name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.imageOpUnop._proof_2 | Mathlib.CategoryTheory.Abelian.Opposite | [
"CategoryTheory.Limits.HasImages.has_image",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Abelian",
"CategoryTheory.instAbelianOpposite",
"Opposite.op",
"CategoryTheory.Category.opposite",
"CategoryTheory.Abelian.instHasStrongEpiMonoFactorisa... | false |
CompactlySupportedContinuousMap.instMulLeftMono | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"CovariantClass.mk",
"HMul.hMul",
"CompactlySupportedContinuousMap.instMulOfContinuousMul._proof_1",
"MulZeroClass.toMul",
"CompactlySupportedContinuousMap",
"ContinuousMap",
"PartialOrder.toPreorder",
"Preorder.toLE",
"mul_le_mul_right",
"MulZeroClass",
"PartialOrder",
"MulLeftMono",
"LE.le... | true |
Field.qsmul_def | Mathlib.Algebra.Field.Defs | [
"Semigroup.toMul",
"Field.toRatCast",
"HMul.hMul",
"Rat",
"Rat.cast",
"Field.qsmul",
"Field.toCommRing",
"Semiring.toMonoid",
"Monoid.toSemigroup",
"CommRing.toRing",
"Ring.toSemiring",
"Eq",
"Field",
"instHMul"
] | true |
Std.Internal.List.DistinctKeys.def | Std.Data.Internal.List.Associative | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.DistinctKeys.def._simp_1_1",
"List.Pairwise",
"congrArg",
"List.map",
"Eq.mp",
"id",
"Sigma.fst",
"List",
"BEq.beq",
"Iff",
"Std.Internal.List.DistinctKeys.mk",
"Std.Internal.List.D... | true |
Std.ExtTreeSet.getGE? | Std.Data.ExtTreeSet.Basic | [
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Unit",
"Std.ExtTreeSet",
"Std.ExtTreeMap.getKeyGE?",
"Option"
] | true |
Lean.Linter.UnusedVariables.FVarDefinition.opts | Lean.Linter.UnusedVariables | [
"Lean.Options",
"Lean.Linter.UnusedVariables.FVarDefinition"
] | true |
MeasureTheory.memLp_re_im_iff | Mathlib.MeasureTheory.Function.LpSpace.Basic | [
"NormedCommRing.toNormedRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"MeasureTheory.MemLp.const_mul",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"RCLike.re_add_im",
"Real",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedRing.toRing",
... | true |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.ExpandedFieldVal.term | Lean.Elab.StructInst | [
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.ExpandedFieldVal",
"Lean.Syntax.Term",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.ExpandedFieldVal.term"
] | true |
Char.isLower | Init.Data.Char.Basic | [
"GE.ge",
"Bool.and",
"UInt32.decLe",
"LE.le",
"Char.val",
"instLEUInt32",
"Bool",
"UInt32",
"Char",
"Decidable.decide",
"Char.ofNat"
] | true |
MeasureTheory.withDensity_zero | Mathlib.MeasureTheory.Measure.WithDensity | [
"MeasureTheory.lintegral_const",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure",
"HMul.hMul",
"MeasurableSet",
"congrArg",
"CommSemiring.toSemiring",
"Set.univ",
"MulZeroClass.zero_mul",
"MeasureTheory.Measure.restrict_apply",
"MeasureTheory.Measure.restrict",
"Pi.instZero",
"E... | true |
FreeMagma | Mathlib.Algebra.Free | [
"FreeMagma.of",
"FreeMagma.mul"
] | true |
Stream'.WSeq.findIndex | Mathlib.Data.WSeq.Defs | [
"Stream'.WSeq.findIndexes",
"Option.getD",
"Computation.instAlternativeComputation",
"instOfNatNat",
"Computation",
"DecidablePred",
"Nat",
"Stream'.WSeq",
"Alternative.toApplicative",
"Applicative.toFunctor",
"OfNat.ofNat",
"Functor.map",
"Stream'.WSeq.head",
"Option"
] | true |
Std.IterM.step_takeWhile | Std.Data.Iterators.Lemmas.Combinators.Monadic.TakeWhile | [
"Pure.pure",
"Eq.mpr",
"Std.Shrink.deflate",
"False",
"Subtype.mk.congr_simp",
"bind_congr",
"Std.Iterators.PostconditionT.operation_pure",
"Std.IterStep",
"congrArg",
"Std.Shrink",
"Monad.toApplicative",
"False.elim",
"Std.IterM.step_takeWhileWithPostcondition.match_3",
"ULift",
"Std.Pl... | true |
Lean.Level.PP.Result.offset | Lean.Level | [
"Lean.Level.PP.Result",
"Nat",
"Lean.Level.PP.Result.offset"
] | true |
_private.Lean.Elab.Parallel.0.Std.Iterators.Types.instIteratorTaskIteratorBaseIO.match_1 | Lean.Elab.Parallel | [
"Unit.unit",
"Std.IterStep",
"Std.IterStep.skip",
"Std.Iterators.Types.TaskIterator",
"Unit",
"Std.IterStep.yield",
"Std.IterStep.done",
"Std.IterM",
"BaseIO",
"Std.IterStep.casesOn"
] | false |
CategoryTheory.RelCat.Hom.ctorIdx | Mathlib.CategoryTheory.Category.RelCat | [
"CategoryTheory.RelCat.Hom",
"CategoryTheory.RelCat",
"Nat"
] | false |
CategoryTheory.Limits.HasImage.casesOn | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.HasImage.mk'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasImage.rec",
"CategoryTheory.Limits.ImageFactorisation",
"Nonempty",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.HasImage",
"CategoryTheory.Category"
] | false |
Matrix._aux_Mathlib_LinearAlgebra_Matrix_ConjTranspose___unexpand_Matrix_conjTranspose_1 | Mathlib.LinearAlgebra.Matrix.ConjTranspose | [
"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 |
PseudoMetric.finsetSup_apply | Mathlib.Topology.MetricSpace.BundledFun | [
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Finset.cons",
"congrArg",
"Finset.sup_singleton",
"PseudoMetric.instSemilatticeSupOfAddLeftMonoOfAddRightMono",
"Finset",
"LinearOrder",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Finset.cons_none... | true |
Std.TreeMap.getKey?_diff | Std.Data.TreeMap.Lemmas | [
"Std.DTreeMap.getKey?_diff",
"Std.TreeMap.instSDiff",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.TreeMap.instDecidableMem",
"Std.TransCmp",
"SDiff.sdiff",
"Option.none",
"Std.TreeMap.instMembership",
"Std.TreeMap.getKey?",
"Eq",
"Std.TreeMap",
"Option",
"ite"
] | true |
AbsoluteValue.instInhabitedIsAdmissibleIntAbs | Mathlib.NumberTheory.ClassNumber.AdmissibleAbs | [
"Int.instIsStrictOrderedRing",
"Int.instLinearOrder",
"Int.euclideanDomain",
"AbsoluteValue.absIsAdmissible",
"Int",
"AbsoluteValue.abs",
"Int.instRing",
"AbsoluteValue.IsAdmissible",
"Inhabited",
"Inhabited.mk"
] | true |
Submodule.idemSemiring._proof_5 | Mathlib.Algebra.Algebra.Operations | [
"Submodule",
"HMul.hMul",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.toModule",
"Submodule.mul",
"Submodule.one",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"One.toOfNat1",
"Submodule.o... | false |
Mathlib.Tactic.Linarith.PComp.noConfusionType | Mathlib.Tactic.Linarith.Oracle.FourierMotzkin | [
"Mathlib.Tactic.Linarith.CompSource",
"Std.TreeSet",
"Ord.compare",
"Mathlib.Tactic.Linarith.Comp",
"Mathlib.Tactic.Linarith.PComp",
"Nat",
"instOrdNat",
"Eq",
"Mathlib.Tactic.Linarith.PComp.casesOn"
] | false |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.Const.minKey?_alterKey_eq_self._simp_1_1 | Std.Data.Internal.List.Associative | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"Eq.symm",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
DihedralGroup.instGroup._proof_13 | Mathlib.GroupTheory.SpecificGroups.Dihedral | [
"Mul.mk",
"One.mk",
"HMul.hMul",
"_private.Mathlib.GroupTheory.SpecificGroups.Dihedral.0.DihedralGroup.one",
"_private.Mathlib.GroupTheory.SpecificGroups.Dihedral.0.DihedralGroup.inv",
"Int",
"npowRec",
"Nat.cast",
"Inv.mk",
"Nat",
"DihedralGroup",
"_private.Mathlib.GroupTheory.SpecificGroups.... | false |
CategoryTheory.MorphismProperty.inverseImage_op_overObj | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Over",
"CategoryTheory.Under.opEquivOpOver",
"Opposite",
"CategoryTheory.MorphismProperty.underObj",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.MorphismProperty.overObj",
"CategoryTheory.MorphismPropert... | true |
kroneckerTMulLinearEquiv._proof_6 | Mathlib.RingTheory.MatrixAlgebra | [
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
ProbabilityTheory.IsGaussian.noAtoms | Mathlib.Probability.Distributions.Gaussian.Fernique | [
"Mathlib.Tactic.Push.not_forall_eq",
"Mathlib.Tactic.Push.not_exists._simp_1",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"ProbabilityTheory.IsGaussian.map_eq_gaussianReal",
"Real.partialOrder",
"Real.instLE",
"ProbabilityTheory.IsGaussian",
"Real",
"Meas... | true |
AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_hom_τl | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"AlgebraicGeometry.Scheme.Modules.pullback",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme.Modules.pushforward",
"AlgebraicGeometry.Scheme",
"Opposite",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"AlgebraicGeometry.Scheme.Modules.pseudofunctor",
... | true |
_private.Mathlib.Algebra.Homology.ShortComplex.PreservesHomology.0.CategoryTheory.ShortComplex.LeftHomologyData.mapCyclesIso_eq._simp_1_1 | Mathlib.Algebra.Homology.ShortComplex.PreservesHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.cyclesMap'",
"CategoryTheory.ShortComplex.cyclesMap'_comp",
"CategoryTheory.ShortComplex.instCat... | false |
MvPolynomial.sumSMulX | Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | [
"Nat.instMulZeroClass",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Finsupp.module",
"CommRing.toNonUnitalCommRing",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"MvPolynomial.instModuleSelf",
"MvPolynomial.X",
"NonUnitalNonAssocRing.toNo... | true |
ReflBEq | Init.Core | [
"ReflBEq.mk",
"BEq"
] | true |
LaurentPolynomial.«term_[T;T⁻¹]» | Mathlib.Algebra.Polynomial.Laurent | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Lean.TrailingParserDescr"
] | true |
DirectLimit.Algebra.hom_ext | Mathlib.Algebra.Colimit.DirectLimit | [
"DirectLimit.setoid",
"DirectLimit.Algebra.of",
"congrArg",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"Preorder.toLE",
"id",
"LE.le",
"AlgHom.ext",
"DirectLimit.instSemiringOfRingHomClass",
"DirectLimit",
"Quotient.mk",
"AlgHomClass",
"CommSemiring",
"IsDirectedOrder",
"Semiring",
"No... | true |
Std.DHashMap.Const.getKey!_insertManyIfNewUnit_list_of_not_mem_of_contains_eq_false | Std.Data.DHashMap.Lemmas | [
"Inhabited.default",
"Std.DHashMap.Const.insertManyIfNewUnit",
"Std.DHashMap.getKey!",
"congrArg",
"instForInOfForIn'",
"Std.DHashMap.Internal.Raw₀.Const.getKey!_insertManyIfNewUnit_list_of_contains_eq_false_of_contains_eq_false",
"List.contains",
"Std.DHashMap.Raw",
"Membership.mem",
"inferInstan... | true |
Lean.PrettyPrinter.Formatter.ident.formatter._regBuiltin.Lean.PrettyPrinter.Formatter.ident.formatter_1 | Lean.Parser | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Lean.PrettyPrinter.Formatter.ident.formatter",
"Unit",
"Lean.Name.mkStr1",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
mabs_le_mabs_of_one_le | Mathlib.Algebra.Order.Group.Unbundled.Abs | [
"Eq.mpr",
"Lattice",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"mabs_of_one_le",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"SemilatticeInf.toPartialOrder",
"MulLeftMono"... | true |
AlternatingMap.toMultilinearMap | Mathlib.LinearAlgebra.Alternating.Basic | [
"AlternatingMap",
"MultilinearMap",
"AddCommMonoid",
"Semiring",
"Module"
] | true |
String._sizeOf_1.eq._@.Mathlib.Util.CompileInductive.3964927263._hygCtx._hyg.24 | Mathlib.Util.CompileInductive | [
"String",
"String._sizeOf_1",
"Nat",
"String._sizeOf_1._@.Mathlib.Util.CompileInductive.3964927263._hygCtx._hyg.23",
"Eq.refl",
"Eq"
] | false |
Std.Tactic.BVDecide.BoolExpr.eval_ite | Std.Tactic.BVDecide.Bitblast.BoolExpr.Basic | [
"cond",
"Std.Tactic.BVDecide.BoolExpr",
"Std.Tactic.BVDecide.BoolExpr.ite",
"Std.Tactic.BVDecide.BoolExpr.eval",
"Bool",
"Eq",
"rfl"
] | true |
groupHomology.H1ToTensorOfIsTrivial.match_1 | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"Submodule",
"Rep.V",
"CommRing",
"CategoryTheory.ShortComplex.moduleCatMkOfKerLERange._proof_1",
"Finsupp.module",
"ModuleCat",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Submodule.addCommMonoid",
"LinearMap.ker",
"LinearMap.instFunLike",
"CategoryTheory.ShortCom... | false |
instCStarAlgebraProd._proof_2 | Mathlib.Analysis.CStarAlgebra.Classes | [
"Prod.cstarRing",
"CStarAlgebra.toNormedRing",
"CStarAlgebra.toStarRing",
"NormedRing.toNonUnitalNormedRing",
"NonUnitalRing.toNonUnitalNonAssocRing",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Prod.nonUnitalNormedRing",
"Prod.instStarRing",
"NonUnitalNormedRing.toNonUnitalRing",
"CStar... | false |
CategoryTheory.Limits.CategoricalPullback.instCategory._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.CategoricalPullback.fst",
"CategoryTheory.Limits.CategoricalPullback",
"CategoryTheory.Category.comp_id",
"CategoryTheory.Functor.map",
"Category... | false |
_private.Mathlib.Order.Defs.Unbundled.0.«term_≺_» | Mathlib.Order.Defs.Unbundled | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.Name.anonymous",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
_private.Mathlib.Topology.Irreducible.0.isIrreducible_iff_sUnion_isClosed._simp_1_12 | Mathlib.Topology.Irreducible | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Set.not_disjoint_iff_nonempty_inter",
"Set.instInter",
"Set.instDistribLattice",
"Inter.inter",
"Set.Nonempty",
"Set.instBoundedOrder",
"BoundedOrder.toOrderBot",
"propext",
... | false |
MeasureTheory.Measure.InnerRegularWRT.of_imp | Mathlib.MeasureTheory.Measure.Regular | [
"MeasureTheory.Measure",
"Preorder.toLT",
"PartialOrder.toPreorder",
"HasSubset.Subset",
"MeasureTheory.Measure.InnerRegularWRT",
"MeasurableSpace",
"And",
"Set.Subset.rfl",
"And.intro",
"LT.lt",
"ENNReal",
"Exists.intro",
"ENNReal.instPartialOrder",
"DFunLike.coe",
"Set.instHasSubset",
... | true |
Subgroup.isComplement'_bot_top | Mathlib.GroupTheory.Complement | [
"Subgroup.isComplement_singleton_univ",
"MulOne.toOne",
"Monoid.toMulOneClass",
"Group",
"DivInvMonoid.toMonoid",
"Subgroup",
"Bot.bot",
"Group.toDivInvMonoid",
"Subgroup.IsComplement'",
"MulOneClass.toMulOne",
"One.toOfNat1",
"Subgroup.instTop",
"Subgroup.instBot",
"Top.top",
"OfNat.ofN... | true |
Algebraic.countable | Mathlib.Algebra.AlgebraicCard | [
"Eq.mpr",
"IsDomain",
"CommRing",
"Cardinal.lift_le_aleph0",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Cardinal.le_aleph0_iff_set_countable",
"CommRing.toNonUnitalCommRing",
"Cardinal.lift_le_aleph0._simp_1",
"IsAlgebraic",
"Cardinal",
"instReflLe",
"congr... | true |
CategoryTheory.op_mono_iff._simp_1 | Mathlib.CategoryTheory.EpiMono | [
"Opposite",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.op_mono_iff",
"Opposite.op",
"propext",
"CategoryTheory.Category.opposite",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Cate... | false |
Batteries.RBSet.union | Batteries.Data.RBMap.Basic | [
"Batteries.RBSet",
"Ordering",
"Batteries.RBSet.insert",
"Batteries.RBSet.foldl"
] | true |
_private.Lean.Meta.Tactic.Grind.VarRename.0.Lean.Meta.Grind.collectMapVars.match_1 | Lean.Meta.Tactic.Grind.VarRename | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Lean.Elab.Tactic.Omega.State.recOn | Lean.Elab.Tactic.Omega.OmegaM | [
"Lean.Elab.Tactic.Omega.State.mk",
"Lean.Elab.Tactic.Omega.State",
"Lean.Expr.instBEq",
"Lean.Expr",
"Std.HashMap",
"Nat",
"Lean.Expr.instHashable",
"Lean.Elab.Tactic.Omega.State.rec"
] | false |
Int.shiftLeft_add | Init.Data.Int.Bitwise.Lemmas | [
"instPowNat",
"HMul.hMul",
"congrArg",
"Int.instHShiftLeftNat",
"Int.mul_assoc",
"HShiftLeft.hShiftLeft",
"Int",
"Int.instNatPow",
"Int.instMul",
"instHAdd",
"HPow.hPow",
"instOfNat",
"HAdd.hAdd",
"Int.shiftLeft_eq",
"Nat",
"congr",
"True",
"eq_self",
"of_eq_true",
"instAddNat"... | true |
TopCat.range_pullback_map | Mathlib.Topology.Category.TopCat.Limits.Pullbacks | [
"_private.Mathlib.Topology.Category.TopCat.Limits.Pullbacks.0.TopCat.range_pullback_map._simp_1_3",
"CategoryTheory.Limits.hasFiniteLimits_of_hasLimits",
"CategoryTheory.Limits.limit.π",
"Set.ext",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.Cone... | true |
_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.eval.match_1.eq_7 | Mathlib.Computability.TuringMachine.Config | [
"Turing.ToPartrec.Code.eval.match_1",
"Turing.ToPartrec.Code.succ",
"Turing.ToPartrec.Code.tail",
"Unit",
"Turing.ToPartrec.Code.comp",
"Turing.ToPartrec.Code.case",
"Eq.refl",
"Turing.ToPartrec.Code.zero'",
"Eq",
"Turing.ToPartrec.Code.fix",
"Turing.ToPartrec.Code.cons",
"Turing.ToPartrec.Cod... | true |
_private.Mathlib.LinearAlgebra.Matrix.PosDef.0.Matrix.posSemidef_diagonal_iff.match_1_1 | Mathlib.LinearAlgebra.Matrix.PosDef | [
"HMul.hMul",
"Ring.toNonAssocRing",
"PartialOrder.toPreorder",
"Finsupp.sum",
"Preorder.toLE",
"PartialOrder",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"LE.le",
"StarAddMonoid.toInvolutiveStar",
"NonAssocRing.toNonUnitalNonAssocRing",
"instDistribOfSemiring",
"And.casesOn",
"Matr... | false |
BitVec.slt_eq_sle_and_ne | Init.Data.BitVec.Lemmas | [
"Iff.mpr",
"instDecidableNot",
"bne",
"Bool.not",
"instLawfulBEq",
"congrArg",
"Decidable.decide.congr_simp",
"Int.decLe",
"Bool.decide_and",
"BitVec",
"Bool.eq_iff_iff",
"Bool.and",
"Ne",
"decide_not",
"Int",
"LE.le",
"instBEqOfDecidableEq",
"instDecidableEqBitVec",
"iff_self",
... | true |
AlgebraicGeometry.PresheafedSpace.Hom.ext._proof_1 | Mathlib.Geometry.RingedSpace.PresheafedSpace | [
"AlgebraicGeometry.PresheafedSpace.Hom",
"CategoryTheory.Functor.op",
"Eq.mpr",
"CategoryTheory.Functor",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"congrArg",
"TopCat.instCategory",... | false |
List.zipWithLeft'TR.go._sunfold | Batteries.Data.List.Basic | [
"Array.push",
"Option.some",
"Prod.mk",
"List.foldl",
"Array.toList",
"Array",
"Option.none",
"List",
"List.zipWithLeft'TR.go",
"List.zipWithLeft'TR.go.match_1",
"Prod",
"List.nil",
"Option"
] | false |
CategoryTheory.Limits.Cocone.precomposeEquivalence._proof_10 | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone.precomposeEquivalence._proof_8",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.Cocone.precompose",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.CoconeMorp... | false |
CategoryTheory.Localization.Construction.LocQuiver.mk.injEq | Mathlib.CategoryTheory.Localization.Construction | [
"CategoryTheory.MorphismProperty",
"Eq.propIntro",
"CategoryTheory.Localization.Construction.LocQuiver",
"CategoryTheory.Localization.Construction.LocQuiver.mk.inj",
"CategoryTheory.Localization.Construction.LocQuiver.mk",
"Eq.ndrec",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"C... | true |
LeftCancelMonoid.groupOfFinite | Mathlib.GroupTheory.OrderOfElement | [
"Semigroup.toMul",
"Finite",
"DivInvMonoid.mk",
"HSub.hSub",
"Group",
"LeftCancelMonoid.toMonoid",
"LeftCancelMonoid.groupOfFinite._proof_5",
"instSubNat",
"DivInvMonoid.div'",
"instOfNatNat",
"Div.mk",
"npowRec",
"Monoid.toPow",
"orderOf",
"LeftCancelMonoid",
"instHSub",
"HPow.hPow"... | true |
CategoryTheory.Limits.isIsoZeroEquiv | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.isIsoZeroEquiv._proof_5",
"CategoryTheory.Limits.isIsoZeroEquiv._proof_1",
"CategoryTheory.CategoryStruct.id",
"Equiv.mk",
"Equiv",
"CategoryTheory.Limit... | true |
_private.Mathlib.ModelTheory.Encoding.0.FirstOrder.Language.Term.listEncode.match_1.splitter | Mathlib.ModelTheory.Encoding | [
"FirstOrder.Language.Term",
"FirstOrder.Language.Term.listEncode.match_1",
"FirstOrder.Language.Term.func",
"FirstOrder.Language.Term.var",
"Nat",
"FirstOrder.Language.Functions",
"FirstOrder.Language",
"Fin"
] | true |
tprod_mulIndicator_of_mem_union_disjoint | Mathlib.Topology.Algebra.InfiniteSum.Basic | [
"MulOne.toOne",
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Monoid.toMulOneClass",
"Set.mulIndicator",
"Disjoint",
"pairwise_disjoint_mono",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"Set.instInter",
"tprod_mulIndicator_of_disjoint_on_mulSuppor... | true |
Int.emod_abs | Mathlib.Algebra.Order.Group.Unbundled.Int | [
"abs",
"Int.instLinearOrder",
"Int.emod_neg",
"instHMod",
"abs_by_cases",
"Int",
"HMod.hMod",
"instLatticeInt",
"Int.instAddGroup",
"Int.instMod",
"Eq",
"rfl"
] | true |
RootPairing.pairingIn_lt_zero_iff | Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear | [
"Left.neg_pos_iff._simp_1",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"CommRing",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Equiv.instEquivLike",
"CommRing.toNonUnitalCommRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"DistribMu... | true |
ContinuousLinearMap.inl | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd | [
"instTopologicalSpaceProd",
"ContinuousLinearMap.id",
"ContinuousLinearMap.zero",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"ContinuousLinearMap.prod",
"Semiring",
"Zero.toOfNat0",
"Module",
"Prod",
"Prod.instModule",
"OfNat.ofNat",
"RingHom.id",
"Semiring.toNonAssocSem... | true |
Lean.Elab.Term.StructInst.FieldLHS.modifyOp.elim | Lean.Elab.StructInst | [
"PULift.up",
"Lean.Elab.Term.StructInst.FieldLHS",
"Lean.Syntax",
"Lean.Elab.Term.StructInst.FieldLHS.modifyOp",
"Lean.Elab.Term.StructInst.FieldLHS.ctorIdx",
"Nat",
"Eq.symm",
"Eq",
"Lean.Elab.Term.StructInst.FieldLHS.ctorElim"
] | false |
HasDerivWithinAt.finsetProd | Mathlib.Analysis.Calculus.Deriv.Mul | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NormedCommRing.toCommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"NormedCommRing",
"ContinuousSMul",
"congrArg",
"Com... | true |
FiniteIndexNormalSubgroup.comap_id | Mathlib.GroupTheory.FiniteIndexNormalSubgroup | [
"Monoid.toMulOneClass",
"Group",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"MonoidHom.id",
"Eq.refl",
"FiniteIndexNormalSubgroup",
"FiniteIndexNormalSubgroup.comap",
"Eq"
] | true |
_private.Init.Data.Iterators.Lemmas.Basic.0.Std.Iter.inductSteps._proof_2 | Init.Data.Iterators.Lemmas.Basic | [
"Std.Iter.TerminationMeasures.Finite.rel_of_yield",
"invImage",
"Std.IterM.TerminationMeasures.Finite",
"Std.Iter.finitelyManySteps",
"Std.Iterators.Finite",
"id",
"Id",
"Std.IterM.TerminationMeasures.instWellFoundedRelationFinite",
"Std.Iterator",
"Std.Iter",
"Std.IterStep.yield",
"Std.Iter.I... | false |
Complex.instTietzeExtension | Mathlib.Analysis.Complex.Tietze | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"NormedSpace.toIsBoundedSMul",
"Real.denselyNormedField",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"Complex.instNormedField",
"FiniteDimensional.rclike_to_... | true |
AlgebraicGeometry.QuasiSeparated | Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Category.toCategoryStruct",
"AlgebraicGeometry.Scheme.instCategory",
"AlgebraicGeometry.QuasiSeparated.mk"
] | true |
Quiver.Path.length_comp._f | Mathlib.Combinatorics.Quiver.Path | [
"Quiver.Hom",
"Quiver.Path.nil",
"_private.Mathlib.Combinatorics.Quiver.Path.0.Quiver.Path.length_comp.match_1_1",
"Quiver.Path",
"congr_arg",
"Quiver.Path.below",
"instHAdd",
"Quiver.Path.cons",
"Unit",
"HAdd.hAdd",
"Nat",
"Quiver.Path.length",
"Quiver",
"instAddNat",
"Quiver.Path.comp"... | false |
Std.DTreeMap.Internal.Impl.insert.congr_simp | Std.Data.DTreeMap.Internal.Model | [
"Ord",
"Std.DTreeMap.Internal.Impl.Balanced",
"Eq.rec",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"Std.DTreeMap.Internal.Impl.insert",
"OfNat.ofNat",
"Eq",
"Std.DTreeMap.Inte... | true |
HNNExtension.NormalWord.cons_toList | Mathlib.GroupTheory.HNNExtension | [
"List.head?",
"HNNExtension.NormalWord",
"HNNExtension.NormalWord.ReducedWord.toList",
"Option.instMembership",
"Group",
"Membership.mem",
"Units",
"Prod.mk",
"Subgroup",
"HNNExtension.NormalWord.TransversalPair.set",
"Int",
"Prod.fst",
"List.cons",
"Int.instMonoid",
"List",
"Option.ma... | true |
NumberField.mixedEmbedding.commMap._proof_2 | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Complex.mul_re",
"Semiring.toModule",
"Pi.addCommMonoid",
"HMul.hMul",
"Real.in... | false |
Set.iInter₂_vadd_subset | Mathlib.Algebra.Group.Pointwise.Set.Lattice | [
"Set.iInter",
"VAdd",
"HasSubset.Subset",
"Set.image2_iInter₂_subset_left",
"HVAdd.hVAdd",
"instHVAdd",
"Set.vadd",
"Set.instHasSubset",
"Set"
] | true |
_private.Init.Data.String.Lemmas.Pattern.TakeDrop.String.0.String.Slice.startsWith_slice_iff._simp_1_7 | Init.Data.String.Lemmas.Pattern.TakeDrop.String | [
"String.toList_inj",
"String",
"List",
"String.toList",
"propext",
"Char",
"Eq.symm",
"Eq"
] | false |
Polynomial.derivative_ofNat | Mathlib.Algebra.Polynomial.Derivative | [
"Polynomial.derivative",
"Semiring.toModule",
"LinearMap.instFunLike",
"LinearMap",
"Polynomial",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Polynomial.semiring",
"Nat",
"Semiring",
"Zero.toOfNat0",
"Polynomial.module",
"Polynomial.derivativ... | true |
CategoryTheory.Limits.Cofork.unop.eq_1 | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers | [
"CategoryTheory.Functor.op",
"CategoryTheory.Limits.Cofork.unop",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.Cocone.precompose",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",... | true |
LightDiagram'._sizeOf_inst | Mathlib.Topology.Category.LightProfinite.Basic | [
"LightDiagram'",
"LightDiagram'._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
_private.Init.Data.BitVec.Lemmas.0.BitVec.toNat_shiftLeftZeroExtend._proof_1_4 | Init.Data.BitVec.Lemmas | [
"instPowNat",
"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",
"Le... | false |
SSet.Truncated.Edge.CompStruct.comp_unique | Mathlib.AlgebraicTopology.Quasicategory.TwoTruncated | [
"SSet.Truncated.Edge",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"SSet.Truncated.Quasicategory₂.fill32",
"Opposite",
"SSet.Truncated.HomotopicL.homotopicR",
"SSet.Truncated.Edge.CompStruct.compId",
"SSet.Truncated",
"SSet.Truncated.HomotopicR",
"SSet.Truncated.Quasicategory₂._proof_1",
"... | true |
Aesop.SimpResult.ctorElim | Aesop.Search.Expansion.Simp | [
"Aesop.SimpResult.ctorElimType",
"Aesop.SimpResult.simplified",
"Lean.MVarId",
"Aesop.SimpResult.unchanged",
"Nat",
"Eq.ndrec",
"PULift.down",
"Aesop.SimpResult.casesOn",
"Lean.Meta.Simp.UsedSimps",
"Eq",
"Aesop.SimpResult.solved",
"Aesop.SimpResult.ctorIdx",
"Aesop.SimpResult"
] | false |
HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject._proof_2 | Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy | [
"HomotopicalAlgebra.BifibrantObject",
"Eq.mpr",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"HomotopicalAlgebra.ModelCategory.cm1a",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.BifibrantObject.homRel._proof_2",
"CategoryTheory.Quotient.category",
"_private.Mat... | false |
instReprExcept | Init.Data.ToString.Basic | [
"Std.Format.instAppend",
"Repr.mk",
"instHAppendOfAppend",
"instReprExcept.match_1",
"Nat",
"Std.Format",
"Repr.addAppParen",
"Except",
"Repr",
"reprArg",
"HAppend.hAppend",
"Std.Format.text"
] | true |
RestrictedProduct.instPow.eq_1 | Mathlib.Topology.Algebra.RestrictedProduct.Basic | [
"SetLike",
"Monoid",
"Monoid.toMulOneClass",
"Pow",
"Filter.Eventually",
"RestrictedProduct.instPow",
"Membership.mem",
"RestrictedProduct.instDFunLike",
"RestrictedProduct",
"Subtype.mk",
"Monoid.toPow",
"Pow.mk",
"SetLike.coe",
"HPow.hPow",
"RestrictedProduct.instPow._proof_1",
"Nat"... | true |
Batteries.Tactic.Lint.instReprLintVerbosity | Batteries.Tactic.Lint.Frontend | [
"Batteries.Tactic.Lint.LintVerbosity",
"Repr.mk",
"Batteries.Tactic.Lint.instReprLintVerbosity.repr",
"Repr"
] | true |
Lean.Grind.CommRing.denoteInt | Init.Grind.Ring.CommSolver | [
"Int.blt'",
"Int",
"Lean.Grind.Semiring.ofNat",
"Lean.Grind.Ring.toNeg",
"instOfNat",
"Lean.Grind.Ring",
"Int.natAbs",
"Bool.rec",
"Bool",
"Lean.Grind.Ring.toSemiring",
"OfNat.ofNat",
"Neg.neg"
] | true |
NumberField.InfinitePlace.IsUnramified.comap | Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | [
"NumberField.InfinitePlace.IsUnramified.comap_algHom",
"Algebra.algebraMap",
"IsScalarTower",
"IsScalarTower.toAlgHom",
"NumberField.InfinitePlace.comap",
"Algebra",
"Algebra.toSMul",
"Field.toSemifield",
"NumberField.InfinitePlace.IsUnramified",
"Semifield.toDivisionSemiring",
"DivisionSemiring... | true |
CategoryTheory.TwoSquare.op | Mathlib.CategoryTheory.Functor.TwoSquare | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.comp",
"CategoryTheory.NatTrans.op",
"CategoryTheory.Category.opposite",
"CategoryTheory.TwoSquare",
"CategoryTheory.Category"
] | true |
Subgroup.le_comap_map | Mathlib.Algebra.Group.Subgroup.Map | [
"Subgroup.gc_map_comap",
"MonoidHom",
"Subgroup.map",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"DivInvMonoid.toMonoid",
"Subgroup",
"GaloisConnection.le_u_l",
"LE.le",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Subgroup.instPartialOrder",
"Subgro... | true |
ContinuousMap.ctorIdx | Mathlib.Topology.ContinuousMap.Defs | [
"ContinuousMap",
"TopologicalSpace",
"Nat"
] | false |
CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.mk.inj | Mathlib.Algebra.Homology.SpectralObject.HasSpectralSequence | [
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore._auto_49",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore._proof_23",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore._proof_40",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore._auto_34",
"Categ... | true |
CasesInfo.mk.injEq | Lean.Meta.CasesInfo | [
"Std.Rco",
"CasesInfo",
"Eq.propIntro",
"Lean.injEq_helper",
"Array",
"And",
"Nat",
"Eq.ndrec",
"CasesInfo.mk",
"Lean.Name",
"Eq.refl",
"CasesInfo.mk.inj",
"Eq",
"CasesAltInfo"
] | true |
dist_prod_prod_le | Mathlib.Analysis.Normed.Group.Basic | [
"Real.instLE",
"Real",
"le_rfl",
"Finset",
"SeminormedCommGroup.toPseudoMetricSpace",
"Membership.mem",
"LE.le",
"Finset.prod",
"Finset.instSetLike",
"dist_prod_prod_le_of_le",
"Real.instAddCommMonoid",
"Dist.dist",
"PseudoMetricSpace.toDist",
"SeminormedCommGroup",
"SeminormedCommGroup.... | true |
Real.partialOrder._proof_3 | Mathlib.Data.Real.Basic | [
"Eq.mpr",
"Real.instLE",
"Real",
"abs",
"Rat",
"Rat.linearOrder",
"id",
"CauSeq.instLEAbs",
"CauSeq.instPreorderAbs",
"Rat.instLattice",
"Rat.instDivisionRing",
"DivisionRing.toRing",
"LE.le",
"Real.mk_le._simp_1",
"Rat.instField",
"implies_congr",
"Real.ind_mk",
"CauSeq",
"Rat.i... | false |
LocallyConstant.constₐ_apply_apply | Mathlib.Topology.LocallyConstant.Algebra | [
"AlgHom",
"AlgHom.funLike",
"LocallyConstant.instSemiring",
"Algebra",
"LocallyConstant",
"CommSemiring",
"TopologicalSpace",
"LocallyConstant.instAlgebra",
"Semiring",
"Eq.refl",
"LocallyConstant.instFunLike",
"LocallyConstant.constₐ",
"Eq",
"DFunLike.coe"
] | true |
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