name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ProbabilityTheory.iSup_bayesRisk_le_minimaxRisk | Mathlib.Probability.Decision.Risk.Basic | [
"ProbabilityTheory.bayesRisk",
"iSup₂_le",
"MeasureTheory.Measure",
"ProbabilityTheory.minimaxRisk",
"iSup",
"CompletelyDistribLattice.toCompleteLattice",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"MeasurableSpace",
"CompleteLinearOrder.toConditionallyCompleteLine... | true |
Std.Internal.List.Const.getValueD_map | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"congrArg",
"Std.Internal.List.containsKey_eq_isSome_getValue?",
"List.map",
"Option.getD",
"Option.some",
"Sigma.fst",
"Bool.true",
"Std.Internal.List.getKey",
"List",
"Std.Internal.List.containsKey",
"EquivBEq",
"Std.Internal.List.getValue?",
"Std.Intern... | true |
Prefunctor.star_fst | Mathlib.Combinatorics.Quiver.Covering | [
"Quiver.Hom",
"Sigma.fst",
"Quiver.Star",
"Prefunctor",
"Quiver",
"Eq.refl",
"Eq",
"Prefunctor.star",
"Prefunctor.obj"
] | true |
Set.Ioc_eq_Icc_same_iff | Mathlib.Order.Interval.Set.Basic | [
"Set.Ioc",
"Preorder.toLE",
"LE.le",
"eq_comm",
"Set.Icc_eq_Ioc_same_iff",
"Iff",
"Set.Icc",
"Iff.trans",
"Eq",
"Not",
"Preorder",
"Set"
] | true |
_private.Lean.Meta.Tactic.Simp.Arith.Int.Basic.0.Lean.Meta.Simp.Arith.Int.ToLinear.toLinearExpr.visit._unsafe_rec | Lean.Meta.Tactic.Simp.Arith.Int.Basic | [
"Pure.pure",
"Unit.unit",
"Lean.Meta.DefEq.isInstMulInt",
"Lean.Expr.isApp",
"Int.Linear.Expr.mulR",
"StateRefT'.instAlternativeOfMonad",
"ReaderT",
"Lean.Meta.State",
"Lean.Expr.cleanupAnnotations",
"instMonadLiftT",
"Lean.Expr",
"Int.Linear.Expr.add",
"Lean.Meta.MetaM",
"IO.RealWorld",
... | false |
ArchimedeanClass.stdPart_ofNat | Mathlib.Algebra.Order.Ring.StandardPart | [
"Real",
"IsOrderedRing",
"LinearOrder",
"AddGroupWithOne.toAddMonoidWithOne",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"AddMonoidWithOne.toNatCast",
"DivisionRing.toRing",
"Nat.cast",
"Field.toSemifield",
"ArchimedeanClass.stdPart_natCast",
"Archim... | true |
Mathlib.Tactic.Coherence.liftHom_WhiskerRight | Mathlib.Tactic.CategoryTheory.Coherence | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"Mathlib.Tactic.Coherence.LiftHom",
"Mathlib.Tactic.Coherence.LiftHom.mk",
"CategoryTheory.FreeMonoidalCategory.instMonoidalCategory",
"Mathlib.Tactic.Coherence.LiftObj_tensor",
"CategoryTheory.MonoidalCategoryS... | true |
Function.Injective.divInvMonoid._proof_1 | Mathlib.Algebra.Group.InjSurj | [
"Eq.mpr",
"Function.Injective.monoid",
"MulOne.toOne",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"instHDiv",
"One",
"Inv",
"HMul.hMul",
"Monoid.toMulOneClass",
"Pow",
"congrArg",
"Mul",
"id",
"MulOne.toMul",
"HDiv.hDiv",
"Div",
"DivInvMonoid.toMonoid",
"div_eq_mul_inv",
"DivInvM... | false |
Lean.Doc.Block.ul.noConfusion | Lean.DocString.Types | [
"Lean.Doc.Block",
"id",
"Lean.Doc.Block.ul",
"Lean.Doc.Block.noConfusion",
"Array",
"heq_of_eq",
"Eq.refl",
"HEq",
"Lean.Doc.ListItem",
"Eq"
] | false |
LinearMap.surjective_comp_linearProjOfIsCompl | Mathlib.LinearAlgebra.Projection | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Submodule.completeLattice",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"Subtype",
"Submodule.instPartialOrder",
"Submodule.module",
"LinearMap",
"AddCommMonoid",
"LinearMap.comp",
"IsCompl",
... | true |
RelIso.embeddingSurjectiveEquivIso | Mathlib.Order.RelIso.Basic | [
"Equiv.mk",
"RelIso.embeddingSurjectiveEquivIso._proof_1",
"RelIso.embeddingSurjectiveEquivIso._proof_2",
"Equiv",
"Subtype",
"Subtype.mk",
"RelIso",
"RelEmbedding",
"RelIso.surjective",
"RelIso.toRelEmbedding",
"RelIso.ofSurjective",
"Subtype.val",
"DFunLike.coe",
"RelEmbedding.instFunLik... | true |
AlgebraicGeometry.Scheme.zeroLocus_iInf | Mathlib.AlgebraicGeometry.AffineScheme | [
"Eq.mpr",
"Submodule",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"iInf",
"Semiring.toModule",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"Iff.of_eq",
"TopologicalSpace.Opens.instPartialOrder",
"congrArg... | true |
Set.nonempty_Ioi | Mathlib.Order.Interval.Set.Basic | [
"Set.Ioi",
"Preorder.toLT",
"NoMaxOrder",
"NoMaxOrder.exists_gt",
"Set.Nonempty",
"Preorder"
] | true |
cond.eq_2 | Init.Grind.Ring.CommSolver | [
"cond",
"Eq.refl",
"Bool.false",
"Eq"
] | true |
IsPrimitiveRoot.zpowers_eq | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"Fintype.card_congr",
"IsDomain",
"Nat.instMulZeroClass",
"CommRing",
"Trans.trans",
"ZMod.commRing",
"CommSemiring.toSemiring",
"Additive",
"ZMod.fintype",
"Subgroup.mul",
"Membership.mem",
"Units",
"Fintype.card",
"Subtype",
"Distrib.toAdd",
"Subgroup",
"Fintype.ofEquiv",
"Units.... | true |
Cardinal.countable_iff_lt_aleph_one | Mathlib.SetTheory.Cardinal.Aleph | [
"Eq.mpr",
"Preorder.toLT",
"Cardinal.le_aleph0_iff_set_countable",
"Cardinal.aleph",
"Ordinal.partialOrder",
"Cardinal",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Cardinal.mk",
"Set.Elem",
"id",
"Cardinal.lt_aleph_one_iff",
"Cardinal.aleph0",
"LE.le",
"Cardi... | true |
Lean.Meta.Grind.Arith.Cutsat.ToIntThms.mk.inj | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Expr",
"Lean.Meta.Grind.Arith.Cutsat.ToIntThms",
"Lean.Meta.Grind.Arith.Cutsat.ToIntThms.mk.noConfusion",
"And",
"And.intro",
"Lean.Meta.Grind.Arith.Cutsat.ToIntThms.mk",
"Eq",
"Option"
] | true |
LaurentPolynomial.algebraMap_eq_toLaurent | Mathlib.Algebra.Polynomial.Laurent | [
"AddMonoidAlgebra.semiring",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"LaurentPolynomial",
"RingHom",
"Int",
"Int.instAddMonoid",
"Polynomial",
"CommSemiring",
"Polynomial.toLaurent",
"RingHom.instFunLike",
"Polynomial.semiring",
"AddMonoidAlgebra.nonAss... | true |
FirstOrder.Field.FieldAxiom.toProp.eq_9 | Mathlib.ModelTheory.Algebra.Field.Basic | [
"One",
"Mul",
"Exists",
"FirstOrder.Field.FieldAxiom.existsPairNE",
"Ne",
"FirstOrder.Field.FieldAxiom.toProp",
"Neg",
"Eq.refl",
"Eq",
"Add",
"Zero"
] | true |
Lean.LibrarySuggestions.Config.maxSuggestions._default | Lean.LibrarySuggestions.Basic | [
"id",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | false |
_private.Aesop.RuleSet.0.Aesop.LocalRuleSet.add._proof_1 | Aesop.RuleSet | [
"Aesop.NormSimpRule.entries",
"congrArg",
"Aesop.SimpTheorems.addSimpEntry",
"Aesop.LocalRuleSet.simpTheoremsArrayNonempty",
"Array.modify",
"Prod.mk",
"instOfNatNat",
"Prod.fst",
"Array.size_modify",
"Array.foldl",
"Aesop.LocalRuleSet",
"Nat",
"LT.lt",
"True",
"Lean.Meta.SimpTheorems",
... | false |
List.flatten.match_1 | Init.Prelude | [
"Unit.unit",
"List.cons",
"List",
"Unit",
"List.casesOn",
"List.nil"
] | false |
_private.Init.Data.Vector.Erase.0.Vector.eraseIdx_set_lt._proof_1 | Init.Data.Vector.Erase | [
"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.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval"... | false |
RingQuot.Rel.sub_right | Mathlib.Algebra.RingQuot | [
"NegZeroClass.toNeg",
"RingQuot.Rel.add_right",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddZeroClass.toAddZero",
"Distrib.toAdd",
"RingQuot.Rel",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"Subtract... | true |
CategoryTheory.Category.toCategoryStruct.hcongr_2 | Mathlib.Topology.Sheaves.Flasque | [
"HEq.refl",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"CategoryTheory.CategoryStruct",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | true |
Lean.Expr.hasMVar | Lean.Expr | [
"Lean.Expr.data",
"Lean.Expr.Data.hasExprMVar",
"Lean.Expr",
"Lean.Expr.Data",
"Lean.Expr.Data.hasLevelMVar",
"Bool",
"Bool.or"
] | true |
MDifferentiableOn.differentiableOn | Mathlib.Geometry.Manifold.MFDeriv.FDeriv | [
"chartedSpaceSelf",
"NormedSpace",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"MDifferentiableOn",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"mdifferentiableOn_iff_differentiableOn",
"DifferentiableOn",
"Iff.mp",
"NontriviallyNormedField",
"NormedAddCommGroup.toAddCommGroup"... | true |
Complex.HadamardThreeLines.sSupNormIm.eq_1 | Mathlib.Analysis.Complex.Hadamard | [
"Norm.norm",
"Real",
"Function.comp",
"Real.instSupSet",
"Set.instSingletonSet",
"Complex.re",
"Complex.HadamardThreeLines.sSupNormIm",
"Set.preimage",
"NormedAddCommGroup.toNorm",
"Eq.refl",
"Set.image",
"Complex",
"Singleton.singleton",
"Eq",
"SupSet.sSup",
"NormedAddCommGroup",
"S... | true |
String.Slice.contains_prop_eq | Init.Data.String.Lemmas.Pattern.Find.Pred | [
"Eq.mpr",
"String.Slice.contains_prop_eq_contains_decide",
"String.Slice.Pattern.CharPred.instToForwardSearcherForallCharBoolDefaultForwardSearcher",
"String.Slice.contains_bool_eq",
"congrArg",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher.instIteratorLoopIdSearchStep",
"String.Slice",... | true |
_private.Mathlib.Topology.Separation.Hausdorff.0.t2_iff_nhds._simp_1_1 | Mathlib.Topology.Separation.Hausdorff | [
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"nhds",
"CompleteLattice.toBoundedOrder",
"t2Space_iff_disjoint_nhds",
"TopologicalSpace",
"T2Space",
"BoundedOrder.toOrderBot",
"Pairwise",
"propext",
"Eq",
"Filter",
"Filter.instPartialOrder"
] | false |
CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_app_iff_mono_rightTriple_leftToRight_app | Mathlib.CategoryTheory.Adjunction.Quadruple | [
"_private.Mathlib.CategoryTheory.Adjunction.Quadruple.0.CategoryTheory.Adjunction.Quadruple.epi_leftTriple_rightToLeft_app_iff_mono_rightTriple_leftToRight_app._simp_1_4",
"CategoryTheory.Adjunction.Quadruple.adj₃",
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.NatIso.isIso_app_of_isIso",
"Equiv.app... | true |
Std.TreeSet.Equiv.rec | Std.Data.TreeSet.Basic | [
"Std.TreeSet",
"Std.TreeMap.Equiv",
"Ordering",
"Std.TreeSet.inner",
"Unit",
"Std.TreeSet.Equiv.mk",
"Std.TreeSet.Equiv"
] | false |
_private.Mathlib.NumberTheory.LSeries.Positivity.0.LSeries.iteratedDeriv_alternating._simp_1_2 | Mathlib.NumberTheory.LSeries.Positivity | [
"Real.instLE",
"Real",
"Real.instZero",
"PartialOrder.toPreorder",
"Complex.instZero",
"Preorder.toLE",
"LE.le",
"Complex.ofReal",
"Complex.zero_le_real",
"propext",
"Zero.toOfNat0",
"Complex",
"OfNat.ofNat",
"Eq",
"Complex.partialOrder"
] | false |
List.tail_attachWith | Init.Data.List.Attach | [
"List.attachWith",
"List.mem_cons_of_mem",
"Membership.mem",
"Subtype",
"List.tail",
"List.mem_of_mem_tail",
"List.cons",
"List",
"List.instMembership",
"List.casesOn",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"Eq.symm",
"Eq",
"List.nil"
] | true |
Int.reduceBinIntNatOp | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Int | [
"Pure.pure",
"Lean.Meta.getNatValue?",
"Lean.Expr.isAppOfArity",
"ReaderT",
"Lean.Meta.State",
"instMonadLiftT",
"Lean.Expr.appArg!",
"Lean.Meta.Simp.MethodsRef",
"ReaderT.instMonad",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Meta.getIntValue?",
"instDecidableEqBool",
"liftM"... | true |
CategoryTheory.ShortComplex.HomologyMapData.noConfusionType | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyMapData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.ShortComplex.HomologyData.left",
"CategoryTheory.ShortComplex.... | false |
ProofWidgets.Component.mk.noConfusion | ProofWidgets.Component.Basic | [
"ProofWidgets.Component.mk",
"Lean.Widget.Module",
"String",
"ProofWidgets.Component",
"id",
"heq_of_eq",
"ProofWidgets.Component.noConfusion",
"Eq.refl",
"Eq"
] | false |
_private.Mathlib.Algebra.Homology.ExactSequence.0.CategoryTheory.ComposableArrows.IsComplex._proof_3 | Mathlib.Algebra.Homology.ExactSequence | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDec... | false |
Algebra.GrothendieckGroup.lift._proof_3 | Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"IsUnit",
"Membership.mem",
"Group.isUnit",
"Subtype",
"DivInvMonoid.toMonoid",
"CommGroup",
"Submonoid.instTop",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"Submonoid.instSetLike",
"CommGroup.toGro... | false |
SeparationQuotient.continuousWithinAt_lift | Mathlib.Topology.Inseparable | [
"ContinuousWithinAt",
"nhds",
"TopologicalSpace",
"Iff",
"Set.preimage",
"SeparationQuotient",
"SeparationQuotient.mk",
"SeparationQuotient.tendsto_lift_nhdsWithin_mk",
"SeparationQuotient.lift",
"instTopologicalSpaceSeparationQuotient",
"Eq",
"Inseparable",
"Set"
] | true |
instNegUniformOnFun._aux_1 | Mathlib.Topology.Algebra.UniformConvergence | [
"Neg",
"UniformOnFun",
"Neg.neg",
"Set"
] | false |
CategoryTheory.Limits.BinaryBicone.category._proof_14 | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.BinaryBiconeMorphism",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.BinaryBicone.inl",
"CategoryTheory.Limits.BinaryBicone.pt",
"CategoryTheory.Limits.BinaryBiconeMorphism.winl_assoc",
"Cat... | false |
groupHomology.cyclesIso₀_inv_comp_iCycles_apply | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"Rep.V",
"CommRing",
"Finsupp.module",
"Nat.instOne",
"ModuleCat",
"congrArg",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"LinearMap.instFunLike",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMono... | true |
Std.Do.SPred.and_nil | Std.Do.SPred.SPred | [
"And",
"Std.Do.SPred",
"Std.Do.SPred.and",
"ULift.up",
"Eq",
"ULift.down",
"rfl",
"List.nil"
] | true |
Stonean.fullyFaithfulToCompHaus._proof_1 | Mathlib.Topology.Category.Stonean.Basic | [
"CompHausLike",
"TopCat.str",
"TopCat.carrier",
"True",
"compHausLikeToCompHaus._proof_1",
"TopCat",
"CompHausLike.toTop",
"ExtremallyDisconnected"
] | false |
Rack.PreEnvelGroup | Mathlib.Algebra.Quandle | [
"Rack.PreEnvelGroup.unit",
"Rack.PreEnvelGroup.inv",
"Rack.PreEnvelGroup.incl",
"Rack.PreEnvelGroup.mul"
] | true |
Std.DHashMap.get!_empty | Std.Data.DHashMap.Lemmas | [
"Inhabited.default",
"LawfulBEq",
"instOfNatNat",
"Std.DHashMap.get!_emptyWithCapacity",
"Nat",
"Std.DHashMap.get!",
"Inhabited",
"Hashable",
"Std.DHashMap.instEmptyCollection",
"EmptyCollection.emptyCollection",
"OfNat.ofNat",
"BEq",
"Eq",
"Std.DHashMap"
] | true |
Vector.forall_cons_iff | Init.Data.Vector.Lemmas | [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Vector.push",
"Vector",
"congrArg",
"HSub.hSub",
"Vector.back",
"id",
"Vector.pop",
"instSubNat",
"instOfNatNat",
"Vector.push_pop_back",
"instHAdd",
"Iff",
"instHSub",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"True",
"Iff.intro",
"eq_self",... | true |
MonoidHom.bijective_of_bijective_of_injective_of_left_exact | Mathlib.Algebra.FiveLemma | [
"MonoidHom.surjective_of_surjective_of_injective_of_left_exact",
"MonoidHom.instFunLike",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"id",
"MonoidHom.comp",
"Div... | true |
DirectLimit.instNonAssocSemiringOfRingHomClass._proof_4 | Mathlib.Algebra.Colimit.DirectLimit | [
"DirectLimit.instMulOneClassOfMonoidHomClass",
"DirectLimit.instNonAssocSemiringOfRingHomClass._proof_2",
"MulOne.toOne",
"HMul.hMul",
"Preorder.toLE",
"MulOne.toMul",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toMulZeroOneClass",
"LE.le",
"MonoidWithZeroHomClass.toMonoidHomClass",... | false |
_private.Mathlib.GroupTheory.Perm.Sign.0.Equiv.Perm.signAux_swap._simp_1_3 | Mathlib.GroupTheory.Perm.Sign | [
"True",
"propext",
"Subsingleton",
"Eq",
"eq_iff_true_of_subsingleton"
] | false |
IsBoundedLinearMap.differentiableWithinAt | Mathlib.Analysis.Calculus.FDeriv.Linear | [
"IsBoundedLinearMap.differentiableAt",
"NormedSpace",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"DifferentiableAt.differentiableWithinAt",
"NormedField.toField",
"Field.toSemifield",
"IsBoundedLinearMap",
"Semifield.toDivisionSemiring",
"SeminormedAddCommGroup.toPseudoMetricSpace... | true |
Polynomial.eq_neg_mul_add_of_roots_quadratic_eq_pair | Mathlib.RingTheory.Polynomial.SmallDegreeVieta | [
"Eq.mpr",
"Polynomial.C",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"IsDomain",
"CommRing",
"Polynomial.roots",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemir... | true |
CategoryTheory.Limits.Fork.ι_postcompose | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheory.Limits.Fork",
"CategoryTheory.Limits... | true |
Manifold.IsImmersionOfComplement.of_opens | Mathlib.Geometry.Manifold.Immersion | [
"PUnit.normedAlgebra",
"NormedCommRing.toSeminormedCommRing",
"PUnit.normedAddCommGroup",
"NormedSpace",
"TopologicalSpace.Opens.instChartedSpace",
"TopologicalSpace.Opens",
"Membership.mem",
"Subtype",
"IsManifold",
"TopologicalSpace.Opens.instSetLike",
"TopologicalSpace",
"ModelWithCorners",... | true |
Std.ExtDHashMap.size_erase | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.ExtDHashMap.instDecidableMem",
"HSub.hSub",
"Membership.mem",
"Std.ExtDHashMap.erase",
"Std.ExtDHashMap.inductionOn",
"instSubNat",
"instOfNatNat",
"LawfulHashable",
"EquivBEq",
"instHSub",
"Std.ExtDHashMap.size",
"Nat",
"Std... | true |
Set.Ico_inter_Iio | Mathlib.Order.Interval.Set.LinearOrder | [
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"SemilatticeInf.toMin",
"Set.instInter",
"Set.Ico",
"Inter.inter",
"Set.Iio",
"Eq",
"_private.Mathlib.Order.Interval.Set.LinearOrder.0.Set.Ico_inter_Iio._proof_1_1",
"instDistribLatticeOfLine... | true |
_private.Mathlib.Data.Num.Lemmas.0.Num.castNum_shiftLeft._simp_1_1 | Mathlib.Data.Num.Lemmas | [
"Num.shiftl",
"HShiftLeft.hShiftLeft",
"Num.shiftl_eq_shiftLeft",
"Num",
"Nat",
"Num.instHShiftLeftNat",
"Eq.symm",
"Eq"
] | false |
Lean.Compiler.LCNF.PP.ppLetDecl | Lean.Compiler.LCNF.PrettyPrinter | [
"Pure.pure",
"Std.instToFormatString",
"Std.Format.instAppend",
"Lean.Compiler.LCNF.PP.ppExpr",
"String",
"Lean.Core.instMonadOptionsCoreM",
"ReaderT.instMonad",
"Lean.instMonadOptionsOfMonadLift",
"IO.RealWorld",
"instDecidableEqBool",
"Lean.Compiler.LCNF.PP.ppLetValue",
"Lean.Compiler.LCNF.P... | true |
TopologicalSpace.CompactOpens.instGeneralizedBooleanAlgebra._proof_4 | Mathlib.Topology.Sets.Compacts | [
"TopologicalSpace.CompactOpens.instPartialOrder",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"TopologicalSpace.CompactOpens.mk",
"DistribLattice.le_sup_inf",
"T2Space.to_quasiSeparatedSpace",
"Iff.rfl",
"PartialOrder.toPreorder",
"BooleanAlgebra.toGeneralizedBooleanAlgebra",
"Preorder.toLE",
"... | false |
Set.union_diff_distrib | Mathlib.Order.BooleanAlgebra.Set | [
"Set.instUnion",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"SDiff.sdiff",
"Set.instBooleanAlgebra",
"sup_sdiff",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",
"Union.union",
"Eq",
"Set.instSDiff",
"Set"
] | true |
_private.Std.Data.String.ToInt.0.String.isSome_toInt?._simp_1_1 | Std.Data.String.ToInt | [
"String.toSlice",
"String.Slice.toInt?",
"String",
"String.toInt?",
"Int",
"String.toInt?_toSlice",
"Eq.symm",
"Eq",
"Option"
] | false |
SSet.Truncated.Edge.mk'._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ConcreteCategory.hom",
"SSet.Truncated.Edge._proof_2",
"Quiver.Hom.op",
"SimplexCategory.Truncated.δ₂",
"SSet.Truncated",
"TypeCat.instFunLikeFun",
"SSet.Truncated.Edge._proof_... | false |
Mathlib.Tactic.rename' | Mathlib.Tactic.Rename | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.sepBy1",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat",
"Mathlib.Tactic.renameArg",
"Bool.false",
"Lean.Name.mkStr1"
] | true |
Frm.instCoeSortType | Mathlib.Order.Category.Frm | [
"CoeSort.mk",
"Frm.carrier",
"Frm",
"CoeSort"
] | true |
Ideal.bot_isMaximal | Mathlib.RingTheory.Ideal.Maximal | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"False",
"Preorder.toLT",
"NeZero.one",
"Semiring.toModule",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Ideal.eq_bot_or_top",
"Submodule.mem_bot._simp_1",
"DivisionSemiring.toGroupWithZero",
"Preorde... | true |
Lean.Linter.MissingDocs.checkSyntaxAbbrev | Lean.Linter.MissingDocs | [
"instOfNatNat",
"Lean.Linter.MissingDocs.SimpleHandler",
"Lean.Linter.MissingDocs.mkSimpleHandler",
"Nat",
"OfNat.ofNat"
] | true |
OrderHom.apply_mono | Mathlib.Order.Hom.Basic | [
"Preorder.toLE",
"OrderHom.instPreorder",
"LE.le",
"OrderHom.mono",
"OrderHom.instFunLike",
"LE.le.trans",
"DFunLike.coe",
"OrderHom",
"Preorder"
] | true |
Finset.image₂_right_comm | Mathlib.Data.Finset.NAry | [
"Eq.mpr",
"Set.image2_right_comm",
"congrArg",
"Finset",
"id",
"Finset.coe_injective",
"SetLike.coe",
"Finset.instSetLike",
"Set.image2",
"congr",
"congrFun'",
"Eq",
"Finset.coe_image₂",
"Eq.trans",
"DecidableEq",
"Finset.image₂",
"Set"
] | true |
minpoly.coeff_zero_eq_zero._simp_1 | Mathlib.FieldTheory.Minpoly.Field | [
"IsDomain",
"minpoly.coeff_zero_eq_zero",
"CommSemiring.toSemiring",
"Algebra",
"instOfNatNat",
"Field.toSemifield",
"Field.toCommRing",
"minpoly",
"Polynomial.coeff",
"CommRing.toCommSemiring",
"IsIntegral",
"Semifield.toDivisionSemiring",
"Nat",
"propext",
"DivisionSemiring.toSemiring"... | false |
Lean.Kernel.Exception.casesOn | Lean.Environment | [
"Lean.Kernel.Exception.other",
"Lean.Kernel.Exception",
"Lean.Kernel.Exception.declTypeMismatch",
"String",
"Lean.Kernel.Exception.declHasFVars",
"Lean.Kernel.Exception.appTypeMismatch",
"Lean.Kernel.Exception.rec",
"Lean.Expr",
"Lean.Kernel.Exception.funExpected",
"Lean.Kernel.Exception.letTypeMi... | false |
exteriorPower.oneEquiv._proof_4 | Mathlib.LinearAlgebra.ExteriorPower.Basic | [
"Fintype.elems",
"Function.update",
"Nat.le_refl",
"HEq.refl",
"Finset",
"List.Mem.tail",
"False.elim",
"instDecidableEqFin",
"noConfusion_of_Nat",
"Membership.mem",
"AddCommGroup",
"exteriorPower.oneEquiv._proof_3",
"Fin.mk",
"Fin.instOfNat",
"SubtractionMonoid.toSubNegZeroMonoid",
"i... | false |
Lean.NameSSet.insert | Lean.Data.NameMap.Basic | [
"Lean.SSet.insert",
"Lean.NameSSet",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.instHashableName"
] | true |
Lean.Lsp.RpcReleaseParams.ctorIdx | Lean.Data.Lsp.Extra | [
"Nat",
"Lean.Lsp.RpcReleaseParams"
] | false |
MeasurableEquiv.ext | Mathlib.MeasureTheory.MeasurableSpace.Embedding | [
"MeasurableEquiv.instEquivLike",
"MeasurableSpace",
"DFunLike.ext'",
"MeasurableEquiv",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
FirstOrder.Language.isEmpty_functions_constantsOn_succ | Mathlib.ModelTheory.LanguageMap | [
"instOfNatNat",
"IsEmpty",
"FirstOrder.Language.constantsOn",
"instHAdd",
"_private.Mathlib.ModelTheory.LanguageMap.0.FirstOrder.Language.isEmpty_functions_constantsOn_succ._proof_1",
"HAdd.hAdd",
"Nat",
"FirstOrder.Language.Functions",
"instAddNat",
"OfNat.ofNat"
] | true |
CompTriple.instComp_id | Mathlib.Logic.Function.CompTypeclasses | [
"congrArg",
"Function.comp",
"id",
"CompTriple",
"True",
"eq_self",
"of_eq_true",
"CompTriple.mk",
"congrFun'",
"Eq",
"CompTriple.IsId.eq_id",
"Eq.trans",
"CompTriple.IsId"
] | true |
CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom_assoc | Mathlib.CategoryTheory.Bicategory.Strict.Pseudofunctor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Pseudofunctor.mapComp'₀₁₃_hom_comp_whiskerLeft_mapComp'_hom._proof_6",
"Eq.mp",
"CategoryTheory.Bicategory.... | true |
Algebra.coe_linearMap | Mathlib.Algebra.Algebra.Defs | [
"Semiring.toModule",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"Algebra",
"RingHom",
"Algebra.toModule",
"Algebra.linearMap",
"LinearMap",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instFunLike",
"NonAssocSemiring.toNonUnitalNonAssoc... | true |
CategoryTheory.Limits.zero_of_source_iso_zero | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.comp_zero",
"CategoryTheory.CategoryStruct.id",
"Eq.mp",
"CategoryTheory.Iso",
"CategoryTheory.Limits.id_zero",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"Tru... | true |
Std.HashSet.diff | Std.Data.HashSet.Basic | [
"Std.HashSet",
"Std.HashMap.diff",
"Unit",
"Std.HashSet.inner",
"Std.HashSet.mk",
"Hashable",
"BEq"
] | true |
CategoryTheory.Functor.toEventualRanges_finite | Mathlib.CategoryTheory.CofilteredSystem | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.toEventualRanges",
"Subtype.finite",
"Finite",
"Membership.mem",
"CategoryTheory.IsCofilteredOrEmpty",
"CategoryTheory.types",
"CategoryTheory.Functor.eventualRange",
"Set.instMembership",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category",
... | true |
Lean.Elab.Tactic.SolveByElim.evalApplyAssumption._regBuiltin.Lean.Elab.Tactic.SolveByElim.evalApplyAssumption.declRange_3 | Lean.Elab.Tactic.SolveByElim | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"Lean.Name.mkStr5",
"IO",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk"
] | false |
Mathlib.Tactic.Linarith.sub_nonpos_of_le | Mathlib.Tactic.Linarith.Lemmas | [
"Ring.toNonAssocRing",
"IsOrderedRing",
"AddGroupWithOne.toAddGroup",
"covariant_swap_add_of_covariant_add",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"PartialOrder",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"LE.le",
"NonAssocRing.toNonUnitalNonAssocRing",
"SubNegMon... | true |
FirstOrder.Language.Substructure.inclusion.congr_simp | Mathlib.ModelTheory.DirectLimit | [
"PartialOrder.toPreorder",
"FirstOrder.Language.Substructure.inducedStructure",
"Preorder.toLE",
"Membership.mem",
"FirstOrder.Language.Substructure.instSetLike",
"Subtype",
"LE.le",
"FirstOrder.Language.Embedding",
"FirstOrder.Language.Substructure",
"FirstOrder.Language.Structure",
"FirstOrder... | true |
QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared | Mathlib.LinearAlgebra.QuadraticForm.Real | [
"SignType.cast",
"Pi.Function.module",
"NegZeroClass.toNeg",
"False",
"Real",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Pi.addCommMonoid",
"zero_eq_neg._simp_1",
"QuadraticForm.equivalent_signType_weighted_sum_squared",
"Real.instZero",
"SignType.instOne",
"congrArg",
"CommSemiring... | true |
AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_homEquiv_apply | Mathlib.AlgebraicGeometry.GammaSpecAdjunction | [
"AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction",
"Opposite",
"Equiv.instEquivLike",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.LocallyRingedSpace.Γ",
"CommRingCat",
"CategoryTheory.Functor.comp",
"Quiver.Hom.unop",
"CategoryTheory.Functor... | true |
LinearMap.convNonUnitalSemiring | Mathlib.RingTheory.Coalgebra.Convolution | [
"Coalgebra.toCoalgebraStruct",
"instSMulOfMul",
"Coalgebra",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"LinearMap",
"AddComm... | true |
CategoryTheory.locallyDiscreteBicategory | Mathlib.CategoryTheory.Bicategory.LocallyDiscrete | [
"CategoryTheory.LocallyDiscrete.categoryStruct",
"CategoryTheory.locallyDiscreteBicategory._proof_11",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"CategoryTheory.locallyDiscreteBicategory._proof_1",
"CategoryTheory.eqToIso",
"CategoryTheory.locallyDiscreteBicateg... | true |
PolynomialLaw.toFun_eq_rTensor_φ_toFun' | Mathlib.RingTheory.PolynomialLaw.Basic | [
"AlgHom.toLinearMap",
"PolynomialLaw.lifts",
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"PolynomialLaw.factorsThrough_toFunLifted_π",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"TensorProduct.addCommMonoid",
... | true |
_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.Code.instantiateValueLevelParams.instAlt | Lean.Compiler.LCNF.Basic | [
"Inhabited.default",
"Lean.Level",
"Lean.Compiler.LCNF.Purity.pure",
"List",
"Lean.Name",
"Inhabited",
"Lean.Compiler.LCNF.Alt",
"Inhabited.mk"
] | true |
CategoryTheory.Sum.functorEquiv._proof_2 | Mathlib.CategoryTheory.Sums.Products | [
"CategoryTheory.Functor",
"CategoryTheory.sum",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Prod.mkHom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"Sum",
"CategoryTheory.Functor.whiskerLeft",
"id",
"Prod.mk",
"CategoryTheory.Sum.inr_",
"Cat... | false |
_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.go._unary._proof_31 | Std.Sat.AIG.CNF | [
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Fanin.gate",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF._proof_15",
"instHashableNat",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF._proof_18",
"And",
"Std.Sat.AIG",
"Nat",
"LT.lt",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.State.IsExtensionBy",
"Decidabl... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.keys_map._simp_1_4 | Std.Data.DTreeMap.Internal.Lemmas | [
"List.Perm",
"Std.DTreeMap.Internal.Impl.Equiv",
"propext",
"Std.DTreeMap.Internal.Impl.toListModel",
"Std.DTreeMap.Internal.Impl.equiv_iff_toListModel_perm",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Sigma"
] | false |
MeasurableEquiv.sumProdSum | Mathlib.MeasureTheory.MeasurableSpace.Embedding | [
"MeasurableEquiv.prodSumDistrib",
"MeasurableEquiv.sumCongr",
"Sum",
"Sum.instMeasurableSpace",
"MeasurableSpace",
"MeasurableEquiv.trans",
"MeasurableEquiv.sumProdDistrib",
"Prod",
"MeasurableEquiv",
"Prod.instMeasurableSpace"
] | true |
_private.Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory.0.CategoryTheory.Triangulated.AbelianSubcategory.eq_zero_of_hom_shift_pos._proof_1_1 | Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Int.Linear.norm_le",
"congrArg",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Int.not_le_eq",
"Eq.mp",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"LE.le",
"Int.Linear.Poly.num",
"Int.instMu... | false |
TrivSqZeroExt.algebraMap_eq_inlHom | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"TrivSqZeroExt",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"MulOpposite.instAlgebra",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"RingHom",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"Algebra.id",
"DistribSMul.toSMulZeroClass",
"IsScalarTower.op_righ... | true |
Lean.ParametricAttributeImpl._sizeOf_1 | Lean.Attributes | [
"Lean.AttributeImplCore",
"Lean.AttrM",
"Lean.Syntax",
"instOfNatNat",
"Lean.ParametricAttributeImpl.rec",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Bool",
"Lean.ParametricAttributeImpl",
"instAddNat",
"Lean.Name",
"SizeOf",
"Lean.AttributeImplCore._sizeOf_inst",
"OfN... | false |
PrimeSpectrum.nonempty_iff_nontrivial | Mathlib.RingTheory.Spectrum.Prime.Basic | [
"Nontrivial",
"PrimeSpectrum.mk",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule.addSubmonoidClass",
"Ideal.exists_maximal",
"Semiring.toModule",
"PrimeSpectrum.isPrime",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"Ne",
"AddCommMon... | true |
MulAction.stabilizer._proof_1 | Mathlib.GroupTheory.GroupAction.Defs | [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHSMul",
"inv_smul_eq_iff",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"id",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"Inv.inv",
"MulAction",
"propext",
"Monoid.toSemigr... | false |
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