | Mathlib.LinearAlgebra.Span.Defs | [
"Eq.mpr",
"Submodule",
"congrArg",
"iSup",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"id",
"Submodule.instPartialOrder",
"LE.le",
"AddCommMonoid",
"iff_self",
"CompleteLattice.toCompleteSem... | true |
CategoryTheory.MorphismProperty.multiplicativeClosure.below.casesOn | Mathlib.CategoryTheory.MorphismProperty.Composition | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.multiplicativeClosure",
"CategoryTheory.MorphismProperty.multiplicativeClosure.below.rec",
"CategoryTheory.MorphismProperty.multiplicativeClosure.of",
"CategoryTheory.CategoryStruc... | false |
Aesop.UnsafeQueueEntry.instToString.match_1 | Aesop.Tree.UnsafeQueue | [
"Aesop.UnsafeRule",
"Aesop.UnsafeQueueEntry",
"Aesop.IndexMatchResult",
"Aesop.UnsafeQueueEntry.unsafeRule",
"Aesop.UnsafeQueueEntry.postponedSafeRule",
"Aesop.UnsafeQueueEntry.casesOn",
"Aesop.PostponedSafeRule"
] | false |
ContinuousMultilinearMap.smulRightL._proof_2 | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"ContinuousMultilinearMap.smulRight",
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddCommGroup",
"Semiring.toModule",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistr... | false |
modelWithCornersEuclideanQuadrant | Mathlib.Geometry.Manifold.Instances.Real | [
"instTopologicalSpaceEuclideanQuadrant",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real.instLE",
"Real",
"PiLp.normedSpace",
"fact_one_le_two_ennreal",
"Real.denselyNormedField",
"Real.instZero",
"Real.instRCLike",
"Set.univ",
"setOf",
"ModelWithCorners.mk",
... | true |
ModularForm.trace | Mathlib.NumberTheory.ModularForms.NormTrace | [
"SlashInvariantForm",
"ModularForm",
"Real",
"Matrix",
"ModularFormClass",
"ModularFormClass.toSlashInvariantFormClass",
"instDecidableEqFin",
"Real.semiring",
"Subgroup",
"IsCusp",
"instOfNatNat",
"Int",
"Units.instGroup",
"Fin.fintype",
"ModularForm.trace._proof_4",
"ModularForm.mk",... | true |
equivShrink_le_equivShrink._simp_1 | Mathlib.Order.Shrink | [
"Equiv.instEquivLike",
"Preorder.toLE",
"instPreorderShrink",
"Equiv",
"LE.le",
"propext",
"Shrink",
"equivShrink_le_equivShrink",
"equivShrink",
"Eq",
"DFunLike.coe",
"Preorder",
"Small",
"EquivLike.toFunLike"
] | false |
OrderDual.instMulOneClass | Mathlib.Algebra.Order.Group.Synonym | [
"MulOne.toOne",
"MulOneClass.mul_one",
"MulOneClass.one_mul",
"MulOne.mk",
"MulOne.toMul",
"MulOneClass.toMulOne",
"MulOneClass.mk",
"OrderDual.instMul",
"OrderDual",
"MulOneClass",
"OrderDual.instOne"
] | true |
CompleteOrthogonalIdempotents.ringEquivOfIsMulCentral._proof_3 | Mathlib.RingTheory.Idempotents | [
"Semigroup.toMul",
"HMul.hMul",
"Exists",
"SemigroupWithZero.toSemigroup",
"NonUnitalSemiring.toSemigroupWithZero",
"Exists.intro",
"Semiring",
"Semiring.toNonUnitalSemiring",
"Eq",
"rfl",
"instHMul"
] | false |
_private.Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs.0.CategoryTheory.IsPushout.inr_isoIsPushout_inv._simp_1_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs | [
"CategoryTheory.Iso.comp_inv_eq",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",
"Eq",
"CategoryTheory.Iso.inv",
"CategoryTheory.Category"
] | false |
Mathlib.Tactic.Ring.Common.evalMul₁._sunfold | Mathlib.Tactic.Ring.Common | [
"Pure.pure",
"Mathlib.Tactic.Ring.Common.Result.mk",
"Lean.Meta.State",
"Lean.Expr.const",
"Lean.Name.mkStr5",
"Mathlib.Tactic.Ring.Common.Result",
"Mathlib.Tactic.Ring.Common.ExSum",
"Lean.Meta.MetaM",
"IO.RealWorld",
"_private.Mathlib.Tactic.Ring.Common.0.Mathlib.Tactic.Ring.Common.evalMul₁.matc... | false |
CommMonCat.forget₂_map_ofHom | Mathlib.Algebra.Category.MonCat.Basic | [
"MonoidHom.instFunLike",
"CommMonCat.instConcreteCategoryMonoidHomCarrier",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CommMonCat.str",
"MonCat",
"MonCat.ofHom",
"MonCat.instCategory",
"CommMonCat.hasForgetToMonCat",
"CategoryTheory.Functor.ma... | true |
Lean.Parser.Term.doHave._regBuiltin.Lean.Parser.Term.doHave_1 | Lean.Parser.Do | [
"IO",
"Lean.Parser.Term.doHave",
"Unit",
"Lean.Parser.addBuiltinLeadingParser",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | false |
_private.Mathlib.Analysis.Complex.OpenMapping.0.AnalyticOnNhd.eq_const_of_re_eq_const._proof_1_2 | Mathlib.Analysis.Complex.OpenMapping | [
"Set.ext",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"False",
"Real",
"Complex.instNormedAddCommGroup",
"eq_false",
"IsConnected",
"Real.denselyNormedField",
"congrArg",
"not_isOpen_singleton",
"exists_exists_and_eq_and._simp_1",
"Set.mem_image._si... | false |
Lean.Doc.Part.below_2 | Lean.DocString.Types | [
"String",
"Lean.Doc.Block",
"Array",
"List",
"PProd",
"PUnit",
"Lean.Doc.Part",
"Lean.Doc.Part.rec_2",
"Lean.Doc.Inline",
"Option"
] | false |
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