name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
SSet.Subcomplex.Pairing.RankFunction.Cell.preimage_filtration_map | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | [
"SSet.Subcomplex.Pairing.RankFunction.rank",
"SSet.Subcomplex.Pairing.RankFunction.Cell.image_horn_lt_subcomplex",
"SSet.N.instPreorder",
"SSet.S.subcomplex",
"Eq.mpr",
"SSet.S",
"SSet.Subcomplex.Pairing.RankFunction.Cell.image_face_index_compl",
"lt_of_le_of_lt",
"False",
"Preorder.toLT",
"Oppo... | true |
Lean.Data.Trie.upsert | Lean.Data.Trie | [
"Lean.Data.Trie",
"String",
"_private.Lean.Data.Trie.0.Lean.Data.Trie.upsert.loop",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"Option"
] | true |
OrderIso.toInitialSeg_toFun | Mathlib.Order.InitialSeg | [
"OrderIso.toInitialSeg",
"Preorder.toLT",
"Preorder.toLE",
"OrderIso",
"instFunLikeOrderIso",
"LT.lt",
"InitialSeg",
"Eq.refl",
"Eq",
"DFunLike.coe",
"InitialSeg.instFunLike",
"Preorder"
] | true |
AlgHom.val_comp_codRestrict | Mathlib.Algebra.Algebra.Subalgebra.Basic | [
"Subalgebra.instSetLike",
"AlgHom",
"AlgHom.funLike",
"Subalgebra.val",
"Algebra",
"Membership.mem",
"Subtype",
"AlgHom.ext",
"CommSemiring",
"Subalgebra.algebra",
"Semiring",
"Subalgebra",
"AlgHom.codRestrict",
"AlgHom.comp",
"Eq",
"DFunLike.coe",
"SetLike.instMembership",
"rfl",
... | true |
Mathlib.Tactic.TermCongr.hasCHole | Mathlib.Tactic.TermCongr | [
"Option.some",
"Lean.Expr",
"Nat",
"Lean.Expr.find?",
"Bool",
"Prod",
"Option.isSome",
"Mathlib.Tactic.TermCongr.cHole?",
"Option"
] | true |
Lean.Meta.Match.Alt | Lean.Meta.Match.Basic | [
"Lean.Meta.Match.Alt.mk"
] | true |
UInt8.toFin_val | Init.Data.UInt.Lemmas | [
"UInt8.toFin",
"UInt8.size",
"Fin.val",
"Nat",
"UInt8.toNat",
"UInt8",
"Eq",
"rfl"
] | true |
_private.Mathlib.ModelTheory.Semantics.0.FirstOrder.Language.BoundedFormula.restrictFreeVar.match_1.eq_3 | Mathlib.ModelTheory.Semantics | [
"FirstOrder.Language.BoundedFormula.imp",
"FirstOrder.Language.BoundedFormula.freeVarFinset",
"Finset",
"Membership.mem",
"FirstOrder.Language.Term",
"Sum",
"Subtype",
"instOfNatNat",
"FirstOrder.Language.BoundedFormula.equal",
"FirstOrder.Language.BoundedFormula.falsum",
"instHAdd",
"Finset.i... | true |
_private.Mathlib.Analysis.Calculus.ContDiff.Defs.0.contDiffOn_infty._simp_1_2 | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"forall_prop_of_true",
"propext",
"Eq"
] | false |
CategoryTheory.CosimplicialObject.truncation | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CosimplicialObject",
"CategoryTheory.Functor.category",
"CategoryTheory.CosimplicialObject.instCategoryTruncated",
"LE.le",
"instLENat",
"CategoryTheory.CosimplicialObject.instCategory",
"CategoryTheory.CosimplicialObject.Truncated",
"Nat",
"CategoryTheory... | true |
_private.Mathlib.Order.Atoms.0.SetLike.isAtom_iff._simp_1_2 | Mathlib.Order.Atoms | [
"Preorder.toLT",
"lt_iff_le_not_ge",
"Preorder.toLE",
"LE.le",
"And",
"LT.lt",
"propext",
"Eq",
"Not",
"Preorder"
] | false |
_private.Lean.Compiler.LCNF.AlphaEqv.0.Lean.Compiler.LCNF.AlphaEqv.eqvType.match_1 | Lean.Compiler.LCNF.AlphaEqv | [
"_private.Lean.Compiler.LCNF.AlphaEqv.0.Lean.Compiler.LCNF.AlphaEqv.eqvType._sparseCasesOn_1",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"_private.Lean.Compiler.LCNF.AlphaEqv.0.Lean.Compiler.LCNF.AlphaEqv.eqvType._sparseCasesOn_2",
"_private.Lean.Compiler.LCNF.AlphaEqv.0.Lean.Compiler.LCNF.AlphaEqv.eqv... | false |
WithZero.lift_symm_apply | Mathlib.Algebra.Group.WithOne.Basic | [
"Equiv.instEquivLike",
"AddHom",
"AddZeroClass.toAddZero",
"Equiv",
"AddHom.funLike",
"WithZero.instAddZeroClass",
"AddZeroClass",
"WithZero",
"WithZero.coe",
"AddZero.toAdd",
"Equiv.symm",
"AddMonoidHom",
"AddMonoidHom.instFunLike",
"Eq",
"DFunLike.coe",
"WithZero.lift",
"Add",
"r... | true |
_private.Mathlib.RingTheory.Flat.Basic.0.LinearMap.rTensor_injective_of_fg._simp_1_3 | Mathlib.RingTheory.Flat.Basic | [
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"LinearMap.instFunLike",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"LinearMap.comp",
"LinearMap.rTensor_comp_apply",
"TensorProduct",
"Module",
"Eq.symm",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring",
"... | false |
Relation.reflTransGen_swap | Mathlib.Logic.Relation | [
"Relation.ReflTransGen.swap",
"Function.swap",
"Iff",
"Iff.intro",
"Relation.ReflTransGen"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity.0.SimpleGraph.antitoneOn_extremalNumber_div_choose_two._simp_1_3 | Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity | [
"le_refl",
"Preorder.toLE",
"LE.le",
"True",
"eq_true",
"Eq",
"Preorder"
] | false |
Std.Http.Method.rebind.elim | Std.Internal.Http.Data.Method | [
"Std.Http.Method",
"PULift.up",
"Std.Http.Method.ctorIdx",
"Std.Http.Method.rebind",
"Nat",
"Eq.symm",
"Std.Http.Method.ctorElim",
"Eq"
] | false |
Lean.Elab.Command.ElabHeaderResult.mk.inj | Lean.Elab.MutualInductive | [
"Lean.Elab.Command.ElabHeaderResult.mk.noConfusion",
"Lean.Expr",
"Lean.Elab.Command.ElabHeaderResult.mk",
"And",
"And.intro",
"Lean.Elab.Command.PreElabHeaderResult",
"Lean.Elab.Command.ElabHeaderResult",
"Eq"
] | true |
_private.Mathlib.Data.Fin.Embedding.0.Fin.range_natAdd_castLEEmb._proof_1_6 | Mathlib.Data.Fin.Embedding | [
"Lean.RArray.leaf",
"False",
"Lean.Grind.ToInt.toInt",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
"Nat.Linear.ExprCnstr.eq_of_toNor... | false |
LawfulMonadStateOf.set_bind_modify_bind | Batteries.Control.LawfulMonadState | [
"Pure.pure",
"LawfulMonadStateOf",
"MonadStateOf",
"congrArg",
"modify",
"Monad.toApplicative",
"MonadState.get",
"LawfulMonad.bind_pure_comp",
"LawfulMonadStateOf.toLawfulMonad",
"LawfulMonadStateOf.modify_eq",
"Applicative.toPure",
"bind_map_left",
"funext",
"PUnit",
"True",
"eq_self... | true |
CategoryTheory.Functor.RightExtension.coneAtFunctor | Mathlib.CategoryTheory.Functor.KanExtension.Pointwise | [
"CategoryTheory.Limits.ConeMorphism.mk",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.RightExtension.coneAtFunctor._proof_1",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.category",
"CategoryTheory.Com... | true |
instIsRightCancelMulMonoidHom | Mathlib.Algebra.Group.Hom.Instances | [
"MonoidHom.instFunLike",
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"MulOne.toMul",
"Function.Injective.isRightCancelMul",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"DFunLike.coe_injective",
"Pi.instMul",
"MonoidHom.mul",
"MulOneClass",
"Pi.instIsRightCancelMul",
"CommMonoid",
... | true |
ContinuousAlgHom.coe_id' | Mathlib.Topology.Algebra.Algebra | [
"ContinuousAlgHom.instFunLike",
"Algebra",
"id",
"CommSemiring",
"TopologicalSpace",
"ContinuousAlgHom.id",
"Semiring",
"ContinuousAlgHom",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
_private.Mathlib.Logic.Relation.0.Acc.of_downward_closed.match_1_1 | Mathlib.Logic.Relation | [
"Exists",
"Exists.casesOn",
"Exists.intro",
"Eq"
] | false |
Int.Linear.Expr.denote.match_1 | Init.Data.Int.Linear | [
"Int.Linear.Expr.mulR",
"Int.Linear.Expr.casesOn",
"Int.Linear.Expr.add",
"Int",
"Int.Linear.Var",
"Int.Linear.Expr",
"Int.Linear.Expr.mulL",
"Int.Linear.Expr.var",
"Int.Linear.Expr.neg",
"Int.Linear.Expr.num",
"Int.Linear.Expr.sub"
] | false |
_private.Std.Data.DTreeMap.Internal.Queries.0.Std.DTreeMap.Internal.Impl.maxEntry?.match_1._arg_pusher | Std.Data.DTreeMap.Internal.Queries | [
"Unit.unit",
"Std.DTreeMap.Internal.Impl.maxEntry?.match_1",
"namedPattern",
"Std.DTreeMap.Internal.Impl.inner",
"id",
"_private.Std.Data.DTreeMap.Internal.Queries.0.Std.DTreeMap.Internal.Impl.maxEntry?.match_1.splitter",
"Unit",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.ndrec",
"Eq.refl",
... | false |
Turing.Tape.mk₂ | Mathlib.Computability.TuringMachine.Tape | [
"Turing.ListBlank.mk",
"Turing.Tape.mk'",
"Turing.Tape",
"List",
"Inhabited"
] | true |
CategoryTheory.Equivalence.inverseFunctorObj'_hom_app | Mathlib.CategoryTheory.Equivalence.Symmetry | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Equivalence.inverseFunctor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Equivalence.inverseFunctorObj'",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence",
"CategoryTheory.CategoryStruct.id",
"Category... | true |
_private.Mathlib.Geometry.Manifold.Bordism.0.SingularManifold.instIsEmptyMEmpty._proof_1 | Mathlib.Geometry.Manifold.Bordism | [
"Real",
"NormedSpace",
"Real.denselyNormedField",
"NormedSpace.toModule",
"IsManifold",
"IsEmpty",
"TopologicalSpace",
"ModelWithCorners",
"SingularManifold.M",
"FiniteDimensional",
"ENat",
"Real.instDivisionRing",
"NormedAddCommGroup.toAddCommGroup",
"Real.normedField",
"DenselyNormedFi... | false |
CategoryTheory.monoidalUnopUnop._proof_16 | Mathlib.CategoryTheory.Monoidal.Opposite | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Category.comp_id",
"CategoryTheory.Functor.map",
"CategoryTheory.MonoidalCateg... | false |
CategoryTheory.MorphismProperty.LeftFractionRel.trans | Mathlib.CategoryTheory.Localization.CalculusOfFractions | [
"CategoryTheory.MorphismProperty.LeftFraction.hs",
"CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Category.assoc",
"CategoryTheory.MorphismProperty.LeftFraction.casesOn",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheo... | true |
Matrix.diagonal_injective | Mathlib.Data.Matrix.Diagonal | [
"Iff.mpr",
"congrArg",
"Matrix",
"Matrix.diagonal_apply_eq",
"Eq.mp",
"funext",
"congr",
"Matrix.ext_iff",
"Function.Injective",
"Eq",
"Matrix.diagonal",
"DecidableEq",
"Zero"
] | true |
CategoryTheory.ShortComplex.Exact.isLimitImage._proof_6 | Mathlib.CategoryTheory.Abelian.Exact | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.NonPreadditiveAbelian.has_cokernels",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Abelian",
"CategoryTheory.Limits.HasCokernels.has_colimit",
"CategoryTheory.NonPreadditiveAbelian.toHasZeroMorphisms",
"Categor... | false |
ProjectiveSpectrum.subset_zeroLocus_iff_le_vanishingIdeal | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology | [
"SetLike",
"Iff.mpr",
"Submodule",
"CommRing",
"Semiring.toModule",
"ChainCompletePartialOrder.instOfCompleteLattice",
"ProjectiveSpectrum.mem_vanishingIdeal",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Preorder.toLE... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.exists_fixed_point_of_prime._simp_1_2 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Finset.eq_univ_iff_forall",
"Finset.univ",
"Finset",
"Membership.mem",
"Fintype",
"Finset.instSetLike",
"propext",
"Eq.symm",
"Eq",
"SetLike.instMembership"
] | false |
_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.insertMin._proof_16 | Std.Data.DTreeMap.Internal.Operations | [
"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",
"Lean.Omega.LinearCombo.coordinate_eva... | false |
ContDiff.fun_comp | Mathlib.Analysis.Calculus.ContDiff.Comp | [
"NormedSpace",
"ContDiff",
"ContDiff.comp",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"NormedAddCommGroup",
"WithTop"
] | true |
_private.Mathlib.Probability.Kernel.Proper.0.ProbabilityTheory.Kernel.IsProper.lintegral_indicator_mul_indicator._simp_1_1 | Mathlib.Probability.Kernel.Proper | [
"HMul.hMul",
"MulZeroClass.toMul",
"Set.indicator",
"MulZeroClass",
"Set.instInter",
"Inter.inter",
"Eq.symm",
"Set.inter_indicator_mul",
"Eq",
"MulZeroClass.toZero",
"instHMul",
"Set"
] | false |
Set.Definable.singleton | Mathlib.ModelTheory.Definability | [
"Set.Definable₁._proof_1",
"FirstOrder.Language.withConstantsStructure",
"FirstOrder.Language.Constants.term",
"setOf",
"Membership.mem",
"Set.Elem",
"Set.instSingletonSet",
"Fin.instOfNat",
"Subtype",
"FirstOrder.Language.withConstants",
"FirstOrder.Language.Term.equal",
"instOfNatNat",
"Su... | true |
RingAut.instGroup._proof_2 | Mathlib.Algebra.Ring.Aut | [
"Mul.mk",
"RingEquiv.refl",
"One.mk",
"HMul.hMul",
"Semigroup.mk",
"Mul",
"RingAut",
"npowRecAuto",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"RingEquiv.trans",
"OfNat.ofNat",
"Eq",
"Add",
"rfl",
"instHMul"
] | false |
Nat.modEq_iff_exists_eq_add | Mathlib.Data.Nat.ModEq | [
"Eq.mpr",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"dvd_def",
"congrArg",
"semigroupDvd",
"HSub.hSub",
"Exists",
"id",
"instSubNat",
"Nat.sub_eq_iff_eq_add'",
"instMulNat",
"Nat.modEq_iff_dvd'",
"Nat.instSemigroup",
"LE.le",
"instLENat",
"instHAdd",
"exists_congr",
"Iff",
"... | true |
Lean.Elab.Tactic.Do.Fuel.unlimited.elim | Lean.Elab.Tactic.Do.VCGen.Basic | [
"PULift.up",
"Lean.Elab.Tactic.Do.Fuel.ctorElim",
"Lean.Elab.Tactic.Do.Fuel",
"Lean.Elab.Tactic.Do.Fuel.ctorIdx",
"Nat",
"Lean.Elab.Tactic.Do.Fuel.unlimited",
"Eq.symm",
"Eq"
] | false |
Orthonormal.tsum_inner_products_le | Mathlib.Analysis.InnerProductSpace.Orthonormal | [
"Real.instIsOrderedRing",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Real.partialOrder",
"Real.instLE",
"Real",
"SeminormedAddCommGroup",
"IsOrderedRing.toPosMulMono",
"_private.Mathlib.Analysis.InnerProductSpace.Orthonormal.0.Orthonormal.tsum_inner_products_le._simp_1_1",
"Real.lattice",
"Ortho... | true |
_private.Init.Data.Iterators.Combinators.Monadic.Take.0.Std.Iterators.Types.Take.instFinitenessRelation._proof_1 | Init.Data.Iterators.Combinators.Monadic.Take | [
"Eq.mpr",
"Decidable.casesOn",
"Prod.lexAccessible",
"WellFounded.apply",
"congrArg",
"Std.IterM.TerminationMeasures.Finite",
"InvImage",
"Decidable",
"Classical.propDecidable",
"Std.IterM.finitelyManySkips",
"Std.Iterators.Types.Take",
"Std.Iterators.Finite",
"dif_pos",
"Nat.lt_wfRel",
... | false |
_private.Init.Data.BitVec.Lemmas.0.BitVec.neg_one_ediv_toInt_eq._proof_1_1 | Init.Data.BitVec.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"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",
"Op... | false |
_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Turing.PartrecToTM2.supports_union._simp_1_2 | Mathlib.Computability.TuringMachine.ToPartrec | [
"or_imp",
"And",
"propext",
"Or",
"Eq"
] | false |
Nat.odd_sub' | Mathlib.Algebra.Ring.Parity | [
"Odd",
"HSub.hSub",
"instSubNat",
"LE.le",
"instLENat",
"Iff",
"instHSub",
"Nat",
"Even",
"instAddNat",
"Nat.instSemiring",
"_private.Mathlib.Algebra.Ring.Parity.0.Nat.odd_sub'._proof_1_1"
] | true |
Lean.Grind.instCommRingUInt8._proof_3 | Init.GrindInstances.Ring.UInt | [
"Int.cast",
"instHSMul",
"HMul.hMul",
"congrArg",
"id",
"Int.instNegInt",
"SMul.mk",
"Int",
"UInt8.neg_mul",
"True",
"instNegUInt8",
"eq_self",
"of_eq_true",
"instMulUInt8",
"UInt8.intCast",
"HSMul.hSMul",
"congrFun'",
"UInt8",
"Eq",
"Neg.neg",
"UInt8.intCast_neg",
"Eq.tran... | false |
_private.Init.Data.Nat.ToString.0.Nat.toDigitsCore.match_1.splitter | Init.Data.Nat.ToString | [
"_private.Init.Data.Repr.0.Nat.toDigitsCore.match_1",
"instOfNatNat",
"List",
"Nat",
"Char",
"OfNat.ofNat",
"Nat.succ"
] | true |
MonoidAlgebra.mapRingEquiv | Mathlib.Algebra.MonoidAlgebra.MapDomain | [
"MonoidAlgebra.semiring",
"MonoidAlgebra.mapRingEquiv._proof_1",
"Monoid",
"Monoid.toMulOneClass",
"RingEquiv.instEquivLike",
"MonoidAlgebra.mapRingEquiv._proof_4",
"MonoidAlgebra.instMul",
"MulOne.toMul",
"Distrib.toAdd",
"MonoidAlgebra.nonAssocSemiring",
"instDistribOfSemiring",
"MonoidAlgeb... | true |
_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.domCongr._simp_1 | Mathlib.Data.Finsupp.Basic | [
"Equiv.trans",
"Finsupp.equivMapDomain",
"Equiv",
"Finsupp.equivMapDomain_trans",
"Eq.symm",
"Eq",
"Finsupp",
"Zero"
] | false |
_private.Mathlib.Algebra.Homology.SpectralObject.FirstPage.0.CategoryTheory.Abelian.SpectralObject.spectralSequenceFirstPageXIso_hom._proof_7 | Mathlib.Algebra.Homology.SpectralObject.FirstPage | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"congrArg",
"Classical.byContradiction",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Int.Linear.Poly.num",
"autoParam",
"Int.instMul",
"Int.Linear.Poly.add",
"Int.Line... | false |
LinearMap.ortho_smul_right | Mathlib.LinearAlgebra.SesquilinearForm.Basic | [
"GroupWithZero.toMonoidWithZero",
"RingHom.instRingHomClass",
"False",
"instHSMul",
"eq_false",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"IsUnit",
"DivisionSemiring.toGroupWit... | true |
Representation.IntertwiningMap.smul_apply | Mathlib.RepresentationTheory.Intertwining | [
"Monoid",
"instHSMul",
"Representation",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Representation.IntertwiningMap.instFunLike",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"Represe... | true |
Mathlib.Tactic.BicategoryLike.Normalize.Result.mk.injEq | Mathlib.Tactic.CategoryTheory.Coherence.PureCoherence | [
"Mathlib.Tactic.BicategoryLike.Normalize.Result.mk",
"Mathlib.Tactic.BicategoryLike.NormalizedHom",
"Mathlib.Tactic.BicategoryLike.Mor₂Iso",
"Eq.propIntro",
"Lean.injEq_helper",
"And",
"Eq.ndrec",
"Eq.refl",
"Mathlib.Tactic.BicategoryLike.Normalize.Result",
"Eq",
"Mathlib.Tactic.BicategoryLike.N... | true |
PrimeSpectrum.isClosedEmbedding_comap_snd | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"Iff.mpr",
"Eq.mpr",
"RingHom.instRingHomClass",
"Prod.instCommSemiring",
"Semiring.toModule",
"PrimeSpectrum.zeroLocus",
"congrArg",
"CommSemiring.toSemiring",
"RingHom",
"id",
"Zero.instNonempty",
"Prod.instSemiring",
"_private.Mathlib.RingTheory.Spectrum.Prime.Topology.0.PrimeSpectrum.isC... | true |
FreeGroup.instGroup._proof_5 | Mathlib.GroupTheory.FreeGroup.Basic | [
"Mul.mk",
"One.mk",
"HMul.hMul",
"FreeGroup.instOne",
"Semigroup.mk",
"npowRecAuto",
"instOfNatNat",
"One.one",
"instHAdd",
"HAdd.hAdd",
"FreeGroup.instGroup._proof_1",
"Mul.mul",
"Nat",
"instAddNat",
"Eq.refl",
"FreeGroup.instMul",
"OfNat.ofNat",
"Eq",
"FreeGroup",
"instHMul"
... | false |
Algebra.GrothendieckAddGroup.instAddCommGroup._proof_6 | Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup | [
"AddSubmonoid.instTop",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"Algebra.GrothendieckAddGroup",
"inferInstance",
"AddSubmonoid",
"AddOreLocalization.instAddCommMonoid",
"AddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"AddCommMonoid.add_comm",
"AddCommMonoid.to... | false |
_private.Init.Data.Iterators.Lemmas.Combinators.Append.0.Std.Iter.step_append.match_1.splitter | Init.Data.Iterators.Lemmas.Combinators.Append | [
"Std.IterStep",
"Std.IterStep.skip",
"Id",
"Std.Iterator",
"Subtype.mk",
"Std.Iter",
"Std.IterStep.yield",
"Std.Iter.IsPlausibleStep",
"Std.IterStep.done",
"Std.Iter.step_append.match_1",
"Std.Iter.Step"
] | true |
Int16.xor | Init.Data.SInt.Basic | [
"Int16",
"BitVec.instXorOp",
"UInt16.ofBitVec",
"BitVec",
"instOfNatNat",
"Nat",
"Int16.toBitVec",
"HXor.hXor",
"OfNat.ofNat",
"instHXorOfXorOp",
"Int16.ofUInt16"
] | true |
TopologicalSpace.isTopologicalBasis_singleton_empty | Mathlib.Topology.Bases | [
"Iff.mpr",
"False",
"TopologicalSpace.IsTopologicalBasis.diff_empty",
"and_true",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"and_self",
"Set.univ",
"sdiff_self",
"Set.sUnion",
"Membership.mem",
"Exists",
"IsEmpty.instSubsingleton",
... | true |
_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice.Pattern.Model.ForwardSliceSearcher.Invariants.not_matchesAt_of_prefixFunction_eq._simp_1_1 | Init.Data.String.Lemmas.Pattern.String.ForwardSearcher | [
"LE.le",
"instLENat",
"String.Pos.Raw",
"Nat",
"String.instLERaw",
"propext",
"String.Pos.Raw.byteIdx",
"String.Pos.Raw.le_iff",
"Eq"
] | false |
NonUnitalStarSubalgebra.instNonUnitalCommRing._proof_9 | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"instSMulOfMul",
"NonUnitalSubalgebra.center.instNonUnitalCommRing._aux_3",
"HMul.hMul",
"NonUnitalStarSubalgebra.instNonUnitalCommRing._proof_1",
"NonUnitalStarSubalgebra.toNonUnitalSemiring",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"SubNegMonoid.mk",
"AddMon... | false |
OpenPartialHomeomorph.univUnitBall._proof_3 | Mathlib.Analysis.Normed.Module.Ball.Homeomorph | [
"Real",
"SeminormedAddCommGroup",
"PseudoMetricSpace.toUniformSpace",
"Metric.ball",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Real.instOne",
"Metric.isOpen_ball",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Semino... | false |
Finset.Ioo_add_one_right_eq_Ioc | Mathlib.Algebra.Order.Interval.Finset.SuccPred | [
"Preorder.toLT",
"One",
"Order.succ",
"Order.succ_eq_add_one",
"congrArg",
"Finset",
"NoMaxOrder",
"LinearOrder",
"SuccAddOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"DistribLattice.toLattice",
"Finset.Ioo_succ_right_eq_Ioc",
"instHAdd",
"HAdd.hAdd",
... | true |
UniformSpace.Completion.instMulActionOfUniformContinuousConstSMul._proof_2 | Mathlib.Topology.Algebra.UniformMulAction | [
"Monoid",
"UniformSpace",
"Eq.mpr",
"UniformSpace.Completion.coe'",
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"congrArg",
"id",
"UniformSpace.Completion.instSMul",
"one_smul",
"MulOneClass.toMulOne",
"UniformSpace.Completion.coe_smul",
"MulAction",
"Monoid.toSemigroup",
"One... | false |
Aesop.Frontend.Parser.phaseNorm | Aesop.Frontend.RuleExpr | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr4"
] | true |
Std.ExtDTreeMap.contains_iff_mem | Std.Data.ExtDTreeMap.Lemmas | [
"Iff.rfl",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Std.ExtDTreeMap.contains",
"Bool.true",
"Iff",
"Std.ExtDTreeMap",
"Bool",
"Eq",
"Std.ExtDTreeMap.instMembershipOfTransCmp"
] | true |
rTensor.inverse_of_rightInverse_comp_rTensor | Mathlib.LinearAlgebra.TensorProduct.RightExactness | [
"Function.Exact",
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"rTensor.inverse_of_rightInverse_apply",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.mk",
"TensorProduct.addCommMonoid",
"LinearMap... | true |
CategoryTheory.GradedObject.mapBifunctorLeftUnitor_hasMap | Mathlib.CategoryTheory.GradedObject.Unitor | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.GradedObject.HasMap",
"CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofanIsColimit",
"CategoryTheory.Functor.category",
"CategoryTheory.GradedObject.mapBifunctorLeftUnitorCofan",
"CategoryTheory.Functor.id",
"CategoryTheory.... | true |
Lean.Meta.Grind.Params.anchorRefs? | Lean.Meta.Tactic.Grind.Main | [
"Lean.Meta.Grind.Params",
"Array",
"Lean.Meta.Grind.AnchorRef",
"Option"
] | true |
Mathlib.Tactic.BicategoryLike.WhiskerLeft.srcM._sunfold | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"Mathlib.Tactic.BicategoryLike.Mor₂",
"Mathlib.Tactic.BicategoryLike.Atom₁",
"Mathlib.Tactic.BicategoryLike.Mor₁.of",
"Mathlib.Tactic.BicategoryLike.Mor₁",
"Mathlib.Tactic.BicategoryLike.MonadMor₁",
"_private.Mathlib.Tactic.CategoryTheory.Coherence.Normalize.0.Mathlib.Tactic.BicategoryLike.WhiskerLeft.e.m... | false |
SubAddAction.instMin.eq_1 | Mathlib.GroupTheory.GroupAction.SubMulAction | [
"SubAddAction.instMin._proof_2",
"Min.mk",
"VAdd",
"Set.instInter",
"Min",
"SubAddAction.mk",
"Inter.inter",
"SubAddAction",
"SetLike.coe",
"SubAddAction.instMin",
"Eq.refl",
"Eq",
"SubAddAction.instSetLike",
"Set"
] | true |
_private.Mathlib.Computability.TuringMachine.StackTuringMachine.0.Option.isSome.match_1.eq_1 | Mathlib.Computability.TuringMachine.StackTuringMachine | [
"Option.isSome.match_1",
"Option.some",
"Option.none",
"Unit",
"Eq.refl",
"Eq",
"Option"
] | true |
Std.DTreeMap.Internal.Impl.filter.congr_simp | Std.Data.DTreeMap.Internal.Operations | [
"Ord",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.filter",
"Eq.rec",
"Std.DTreeMap.Internal.Impl.BalancedTree",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | true |
CategoryTheory.Limits.pasteHorizIsPullback | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | [
"CategoryTheory.Limits.PullbackCone.isLimitAux'",
"CategoryTheory.Limits.pasteHorizIsPullback._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Subtype.casesOn",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.PullbackCone.fst",
"Subtype",
"CategoryTheory... | true |
_private.Mathlib.Data.Seq.Computation.0.Computation.Corec.f.match_1.eq_1 | Mathlib.Data.Seq.Computation | [
"Sum",
"Computation.Corec.f.match_1",
"Sum.inl",
"Sum.inr",
"Eq.refl",
"Eq"
] | true |
BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged | Mathlib.Analysis.BoxIntegral.Partition.Tagged | [
"Real",
"Set.Ioi",
"pseudoMetricSpacePi",
"BoxIntegral.Prepartition",
"Real.instZero",
"BoxIntegral.Box.Icc",
"BoxIntegral.TaggedPrepartition.IsSubordinate",
"Membership.mem",
"Set.Elem",
"HasSubset.Subset",
"Iff",
"Fintype",
"Set.instLE",
"BoxIntegral.Box.instLE",
"BoxIntegral.Prepartit... | true |
Lean.Grind.Linarith.Expr.natMul.noConfusion | Init.Grind.Ordered.Linarith | [
"Lean.Grind.Linarith.Expr",
"Lean.Grind.Linarith.Expr.natMul",
"id",
"Lean.Grind.Linarith.Expr.noConfusion",
"Nat",
"Eq"
] | false |
_private.Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory.0.CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.unitIso._proof_8 | Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory | [
"CategoryTheory.ComonObj.comul",
"Eq.mpr",
"_private.Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory.0.CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.unitIso._proof_3",
"CategoryTheory.Functor",
"CategoryTheory.Comon.ext",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTr... | false |
Int.Linear.instReprPoly_lean.repr._unsafe_rec | Lean.Meta.Tactic.Simp.Arith.Int.Basic | [
"_private.Lean.Meta.Tactic.Simp.Arith.Int.Basic.0.Int.Linear.instReprPoly_lean.repr.match_1",
"Std.Format.instAppend",
"Std.Format.line",
"Std.Format.group",
"GE.ge",
"instOfNatNat",
"Int",
"Int.Linear.Var",
"instLENat",
"Int.Linear.instReprPoly_lean.repr._unsafe_rec",
"instHAppendOfAppend",
"... | false |
Lean.Meta.CustomEliminator.elimName | Lean.Meta.Tactic.ElimInfo | [
"Lean.Meta.CustomEliminator",
"Lean.Name"
] | true |
_private.Mathlib.CategoryTheory.Sites.Sheaf.0.CategoryTheory.Presheaf.isLimit_iff_isSheafFor._simp_1_1 | Mathlib.CategoryTheory.Sites.Sheaf | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Presieve.FamilyOfElements.SieveCompatible",
"CategoryTheory.Sieve",
"CategoryTheory.types",
"propext",
"CategoryTheory.Category.opposite",
"CategoryTheory.Presieve.FamilyOfElements",
"CategoryTheory.Presieve.compa... | false |
Polynomial.splits_X_sub_C | Mathlib.Algebra.Polynomial.Splits | [
"Polynomial.C",
"HSub.hSub",
"RingHom",
"Polynomial",
"RingHom.instFunLike",
"instHSub",
"Polynomial.Splits.X_sub_C",
"Polynomial.semiring",
"Polynomial.instSub",
"Polynomial.Splits",
"Polynomial.X",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"DFunLike.coe",
"Ring"
] | true |
CategoryTheory.ShortComplex.HasLeftHomology.of_hasKernel_of_hasCokernel | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Limits.kernel",
"CategoryTheory.Limits.HasKernel",
"CategoryTheory.Limits.HasCokernel",
"CategoryTheory.ShortComplex.zero",
"CategoryTheory.ShortComplex.HasLeftHomology",
"Categ... | true |
Finset.Nat.instHasAntidiagonal._proof_1 | Mathlib.Data.Finset.NatAntidiagonal | [
"Eq.mpr",
"AddMonoid.toAddSemigroup",
"congrArg",
"Finset",
"Iff.rfl",
"Multiset.Nat.mem_antidiagonal",
"Nat.instAddMonoid",
"Membership.mem",
"Multiset",
"id",
"Multiset.Nat.antidiagonal",
"Finset.val",
"Prod.fst",
"Multiset.instMembership",
"instHAdd",
"AddSemigroup.toAdd",
"Iff",
... | false |
_private.Mathlib.Geometry.Manifold.Riemannian.Basic.0.setOf_riemannianEDist_lt_subset_nhds._simp_1_2 | Mathlib.Geometry.Manifold.Riemannian.Basic | [
"GT.gt",
"LT.lt",
"gt_iff_lt",
"propext",
"Eq",
"LT"
] | false |
Filter.mem_comk._simp_1 | Mathlib.Order.Filter.Defs | [
"Filter.instMembership",
"Compl.compl",
"Filter.mem_comk",
"Membership.mem",
"Set.instUnion",
"HasSubset.Subset",
"Set.instCompl",
"propext",
"Set.instEmptyCollection",
"Union.union",
"EmptyCollection.emptyCollection",
"Eq",
"Filter.comk",
"Filter",
"Set.instHasSubset",
"Set"
] | false |
exists_dist_le_lt | Mathlib.Analysis.Normed.Module.Ball.Pointwise | [
"Real.instIsOrderedRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
"instHDiv",
"SeminormedAddCommGroup",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"DivisionCom... | true |
Std.Do.SPred.bientails.eq_2 | Std.Do.SPred.Laws | [
"Std.Do.SPred.bientails",
"List.cons",
"List",
"Std.Do.SPred",
"Eq.refl",
"Eq"
] | true |
Lean.Meta.SimpTheorems.mk.injEq | Lean.Meta.Tactic.Simp.SimpTheorems | [
"Eq.propIntro",
"Lean.PHashMap",
"Lean.Meta.instHashableOrigin",
"Lean.injEq_helper",
"Lean.Meta.instBEqOrigin",
"Lean.PHashSet",
"Array",
"Lean.Meta.SimpTheoremTree",
"And",
"Lean.Meta.SimpTheorems",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Lean.Meta.SimpTheorems.mk.inj",
"Lean.Meta.Origin"... | true |
MvQPF.Fix.rec_unique | Mathlib.Data.QPF.Multivariate.Constructions.Fix | [
"Eq.mpr",
"congrArg",
"MvQPF.Fix.mk",
"id",
"TypeVec.append1",
"instOfNatNat",
"MvQPF.Fix.ind_rec",
"MvQPF.toMvFunctor",
"funext",
"instHAdd",
"MvQPF.Fix",
"HAdd.hAdd",
"Nat",
"TypeVec.appendFun",
"instAddNat",
"Eq.refl",
"MvQPF",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"MvFunctor.ma... | true |
_private.Aesop.Tree.ExtractProof.0.Aesop.SafePrefixState.recOn | Aesop.Tree.ExtractProof | [
"Lean.MVarId",
"_private.Aesop.Tree.ExtractProof.0.Aesop.SafePrefixState.rec",
"Array",
"_private.Aesop.Tree.ExtractProof.0.Aesop.SafePrefixState",
"_private.Aesop.Tree.ExtractProof.0.Aesop.SafePrefixState.mk"
] | false |
_private.Init.Data.Iterators.Lemmas.Consumers.Access.0.Std.Iter.atIdxSlow?_eq_match.match_1.eq_1 | Init.Data.Iterators.Lemmas.Consumers.Access | [
"Unit.unit",
"Std.Iter.atIdxSlow?_eq_match.match_1",
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
Rat.lt_sub_right_iff_add_lt | Init.Data.Rat.Lemmas | [
"Rat.instSub",
"Eq.mpr",
"congrArg",
"Rat",
"HSub.hSub",
"Eq.rec",
"id",
"Rat.sub_add_cancel",
"iff_self",
"instHAdd",
"Iff",
"instHSub",
"HAdd.hAdd",
"LT.lt",
"True",
"propext",
"Rat.instAdd",
"of_eq_true",
"Rat.instLT",
"Eq.refl",
"congrFun'",
"Eq.symm",
"Eq",
"Rat.ad... | true |
Pi.rightCancelSemigroup._proof_1 | Mathlib.Algebra.Group.Pi.Basic | [
"Semigroup.toMul",
"RightCancelSemigroup.toSemigroup",
"mul_right_cancel",
"IsRightCancelMul.mk",
"Pi.semigroup",
"RightCancelSemigroup",
"Pi.instIsRightCancelMul",
"RightCancelSemigroup.toIsRightCancelMul",
"IsRightCancelMul"
] | false |
_private.Batteries.Data.Array.Scan.0.Array.getElem_scanr._proof_1_4 | Batteries.Data.Array.Scan | [
"False",
"Lean.Grind.nestedProof",
"eq_false",
"List.scanr",
"Array.drop",
"congrArg",
"List.getElem_toArray._proof_1",
"List.getElem_scanr",
"Classical.byContradiction",
"Eq.rec",
"Eq.mp",
"id",
"instOfNatNat",
"Array.extract",
"Array.toList_drop",
"Array.toList",
"List.toArray",
... | false |
omegaLimit_inter | Mathlib.Dynamics.OmegaLimit | [
"omegaLimit",
"omegaLimit_mono_right",
"Set.inter_subset_left",
"HasSubset.Subset",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"Set.subset_inter",
"Filter",
"Set.inter_subset_right",
"Set.instHasSubset",
"Set"
] | true |
Valuation.HasExtension.instIsLocalHomSubtypeMemValuationSubringValuationSubringRingHomAlgebraMap | Mathlib.RingTheory.Valuation.Extension | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"RingHom.instRingHomClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"instIsLocalHomOfMonoidWithZeroHomClassOfNontrivial",
"Algebra.algebraMap",
"outParam",
"CommSemiring.toSemiring",
"Algebra... | true |
_private.Mathlib.Topology.Compactness.DeltaGeneratedSpace.0.DeltaGeneratedSpace.continuous_iff._simp_1_3 | Mathlib.Topology.Compactness.DeltaGeneratedSpace | [
"Sigma.forall",
"propext",
"Sigma.mk",
"Eq",
"Sigma"
] | false |
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