name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
List.decidableSortedGE | Mathlib.Data.List.Sort | [
"List.sortedGE_iff_isChain",
"Preorder.toLE",
"GE.ge",
"List.IsChain",
"List",
"DecidableLE",
"DecidablePred",
"List.instDecidableIsChainOfDecidableRel",
"decidable_of_iff'",
"List.SortedGE",
"Preorder"
] | true |
SimpleGraph._aux_Mathlib_Combinatorics_SimpleGraph_Copy___unexpand_SimpleGraph_IsIndContained_1 | Mathlib.Combinatorics.SimpleGraph.Copy | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.mem_of_mem_insertMany_list._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
apply_wcovBy_apply_iff._simp_1 | Mathlib.Order.Cover | [
"apply_wcovBy_apply_iff",
"Preorder.toLE",
"OrderIsoClass",
"EquivLike",
"WCovBy",
"propext",
"Eq",
"DFunLike.coe",
"Preorder",
"EquivLike.toFunLike"
] | false |
LSeries.term_sum_apply | Mathlib.NumberTheory.LSeries.Linearity | [
"False",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Pi.addCommMonoid",
"GroupWithZero.toDivInvMonoid",
"eq_false",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Complex.instNormedField",
"Finset.sum_apply",
"Complex.instZero",
"LSeries.term_of_ne_zero",
"DivisionSem... | true |
Std.TreeMap.contains_emptyc | Std.Data.TreeMap.Lemmas | [
"Ordering",
"Std.DTreeMap.contains_emptyc",
"Std.TreeMap.contains",
"Bool",
"Std.TreeMap.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Bool.false",
"Eq",
"Std.TreeMap"
] | true |
_private.Std.Data.DHashMap.Basic.0.Std.DHashMap.Const.insertMany._proof_1 | Std.Data.DHashMap.Basic | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.WF.insert₀",
"Std.DHashMap.Raw",
"Std.DHashMap.wf",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"Id",
"Subtype.mk",
"Std.DHashMap.Internal.Raw₀.insert",
"Std.DHashMap.inner",
"ForIn",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"_priva... | false |
Topology.WithLowerSet.toLowerSet_symm | Mathlib.Topology.Order.UpperLowerSetTopology | [
"Topology.WithLowerSet.ofLowerSet",
"Equiv",
"Equiv.symm",
"Topology.WithLowerSet",
"Eq",
"rfl",
"Topology.WithLowerSet.toLowerSet"
] | true |
NonUnitalSubalgebra.iSupLift._proof_4 | Mathlib.Algebra.Algebra.NonUnitalSubalgebra | [
"Eq.mpr",
"NonUnitalSubalgebra",
"instSMulOfMul",
"congrArg",
"CommSemiring.toSemiring",
"iSup",
"DistribMulAction.toDistribSMul",
"Directed",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toConditionallyCompleteLattice",
"AddZero... | false |
curveIntegralFun_symm | Mathlib.MeasureTheory.Integral.CurveIntegral.Basic | [
"NegZeroClass.toNeg",
"Real",
"Pi.instNeg",
"Path.symm",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"Real.instSub",
"curveIntegralFun_symm_apply",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"SubtractionMonoid.toSubNegZeroMonoid",
"Su... | true |
Nat.mul_ne_mul_left | Init.Data.Nat.Lemmas | [
"HMul.hMul",
"Ne",
"instMulNat",
"instOfNatNat",
"Iff",
"Nat",
"Nat.mul_left_inj",
"OfNat.ofNat",
"Eq",
"not_congr",
"instHMul"
] | true |
GradedRingHom.map_one | Mathlib.RingTheory.GradedAlgebra.RingHom | [
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"GradedRingHom",
"MonoidHomClass.toOneHomClass",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"MonoidWithZeroHomClass.toMonoidHomClass",
"MulZeroOneCla... | true |
CategoryTheory.Bicategory.Adj.forget₁._proof_7 | Mathlib.CategoryTheory.Bicategory.Adjunction.Adj | [
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Bicategory.Adj.Hom.l",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Iso.refl",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory.Adj.Hom₂.τl",
... | false |
OpenPartialHomeomorph.extend_image_nhds_mem_nhds_of_boundaryless | Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | [
"Filter.instMembership",
"Eq.mpr",
"OpenPartialHomeomorph.map_extend_nhds_of_boundaryless",
"NormedSpace",
"congrArg",
"Filter.map",
"ModelWithCorners.Boundaryless",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"nhds",
"Filter.mp_mem",
"id",
"TopologicalSpace",
"ModelWi... | true |
Lean.Meta.Grind.EMatchTheoremKind.leftRight.sizeOf_spec | Lean.Meta.Tactic.Grind.Extension | [
"instOfNatNat",
"Lean.Meta.Grind.EMatchTheoremKind",
"Nat",
"SizeOf.sizeOf",
"Lean.Meta.Grind.EMatchTheoremKind.leftRight",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Meta.Grind.EMatchTheoremKind._sizeOf_inst"
] | true |
FiniteDimensional.basisSingleton._proof_5 | Mathlib.LinearAlgebra.FiniteDimensional.Basic | [
"IsNoetherianRing.strongRankCondition",
"PrincipalIdealRing.isNoetherianRing",
"Ring.toNonAssocRing",
"DivisionRing.toDivisionSemiring",
"DivisionRing.toRing",
"DivisionSemiring.isPrincipalIdealRing",
"NonAssocRing.toNonUnitalNonAssocRing",
"DivisionRing.isSimpleRing",
"StrongRankCondition",
"Divi... | false |
MulAction.is_one_pretransitive_iff | Mathlib.GroupTheory.GroupAction.MultipleTransitivity | [
"Fin.instUnique",
"Group",
"MulAction.IsPretransitive",
"MulAction.oneEmbedding_isPretransitive_iff",
"DivInvMonoid.toMonoid",
"instOfNatNat",
"Group.toDivInvMonoid",
"Iff",
"Nat",
"MulAction",
"MulAction.IsMultiplyPretransitive",
"Monoid.toSemigroup",
"SemigroupAction.toSMul",
"MulAction.... | true |
ContinuousMap.inv_apply | Mathlib.Topology.ContinuousMap.Algebra | [
"Inv",
"ContinuousMap.instInvOfContinuousInv",
"ContinuousMap",
"TopologicalSpace",
"Inv.inv",
"ContinuousInv",
"Eq",
"ContinuousMap.instFunLike",
"DFunLike.coe",
"rfl"
] | true |
_private.Init.Data.List.Nat.TakeDrop.0.List.take_set_of_le._proof_1_1 | Init.Data.List.Nat.TakeDrop | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.LinearC... | false |
Lists.Subset.decidable.match_1 | Mathlib.SetTheory.Lists | [
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Lists'.atom",
"Lists'.cons'",
"Bool.ctorIdx",
"Bool.true",
"Lists'.casesOn",
"Bool",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Bool.false",
"Eq",
"Lists'.nil",
"Lists'"
] | false |
Unique.rec | Mathlib.Logic.Unique | [
"Inhabited.default",
"Unique.mk",
"Unique",
"Inhabited",
"Eq"
] | false |
List.get_length_sub_one._proof_1 | Mathlib.Data.List.Basic | [
"False",
"HSub.hSub",
"instSubNat",
"Ne",
"instOfNatNat",
"List",
"instHSub",
"Nat",
"Nat.lt_irrefl",
"LT.lt",
"Eq.ndrec",
"instLTNat",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"List.length",
"List.nil"
] | false |
OrderIso.sumLexIicIoi | Mathlib.Order.Hom.Lex | [
"OrderIso.sumLexIioIci._proof_2",
"instTrichotomousLt",
"OrderIso.setCongr",
"Sum.Lex.LE",
"Set.Ioi",
"Preorder.toLT",
"OrderIso.sumLexIicIoi._proof_1",
"Lex",
"LinearOrder",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Set.Elem... | true |
Std.DHashMap.Internal.Raw₀.insertListₘ | Std.Data.DHashMap.Internal.Model | [
"List.brecOn",
"Std.DHashMap.Internal.Raw₀.insertListₘ._f",
"List",
"Hashable",
"BEq",
"Std.DHashMap.Internal.Raw₀",
"Sigma"
] | true |
fderiv_fun_smul | Mathlib.Analysis.Calculus.FDeriv.Mul | [
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousLinearMap.smulRight",
"NormedAddCommGroup.toMetricSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddComm... | true |
CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac | Mathlib.Algebra.Homology.ExactSequenceFour | [
"CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac._auto_1",
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComposableArrows.IsComplex",
"Cate... | true |
CategoryTheory.StructuredArrow.eta_hom_right | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.StructuredArrow.hom",
"CategoryTheory.CommaMorphism.right",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.StructuredArro... | true |
Real.cos_sub_nat_mul_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Real",
"Real.pi",
"HMul.hMul",
"Real.cos",
"Real.instSub",
"HSub.hSub",
"Real.instRing",
"Real.commRing",
"CommRing.toNonAssocCommRing",
"Nat.cast",
"Monoid.toPow",
"Real.instOne",
"Real.instMonoid",
"instHSub",
"HPow.hPow",
"Nat",
"Real.instMul",
"Real.cos_antiperiodic",
"Real.... | true |
DFinsupp.addCommGroup._proof_7 | Mathlib.Data.DFinsupp.Defs | [
"AddGroup.toSubtractionMonoid",
"instHSMul",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"DFinsupp.instDFunLike",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"DFinsupp.hasIntScalar",
"AddGroup.toSubNegMonoid",
"P... | false |
ProofWidgets.CheckRequestResponse.done | ProofWidgets.Cancellable | [
"Lean.Json",
"ProofWidgets.CheckRequestResponse",
"ProofWidgets.CheckRequestResponse.done",
"ProofWidgets.LazyEncodable"
] | true |
Set.card_image_of_inj_on | Mathlib.Data.Set.Finite.Basic | [
"Trans.trans",
"congrArg",
"Finset",
"Set.mem_image._simp_1",
"Finset.mem_image._simp_1",
"Classical.propDecidable",
"Membership.mem",
"Exists",
"Set.Elem",
"Fintype.card",
"Fintype.card_of_finset'",
"Set.toFinset",
"iff_self",
"instTransEq",
"funext",
"And",
"Iff",
"Fintype",
"S... | true |
HasStrictFDerivAt.snd | Mathlib.Analysis.Calculus.FDeriv.Prod | [
"ContinuousLinearMap.comp",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"NormedField.toField",
"nhds",
"Prod.mk",
"ContinuousLinearMap.snd",
"Field.toSemifield",
"ContinuousLinearMap",
"Semifield.toDiv... | true |
Vector.set_eraseIdx._proof_2 | Init.Data.Vector.Erase | [
"LE.le",
"instLENat",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Nat.decLt",
"_private.Init.Data.Vector.Erase.0.Vector.set_eraseIdx._proof_1",
"instLTNat",
"Not"
] | false |
Rack.PreEnvelGroupRel'._sizeOf_inst | Mathlib.Algebra.Quandle | [
"Rack.PreEnvelGroupRel'",
"Rack",
"Rack.PreEnvelGroupRel'._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Rack.PreEnvelGroup"
] | false |
_private.Batteries.Tactic.Alias.0.Batteries.Tactic.Alias.AliasInfo.name.match_1 | Batteries.Tactic.Alias | [
"Batteries.Tactic.Alias.AliasInfo.plain",
"Batteries.Tactic.Alias.AliasInfo.casesOn",
"Batteries.Tactic.Alias.AliasInfo.forward",
"Batteries.Tactic.Alias.AliasInfo.reverse",
"Batteries.Tactic.Alias.AliasInfo",
"Lean.Name"
] | false |
IsLocalization.height_comap | Mathlib.RingTheory.Ideal.Height | [
"CommRing",
"IsLocalization",
"CommSemiring.toSemiring",
"Algebra",
"IsLocalization.height_under",
"Ideal",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommRing.toCommSemiring",
"ENat",
"Ideal.height",
"Eq",
"Submonoid",
"Ideal.under"
] | true |
Int.instIsCancelMulZero | Mathlib.Algebra.Ring.Int.Defs | [
"Int.mul_eq_mul_left_iff",
"Int.mul_eq_mul_right_iff",
"HMul.hMul",
"CommSemiring.toSemiring",
"IsRightCancelMulZero.mk",
"IsCancelMulZero.mk",
"IsLeftCancelMulZero.mk",
"Ne",
"Int",
"IsCancelMulZero",
"Int.instMul",
"CommRing.toCommSemiring",
"Int.instCommRing",
"Iff.mp",
"Zero.toOfNat0... | true |
_private.Mathlib.CategoryTheory.PathCategory.MorphismProperty.0.CategoryTheory.MorphismProperty.instIsMultiplicativeStrictMapPathsPathsPathComposition.match_1 | Mathlib.CategoryTheory.PathCategory.MorphismProperty | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"CategoryTheory.pathComposition",
"CategoryTheory.MorphismProperty.paths",
"CategoryTheory.Functor.map",
"CategoryTheory.MorphismProp... | false |
_private.Mathlib.Data.Set.Image.0.Set.image_singleton._proof_1_1 | Mathlib.Data.Set.Image | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"Set.ext",
"of_eq_false",
"False",
"forall_not_of_not_exists",
"Lean.Grind.not_not",
"Lean.Grind.not_and",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"HEq.refl",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_... | false |
_private.Mathlib.NumberTheory.Padics.ProperSpace.0.PadicInt.totallyBounded_univ._simp_1_3 | Mathlib.NumberTheory.Padics.ProperSpace | [
"Real",
"Real.instLT",
"Membership.mem",
"Metric.ball",
"Metric.mem_ball",
"PseudoMetricSpace",
"LT.lt",
"propext",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.Combinatorics.Matroid.Dual.0.Matroid.IsBase.compl_inter_isBasis_of_inter_isBasis._simp_1_2 | Mathlib.Combinatorics.Matroid.Dual | [
"And",
"propext",
"not_and",
"Eq",
"Not"
] | false |
HomologicalComplex.homologyι | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.HasHomology",
"HomologicalComplex.opcycles",
"HomologicalComplex",
"ComplexShape",
"HomologicalComplex.sc",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ShortComplex... | true |
QuaternionAlgebra.instNeg | Mathlib.Algebra.Quaternion | [
"QuaternionAlgebra.imI",
"Neg.mk",
"QuaternionAlgebra.re",
"QuaternionAlgebra.mk",
"QuaternionAlgebra",
"Neg",
"QuaternionAlgebra.imK",
"Neg.neg",
"QuaternionAlgebra.imJ"
] | true |
CompleteSublattice.subtype_apply | Mathlib.Order.CompleteSublattice | [
"Sublattice",
"Sublattice.subtype",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"Subtype",
"LatticeHom",
"Sublattice.instSetLike",
"LatticeHom.instFunLike",
"ConditionallyCompleteLattice.toLattice",
"CompleteLattice",
"Subtype.val",
"Eq",
"DFunLike.coe",
"SetLike.in... | true |
NonarchAddGroupSeminorm.add_bddBelow_range_add | Mathlib.Analysis.Normed.Group.Seminorm | [
"Real.partialOrder",
"Real.instLE",
"Real",
"AddGroupSeminormClass.toNonnegHomClass",
"Real.instZero",
"Real.instAddMonoid",
"lowerBounds",
"NonarchAddGroupSeminorm.funLike",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HSub.hSub",
"NonarchAddGroupSeminorm",
"Preorder.toLE",
"Ad... | true |
ProbabilityTheory.Kernel.ext_fun_iff | Mathlib.Probability.Kernel.Defs | [
"Eq.mpr",
"MeasureTheory.Measure",
"congrArg",
"Measurable",
"ENNReal.measurableSpace",
"ProbabilityTheory.Kernel.ext_fun",
"ProbabilityTheory.Kernel.instFunLike",
"id",
"MeasurableSpace",
"Iff",
"Iff.intro",
"ENNReal",
"Eq.refl",
"Eq",
"DFunLike.coe",
"MeasureTheory.lintegral",
"Pro... | true |
strictConvexOn_rpow | Mathlib.Analysis.Convex.SpecificFunctions.Basic | [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Iff.mpr",
"sub_pos",
"add_sub_assoc",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"IsOrderedModule.toPosSMulMono",
"Real.instPow",
"Real.part... | true |
BitVec.extractLsb'_eq_zero | Init.Data.BitVec.Lemmas | [
"BitVec.extractLsb'",
"BitVec",
"instDecidableEqBool",
"instOfNatNat",
"BitVec.ofNat",
"GetElem.getElem",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.extractLsb'_eq_zero._proof_1_1",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Bool",
"BitVec.instGetElemNatBoolLt",
"instLTNat",
"BitVec.eq_... | true |
RightCancelMonoid | Mathlib.Algebra.Group.Defs | [
"RightCancelMonoid.mk"
] | true |
_private.Mathlib.Tactic.Positivity.Core.0.Mathlib.Meta.Positivity.normNumPositivity._proof_1 | Mathlib.Tactic.Positivity.Core | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Qq.Quoted.unsafeMk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Qq.QuotedDefEq.unsafeIntro",
"List.nil"
] | false |
CategoryTheory.ShortComplex.SnakeInput.φ₁_L₂_f_assoc | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.assoc",
"CategoryTheory.ShortComplex.SnakeInput.L₂",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.SnakeInput",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Abelian",
"CategoryT... | true |
_private.Batteries.Tactic.Trans.0.Batteries.Tactic.getRel.match_1 | Batteries.Tactic.Trans | [
"Lean.Expr",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Lean.Meta.LazyDiscrTree.PartialMatch.score | Lean.Meta.LazyDiscrTree | [
"Lean.Meta.LazyDiscrTree.PartialMatch",
"Nat"
] | true |
ContinuousAt.comp₂_of_eq | Mathlib.Topology.Constructions.SumProd | [
"ContinuousAt.comp₂",
"congrArg",
"ContinuousAt",
"instTopologicalSpaceProd",
"Eq.mp",
"Prod.mk",
"TopologicalSpace",
"Prod",
"Eq.symm",
"Eq"
] | true |
_private.Mathlib.Tactic.Positivity.Basic.0.Mathlib.Meta.Positivity.evalIte._proof_1 | Mathlib.Tactic.Positivity.Basic | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Qq.Quoted.unsafeMk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Qq.QuotedDefEq.unsafeIntro",
"List.nil"
] | false |
_private.Mathlib.Algebra.Lie.Basis.0.LieAlgebra.Basis.coroot_eq_h'.match_1_2 | Mathlib.Algebra.Lie.Basis | [
"LieSubalgebra.instSetLike",
"Subtype.casesOn",
"Membership.mem",
"Subtype",
"LieAlgebra.Basis.cartan",
"Finite.of_fintype",
"Field.toCommRing",
"Subtype.mk",
"LieRing",
"Fintype",
"LieAlgebra.Basis",
"LieSubalgebra",
"LieAlgebra",
"Field",
"SetLike.instMembership"
] | false |
ContinuousENorm.toENorm | Mathlib.Analysis.Normed.Group.Defs | [
"ContinuousENorm",
"TopologicalSpace",
"ENorm"
] | true |
Submonoid.instCompleteLattice.eq_1 | Mathlib.Algebra.Group.Submonoid.Basic | [
"SemilatticeSup.mk",
"Submonoid.instCompleteLattice._proof_4",
"LT.mk",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Submonoid.mem_top",
"Submonoid.instCompleteLattice._proof_13",
"completeLatticeOfInf",
"CompleteLattice.toLattice",
"Submonoid.instCompleteLattice._proof_9",
"Submonoid.instCompl... | true |
IO.Error.mkInterrupted | Init.System.IOError | [
"String",
"UInt32",
"IO.Error",
"IO.Error.interrupted"
] | true |
TensorProduct.assoc._proof_3 | Mathlib.LinearAlgebra.TensorProduct.Associator | [
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"CommMonoid.toMonoid",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"TensorProduct",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.toAddMonoid",
"Mod... | false |
CategoryTheory.monoidalCategoryMop._proof_9 | Mathlib.CategoryTheory.Monoidal.Opposite | [
"CategoryTheory.MonoidalOpposite.mop",
"CategoryTheory.Category.assoc",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.MonoidalOpposite.unmop",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalOpposite",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor"... | false |
_private.Mathlib.Analysis.SpecialFunctions.Complex.Arg.0.Complex.arg_mul_coe_angle._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Complex.Arg | [
"Real",
"Real.Angle",
"Real.Angle.coe",
"AddCommGroup.toAddCommMonoid",
"Real.Angle.coe_add",
"Real.instAdd",
"instHAdd",
"HAdd.hAdd",
"NormedAddCommGroup.toAddCommGroup",
"AddCommSemigroup.toAddCommMagma",
"Eq.symm",
"AddCommMonoid.toAddCommSemigroup",
"Eq",
"Real.instNormedAddCommGroupAn... | false |
Lean.ReducibilityHints.isAbbrev | Lean.Declaration | [
"Lean.ReducibilityHints",
"Bool.true",
"Unit",
"Bool",
"_private.Lean.Declaration.0.Lean.ReducibilityHints.isAbbrev.match_1",
"Bool.false"
] | true |
_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.checkNameExists._sparseCasesOn_1 | Lean.Elab.DocString.Builtin | [
"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 |
CategoryTheory.compCreatesLimit._proof_1 | Mathlib.CategoryTheory.Limits.Creates | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.ReflectsLimit",
"CategoryTheory.Functor.comp",
"CategoryTheory.CreatesLimit",
"CategoryTheory.CreatesLimit.toReflectsLimit",
"CategoryTheory.Limits.comp_reflectsLimit",
"CategoryTheory.Category"
] | false |
AffineSubspace.direction_top | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"Submodule",
"Lattice.toSemilatticeSup",
"AddMonoid.toAddSemigroup",
"CompleteLattice.toLattice",
"congrArg",
"AffineSubspace.vsub_mem_direction",
"AddCommGroup.toAddCommMonoid",
"imp_intro",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"CompleteLa... | true |
Filter.disjoint_pure_pure._simp_1 | Mathlib.Order.Filter.Bases.Basic | [
"Pure.pure",
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"CompleteLattice.toBoundedOrder",
"Ne",
"Filter.disjoint_pure_pure",
"Filter.instPure",
"BoundedOrder.toOrderBot",
"propext",
"Eq",
"Filter",
"Filter.instPartialOrder"
] | false |
CategoryTheory.PreZeroHypercover.refineOneHypercover_p₁ | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"CategoryTheory.Limits.pullback",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover",
"CategoryTheory.Limits.pullback.fst",
"CategoryTheory.Categ... | true |
NumberField.InfinitePlace.instMulActionAlgEquiv._proof_1 | Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | [
"AlgEquiv.instEquivLike",
"Algebra",
"AlgEquivClass.toAlgHomClass",
"Field.toSemifield",
"AlgEquiv.instAlgEquivClass",
"Semifield.toDivisionSemiring",
"AlgEquiv",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"AlgHomClass.toRingHomClass",
"Semiring.toNonAssocSemiring",
"Field",
... | false |
CategoryTheory.Discrete.discreteCases | Mathlib.CategoryTheory.Discrete.Basic | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.SourceInfo",
"Lean.Syntax.atom",
"Lean.Elab.Tactic.Context",
"Lean.TSyntax.mk",
"Lean.Name.mkStr3",
"Lean.MonadQuotation.toMonadRef",
"Lean... | true |
CategoryTheory.TwoSquare | Mathlib.CategoryTheory.Functor.TwoSquare | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.elabMutualDef._sparseCasesOn_13 | Lean.Elab.MutualDef | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"Lean.ReducibilityStatus.rec",
"instOfNatNat",
"Lean.ReducibilityStatus.implicitReducible",
"Nat.land",
"Lean.ReducibilityStatus.semireducible",
"Lean.ReducibilityStatus.ctorIdx",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.fa... | false |
_private.Mathlib.LinearAlgebra.LinearIndependent.BaseChange.0.LinearIndependent.linearIndependent_algebraMap_comp_aux | Mathlib.LinearAlgebra.LinearIndependent.BaseChange | [
"Set.mem_range_self",
"LinearIndepOn.extend",
"Eq.mpr",
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Algebra.to_smulCommClass",
"instHSMul",
"Fintype.ofFinite",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"IsScal... | true |
Real.rpow_two | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Real.instPow",
"Real",
"congrArg",
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"Monoid.toPow",
"Real.instMonoid",
"HPow.hPow",
"Nat.instNeZeroSucc",
"Nat",
"True",
"eq_self",
"Real.rpow_ofNat",
"of_eq_true",
"congrFun'",
"instHPow",
"OfNat.ofNat",
"Eq",
"instOfNatAtLeastTwo",... | true |
CategoryTheory.ShortComplex.SnakeInput.exact_C₁_up._proof_1 | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.ShortComplex.SnakeInput.L₂",
"CategoryTheory.ShortComplex.comp_τ₁",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.Hom.τ₁",
"CategoryTheory.ShortComplex.SnakeInput.L₀",
"CategoryTheo... | false |
_private.Std.Data.HashMap.IteratorLemmas.0.Std.HashMap.Raw.keysIter.eq_1 | Std.Data.HashMap.IteratorLemmas | [
"Pure.pure",
"Std.Iterators.Types.ArrayIterator",
"Monad.toApplicative",
"MonadLiftT.monadLift",
"instMonadLiftT",
"Sigma.fst",
"Std.Iter.toIterM",
"Id",
"Applicative.toPure",
"Std.HashMap.Raw",
"Std.DHashMap.Internal.AssocList.AssocListIterator",
"Std.Iterators.instMonadPostconditionT",
"St... | true |
mul_lt_mul_of_pos_right | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | [
"Preorder.toLT",
"HMul.hMul",
"Mul",
"MulPosStrictMono.mul_lt_mul_of_pos_right",
"MulPosStrictMono",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat",
"Preorder",
"instHMul",
"Zero"
] | true |
IsLocalFrameOn.mdifferentiableAt_of_coeff | Mathlib.Geometry.Manifold.VectorBundle.LocalFrame | [
"Filter.instMembership",
"Pi.Function.module",
"NormedCommRing.toSeminormedCommRing",
"WithTop.charZero",
"instHSMul",
"Prod.normedSpace",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"chartedSpaceSelf... | true |
_private.Batteries.Data.Array.Monadic.0.cond.match_1.eq_1 | Batteries.Data.Array.Monadic | [
"Unit.unit",
"cond.match_1",
"Bool.true",
"Unit",
"Bool",
"Eq.refl",
"Bool.false",
"Eq"
] | true |
Units.cfcRpow._proof_3 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"Units.val",
"Units.cfcRpow._proof_2",
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"instStarRingReal",
"HMul.hMul",
"Ring.toNonAssocRing",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Algebra",
"Preorder.toLE",
"CFC.nnrpow._proof_1",
"Units",
"PartialOrder",
"Alg... | false |
CategoryTheory.LaxFunctor.map₂_rightUnitor._autoParam | Mathlib.CategoryTheory.Bicategory.Functor.Lax | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CompactlyGenerated.isoEquivHomeo_symm_apply | Mathlib.Topology.Category.CompactlyGenerated | [
"CompactlyGenerated.instCategory",
"Equiv.instEquivLike",
"CompactlyGenerated.isoOfHomeo",
"Equiv",
"CategoryTheory.Iso",
"TopCat.str",
"TopCat.carrier",
"Homeomorph",
"Eq.refl",
"Equiv.symm",
"CompactlyGenerated.isoEquivHomeo",
"Eq",
"DFunLike.coe",
"CompactlyGenerated",
"EquivLike.toFu... | true |
CategoryTheory.MonoidalCategoryStruct.whiskerRight | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
ContinuousMap.mk | Mathlib.Topology.ContinuousMap.Defs | [
"Continuous",
"ContinuousMap.mk",
"ContinuousMap",
"autoParam",
"TopologicalSpace",
"ContinuousMap.continuous_toFun._autoParam"
] | true |
OrderIso.Icc._proof_5 | Mathlib.Order.Hom.Set | [
"Lattice",
"Subtype.mk.congr_simp",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Set.Elem",
"Subtype",
"OrderIso",
"OrderIso.symm",
"Subtype.mk",
"Set.Icc",
"instFunLikeOrderIso",
"Subtype.coe_eta",
"True",
"eq_self",
"... | false |
CategoryTheory.Abelian.SpectralObject.mapFourδ₁Toδ₀'_mapFourδ₃Toδ₃' | Mathlib.Algebra.Homology.SpectralObject.EpiMono | [
"Eq.mpr",
"CategoryTheory.Abelian.SpectralObject.E",
"CategoryTheory.Abelian.SpectralObject.mapFourδ₄Toδ₃'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Preorder.toLE",
"CategoryTheory.Abelian",
"CategoryTheor... | true |
Equiv.Perm.equivUnitsEnd._proof_6 | Mathlib.Algebra.Group.End | [
"Equiv.instEquivLike",
"HMul.hMul",
"Equiv.symm_comp_self",
"Function.comp",
"id",
"Equiv",
"Equiv.Perm",
"Equiv.Perm.instMul",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"instHMul"
] | false |
_private.Mathlib.Data.Int.Bitwise.0.Int.shiftLeft_eq_mul_pow.match_1_1 | Mathlib.Data.Int.Bitwise | [
"Int.casesOn",
"Int.ofNat",
"Int",
"Nat",
"Int.negSucc"
] | false |
Lean.Meta.Grind.Extension.addEMatchAttrAndSuggest | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"Lean.getConstInfo",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Bool.not",
"Lean.Core.instMonadResolveNameCoreM",
"Lean.ConstantInfo.isAxiom",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.Meta.Grind.Entry.ematch",
"Lean.Meta.Grind.Extens... | true |
SimpleGraph.Copy.mapNeighborSet._proof_2 | Mathlib.Combinatorics.SimpleGraph.Copy | [
"RelHom.instFunLike",
"SimpleGraph.Adj",
"Membership.mem",
"SimpleGraph.neighborSet",
"SimpleGraph.Copy",
"Set.Elem",
"SimpleGraph",
"Subtype.prop",
"SimpleGraph.Copy.toHom",
"SimpleGraph.Hom",
"Subtype.val",
"Set.instMembership",
"DFunLike.coe",
"SimpleGraph.Hom.apply_mem_neighborSet",
... | false |
IsReduced.mk | Mathlib.Algebra.GroupWithZero.Basic | [
"Pow",
"Nat",
"IsReduced.mk",
"Zero.toOfNat0",
"OfNat.ofNat",
"IsNilpotent",
"Eq",
"IsReduced",
"Zero"
] | true |
ArchimedeanOrder.instLE | Mathlib.Algebra.Order.Archimedean.Class | [
"Lattice",
"instHSMul",
"Equiv.instEquivLike",
"abs",
"PartialOrder.toPreorder",
"AddMonoid.toNSMul",
"ArchimedeanOrder.val",
"Preorder.toLE",
"Exists",
"SemilatticeInf.toPartialOrder",
"Equiv",
"LE.le",
"LE",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Nat",
"LE.mk",
"ArchimedeanOrder... | true |
Plausible.TestResult.ctorElim | Plausible.Testable | [
"Plausible.TestResult.ctorElimType",
"String",
"PSum",
"Plausible.TestResult.failure",
"Plausible.TestResult",
"List",
"Unit",
"Plausible.TestResult.ctorIdx",
"Nat",
"Plausible.TestResult.casesOn",
"Plausible.TestResult.success",
"Eq.ndrec",
"PULift.down",
"Plausible.TestResult.gaveUp",
... | false |
CategoryTheory.ComposableArrows.sc'._auto_5 | Mathlib.Algebra.Homology.ExactSequence | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Meta.StructProjDecl.projName | Lean.Meta.Structure | [
"Lean.Name",
"Lean.Meta.StructProjDecl"
] | true |
HomologicalComplex.evalCompCoyonedaCorepresentableBySingle._proof_3 | Mathlib.Algebra.Homology.Double | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"Opposite",
"CategoryTheory.coyoneda",
"HomologicalComplex.mkHomFromSingle",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"False.elim",
"Cat... | false |
WithBot.ofDual_lt_ofDual_iff | Mathlib.Order.WithBot | [
"WithTop.not_top_lt._simp_1",
"False",
"WithBot.some",
"WithBot",
"WithBot.instLT",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"congrArg",
"OrderDual.ofDual_lt_ofDual._simp_1",
"Equiv",
"OrderDual.instLT",
"Bot.bot",
"WithTop.coe_lt_top._simp_1",
"WithTop.coe_lt_coe._simp_1",
"WithTop.so... | true |
_private.Mathlib.RingTheory.Perfectoid.BDeRham.0.«_aux_Mathlib_RingTheory_Perfectoid_BDeRham___macroRules__private_Mathlib_RingTheory_Perfectoid_BDeRham_0_term𝔹_dR^+(_)_1» | Mathlib.RingTheory.Perfectoid.BDeRham | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
Matrix.det_isEmpty | Mathlib.LinearAlgebra.Matrix.Determinant.Basic | [
"Matrix.det_apply",
"MulOne.toOne",
"Units.instMulAction",
"CommRing",
"instHSMul",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Equiv.instEquivLike",
"CommRing.toNonUnitalCommRing",
"Equiv.Perm.instOne",
"Finset.univ",
"MonoidHom",
"Monoid.toMulOneClass",
"Ad... | true |
Lean.JsonRpc.RequestID.num.inj | Lean.Data.JsonRpc | [
"Lean.JsonNumber",
"Lean.JsonRpc.RequestID.num",
"Lean.JsonRpc.RequestID.num.noConfusion",
"Lean.JsonRpc.RequestID",
"Eq"
] | true |
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