name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
TopModuleCat | Mathlib.Algebra.Category.ModuleCat.Topology.Basic | [
"TopologicalSpace",
"Ring",
"TopModuleCat.mk"
] | true |
Lean.Lsp.Ipc.CallHierarchy.rec_2 | Lean.Data.Lsp.Ipc | [
"Lean.Lsp.CallHierarchyItem",
"List.cons",
"Lean.Lsp.Ipc.CallHierarchy",
"Array",
"List",
"Lean.Lsp.Ipc.CallHierarchy.mk",
"Lean.Lsp.Range",
"Array.mk",
"List.nil"
] | false |
CategoryTheory.SmallObject.hasPushouts | Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument | [
"CategoryTheory.MorphismProperty",
"Cardinal.IsRegular",
"Cardinal",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"SemilatticeInf.toPartialOrder",
"Fact",
"DistribLattice.toLattice",
"linearOrder_toType",
"Cardinal.ord",
"CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgum... | true |
AddSubgroup.op.instNormal | Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas | [
"AddOpposite",
"AddSubgroup",
"AddSubgroup.Normal",
"AddSubgroup.Normal.op",
"AddSubgroup.op",
"AddGroup",
"AddOpposite.instAddGroup"
] | true |
LinearMap.BilinForm.apply_apply_same_eq_zero_iff | Mathlib.LinearAlgebra.SesquilinearForm.Basic | [
"Eq.mpr",
"Submodule",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"AddGroupWithOne.toAddGroup",
"LinearMap.ext",
"LinearMap.BilinForm",
"congrArg",
"CommSemiring.toSemiring",
"... | true |
AnalyticAt.comp_of_eq' | Mathlib.Analysis.Analytic.Composition | [
"NormedSpace",
"AnalyticAt.comp_of_eq",
"AnalyticAt",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Eq",
"NormedAddCommGroup"
] | true |
Equiv.piCongr'.eq_1 | Mathlib.Logic.Equiv.Basic | [
"Equiv.instEquivLike",
"Equiv",
"Equiv.piCongr'",
"Equiv.piCongr",
"Eq.refl",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Fin.cast_addNat | Init.Data.Fin.Lemmas | [
"Fin.natAdd",
"Fin.ext",
"Fin.val",
"instHAdd",
"Fin.cast",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Fin",
"Eq",
"Fin.addNat",
"Nat.add_comm"
] | true |
_private.Mathlib.Topology.Metrizable.Uniformity.0.UniformSpace.metrizable_uniformity._simp_1_5 | Mathlib.Topology.Metrizable.Uniformity | [
"True",
"propext",
"Eq",
"eq_self_iff_true"
] | false |
List.nodup_iff_forall_not_duplicate | Mathlib.Data.List.Duplicate | [
"Eq.mpr",
"congrArg",
"_private.Mathlib.Data.List.Duplicate.0.List.nodup_iff_forall_not_duplicate._simp_1_1",
"id",
"_private.Mathlib.Data.List.Duplicate.0.List.nodup_iff_forall_not_duplicate._simp_1_2",
"List.cons",
"List.Nodup",
"iff_self",
"List",
"List.Duplicate",
"Iff",
"True",
"of_eq_t... | true |
instLinearOrderEReal._aux_10 | Mathlib.Data.EReal.Basic | [
"Real",
"WithBot",
"LinearOrder.toDecidableEq",
"WithBot.decidableEq",
"EReal",
"WithTop.linearOrder",
"Real.linearOrder",
"WithTop",
"DecidableEq"
] | false |
LiouvilleWith.sub_nat_iff._simp_1 | Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith | [
"Real",
"Real.instSub",
"HSub.hSub",
"LiouvilleWith",
"Nat.cast",
"instHSub",
"Nat",
"LiouvilleWith.sub_nat_iff",
"propext",
"Eq",
"Real.instNatCast"
] | false |
CategoryTheory.Subfunctor.Subpresheaf.toPresheaf_map_coe | Mathlib.CategoryTheory.Subfunctor.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"Membership.mem",
"CategoryTheory.Subfunctor.obj",
"TypeCat.ofHom",
"Set.Elem",
"CategoryTheory.Subfunctor.toFunctor_map",
"CategoryTheory.Subfunctor... | true |
Std.TreeMap.Raw.insertMany_list_equiv_foldl | Std.Data.TreeMap.Raw.Lemmas | [
"Eq.mpr",
"List.foldl_hom",
"Std.TreeMap.Raw.insert",
"congrArg",
"Std.DTreeMap.Raw.Const.insertMany_list_equiv_foldl",
"instForInOfForIn'",
"Ordering",
"inferInstance",
"id",
"Std.DTreeMap.Raw.Equiv",
"Std.TreeMap.Raw.Equiv",
"List.foldl",
"Id",
"Std.TreeMap.Raw.inner",
"Membership",
... | true |
CategoryTheory.ObjectProperty.productTo | Mathlib.CategoryTheory.Generator.Basic | [
"CategoryTheory.Limits.HasProduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.ObjectProperty.productToFamily",
"CategoryTheory.StructuredArrow.hom",
"CategoryTheory.Limits.piObj",
"CategoryTheory.Limits.Pi.lift",
"CategoryTheory.Catego... | true |
Finset.zero_mem_neg_add_iff._simp_1 | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Finset",
"AddMonoid.toAddZeroClass",
"Finset.zero_mem_neg_add_iff",
"Disjoint",
"Membership.mem",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"Finset.partialOrder",
"SubNegZeroMonoid.toNegZeroClass",
"instHAdd",
"Ad... | false |
Nat.ppred | Mathlib.Data.Nat.PSub | [
"Option.some",
"Option.none",
"Unit",
"Nat",
"Nat.ppred.match_1",
"Option"
] | true |
Polynomial.exists_mul_sq_add_linear_part_eq_eval_add | Mathlib.Algebra.Polynomial.Taylor | [
"Polynomial.taylor_eval",
"Polynomial.derivative",
"Eq.mpr",
"Polynomial.eval",
"MulOne.toOne",
"Semigroup.toMul",
"Semiring.toModule",
"HMul.hMul",
"Monoid.toMulOneClass",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"pow_succ",
"AddMonoid.toA... | true |
String.startsWith_slice_iff | Init.Data.String.Lemmas.Pattern.TakeDrop.String | [
"String.toSlice",
"congrArg",
"String",
"String.Slice.startsWith_slice_iff._simp_1",
"String.Slice",
"String.Slice.Pattern.ForwardSliceSearcher.instForwardPattern",
"String.Slice.startsWith",
"String.startsWith",
"iff_self",
"Bool.true",
"String.Slice.copy",
"List",
"Iff",
"List.IsPrefix",... | true |
Matrix.instNonUnitalRing._proof_1 | Mathlib.Data.Matrix.Mul | [
"SubNegMonoid.sub_eq_add_neg",
"AddMonoid.toAddSemigroup",
"Matrix",
"NonUnitalNonAssocRing.toAddCommGroup",
"HSub.hSub",
"Matrix.addCommGroup",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"SubNegMonoid.toSub",
"instHAdd",
"AddSemigroup.toAdd",
"instHSub",
"AddGroup.t... | false |
Tree.noConfusionType | Mathlib.Data.Tree.Basic | [
"Tree.casesOn",
"Tree",
"HEq"
] | false |
LinearEquiv._sizeOf_inst | Mathlib.Algebra.Module.Equiv.Defs | [
"RingHom",
"AddCommMonoid",
"RingHomInvPair",
"SizeOf.mk",
"LinearEquiv",
"Semiring",
"SizeOf",
"Module",
"Semiring.toNonAssocSemiring",
"LinearEquiv._sizeOf_1"
] | false |
Cycle.length_nil | Mathlib.Data.List.Cycle | [
"instOfNatNat",
"Cycle.length",
"Nat",
"OfNat.ofNat",
"Eq",
"rfl",
"Cycle.nil"
] | true |
Lean.Elab.Command.elabEvalCoreUnsafe | Lean.Elab.BuiltinEvalCommand | [
"guard",
"_private.Lean.Elab.BuiltinEvalCommand.0.Lean.Elab.Command.EvalAction",
"Pure.pure",
"Lean.instMonadEnvOfMonadLift",
"Functor.discard",
"Lean.MessageData",
"Lean.MonadError.mk",
"Std.instInhabitedFormat",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.mkAppOptM",
"Std... | true |
CoxeterSystem.length_eq_one_iff | Mathlib.GroupTheory.Coxeter.Length | [
"CoxeterSystem.exists_isReduced",
"Group",
"CoxeterSystem.IsReduced",
"Exists",
"CoxeterSystem.simple",
"instOfNatNat",
"CoxeterMatrix",
"List.length_eq_one_iff",
"List.cons",
"CoxeterSystem.wordProd_singleton",
"And.casesOn",
"CoxeterSystem.length",
"List",
"And",
"Iff",
"Exists.cases... | true |
Multiplicative.mulAction_isPretransitive | Mathlib.Algebra.Group.Action.Pretransitive | [
"AddAction.exists_vadd_eq",
"Multiplicative.smul",
"AddMonoid.toAddSemigroup",
"MulAction.IsPretransitive.mk",
"MulAction.IsPretransitive",
"Multiplicative",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddSemigroupAction.toVAdd",
"AddMonoid",
"AddAction.IsPretransitive"
] | true |
LawfulMonadAttach.eq_of_canReturn_pure | Init.Control.Lawful.MonadAttach.Lemmas | [
"Pure.pure",
"congrArg",
"Monad.toApplicative",
"Eq.mp",
"Subtype",
"LawfulMonad",
"Applicative.toPure",
"Subtype.mk",
"LawfulMonadAttach.canReturn_map_imp",
"True",
"MonadAttach",
"eq_self",
"of_eq_true",
"Applicative.toFunctor",
"LawfulMonad.toLawfulApplicative",
"LawfulApplicative.m... | true |
MeasureTheory.integral_prod_swap | Mathlib.MeasureTheory.Integral.Prod | [
"MeasurableEquiv.measurableEmbedding",
"MeasureTheory.MeasurePreserving.integral_comp",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"MeasurableSpace",
"MeasureTheory.SFinite",
"MeasureTheory.Measure.prod",
"MeasurableEquiv.prodComm",
"MeasureTheory.integral",
"Real.normedField",
"Prod.swap... | true |
Mathlib.Tactic.Linarith.Comp.scale | Mathlib.Tactic.Linarith.Datatypes | [
"Int",
"Nat.cast",
"Mathlib.Tactic.Linarith.Comp",
"Mathlib.Tactic.Linarith.Comp.coeffs",
"Mathlib.Tactic.Linarith.Comp.str",
"Nat",
"Mathlib.Tactic.Linarith.Comp.mk",
"instNatCastInt",
"Mathlib.Tactic.Linarith.Linexp.scale"
] | true |
mul_le_of_mul_le_left | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"HMul.hMul",
"Preorder.toLE",
"Mul",
"MulLeftMono",
"LE.le",
"instIsTransLe",
"act_rel_of_rel_of_act_rel",
"Preorder",
"instHMul"
] | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.reduce_fold_fn_preserves_induction_motive._simp_1_4 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
div_div_eq_mul_div | Mathlib.Algebra.Group.Basic | [
"Semigroup.toMul",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"mul_assoc",
"DivisionMonoid",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"DivisionMonoid.toInvolutiveInv",
"div_eq_mul_inv",
"DivisionMonoid.toDivInvMonoid",
"MulOneClass.toM... | true |
Lean.Compiler.LCNF.AuxDeclCacheKey.casesOn | Lean.Compiler.LCNF.AuxDeclCache | [
"Lean.Compiler.LCNF.AuxDeclCacheKey.mk",
"Lean.Compiler.LCNF.Decl",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.AuxDeclCacheKey.rec",
"Lean.Compiler.LCNF.AuxDeclCacheKey"
] | false |
HomogeneousSubsemiring.ext | Mathlib.RingTheory.GradedAlgebra.Homogeneous.Subsemiring | [
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddZeroClass",
"AddSubmonoidClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Subsemiring",
"GradedRing",
"HomogeneousSubsemiring.toSubsemiring_injective",
"AddMonoid",
"Semiring",
"AddMonoidWithOne.toAddMonoid",
"Homogeneous... | true |
CategoryTheory.Limits.IsLimit.pushoutOfHasExactLimitsOfShape._proof_2 | Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Connected | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category... | false |
perfectClosure.eq_bot_of_isSeparable | Mathlib.FieldTheory.PurelyInseparable.PerfectClosure | [
"IntermediateField.isScalarTower_mid'",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"CompleteLattice.toLattice",
"IntermediateField",
"perfectClosure",
"OrderBot.toBot",
"IntermediateField.toField",
"PartialOrder.t... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.IsBipartite.exists_isBipartiteWith._proof_1_3 | Mathlib.Combinatorics.SimpleGraph.Bipartite | [
"Zero.ofOfNat0",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"NeZero",
"OfNat.ofNat"
] | false |
ContinuousLinearMap.flipMultilinearEquiv._proof_4 | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"ContinuousMultilinearMap.seminorm._proof_2",
"Real.instLE",
"LinearEquiv.symm",
"MultilinearMap.mk",
"Real",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"Uniform... | false |
Std.Internal.List.getEntry?._sunfold | Std.Data.Internal.List.Associative | [
"cond",
"Option.some",
"Option.none",
"List",
"BEq.beq",
"Unit",
"Std.Internal.List.getEntry?",
"Sigma.mk",
"BEq",
"Sigma",
"Option",
"_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.getEntry?.match_1"
] | false |
_private.Mathlib.GroupTheory.Submonoid.Inverses.0.Submonoid.leftInvEquiv._simp_2 | Mathlib.GroupTheory.Submonoid.Inverses | [
"Monoid",
"Units.val",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"Units",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Inv.inv",
"propext",
"One.toOfNat1",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Units.instInv",
"Units.mul_eq_one_iff_inv_eq",
"instHMul"
] | false |
Lean.Parser.Term.leading_parser._regBuiltin.Lean.Parser.Term.withAnonymousAntiquot.parenthesizer_19 | Lean.Parser.Term | [
"Lean.Name.mkStr5",
"IO",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.PrettyPrinter.parenthesizerAttribute",
"Lean.Parser.Term.withAnonymousAntiquot.parenthesizer",
"Unit",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
Int.fib_neg_one | Mathlib.Data.Int.Fib.Basic | [
"Int.fib",
"Int.instNegInt",
"Int",
"instOfNat",
"OfNat.ofNat",
"Eq",
"Neg.neg",
"rfl"
] | true |
MonadReader.casesOn | Init.Prelude | [
"MonadReader.mk",
"MonadReader",
"MonadReader.rec"
] | false |
NumberField.instIsAlgebraicSubtypeMemSubfield | Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex | [
"Subfield.toDivisionRing",
"Subfield.toAlgebra",
"Semiring.toModule",
"Algebra.IsAlgebraic.tower_top",
"AddCommGroup.toAddCommMonoid",
"Subfield.instSubfieldClass",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Rat.commSemiring",
"Membership.mem",
"Field.toDivisionRing",
"DivisionRing.toDivisi... | true |
Set.graphOn_singleton | Mathlib.Data.Set.Prod | [
"Set.image_singleton",
"Set.instSingletonSet",
"Prod.mk",
"Set.graphOn",
"Prod",
"Singleton.singleton",
"Eq",
"Set"
] | true |
_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.Padic.norm_intCast_eq_one_iff._simp_1_3 | Mathlib.NumberTheory.Padics.PadicNumbers | [
"Int.gcd",
"Int.isCoprime_iff_gcd_eq_one",
"instOfNatNat",
"Int",
"Nat",
"propext",
"Int.instCommSemiring",
"OfNat.ofNat",
"Eq",
"IsCoprime"
] | false |
mul_le_mul_left_of_neg._simp_1 | Mathlib.Algebra.Order.Ring.Unbundled.Basic | [
"Preorder.toLT",
"HMul.hMul",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"AddRightMono",
"DistribLattice.toLattice",
"Distrib.toAdd",
"mul_le_mul_left_of_neg",
"LE.le",
"instDistribOfSemiring",
"ExistsAddOfLE",
"AddRightReflectLE",
"Distri... | false |
linearIndependent_fin_succ | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | [
"Submodule",
"instNeZeroNatHAdd_1",
"AddCommGroup.toAddCommMonoid",
"Membership.mem",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"Fin.instOfNat",
"instOfNatNat",
"instHAdd",
"And",
"Iff",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"Submodule.setLike",
"LinearIndependent",
"lin... | true |
subset_affineSpan | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"HasSubset.Subset",
"AffineSubspace.instSetLike",
"affineSpan",
"SetLike.coe",
"AddTorsor",
"Module",
"Ring.toSemiring",
"subset_spanPoints",
"Ring",
"AffineSubspace",
"Set.instHasSubset",
"Set"
] | true |
Lean.ScopedEnvExtension.State.mk.injEq | Lean.ScopedEnvExtension | [
"Eq.propIntro",
"Lean.NameSet",
"Lean.ScopedEnvExtension.State",
"Lean.injEq_helper",
"Lean.ScopedEnvExtension.State.mk.inj",
"And",
"Lean.ScopedEnvExtension.State.mk",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts.0.CategoryTheory.hasCoproduct_fin | Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts | [
"Nat.brecOn",
"CategoryTheory.Limits.HasCoproduct",
"Nat",
"_private.Mathlib.CategoryTheory.Limits.Constructions.FiniteProductsOfBinaryProducts.0.CategoryTheory.hasCoproduct_fin._f",
"CategoryTheory.Limits.HasBinaryCoproducts",
"Fin",
"CategoryTheory.Limits.HasInitial",
"CategoryTheory.Category"
] | true |
Lean.Parser.Command.structExplicitBinder | Lean.Parser.Command | [
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.leadingNode",
"Lean.Parser.Term.binderDefault",
"Lean.Parser.optional",
"instHAndThenOfAndThen",
"Lean.Parser.Command.optDeclSig",
"HOrElse.hOrElse",
"Lean.Parser.Term.binderTactic",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.with... | true |
Lean.Meta.Contradiction.Config.emptyType | Lean.Meta.Tactic.Contradiction | [
"Lean.Meta.Contradiction.Config",
"Bool"
] | true |
CoxeterSystem.length_wordProd_le | Mathlib.GroupTheory.Coxeter.Length | [
"Group",
"Classical.propDecidable",
"Exists",
"_private.Mathlib.GroupTheory.Coxeter.Length.0.CoxeterSystem.exists_word_with_prod",
"LE.le",
"instLENat",
"CoxeterMatrix",
"CoxeterSystem.length",
"List",
"And",
"Nat.find_min'",
"Nat",
"And.intro",
"Exists.intro",
"CoxeterSystem.wordProd",
... | true |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point.0._aux_Mathlib_AlgebraicGeometry_EllipticCurve_Projective_Point___macroRules__private_Mathlib_AlgebraicGeometry_EllipticCurve_Projective_Point_0_termZ_1 | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.node5",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSy... | false |
Pi.Colex.instCompleteLinearOrderColexForall._proof_10 | Mathlib.Order.CompleteLattice.PiLex | [
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Pi.Colex.completeLattice",
"Colex",
"LinearOrder",
"WellFoundedGT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toBoundedOrder",
"DistribLattice.toLattice",
"Pi.Colex.linearOrder",
"BiheytingAlgeb... | false |
MoritaEquivalence.mk.injEq | Mathlib.RingTheory.Morita.Basic | [
"MoritaEquivalence",
"MoritaEquivalence.linear._autoParam",
"ModuleCat",
"Eq.propIntro",
"CommSemiring.toSemiring",
"CategoryTheory.Functor.Linear",
"MoritaEquivalence.mk.inj",
"CategoryTheory.Equivalence",
"Algebra",
"CategoryTheory.Equivalence.functor",
"ModuleCat.Algebra.instLinear",
"autoP... | true |
HomotopicalAlgebra.FibrantObject.homMk_id | Mathlib.AlgebraicTopology.ModelCategory.Bifibrant | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"HomotopicalAlgebra.FibrantObject",
"HomotopicalAlgebra.IsFibrant",
"CategoryTheory.Category.toCategoryStruct",
"HomotopicalAlgebra.FibrantObject.mk",
"CategoryTheory.ObjectProperty.FullSubcategory.category",
... | true |
Equiv.Perm.sign_inv | Mathlib.GroupTheory.Perm.Sign | [
"Int.instCommMonoid",
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"DivInvMonoid.toInv",
"MonoidHom.instFunLike",
"map_inv",
"DivisionCommMonoid.toDivisionMonoid",
"Equiv.Perm.instInv",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Equiv.Perm.sign",
"Int.units_inv_eq_self",
"Units",
"id... | true |
RootableBy.mk._flat_ctor | Mathlib.GroupTheory.Divisible | [
"Monoid",
"MulOne.toOne",
"Monoid.toMulOneClass",
"Pow",
"RootableBy.mk",
"Ne",
"RootableBy",
"MulOneClass.toMulOne",
"HPow.hPow",
"One.toOfNat1",
"Zero.toOfNat0",
"instHPow",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
HahnEmbedding.Seed.hahnCoeff_apply | Mathlib.Algebra.Order.Module.HahnEmbedding | [
"Eq.mpr",
"DirectSum.coeAddMonoidHom",
"instDecidableNot",
"Submodule",
"Submodule.addSubmonoidClass",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"SetLike.coe_subset_coe._simp_1",
"SemilinearMapClass.distribMulActionSemiHomClass",
"LinearOrder.toDecidableEq",
"Submodule.mem_comap._simp_1",... | true |
Std.TreeMap.getKeyLT | Std.Data.TreeMap.AdditionalOperations | [
"Std.DTreeMap.getKeyLT",
"Std.TreeMap.inner",
"Membership.mem",
"Exists",
"Ordering",
"Std.TransCmp",
"And",
"Std.TreeMap.instMembership",
"Ordering.lt",
"Eq",
"Std.TreeMap"
] | true |
TensorProduct.induction_on | Mathlib.LinearAlgebra.TensorProduct.Defs | [
"Eq.mpr",
"AddMonoid.toAddSemigroup",
"addConGen",
"TensorProduct.Eqv",
"FreeAddMonoid.of",
"congrArg",
"AddCon.induction_on",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddCon.hasAdd",
"FreeAddMonoid.instAddCancelMonoid",
"AddCancelMonoid.toAddRightCancelMonoid",
"AddZeroClass.... | true |
Finset.isPWO_support_addAntidiagonal | Mathlib.Data.Finset.MulAntidiagonal | [
"Set.IsPWO",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"setOf",
"AddZeroClass.toAddZero",
"PartialOrder",
"AddCommMonoid",
"instHAdd",
"Set.add",
"HAdd.hAdd",
"Finset.support_addAntidiagonal_subset_add",
"Finset.Nonempty",
"Set.IsPWO.add",
"Finset.addAntidiagonal",
"AddZero.... | true |
SSet.relativeCellComplexOfMono.Cell.ctorIdx | Mathlib.AlgebraicTopology.SimplicialSet.Skeleton | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"SSet",
"Nat",
"CategoryTheory.types",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"CategoryTheory.Category.toCategoryStruct",
"SimplexCategory.smallCategory",
"SSet.relativeCellCo... | false |
_private.Mathlib.Data.Analysis.Filter.0.Filter.Realizer.ne_bot_iff._simp_1_1 | Mathlib.Data.Analysis.Filter | [
"Set.not_nonempty_iff_eq_empty",
"Set.Nonempty",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Not",
"Set"
] | false |
CategoryTheory.Abelian.SpectralObject.leftHomologyDataShortComplex._proof_11 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Abelian",
"CategoryTheory.Abelian.SpectralObject",
"Int",
"CategoryTheory.Abelian.SpectralObject.shortComplex",
"CategoryTheory.Abelian.SpectralObject.sho... | false |
CategoryTheory.Limits.hasFiniteLimits_of_hasLimitsLimits_of_createsFiniteLimits | Mathlib.CategoryTheory.Limits.Preserves.Creates.Finite | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasFiniteLimits",
"CategoryTheory.SmallCategory",
"CategoryTheory.Limits.HasFiniteLimits.mk",
"CategoryTheory.FinCategory",
"CategoryTheory.Limits.CreatesFiniteLimits",
"CategoryTheory.hasLimitsOfShape_of_hasLimitsOfShape_createsLimitsOfShape",
"Categor... | true |
_private.Init.Data.SInt.Lemmas.0.Int32.toInt64_lt._simp_1_2 | Init.Data.SInt.Lemmas | [
"Int64.toInt",
"instLTInt64",
"Int64",
"Int",
"Int.instLTInt",
"Int64.lt_iff_toInt_lt",
"LT.lt",
"propext",
"Eq"
] | false |
SSet.finite_of_hasDimensionLT | Mathlib.AlgebraicTopology.SimplicialSet.Finite | [
"SSet.S.simplex",
"False",
"Opposite",
"Set.mem_empty_iff_false._simp_1",
"SSet.N.mk",
"congrArg",
"False.elim",
"Finite",
"PartialOrder.toPreorder",
"SSet.nonDegenerate",
"Preorder.toLE",
"Fin.isLt",
"Membership.mem",
"Exists",
"Eq.mp",
"Set.Elem",
"Fin.mk",
"Finite.instSigma",
... | true |
Language.one_add_self_mul_kstar_eq_kstar | Mathlib.Computability.Language | [
"Eq.mpr",
"MulOne.toOne",
"instCompleteAtomicBooleanAlgebraLanguage",
"Language.instOne",
"HMul.hMul",
"Language.instAdd",
"Monoid.toMulOneClass",
"congrArg",
"iSup",
"KStar.kstar",
"id",
"MulOne.toMul",
"_private.Mathlib.Computability.Language.0.Language.one_add_self_mul_kstar_eq_kstar._sim... | true |
Int16.add_eq_left._simp_1 | Init.Data.SInt.Lemmas | [
"Int16",
"Int16.instOfNat",
"Int16.add_eq_left",
"instHAdd",
"HAdd.hAdd",
"propext",
"instAddInt16",
"OfNat.ofNat",
"Eq"
] | false |
Std.ExtDHashMap.getKey_eq_getKey! | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.inner",
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.ExtDHashMap.getKey!",
"Quot.pliftOn._proof_2",
"Membership.mem",
"Std.ExtDHashMap.inductionOn",
"Std.ExtDHashMap.getKey",
"Std.ExtDHashMap.mk",
"_private.Std.Data.ExtDHashMap.Basic.0.Std.ExtDHashMap.getKey._pro... | true |
_private.Mathlib.Order.Filter.Map.0.Filter.compl_mem_kernMap._simp_1_1 | Mathlib.Order.Filter.Map | [
"Filter.instMembership",
"Compl.compl",
"Membership.mem",
"Exists",
"Set.instCompl",
"Filter.mem_kernMap_iff_compl",
"And",
"propext",
"Set.image",
"Eq",
"Filter",
"Filter.kernMap",
"Set"
] | false |
divp_mul_eq_mul_divp | Mathlib.Algebra.Group.Units.Basic | [
"Units.val",
"Eq.mpr",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"Monoid.toMulOneClass",
"congrArg",
"Units",
"id",
"MulOne.toMul",
"CommMagma.toMul",
"divp",
"MulOneClass.toMulOne",
"divp.eq_1",
"Inv.inv",
"CommMonoid.toMonoid",
"mul_right_comm",
"CommSemigroup.toCommMagma",
"Eq.... | true |
Std.Do.SPred.Tactic.instIsPure | Std.Do.SPred.DerivedLaws | [
"Std.Do.SPred.Tactic.IsPure.to_pure",
"Std.Do.SPred.Tactic.IsPure.mk",
"Std.Do.SPred.pure",
"Std.Do.SPred.bientails",
"List.cons",
"List",
"Iff.mp",
"Std.Do.SPred",
"Std.Do.SPred.bientails_cons",
"iff_of_eq",
"Std.Do.SPred.Tactic.IsPure"
] | true |
String.Slice.RevByteIterator.ctorIdx | Init.Data.String.Iterate | [
"String.Slice.RevByteIterator",
"Nat"
] | false |
NonUnitalSubsemiring.corner._proof_4 | Mathlib.RingTheory.Idempotents | [
"Semigroup.toMul",
"HMul.hMul",
"Membership.mem",
"SemigroupWithZero.toSemigroup",
"NonUnitalSemiring.toSemigroupWithZero",
"NonUnitalSemiring",
"Subsemigroup.carrier",
"Subsemigroup.mul_mem'",
"Subsemigroup.corner",
"Set.instMembership",
"instHMul",
"Set"
] | false |
Std.DTreeMap.Internal.Impl.get_insertIfNew! | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"instDecidableNot",
"instDecidableEqOrdering",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.insertIfNew_eq_insertIfNew!",
"cast",
"Membership.mem",
"Ordering",
"Ordering.eq",
"Eq.mp",
"Std.DTreeMap.Internal.Im... | true |
Std.Tactic.BVDecide.LRAT.Internal.DefaultClause.delete_iff | Std.Tactic.BVDecide.LRAT.Internal.Clause | [
"Membership.mem",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultClause.toList",
"Ne",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultClause.delete",
"_private.Std.Tactic.BVDecide.LRAT.Internal.Clause.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultClause.delete_iff._proof_1_2",
"And",
"Iff",
"List.instMembership",
... | true |
_private.Mathlib.FieldTheory.IsAlgClosed.Basic.0.IsAlgClosed.liftAux | Mathlib.FieldTheory.IsAlgClosed.Basic | [
"AlgHom",
"Classical.choice",
"Algebra",
"Field.toDivisionRing",
"DivisionRing.toRing",
"Algebra.IsAlgebraic",
"Field.toSemifield",
"Field.toCommRing",
"Semifield.toDivisionSemiring",
"IsAlgClosed",
"DivisionSemiring.toSemiring",
"_private.Mathlib.FieldTheory.IsAlgClosed.Basic.0.IsAlgClosed.li... | true |
_private.Mathlib.GroupTheory.Subgroup.Centralizer.0.Subgroup.normalizerMonoidHom_ker._simp_1_6 | Mathlib.GroupTheory.Subgroup.Centralizer | [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"eq_mul_inv_iff_mul_eq",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"propext",
"InvOneClass.... | false |
_private.Mathlib.Data.Set.SMulAntidiagonal.0.Set.SMulAntidiagonal.finite_of_finite_fst._proof_1_3 | Mathlib.Data.Set.SMulAntidiagonal | [
"False",
"instHSMul",
"eq_false",
"Set.mem_smulAntidiagonal",
"Lean.Grind.iff_eq",
"congrArg",
"SMul",
"Classical.byContradiction",
"Membership.mem",
"Eq.mp",
"id",
"Prod.mk",
"Prod.fst",
"IsLeftCancelSMul.left_cancel",
"And",
"Iff",
"Set.smulAntidiagonal",
"congr",
"True",
"eq... | false |
_private.Lean.Meta.Basic.0.Lean.Meta.isSyntheticMVar.match_1 | Lean.Meta.Basic | [
"Unit.unit",
"Lean.MetavarKind.syntheticOpaque",
"Nat.hasNotBit",
"Lean.MetavarKind.synthetic",
"Unit",
"Lean.MetavarKind.ctorIdx",
"_private.Lean.Meta.Basic.0.Lean.Meta.isSyntheticMVar._sparseCasesOn_1",
"Lean.MetavarKind"
] | false |
CategoryTheory.Pseudofunctor.DescentData.toDescentDataCompPullFunctorIso | Mathlib.CategoryTheory.Sites.Descent.DescentData | [
"CategoryTheory.Functor",
"CategoryTheory.Pseudofunctor.DescentData.toDescentDataCompPullFunctorIso._proof_8",
"Opposite",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.Pseudofunctor.DescentData.toDescentDataCompPullFunctorIso._proof_4",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"... | true |
MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuousMap_continuous_integral | Mathlib.MeasureTheory.Measure.ProbabilityMeasure | [
"Real",
"Continuous",
"ContinuousMap.equivBoundedOfCompact",
"ContinuousMap",
"Equiv.forall_congr_left",
"PseudoMetricSpace.toUniformSpace",
"BoundedContinuousFunction.instFunLike",
"MeasureTheory.ProbabilityMeasure",
"Real.normedAddCommGroup",
"CompactSpace",
"MeasureTheory.ProbabilityMeasure.i... | true |
Metric.frontier_thickening_disjoint | Mathlib.Topology.MetricSpace.Thickening | [
"Iff.mpr",
"frontier",
"Real",
"Preorder.toLT",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"HEq.refl",
"PartialOrder.toPreorder",
"setOf",
"Set.disjoint_singleton",
... | true |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable.0.EisensteinSeries.E2_eq_tsum_cexp._simp_1_6 | Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | [
"False",
"eq_false",
"pow_ne_zero",
"Ne",
"Monoid.toPow",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Nat",
"Zero.toOfNat0",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"MonoidWithZero.toMonoid",
"MulZeroClass.toZero",
"IsReduced"
] | false |
Lean.Elab.Term.MatchExpr.ElseAlt.mk.sizeOf_spec | Lean.Elab.MatchExpr | [
"Lean.Syntax._sizeOf_inst",
"Lean.Syntax",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Lean.Elab.Term.MatchExpr.ElseAlt",
"SizeOf.sizeOf",
"Lean.Elab.Term.MatchExpr.ElseAlt.mk",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Elab.Term.MatchExpr.ElseAlt._sizeOf_inst"
] | true |
_private.Mathlib.Tactic.NormNum.NatFactorial.0.Mathlib.Meta.NormNum.evalNatDescFactorial._proof_2 | Mathlib.Tactic.NormNum.NatFactorial | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Qq.Quoted.unsafeMk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Qq.QuotedDefEq.unsafeIntro",
"List.nil"
] | false |
denselyOrdered_multiplicative_iff | Mathlib.GroupTheory.ArchimedeanDensely | [
"Iff.rfl",
"Multiplicative",
"Iff",
"instLTMultiplicative",
"DenselyOrdered",
"LT"
] | true |
Lean.Lsp.SemanticTokenType.method.sizeOf_spec | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SemanticTokenType.method",
"Lean.Lsp.SemanticTokenType",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Lsp.SemanticTokenType._sizeOf_inst"
] | true |
RatFunc.valuation_isEquiv_adic_of_valuation_X_le_one | Mathlib.NumberTheory.RatFunc.Ostrowski | [
"Int.instAddCommMonoid",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemirin... | true |
GrpCat.uliftFunctor_preservesLimitsOfSize | Mathlib.Algebra.Category.Grp.Ulift | [
"GrpCat",
"CategoryTheory.Limits.PreservesLimitsOfSize.mk",
"inferInstance",
"GrpCat.uliftFunctor_preservesLimitsOfShape",
"GrpCat.uliftFunctor",
"GrpCat.instCategory",
"CategoryTheory.Limits.PreservesLimitsOfSize",
"CategoryTheory.Limits.PreservesLimitsOfShape",
"CategoryTheory.Category"
] | true |
MeasureTheory.regular_inv_iff | Mathlib.MeasureTheory.Group.Measure | [
"MeasureTheory.Measure",
"DivInvOneMonoid.toInvOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"BorelSpace",
"MeasureTheory.Measure.Regular",
"DivisionMonoid.toInvolutiveInv",
"Homeomorph.inv",
"MeasurableSpace",
"TopologicalSpace",
"Iff",
"IsTopologicalGrou... | true |
_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.alter.match_3.eq_3 | Std.Data.DTreeMap.Internal.Operations | [
"Ordering.gt",
"Ordering",
"Ordering.eq",
"Ordering.lt",
"Std.DTreeMap.Internal.Impl.alter.match_3",
"Eq.refl",
"Eq"
] | true |
ULift.semiring._proof_5 | Mathlib.Algebra.Ring.ULift | [
"Monoid.npow",
"Semigroup.toMul",
"HMul.hMul",
"ULift",
"ULift.monoid",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Monoid.npow_succ",
"Semiring.toMonoid",
"Monoid.toSemigroup",
"Semiring",
"instAddNat",
"OfNat.ofNat",
"Eq",
"instHMul"
] | false |
_private.Mathlib.FieldTheory.Extension.0.IntermediateField.nonempty_algHom_adjoin_of_splits.match_1_1 | Mathlib.FieldTheory.Extension | [
"IntermediateField.instPartialOrder",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"IntermediateField",
"AlgHom",
"OrderBot.toBot",
"IntermediateField.toField",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"Membership.mem",
"Exis... | false |
CategoryTheory.Limits.CatCospanTransform.inv_whiskerRight | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | [
"CategoryTheory.IsIso.inv_eq_of_hom_inv_id",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.CatCospanTransformMorphism.whiskerRight",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.CatCospanTran... | true |
EReal.abs_neg | Mathlib.Data.EReal.Inv | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"EReal.abs",
"NegZeroClass.toNeg",
"abs_neg",
"Real",
"Real.lattice",
"ENNReal.ofReal",
"abs",
"congrArg",
"EReal.coe_neg",
"EReal.instNeg",
"EReal",
"instTopEReal",
"id",
"Real.instAddGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"Bot.bo... | true |
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