name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
AddMonoid.End.instAddCommGroup._proof_9 | Mathlib.Algebra.Group.Hom.Instances | [
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Int",
"Nat.cast",
"autoParam",
"AddMonoid.End.instAddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"AddMonoidHom.instAddCommGroup._pr... | false |
_private.Mathlib.Topology.CWComplex.Classical.Basic.0.Topology.RelCWComplex.cellFrontier_subset_finite_openCell._simp_1_3 | Mathlib.Topology.CWComplex.Classical.Basic | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
Sat.Literal.pos.noConfusion | Mathlib.Tactic.Sat.FromLRAT | [
"id",
"Sat.Literal.pos",
"Nat",
"Sat.Literal.noConfusion",
"Sat.Literal",
"Eq"
] | false |
Module.Basis.instFunLike._proof_1 | Mathlib.LinearAlgebra.Basis.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"LinearEquiv.symm",
"Semiring.toModule",
"Finsupp.module",
"AddMonoid.toAddZeroClass",
"Finsupp.lhom_ext'",
"AddZeroClass.toAddZero",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Module.Basis.repr",
"LinearMap",
"AddCommMonoid",
"Finsupp.instAddCommMon... | false |
Units.toAut_inv | Mathlib.CategoryTheory.SingleObj | [
"Monoid",
"Units.val",
"MulOne.toOne",
"MulEquiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Monoid.toMulOneClass",
"Units",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"CategoryTheory.SingleObj.star",
"CategoryTheory.End.mul",
"CategoryTheory.End",
"Group.toDivIn... | true |
CategoryTheory.SplitMono.map.eq_1 | Mathlib.CategoryTheory.EpiMono | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SplitMono.mk",
"CategoryTheory.SplitMono.map._proof_1",
"CategoryTheory.SplitMono.map",
"CategoryTheory.Functor.map",
"CategoryTheory.SplitMono.retraction",
"Eq.refl",
"CategoryTheory.Category.toCateg... | true |
Sum.update_inr_apply_inl | Mathlib.Data.Sum.Basic | [
"Sum.inl_ne_inr",
"Function.update",
"Sum",
"Sum.inl",
"Sum.inr",
"Eq",
"DecidableEq",
"Function.update_of_ne"
] | true |
Set.image_const_sub_Ici | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"Set.image_neg_eq_neg",
"Set.Ici",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"sub_eq_add_neg",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Function... | true |
_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.diseqs.inj | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.ParentSet",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.diseqs.noConfusion",
"And",
"Nat",
"And.intro",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.diseqs",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lea... | true |
AdjoinRoot.algEquivOfEq_symm | Mathlib.RingTheory.AdjoinRoot | [
"CommRing",
"AdjoinRoot",
"AlgEquiv.symm",
"CommSemiring.toSemiring",
"Algebra",
"AdjoinRoot.algEquivOfEq",
"Polynomial",
"AdjoinRoot.instAlgebra",
"CommRing.toCommSemiring",
"AlgEquiv",
"AdjoinRoot.instCommRing",
"Eq.symm",
"Eq",
"rfl"
] | true |
_private.Mathlib.NumberTheory.Height.Basic.0.Height.hasFiniteMulSupport_iSup_nonarchAbsVal._proof_1_3 | Mathlib.NumberTheory.Height.Basic | [
"Lean.Grind.eq_false_of_not_eq_true",
"False",
"Lean.Grind.not_not",
"Classical.byContradiction",
"Eq.mp",
"id",
"Subtype",
"Ne",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"True",
"eq_true",
"DivisionSemiring.toSemiring",
"Lean.Grind.intro_with_eq",
"Zero.toOfNat0",
"OfNat.o... | false |
Nat.leRec._proof_1 | Mathlib.Data.Nat.Init | [
"Nat.le_refl",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat",
"OfNat.ofNat"
] | false |
Mathlib.Meta.NormNum.isInt_ratCast | Mathlib.Tactic.NormNum.Inv | [
"Int.cast",
"Rat.cast_intCast",
"DivisionRing.toRatCast",
"congrArg",
"Rat",
"Rat.cast",
"Rat.instDivisionRing",
"DivisionRing.toRing",
"Int",
"AddGroupWithOne.toIntCast",
"Mathlib.Meta.NormNum.IsInt.mk",
"True",
"eq_self",
"of_eq_true",
"DivisionRing",
"congrFun'",
"Mathlib.Meta.Nor... | true |
NonemptyInterval.pure_natCast | Mathlib.Algebra.Order.Interval.Basic | [
"NonemptyInterval.pure",
"Preorder.toLE",
"NatCast",
"Nat.cast",
"Nat",
"NonemptyInterval.instNatCast",
"Eq",
"rfl",
"Preorder",
"NonemptyInterval"
] | true |
MvPolynomial.comp_aeval_apply | Mathlib.Algebra.MvPolynomial.Eval | [
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"MvPolynomial.aeval",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"Algebra",
"Nat.instAddMonoid",
"Function.comp",
"Algebra.id",
"id",
"CommSemirin... | true |
_private.Mathlib.Algebra.Polynomial.HasseDeriv.0.Polynomial.factorial_smul_hasseDeriv._simp_1_2 | Mathlib.Algebra.Polynomial.HasseDeriv | [
"Nat.cast_succ",
"AddMonoid.toAddSemigroup",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"AddMonoidWithOne.toOne",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat",
"One.toOfNat1",
"AddMonoidWithOne.toAddMonoid",
"OfNat.ofNat",
"Eq.symm",
"Nat.succ",
"Eq",
"AddMonoidWithOne"
] | false |
InfHom.instPartialOrder.eq_1 | Mathlib.Order.Hom.Lattice | [
"InfHom.instPartialOrder._proof_1",
"SemilatticeInf.toPartialOrder",
"PartialOrder",
"InfHom",
"SemilatticeInf.toMin",
"Min",
"SemilatticeInf",
"Pi.partialOrder",
"Eq.refl",
"InfHom.instFunLike",
"Eq",
"DFunLike.coe",
"InfHom.instPartialOrder",
"PartialOrder.lift"
] | true |
Std.DTreeMap.Raw.getKey!_eq_of_contains | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Internal.Impl.getKey!_eq_of_contains",
"Ord.mk",
"Ordering",
"Std.TransCmp",
"Std.DTreeMap.Raw.getKey!",
"Bool.true",
"Std.DTreeMap.Raw.WF.out",
"Std.LawfulEqCmp",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Raw.contains",
"Bool",
"Inhabited",
"Eq",
"Std.DTreeMap.Raw.WF",
"Std.... | true |
CompletelyPositiveMap.noConfusion | Mathlib.Analysis.CStarAlgebra.CompletelyPositiveMap | [
"CStarMatrix.instZero",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"CompletelyPositiveMap.noConfusionType",
"HEq.refl",
"CompletelyPositiveMap.casesOn",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"Complex.instNormedField",
"LinearMap.instFunLike",
"NonUnitalNonAssocSemiring.toMulZeroCl... | false |
_private.Mathlib.Algebra.Module.Submodule.Pointwise.0.Submodule.set_smul_eq_iSup._simp_1_2 | Mathlib.Algebra.Module.Submodule.Pointwise | [
"iSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"propext",
"CompleteSemilatticeSup.toSupSet",
"CompleteLattice.toCompleteSemilatticeSup",
"iSup_le_iff",
"CompleteLattice",
"Eq"
] | false |
_private.Mathlib.Data.Finmap.0.Finmap.any._simp_1 | Mathlib.Data.Finmap | [
"imp_true_iff",
"True",
"propext",
"Eq"
] | false |
PerfectClosure.mk_inv | Mathlib.FieldTheory.PerfectClosure | [
"Nat.Prime",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"AddGroupWithOne.toAddMonoidWithOne",
"DivisionMonoid.toDivInvOneMonoid",
"Field.toDivisionRing",
"Fact",
"Prod.mk",
"DivisionRing.toRing",
"Field.toSemifield",
"Field.toCommRing",
"Prod.fst",
"Inv.inv",
"... | true |
_private.Mathlib.Probability.Kernel.IonescuTulcea.Traj.0.ProbabilityTheory.Kernel.condExp_traj'._simp_1_1 | Mathlib.Probability.Kernel.IonescuTulcea.Traj | [
"Preorder.toLE",
"Membership.mem",
"LE.le",
"propext",
"Set.mem_Iic",
"Set.Iic",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | false |
LieSubmodule.subset_lieSpan | Mathlib.Algebra.Lie.Submodule | [
"LieSubmodule.instSetLike",
"Eq.mpr",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieSubmodule",
"Membership.mem",
"AddCommGroup",
"id",
"HasSubset.Subset",
"LieRing",
"CommRing.toCommSemiring",
"SetLike.coe",
"SetLike.mem_coe",
"LieSubmodule.lie... | true |
IsContDiffImplicitAt.apply_implicitFunction | Mathlib.Analysis.Calculus.ImplicitContDiff | [
"ContinuousLinearMap.comp",
"ContDiffAt",
"Prod.normedSpace",
"CompleteSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Filter.Eventually",
"NormedSpace.toModule",
"ContinuousLinearMap.IsInvertible",
"PseudoMetricSpace.toUniformSpace... | true |
CategoryTheory.Monad.ForgetCreatesLimits.liftedConeIsLimit._proof_4 | Mathlib.CategoryTheory.Monad.Limits | [
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Monad",
"CategoryTheory.Functor",
"CategoryTheory.Monad.forget",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Monad.Algebra.Hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Monad.Algebra.a",
"congrArg",
"Ca... | false |
RatFunc.toFractionRingRingEquiv._proof_8 | Mathlib.FieldTheory.RatFunc.Basic | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"FractionRing",
"nonZeroDivisors",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"RatFunc.toFractionRing",
"Polynomial",
"RatFunc.ofFr... | false |
Int.subNatNat_elim | Init.Data.Int.Lemmas | [
"Nat.le_of_sub_eq_zero",
"Eq.mpr",
"congrArg",
"_private.Init.Data.Int.Lemmas.0.Int.subNatNat_elim.match_1_1",
"HSub.hSub",
"Exists",
"Nat.add_sub_cancel_left",
"Eq.mp",
"id",
"Nat.sub_eq_iff_eq_add",
"instSubNat",
"Int.ofNat",
"instOfNatNat",
"Int",
"Nat.le_of_lt",
"Nat.cast",
"inst... | true |
ContinuousLinearMap.toSpanSingleton_inj | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"ContinuousSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddCommM... | true |
ArithmeticFunction.LSeries_mul | Mathlib.NumberTheory.LSeries.Convolution | [
"Preorder.toLT",
"HMul.hMul",
"ArithmeticFunction.instFunLikeNat",
"ArithmeticFunction.instMul",
"PartialOrder.toPreorder",
"ArithmeticFunction.coe_mul",
"EReal",
"Complex.instZero",
"Complex.instMul",
"Eq.rec",
"LSeries.convolution",
"LSeries",
"Complex.re",
"Nat",
"LT.lt",
"Arithmeti... | true |
PFunctor.mk._flat_ctor | Mathlib.Data.PFunctor.Univariate.Basic | [
"PFunctor",
"PFunctor.mk"
] | false |
DirectSum.GradeZero.ring._proof_2 | Mathlib.Algebra.DirectSum.Ring | [
"AddMonoidHom.map_zero",
"instAddCommMonoidDirectSum",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddCommGroup",
"AddZero.toZero",
"AddMonoid",
"DirectSum.of",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"AddMonoidHom",
"AddMonoidHom.instFunLike"... | false |
Std.Http.Header.ContentLength.mk._flat_ctor | Std.Internal.Http.Data.Headers.Basic | [
"Std.Http.Header.ContentLength",
"Nat",
"Std.Http.Header.ContentLength.mk"
] | false |
Lean.HeadIndex.sort | Lean.HeadIndex | [
"Lean.HeadIndex.sort",
"Lean.HeadIndex"
] | true |
_private.Mathlib.Topology.Constructions.SumProd.0.isClosed_sum_iff._simp_1_1 | Mathlib.Topology.Constructions.SumProd | [
"Compl.compl",
"Set.instCompl",
"IsClosed",
"TopologicalSpace",
"propext",
"IsOpen",
"Eq.symm",
"Eq",
"isOpen_compl_iff",
"Set"
] | false |
mdifferentiableWithinAt_comp_projIcc_iff | Mathlib.Geometry.Manifold.Instances.Icc | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"WithTop.charZero",
"Real",
"PiLp.normedSpace",
"fact_one_le_two_ennreal",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"chartedSpaceSelf",
"ContMDiffAt.mdifferentiableAt",
"NormedSpace",
"mdifferentiableW... | true |
QuadraticMap.polar_smul_left_of_tower | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"Eq.mpr",
"CommRing",
"instHSMul",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"AddCommGroup.toAddGroup",
"RingHom",
"Algebra.toSMul",
"AddZeroClass.... | true |
NumberField.dedekindZeta_residue_pos | Mathlib.NumberTheory.NumberField.DedekindZeta | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Real.instIsOrderedRing",
"Int.cast",
"NonAssocSemiring.toAddCommMonoidWithOne",
"pow_pos",
"Real.partialOrder",
"Real",
"NumberField.Units.torsionOrder_pos",
"Preorder.toLT",
"Nat.cast_pos",
"Real.pi",
"HMul.hMul",
"Real.lattice",
"MulZeroClass... | true |
Std.DHashMap.Const.isEmpty_of_isEmpty_insertManyIfNewUnit | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.Const.insertManyIfNewUnit",
"Std.DHashMap.Raw",
"Std.DHashMap.wf",
"instOfNatNat",
"Id",
"LawfulHashable",
"Subtype.mk",
"Bool.true",
"Unit",
"EquivBEq",
"Std.DHashMap.inner",
"ForIn",
"Nat",
"Std.DHashMap.Raw.buckets",
"Std.DHashMap.Internal.Raw₀.Const.isEmpty_of_isEmpty_i... | true |
EStateM.run_throw | Init.Control.Lawful.Instances | [
"instMonadExceptOfMonadExceptOf",
"EStateM.Result",
"MonadExcept.throw",
"EStateM.run",
"PUnit",
"EStateM.instMonadExceptOfOfBacktrackable",
"EStateM",
"EStateM.Result.error",
"Eq",
"rfl",
"EStateM.nonBacktrackable"
] | true |
ConvexBody.ext_iff | Mathlib.Analysis.Convex.Body | [
"Real",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Real.semiring",
"Eq.casesOn",
"DistribSMul.toSMulZeroClass",
"ConvexBody.ext",
"Real.instMonoid",
"Topolog... | true |
Equiv.swapCore_self | Mathlib.Logic.Equiv.Basic | [
"Equiv.swapCore",
"Eq.mpr",
"congrArg",
"id",
"if_pos",
"dite",
"True",
"eq_self",
"of_eq_true",
"Eq.refl",
"congrFun'",
"ite_congr",
"Eq",
"if_neg",
"Not",
"Eq.trans",
"DecidableEq",
"ite"
] | true |
_private.Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Relations.0.RootPairing.GeckConstruction.lie_e_f_ne._simp_1_1 | Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Relations | [
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"SubNegMonoid",
"AddZeroClass.toAddZero",
"SubNegMonoid.toSub",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"SubNegMonoid.toNeg",
"AddZero.toAdd",
"SubNegMonoid.toAddMonoid",
"Eq.symm",
"Eq",
"Neg.neg"
] | false |
Lean.Elab.Tactic.instInhabitedState | Lean.Elab.Term.TermElabM | [
"Lean.Elab.Tactic.instInhabitedState.default",
"Inhabited",
"Lean.Elab.Tactic.State",
"Inhabited.mk"
] | true |
_private.Mathlib.Data.Finset.Card.0.Finset.card_insert_le._proof_1_1 | Mathlib.Data.Finset.Card | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"eq_false",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Finset",
"Finset.card_le_card",
"Classical.byContradiction",
"Pa... | false |
Affine.Simplex.centroidWeightsWithCircumcenter.eq_2 | Mathlib.Geometry.Euclidean.Circumcenter | [
"Real",
"Real.instZero",
"Finset",
"Affine.Simplex.centroidWeightsWithCircumcenter",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Zero.toOfNat0",
"Eq.refl",
"OfNat.ofNat",
"Fin",
"Affine.Simplex.PointsWithCircumcenterIndex.circumcenterIndex",
"Eq"
] | true |
IsPreconnected.eq_or_eq_neg_of_sq_eq | Mathlib.Topology.Algebra.Field | [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"IsDomain.to_noZeroDivisors",
"Pi.instNeg",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"HMul.hMul",
"Field.isDomain",
"GroupWithZero.toDivInvMonoid",
"Co... | true |
CategoryTheory.SimplicialObject.Augmented.whiskering._proof_3 | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.constComp",
"congrArg",
"CategoryTheory.SimplicialObject.const",
"CategoryTheory.SimplicialObject.Augmented.point",
"CategoryTheory.Functor.category",... | false |
Lean.Grind.instLEUSizeUintNumBits | Init.GrindInstances.ToInt | [
"Eq.mpr",
"Lean.Grind.ToInt.toInt",
"congrArg",
"Int.ofNat_le._simp_1",
"instLEUSize",
"USize.le_iff_toBitVec_le",
"Lean.Grind.ToInt.LE",
"Lean.Grind.ToInt.LE.mk",
"id",
"Lean.Grind.IntInterval.uint",
"Int",
"LE.le",
"instLENat",
"System.Platform.numBits",
"Iff",
"USize.toNat",
"Lean... | true |
AbsoluteValue._sizeOf_1 | Mathlib.Algebra.Order.AbsoluteValue.Basic | [
"MulHom",
"MulHom._sizeOf_inst",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Distrib.toAdd",
"instOfNatNat",
"LE.le",
"instDistribOfSemiring",
"instHAdd",
"MulHom.toFun",
"Iff",
"Distrib.toMul",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Semiring",
"instAddNat",
"Zero... | false |
String.Pos.Raw.offsetBy_sliceRawEndPos_left | Init.Data.String.Defs | [
"congrArg",
"String.Slice.byteIdx_rawEndPos",
"String.Slice.rawEndPos",
"String.Slice",
"_private.Init.Data.String.Defs.0.String.Pos.Raw.offsetBy_sliceRawEndPos_left._simp_1_1",
"String.Slice.utf8ByteSize",
"String.Pos.Raw",
"String.Pos.Raw.byteIdx_offsetBy",
"String.instHAddRawSlice",
"instHAdd",... | true |
HasDerivWithinAt.lhopital_zero_nhdsWithin_convex | Mathlib.Analysis.Calculus.LHopital | [
"Filter.instMembership",
"Iff.mpr",
"Eq.mpr",
"Convex.nhdsWithin_diff_eq_nhdsNE",
"NormedCommRing.toSeminormedCommRing",
"Set.diff_subset",
"Real.partialOrder",
"Real",
"Set.Ioi",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"NormedSpac... | true |
_private.Mathlib.NumberTheory.ArithmeticFunction.Misc.0.ArithmeticFunction.sum_Ioc_mul_eq_sum_sum._simp_1_2 | Mathlib.NumberTheory.ArithmeticFunction.Misc | [
"Finset",
"Membership.mem",
"And",
"Finset.instSetLike",
"DecidablePred",
"propext",
"Finset.mem_filter",
"Finset.filter",
"Eq",
"SetLike.instMembership"
] | false |
_private.Lean.Linter.UnusedSimpArgs.0.Lean.Linter.unusedSimpArgs.match_4 | Lean.Linter.UnusedSimpArgs | [
"Lean.Syntax.Range",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Lean.Linter.UnusedSimpArgs.0.Lean.Linter.unusedSimpArgs._sparseCasesOn_1",
"Option"
] | false |
CategoryTheory.instAdditiveObjFunctorAdditiveFunctor | Mathlib.CategoryTheory.Preadditive.AdditiveFunctor | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryTheory.ObjectProperty.FullSubcategory.property",
"CategoryTheory.additiveFunctor",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.Preadditive",
"CategoryTheory.Category",
"C... | true |
_private.Mathlib.Combinatorics.SimpleGraph.StronglyRegular.0.SimpleGraph.IsSRGWith.param_eq._simp_1_8 | Mathlib.Combinatorics.SimpleGraph.StronglyRegular | [
"Ne.eq_def",
"Ne",
"Eq.symm",
"Eq",
"Not"
] | false |
Aesop.CasesTarget.patterns | Aesop.RuleTac.Basic | [
"Aesop.CasesTarget.patterns",
"Array",
"Aesop.CasesPattern",
"Aesop.CasesTarget"
] | true |
Lean.Parser.Command.tactic_extension | Lean.Parser.Command | [
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.leadingNode",
"Lean.Parser.optional",
"instHAndThenOfAndThen",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.Command.docComment",
"Lean.Parser.withAntiquot",
"Bool.true",
"Unit",
"Nat",
"Lean.Parser.ppLine",
"Lean.Parser.ident",
... | true |
Stream'.Seq.zipWith_map_right | Mathlib.Data.Seq.Basic | [
"Eq.mpr",
"Stream'.Seq",
"Stream'.Seq.zipWith",
"Stream'.Seq.map_id",
"congrArg",
"HEq.refl",
"Stream'.Seq.map",
"Eq.casesOn",
"id",
"funext",
"True",
"eq_self",
"of_eq_true",
"eq_of_heq",
"Eq.ndrec",
"Stream'.Seq.zipWith_map",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"Eq.trans"
] | true |
_private.Init.Data.List.Erase.0.List.filterMap.match_1.eq_1 | Init.Data.List.Erase | [
"Unit.unit",
"Option.some",
"List.filterMap.match_1",
"Option.none",
"Unit",
"Eq.refl",
"Eq",
"Option"
] | true |
LinearMap.tracePositiveLinearMap._proof_1 | Mathlib.Analysis.InnerProductSpace.Positive | [
"InnerProductSpace.toNormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"Field.toSemifield",
"Field.toCommRing",
"smulCommClass_self",
"RCLike.toDenselyNormedField",
"RCLike",
"Semifield.toDivisionSemiring",
"CommMonoid.toMonoid",
"Monoid.toSemigroup",... | false |
Lean.Meta.Sym.ProofInstArgInfo.noConfusion | Lean.Meta.Sym.SymM | [
"Lean.Meta.Sym.ProofInstArgInfo.casesOn",
"Lean.Meta.Sym.ProofInstArgInfo",
"Lean.Meta.Sym.ProofInstArgInfo.noConfusionType",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | false |
OrderIso.dualAntisymmetrization._proof_6 | Mathlib.Order.Antisymmetrization | [
"OrderDual.instLE",
"AntisymmRel.setoid",
"OrderIso.dualAntisymmetrization._proof_4",
"Preorder.toLE",
"Quotient.inductionOn'",
"id",
"OrderIso.dualAntisymmetrization._proof_5",
"LE.le",
"Antisymmetrization",
"instIsPreorderLe",
"OrderIso.dualAntisymmetrization._proof_1",
"Quotient.map'",
"O... | false |
RingHom.ENatMap._proof_1 | Mathlib.Data.ENat.Basic | [
"Nontrivial",
"MulOne.toOne",
"WithTop.instMulZeroOneClass",
"ZeroHom.toFun",
"CommSemiring.toSemiring",
"RingHom.toMonoidWithZeroHom",
"MonoidWithZeroHom.toZeroHom",
"RingHom",
"NonAssocSemiring.toMulZeroOneClass",
"MonoidWithZeroHom.map_one'",
"Nat.instNonAssocSemiring",
"MulZeroOneClass.toM... | false |
CompactExhaustion.iUnion_eq | Mathlib.Topology.Compactness.SigmaCompact | [
"Set.univ",
"TopologicalSpace",
"Nat",
"CompactExhaustion",
"CompactExhaustion.instFunLikeNatSet",
"Eq",
"DFunLike.coe",
"Set.iUnion",
"CompactExhaustion.iUnion_eq'",
"Set"
] | true |
MeasureTheory.measureReal_diff._auto_1 | Mathlib.MeasureTheory.Measure.Real | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
SimpleGraph.Walk.getVert_eq_support_getElem? | Mathlib.Combinatorics.SimpleGraph.Walk.Traversal | [
"Eq.mpr",
"congrArg",
"SimpleGraph.Walk.length",
"List.instGetElem?NatLtLength",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Option.some",
"SimpleGraph.Walk.length_support",
"Eq.rec",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"SimpleGraph.Walk.getVert_eq_support_getElem",
"Nat.lt_... | true |
Metric.ediam_pos_iff' | Mathlib.Topology.EMetricSpace.Diam | [
"Preorder.toLT",
"_private.Mathlib.Topology.EMetricSpace.Diam.0.Metric.ediam_pos_iff'._simp_1_1",
"congrArg",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"EMetricSpace.toPseudoEMetricSpace",
"Ne",
"EMetricSpace",
"iff_self",
"Metric.ediam",
"And",
"Iff",
"LT.lt",
"True",
"EN... | true |
Std.ExtDHashMap.get?_eq_none_of_contains_eq_false | Std.Data.ExtDHashMap.Lemmas | [
"Std.DHashMap.get?_eq_none_of_contains_eq_false",
"instLawfulHashableOfLawfulBEq",
"LawfulBEq",
"Std.ExtDHashMap.contains",
"Std.ExtDHashMap.inductionOn",
"Option.none",
"Std.ExtDHashMap",
"Bool",
"Hashable",
"instEquivBEqOfLawfulBEq",
"Bool.false",
"BEq",
"Eq",
"Std.DHashMap",
"Option",... | true |
Pi.distrib | Mathlib.Algebra.Ring.Pi | [
"Pi.distrib._proof_2",
"Distrib.toAdd",
"Pi.instAdd",
"Distrib.toMul",
"Distrib",
"Pi.distrib._proof_1",
"Pi.instMul",
"Distrib.mk"
] | true |
Subsemiring.mem_unop | Mathlib.Algebra.Ring.Subsemiring.MulOpposite | [
"Subsemiring.instSetLike",
"Iff.rfl",
"MulOpposite",
"Membership.mem",
"Subsemiring",
"Iff",
"NonAssocSemiring",
"Subsemiring.unop",
"SetLike.instMembership",
"MulOpposite.instNonAssocSemiring",
"MulOpposite.op"
] | true |
LieAlgebra.Extension.casesOn | Mathlib.Algebra.Lie.Extension | [
"LieHom",
"CommRing",
"LieAlgebra.Extension",
"LieAlgebra.Extension.rec",
"LieRing",
"LieAlgebra.IsExtension",
"LieAlgebra",
"LieAlgebra.Extension.mk"
] | false |
SSet.Truncated.HomotopyCategory.homToNerveMk_app_edge | Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | [
"SSet.Truncated.Edge",
"Eq.mpr",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"SSet.Truncated.Edge._proof_2",
"SSet.Truncated.Edge.edge",
"Quiver.Hom.op",
"... | true |
PFunctor.M.IsPath.cons | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"PFunctor.A",
"PFunctor.M",
"PFunctor.B",
"PFunctor.Approx.Path",
"List.cons",
"PFunctor.M.IsPath",
"Sigma.mk",
"PFunctor.Idx",
"Eq",
"PFunctor.M.IsPath.cons",
"PFunctor.M.mk"
] | true |
Std.ExtDHashMap.Const.size_alter_le_size | Std.Data.ExtDHashMap.Lemmas | [
"Std.DHashMap.Const.size_alter_le_size",
"Std.ExtDHashMap.Const.alter",
"Std.ExtDHashMap.inductionOn",
"instOfNatNat",
"LE.le",
"instLENat",
"LawfulHashable",
"instHAdd",
"EquivBEq",
"HAdd.hAdd",
"Std.ExtDHashMap.size",
"Nat",
"Std.ExtDHashMap",
"instAddNat",
"Hashable",
"OfNat.ofNat",... | true |
RingEquiv.map_sub | Mathlib.Algebra.Ring.Equiv | [
"NonUnitalNonAssocRing",
"map_sub",
"RingEquivClass.toNonUnitalRingHomClass",
"RingEquiv.instEquivLike",
"NonUnitalNonAssocRing.toAddCommGroup",
"RingEquiv.instRingEquivClass",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Subtract... | true |
Std.Internal.List.getKey?_filter_containsKey_of_containsKey_right | Std.Data.Internal.List.Associative | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"congrArg",
"Std.Internal.List.getKey?_filter_containsKey",
"id",
"instDecidableEqBool",
"Sigma.fst",
"ite_cond_eq_true",
"Bool.true",
"Option.none",
"List",
"Std.Internal.List.containsKey",
"EquivBEq",
"List.filter",
"True",
"eq_self",
"Bo... | true |
HomotopicalAlgebra.Precylinder.LeftHomotopy.refl._proof_2 | Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HomotopicalAlgebra.Precylinder.I",
"HomotopicalAlgebra.Precylinder.π",
"HomotopicalAlgebra.Precylinder",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"CategoryTheory.Category.toCategoryStruct",
"cong... | false |
CategoryTheory.yoneda_preservesLimits | Mathlib.CategoryTheory.Limits.Yoneda | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.PreservesLimitsOfSize.mk",
"CategoryTheory.yoneda",
"inferInstance",
"CategoryTheory.yoneda_preservesLimitsOfShape",
"CategoryTheory.types",
"CategoryTheory.Limits.PreservesLimitsOfSize",
"CategoryTheor... | true |
ZFSet.mem_pairSep._simp_1 | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"Membership.mem",
"Exists",
"ZFSet.mem_pairSep",
"ZFSet.pairSep",
"And",
"ZFSet.pair",
"propext",
"Eq",
"ZFSet.instSetLike",
"SetLike.instMembership"
] | false |
Finpartition.mem_part_self | Mathlib.Order.Partition.Finpartition | [
"dite_cond_eq_true",
"Iff.mpr",
"False",
"eq_false",
"congrArg",
"Finset",
"Finset.choose",
"Finpartition.part",
"Finpartition.part_eq_empty",
"Membership.mem",
"Finpartition.parts",
"Finset.instEmptyCollection",
"dite",
"iff_self",
"Iff",
"Finset.notMem_empty._simp_1",
"Finset.instS... | true |
AddUnits.recOn | Mathlib.Algebra.Group.Units.Defs | [
"AddMonoid.toAddSemigroup",
"AddUnits.rec",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"AddMonoid",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"AddUnits",
"AddUnits.mk"
] | false |
SimplexCategory.Truncated.δ₂_one_comp_σ₂_zero._auto_3 | Mathlib.AlgebraicTopology.SimplexCategory.Truncated | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.Topology.UniformSpace.Cauchy.0.Filter.totallyBounded_iSup._simp_1_1 | Mathlib.Topology.UniformSpace.Cauchy | [
"Filter.instMembership",
"Filter.le_principal_iff",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"propext",
"Filter.principal",
"Eq.symm",
"Eq",
"Filter",
"Filter.instPartialOrder",
"Set"
] | false |
Homeomorph.sumArrowHomeomorphProdArrow._proof_4 | Mathlib.Topology.Homeomorph.Lemmas | [
"Continuous.comp'",
"Continuous",
"Pi.topologicalSpace",
"instTopologicalSpaceProd",
"continuous_fst",
"Sum",
"Sum.inl",
"Prod.fst",
"TopologicalSpace",
"continuous_apply",
"Prod",
"Equiv.invFun",
"Equiv.sumArrowEquivProdArrow"
] | false |
CategoryTheory.Functor.ext_of_iso | Mathlib.CategoryTheory.EqToHom | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.ext",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.Iso",
... | true |
CategoryTheory.ReflQuiv.isoOfQuivIso._proof_1 | Mathlib.CategoryTheory.Category.ReflQuiv | [
"Equiv.instEquivLike",
"CategoryTheory.Quiv.str'",
"CategoryTheory.ReflQuiver.homOfEq_id",
"CategoryTheory.Quiv.hom_map_inv_map_of_iso._proof_1",
"Quiver.Hom",
"congrArg",
"Quiver.homOfEq",
"CategoryTheory.Quiv.of",
"CategoryTheory.Quiv.homEquivOfIso",
"Equiv",
"CategoryTheory.Iso",
"CategoryT... | false |
_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.subset_union_prime._simp_1_1 | Mathlib.RingTheory.Ideal.Operations | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
MeasureTheory.OuterMeasure.comap_iInf | Mathlib.MeasureTheory.OuterMeasure.OfFunction | [
"Eq.mpr",
"_private.Mathlib.MeasureTheory.OuterMeasure.OfFunction.0.MeasureTheory.OuterMeasure.comap_iInf._simp_1_2",
"iInf",
"ENNReal.tsum_le_tsum",
"Semiring.toModule",
"IsScalarTower.right",
"ENNReal.instAddCommMonoid",
"Iff.of_eq",
"congrArg",
"CommSemiring.toSemiring",
"MeasureTheory.OuterM... | true |
Configuration.HasLines.toNondegenerate | Mathlib.Combinatorics.Configuration | [
"Membership",
"Configuration.Nondegenerate",
"Configuration.HasLines"
] | true |
CategoryTheory.uliftCategory._proof_4 | Mathlib.CategoryTheory.Category.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ULift",
"CategoryTheory.CategoryStruct.id",
"_private.Mathlib.CategoryTheory.Category.Basic.0.CategoryTheory.uliftCategory._proof_3",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"ULift.down",
"Cate... | false |
_private.Mathlib.Probability.Distributions.Gaussian.Real.0.ProbabilityTheory.integrable_gaussianPDFReal._simp_1_12 | Mathlib.Probability.Distributions.Gaussian.Real | [
"False",
"HMul.hMul",
"eq_false",
"Mul",
"Ne",
"NoZeroDivisors",
"Zero.toOfNat0",
"mul_ne_zero",
"OfNat.ofNat",
"Eq",
"instHMul",
"Zero"
] | false |
CompHausLike.LocallyConstant.counitApp.eq_1 | Mathlib.Condensed.Discrete.Colimit | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompHausLike.HasExplicitFiniteCoproducts",
"instMetricSpacePUnit",
"instIndiscreteTopologyPUnit",
"EMetricSpace.metrizableSpace",
"CategoryTheory.Functor.category",
"CompHausLike.LocallyConstant.counitAp... | true |
_private.Lean.Elab.Term.TermElabM.0.Lean.Elab.Term.synthesizeInstMVarCore._sparseCasesOn_4 | Lean.Elab.Term.TermElabM | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
PolynomialLaw.instSMul | Mathlib.RingTheory.PolynomialLaw.Basic | [
"CommSemiring.toSemiring",
"SMul",
"PolynomialLaw",
"SMul.mk",
"AddCommMonoid",
"CommSemiring",
"PolynomialLaw.smul",
"Module"
] | true |
Subfield.relrank_eq_of_inf_eq | Mathlib.FieldTheory.Relrank | [
"SetLike",
"NonUnitalNonAssocRing",
"Subfield.toDivisionRing",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Subfield.relrank",
"Subfield.toAlgebra",
"Semiring.toModule",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"Subfield.relrank._proof_1",
"outParam",
"Cardinal",
"... | true |
TannakaDuality.FiniteGroup.rightFDRep._proof_1 | Mathlib.RepresentationTheory.Tannaka | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Finite",
"Pi.module",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Module.Finite... | false |
Std.TreeMap.Equiv.maxKey_eq | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.Equiv",
"Std.TreeMap.Equiv.isEmpty_eq",
"Std.TreeMap.Equiv.inner",
"Std.TreeMap.inner",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.isEmpty",
"Std.TreeMap.maxKey",
"Bool",
"Std.DTreeMap.Equiv.maxKey_eq",
"Eq.symm",
"Bool.false",
"Eq",
"Std.TreeMap",
"Eq.trans"
] | true |
String.Slice.toNat?_eq_none_iff | Std.Data.String.ToNat | [
"Option.isNone",
"String.Slice.toNat?",
"Bool.not",
"congrArg",
"_private.Std.Data.String.ToNat.0.String.Slice.toNat?_eq_none_iff._simp_1_1",
"String.Slice",
"String.Slice.isSome_toNat?",
"_private.Std.Data.String.ToNat.0.String.Slice.toNat?_eq_none_iff._simp_1_2",
"iff_self",
"Bool.true",
"Opti... | true |
Matrix.instLieRingToLieAlgebra._proof_27 | Mathlib.Algebra.Lie.SerreConstruction | [
"LieAlgebra.toModule",
"Matrix.instLieRingToLieAlgebra._proof_16",
"CommRing",
"Matrix.instLieRingToLieAlgebra._aux_12",
"FreeLieAlgebra.instLieRing",
"AddMonoid.toAddSemigroup",
"LieRing.toAddCommGroup",
"Matrix",
"SubNegMonoid.mk",
"Add.mk",
"Neg.mk",
"Matrix.instLieRingToLieAlgebra._proof_2... | false |
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