name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Subgroup.Normal.conj_smul_eq_self | Mathlib.Algebra.Group.Subgroup.Pointwise | [
"instHSMul",
"MonoidHom.instFunLike",
"MulAut.applyMulDistribMulAction",
"MonoidHom",
"Monoid.toMulOneClass",
"Subgroup.Normal.conjAct",
"MulAut.instGroup",
"Group",
"MulAut",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Subgroup",
"MulAut.conj",
"Group.toDivInvMonoid",
"MulOneClass.toMulOn... | true |
_private.Init.Data.Nat.SOM.0.Nat.SOM.Mon.mul.go.match_1.eq_2 | Init.Data.Nat.SOM | [
"False",
"_private.Init.Data.Nat.SOM.0.Nat.SOM.Mon.mul.go.match_1",
"id",
"List.rec",
"List.cons",
"Nat.SOM.Mon",
"List",
"Nat.Linear.Var",
"absurd",
"List.casesOn",
"Eq.refl",
"Eq",
"List.nil"
] | true |
AlgebraicGeometry.specTargetImageFactorization._proof_1 | Mathlib.AlgebraicGeometry.AffineScheme | [
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"Semiring.toModule",
"le_rfl",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"CommRingCat",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Submodule.instPartialOrder",
"LE.le",
"... | false |
_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.tendsto_nhds_top_iff_real._simp_1_1 | Mathlib.Topology.Instances.EReal.Lemmas | [
"Set.Ioi",
"Preorder.toLT",
"Membership.mem",
"Set.mem_Ioi",
"LT.lt",
"propext",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | false |
Real.sinOrderIso._proof_1 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Real",
"instHDiv",
"Real.pi",
"Real.instDivInvMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"HDiv.hDiv",
"instOfNatNat",
"Set.BijOn.image_eq",
"Real.instOne",
"Real.bijOn_sin",
"Real.pi._proof_1",
"Set.Icc",
"Nat.instNeZeroSucc",
"Nat",
"Real.instNeg",
"DivInvMonoid.toDiv",
"One.toOfNat1"... | false |
UInt8.not_le | Init.Data.UInt.Lemmas | [
"UInt8.le_iff_toBitVec_le._simp_1",
"congrArg",
"BitVec",
"UInt8.lt_iff_toBitVec_lt._simp_1",
"instLTUInt8",
"instOfNatNat",
"LE.le",
"UInt8.toBitVec",
"iff_self",
"Iff",
"instLTBitVec",
"Nat",
"congr",
"LT.lt",
"True",
"of_eq_true",
"instLEBitVec",
"OfNat.ofNat",
"UInt8",
"Bit... | true |
Std.BundledIterM.Equiv._proof_1 | Std.Data.Iterators.Lemmas.Equivalence.Basic | [
"Std.BundledIterM.step",
"Std.IterStep",
"Lean.Order.instCompleteLatticePi",
"Std.Iterators.HetT.comp_map",
"congrArg",
"_private.Std.Data.Iterators.Lemmas.Equivalence.Basic.0.Std.quotOfQuot",
"Lean.Order.ReverseImplicationOrder",
"Monad.toApplicative",
"Std.BundledIterM.iterator",
"Std.IterStep.m... | false |
RestrictedProduct.mk.congr_simp | Mathlib.Topology.Algebra.RestrictedProduct.Units | [
"Filter.Eventually",
"Membership.mem",
"Eq.rec",
"RestrictedProduct.mk",
"RestrictedProduct",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Set.instMembership",
"Filter",
"Set"
] | true |
Matrix.toMatrix₂Aux_toLinearMap₂'Aux | Mathlib.LinearAlgebra.Matrix.SesquilinearForm | [
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"Pi.addCommMonoid",
"Matrix.module",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Matrix",
"LinearMap.instSMulCommClass",
"Matrix.toLinearMap₂'Aux_single",
"AddMonoid.toAddZeroCla... | true |
LowerSet.prod_self_lt_prod_self._simp_1 | Mathlib.Order.UpperLower.Prod | [
"Preorder.toLT",
"LowerSet.prod_self_lt_prod_self",
"Prod.instLE_mathlib",
"SProd.sprod",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LowerSet.instPartialOrder",
"LT.lt",
"propext",
"Prod",
"LowerSet",
"Eq",
"LowerSet.instSProd",
"Preorder"
] | false |
Lean.Meta.Grind.Methods.evalTactic | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.EvalTactic",
"Lean.Meta.Grind.Methods"
] | true |
_private.Mathlib.Algebra.Homology.ExactSequenceFour.0.CategoryTheory.ComposableArrows.IsComplex.cokerToKer'._proof_3 | Mathlib.Algebra.Homology.ExactSequenceFour | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.ev... | false |
Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_top | Mathlib.RingTheory.Polynomial.Ideal | [
"Subalgebra.instSetLike",
"Iff.mpr",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Polynomial.instOne",
"Semigroup.toMul",
"Ideal.one_eq_top",
"CommRing",
"Dvd.dvd",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule"... | true |
ULift.semiring._proof_9 | Mathlib.Algebra.Ring.ULift | [
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"ULift",
"NonUnitalNonAssocSemiring.toMul",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"ULift.nonUnitalSemiring",
"HAdd.hAdd",
"NonUnitalNonAssocSemiring.right_distrib",
... | false |
OrderedFinpartition.extendLeft._proof_14 | Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | [
"Fin.cons_succ",
"OrderedFinpartition.partSize_pos",
"Fin.succ",
"congrArg",
"Fin.cons",
"OrderedFinpartition",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"True",
"OrderedFinpartition.partSize",
"eq_true",
"of_eq_true",
"instAddNat",
"implies_true",
"instLTNat",
"Of... | false |
Lean.Meta.Match.Overlaps.noConfusionType | Lean.Meta.Match.MatcherInfo | [
"Std.TreeSet",
"Lean.Meta.Match.Overlaps",
"Lean.Meta.Match.Overlaps.casesOn",
"Std.HashMap",
"instHashableNat",
"instBEqOfDecidableEq",
"Ord.compare",
"Nat",
"instDecidableEqNat",
"instOrdNat",
"Eq"
] | false |
BoundedContinuousFunction.instModule'._proof_8 | Mathlib.Topology.ContinuousMap.Bounded.Normed | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"BoundedContinuousFunction.ext",
"BoundedContinuousFunction.instModule'._proof... | false |
CategoryTheory.Triangulated.Octahedron.map_m₁ | Mathlib.CategoryTheory.Triangulated.Functor | [
"CategoryTheory.Functor.IsTriangulated",
"CategoryTheory.Functor",
"CategoryTheory.Triangulated.Octahedron",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTheory.Pretriangulated.Triangle.obj₃",
"Cat... | true |
CharacterModule.instModule._proof_5 | Mathlib.Algebra.Module.CharacterModule | [
"Rat.instOfNat",
"DomMulAct",
"ZeroHom.funLike",
"Module.compHom._proof_1",
"CommRing",
"instHSMul",
"Equiv.instEquivLike",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"CharacterModule._proof_1",
"RingHom.toMono... | false |
_private.Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic.0.CategoryTheory.IsPullback.of_iso'._simp_1_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic | [
"CategoryTheory.Iso.comp_inv_eq",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",
"Eq",
"CategoryTheory.Iso.inv",
"CategoryTheory.Category"
] | false |
IsPurelyInseparable.surjective_algebraMap_of_isSeparable | Mathlib.FieldTheory.PurelyInseparable.Basic | [
"CommRing",
"Algebra.IsSeparable.isSeparable",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.IsSeparable",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"DFunLike.coe",
"Ring",
"Function.Surjective",
... | true |
CategoryTheory.Lax.OplaxTrans.homCategory._proof_4 | Mathlib.CategoryTheory.Bicategory.Modification.Lax | [
"CategoryTheory.Lax.OplaxTrans.Hom.as",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Lax.OplaxTrans.instCategoryStructLaxFunctor",
"id",
"CategoryTheory.Lax.OplaxTrans.app",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Category.comp_id",
"Cat... | false |
Lean.Elab.CheckTactic.expandCheckSimp._regBuiltin.Lean.Elab.CheckTactic.expandCheckSimp.declRange_3 | Lean.Elab.CheckTactic | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"IO",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk",
"Lean.Name.mkStr4"
] | false |
Lean.Order.CompleteLattice.casesOn | Init.Internal.Order.Basic | [
"Exists",
"Lean.Order.CompleteLattice.rec",
"Lean.Order.CompleteLattice",
"Lean.Order.PartialOrder",
"Lean.Order.CompleteLattice.mk",
"Lean.Order.is_sup"
] | false |
Matrix.transpose_fromRows | Mathlib.Data.Matrix.ColumnRowPartitioned | [
"Matrix.fromCols",
"Matrix",
"Sum.casesOn",
"Sum",
"Matrix.transpose",
"eq_self",
"Matrix.fromRows",
"of_eq_true",
"Eq",
"Matrix.ext"
] | true |
LinearMap.ofIsCompl_eq_add | Mathlib.LinearAlgebra.Projection | [
"Submodule",
"LinearMap.ext",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Submodule.completeLattice",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Exists",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"m... | true |
RingEquiv.prodProdProdComm._proof_3 | Mathlib.Algebra.Ring.Prod | [
"MulEquiv.prodProdProdComm",
"HMul.hMul",
"Prod.instMul",
"MulEquiv.map_mul'",
"MulOne.toMul",
"MulEquiv.toEquiv",
"NonAssocSemiring.toMulZeroOneClass",
"Equiv.toFun",
"MulZeroOneClass.toMulOneClass",
"MulOneClass.toMulOne",
"NonAssocSemiring",
"Prod",
"Eq",
"instHMul"
] | false |
_private.Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily.0.CategoryTheory.PreZeroHypercoverFamily.mem_precoverage_iff.match_1_1 | Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily | [
"CategoryTheory.Presieve",
"HEq.refl",
"CategoryTheory.PreZeroHypercover.presieve₀",
"CategoryTheory.PreZeroHypercoverFamily.precoverage",
"Membership.mem",
"CategoryTheory.PreZeroHypercoverFamily.presieve.mk",
"CategoryTheory.PreZeroHypercoverFamily.presieve.casesOn",
"CategoryTheory.PreZeroHypercove... | false |
IO.FS.Mode.recOn | Init.System.IO | [
"IO.FS.Mode.readWrite",
"IO.FS.Mode.write",
"IO.FS.Mode",
"IO.FS.Mode.read",
"IO.FS.Mode.append",
"IO.FS.Mode.writeNew",
"IO.FS.Mode.rec"
] | false |
Vector.flatMap_push | Init.Data.Vector.Lemmas | [
"Array.instAppend",
"Vector.push",
"Vector.flatMap_push._proof_1",
"HMul.hMul",
"Vector.mk_eq._simp_1",
"Vector.instHAppendHAddNat",
"Vector",
"Array.push",
"congrArg",
"Vector.push_mk._proof_1",
"Vector.casesOn",
"Eq.rec",
"Array.flatMap",
"instMulNat",
"instOfNatNat",
"Vector.flatMap... | true |
_private.Std.Data.DHashMap.Internal.WF.0.Std.DHashMap.Raw.Internal.foldRev.eq_1 | Std.Data.DHashMap.Internal.WF | [
"Pure.pure",
"Monad.toApplicative",
"Std.DHashMap.Raw",
"Id.run",
"Id",
"Applicative.toPure",
"Std.DHashMap.Raw.Internal.foldRev",
"Std.DHashMap.Raw.Internal.foldRevM",
"Eq.refl",
"Id.instMonad",
"Eq"
] | true |
UInt8.reduceAdd | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | [
"instOfNatNat",
"instAddUInt8",
"instHAdd",
"HAdd.hAdd",
"Nat",
"UInt8.reduceBin._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.781669616._hygCtx._hyg.3",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"UInt8"
] | true |
LocallyConstant.desc | Mathlib.Topology.LocallyConstant.Basic | [
"LocallyConstant.mk",
"Function.comp",
"LocallyConstant",
"TopologicalSpace",
"LocallyConstant.instFunLike",
"Function.Injective",
"LocallyConstant.desc._proof_1",
"Eq",
"DFunLike.coe"
] | true |
DFinsupp.filter.congr_simp | Mathlib.Data.DFinsupp.Defs | [
"instSubsingletonDecidable",
"Decidable",
"Eq.rec",
"Pi.instSubsingleton",
"DecidablePred",
"DFinsupp.filter",
"Eq.ndrec",
"Eq.refl",
"DFinsupp",
"Subsingleton.elim",
"Eq",
"Zero"
] | true |
CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory_leftUnitor_inv_as_app | Mathlib.CategoryTheory.Bicategory.FunctorBicategory.Lax | [
"CategoryTheory.Lax.OplaxTrans.Hom.as",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Lax.OplaxTrans.instCategoryStructLaxFunctor",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Lax.OplaxTrans.app",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFun... | true |
ComplexShape.TensorSigns.casesOn | Mathlib.Algebra.Homology.ComplexShapeSigns | [
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"AddMonoid.toAddSemigroup",
"MonoidHom",
"AddMonoid.toAddZeroClass",
"Units.instNeg",
"Units",
"Multiplicative.mulOneClass",
"ComplexShape.TensorSigns.mk",
"Int",
"ComplexShape",
"Int.in... | false |
CategoryTheory.Subobject.ofLEMk_comp | Mathlib.CategoryTheory.Subobject.Basic | [
"CategoryTheory.Subobject.ofLE_arrow",
"CategoryTheory.Category.assoc",
"CategoryTheory.Subobject.arrow",
"CategoryTheory.Subobject.underlying",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.Subobject.ofLE",
... | true |
_private.Mathlib.Analysis.Normed.Group.Basic.0.enorm'_eq_iff_norm_eq._simp_1_1 | Mathlib.Analysis.Normed.Group.Basic | [
"Norm.norm",
"ENNReal.ofReal",
"ofReal_norm'",
"SeminormedGroup",
"ENorm.enorm",
"SeminormedGroup.toNNNorm",
"SeminormedGroup.toNorm",
"ENNReal",
"NNNorm.toENorm",
"Eq.symm",
"Eq"
] | false |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable.0.EisensteinSeries.tendsto_double_sum_S_act._simp_1_1 | Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | [
"Filter.map",
"Filter.tendsto_map'_iff",
"Function.comp",
"Filter.Tendsto",
"propext",
"Eq",
"Filter"
] | false |
ENat.toENNReal_strictMono | Mathlib.Data.Real.ENatENNReal | [
"StrictMono",
"PartialOrder.toPreorder",
"OrderEmbedding.strictMono",
"instPreorderENat",
"ENat.toENNReal",
"ENat.toENNRealOrderEmbedding",
"ENat",
"ENNReal",
"ENNReal.instPartialOrder"
] | true |
CategoryTheory.CommRingObjCat.instCategory | Mathlib.CategoryTheory.Monoidal.Ring | [
"CategoryTheory.CommRingObjCat.instCategory._proof_3",
"Quiver.mk",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.CommRingObjCat.X",
"CategoryTheory.Category.mk",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoi... | true |
Lean.Elab.Tactic.throwOrLogError | Lean.Elab.Tactic.Basic | [
"Lean.MessageData",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.MonadRef.getRef",
"Lean.Elab.Tactic.Context",
"Lean.Syntax",
"Lean.MonadQuotation.toMonadRef",
"IO.RealWorld",
"StateRefT'.instMonadFunctor",
"ReaderT.instMonadFunctor",
"ReaderT.instMonadLift",
"Lean.Elab.Tactic.instMona... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Basic.0.Equiv.Perm.IsCycle.commute_iff._simp_1_1 | Mathlib.GroupTheory.Perm.Cycle.Basic | [
"DivInvMonoid.toZPow",
"Group",
"Membership.mem",
"Exists",
"Subgroup",
"Int",
"Group.toDivInvMonoid",
"HPow.hPow",
"Subgroup.zpowers",
"propext",
"instHPow",
"Subgroup.mem_zpowers_iff",
"Eq",
"SetLike.instMembership",
"Subgroup.instSetLike"
] | false |
descPochhammer_one | Mathlib.RingTheory.Polynomial.Pochhammer | [
"Polynomial.instOne",
"HMul.hMul",
"congrArg",
"descPochhammer",
"HSub.hSub",
"instOfNatNat",
"Polynomial",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"instHSub",
"Polynomial.one_comp",
"Polynomial.semiring",
"Nat",
"True",
"Polynomial.instSub",
"eq_self",
"of_... | true |
Lean.Meta.Simp.Arith.Int.ToLinear.State.mk.inj | Lean.Meta.Tactic.Simp.Arith.Int.Basic | [
"Lean.Meta.Simp.Arith.Int.ToLinear.State.mk",
"Lean.Expr",
"Array",
"And",
"Nat",
"And.intro",
"Eq",
"Lean.Meta.KExprMap",
"Lean.Meta.Simp.Arith.Int.ToLinear.State",
"Lean.Meta.Simp.Arith.Int.ToLinear.State.mk.noConfusion"
] | true |
_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.lt_find_iff._simp_1_2 | Mathlib.Data.Fin.Tuple.Basic | [
"Exists",
"not_exists",
"propext",
"Eq",
"Not"
] | false |
Set.fintypeUnion._proof_1 | Mathlib.Data.Set.Finite.Basic | [
"Finset.instUnion",
"congrArg",
"Finset",
"Membership.mem",
"Set.instUnion",
"Set.Elem",
"Finset.mem_union._simp_1",
"Set.toFinset",
"iff_self",
"Iff",
"Fintype",
"Finset.instSetLike",
"congr",
"True",
"of_eq_true",
"Or",
"implies_true",
"Set.mem_union._simp_1",
"Union.union",
... | false |
ContinuousAlternatingMap.instNormedSpace | Mathlib.Analysis.Normed.Module.Alternating.Basic | [
"SeminormedAddCommGroup",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousAlternatingMap.instNormedSpace._proof_1",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedField.toField",
... | true |
WithBot.bot_lt_coe | Mathlib.Order.WithBot | [
"False",
"WithBot.some",
"WithBot",
"WithBot.instLT",
"congrArg",
"and_self",
"false_and",
"Exists",
"_private.Mathlib.Order.WithBot.0.WithBot.bot_lt_coe._simp_1_1",
"Bot.bot",
"funext",
"And",
"exists_false._simp_1",
"congr",
"LT.lt",
"True",
"eq_self",
"of_eq_true",
"or_false",... | true |
Lean.Lsp.DiagnosticRelatedInformation.mk.noConfusion | Lean.Data.Lsp.Diagnostics | [
"Lean.Lsp.Location",
"String",
"Lean.Lsp.DiagnosticRelatedInformation",
"Lean.Lsp.DiagnosticRelatedInformation.mk",
"id",
"Lean.Lsp.DiagnosticRelatedInformation.noConfusion",
"Eq"
] | false |
instInhabitedBool.default | Init.Prelude | [
"Bool",
"Bool.false"
] | true |
_private.Mathlib.LinearAlgebra.Matrix.Notation.0.Matrix.delabMatrixNotation._sparseCasesOn_1 | Mathlib.LinearAlgebra.Matrix.Notation | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
WeierstrassCurve.integralModel | Mathlib.AlgebraicGeometry.EllipticCurve.Reduction | [
"CommRing",
"Algebra",
"WeierstrassCurve",
"Field.toSemifield",
"Field.toCommRing",
"CommRing.toCommSemiring",
"Semifield.toDivisionSemiring",
"WeierstrassCurve.baseChange",
"DivisionSemiring.toSemiring",
"Exists.choose",
"WeierstrassCurve.IsIntegral.integral",
"Eq",
"Field",
"WeierstrassC... | true |
_private.Mathlib.MeasureTheory.SetSemiring.0.MeasureTheory.IsSetSemiring.empty_notMem_disjointOfDiffUnion._simp_1_4 | Mathlib.MeasureTheory.SetSemiring | [
"False",
"True",
"propext",
"not_true",
"Eq",
"Not"
] | false |
_private.Std.Time.Date.Unit.Weekday.0.Std.Time.Weekday.toOrdinal.eq_5 | Std.Time.Date.Unit.Weekday | [
"Std.Time.Weekday.friday",
"Std.Time.Weekday.toOrdinal",
"Std.Time.Weekday.Ordinal",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Std.Time.Weekday.instOfNatOrdinal"
] | true |
Int.fib_dvd | Mathlib.Data.Int.Fib.Basic | [
"_private.Mathlib.Data.Int.Fib.Basic.0.Int.fib_natCast_dvd",
"Int.instCommMonoid",
"False",
"Nat.instMulZeroClass",
"Dvd.dvd",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"isUnit_pow_iff._simp_3",
"IsUnit.mul_left_dvd._simp_1",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Nat.instOne",
"... | true |
ZMod.inv | Mathlib.Data.ZMod.Basic | [
"Int.cast",
"ZMod.commRing",
"Int.sign",
"instOfNatNat",
"AddGroupWithOne.toIntCast",
"ZMod",
"ZMod.inv.match_1",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Nat.gcdA",
"instAddNat",
"CommRing.toRing",
"OfNat.ofNat",
"Ring.toAddGroupWithOne",
"ZMod.val"
] | true |
Aesop.instBEqPhaseName.beq | Aesop.Rule.Name | [
"instBEqOfDecidableEq",
"Aesop.PhaseName",
"BEq.beq",
"Nat",
"Bool",
"instDecidableEqNat",
"Aesop.PhaseName.ctorIdx"
] | true |
AbsConvexOpenSets.coe_isOpen | Mathlib.Analysis.LocallyConvex.AbsConvexOpen | [
"SMul",
"AbsConvex",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"PartialOrder",
"AbsConvexOpenSets",
"AddCommMonoid",
"TopologicalSpace",
"AddZero.toZero",
"And",
"And.right",
"And.left",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"IsOpen",
"OfNat.ofNa... | true |
_private.Mathlib.Order.Interval.Set.Disjoint.0.Set.Ioo_disjoint_Ioo._simp_1_2 | Mathlib.Order.Interval.Set.Disjoint | [
"Preorder.toLT",
"LT.lt",
"propext",
"Set.instEmptyCollection",
"DenselyOrdered",
"Set.Ioo_eq_empty_iff",
"EmptyCollection.emptyCollection",
"Eq",
"Not",
"Set.Ioo",
"Preorder",
"Set"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.IsPath.snd_of_toSubgraph_adj._proof_1_7 | Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | [
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"SimpleGraph.Walk.length",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"SimpleGraph.Walk",
"Eq.mp",
"Lean.RArray.b... | false |
_private.Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots.0.IsPrimitiveRoot.card_nthRoots._simp_1_1 | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"Multiset.card_eq_zero",
"Multiset",
"instOfNatNat",
"Nat",
"propext",
"Zero.toOfNat0",
"Multiset.card",
"OfNat.ofNat",
"Eq",
"Multiset.instZero"
] | false |
Lean.Meta.Grind.Arith.Cutsat.SymbolicBound.rec | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Expr",
"Int",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicBound.mk",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicBound",
"Option"
] | false |
Std.TreeSet.isNone_max?_eq_isEmpty | Std.Data.TreeSet.Lemmas | [
"Option.isNone",
"Std.TreeSet",
"Std.TreeSet.max?",
"Std.TreeSet.isEmpty",
"Ordering",
"Std.TreeSet.inner",
"Std.TransCmp",
"Unit",
"Std.TreeMap.isNone_maxKey?_eq_isEmpty",
"Bool",
"Eq"
] | true |
Std.TreeMap.Raw.size_insert | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.contains",
"Std.TreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.size_insert",
"Std.TreeMap.Raw.insert",
"Ordering",
"instDecidableEqBool",
"Std.TreeMap.Raw.size",
"instOfNatNat",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Bool.true",
"instHAd... | true |
Lean.reservedMacroScope | Init.Prelude | [
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | true |
cfcₙ_comp_smul._auto_3 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Std.TreeMap.getKey!_union | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.getKey!",
"Std.TreeMap.inner",
"Ordering",
"Std.DTreeMap.getKey!_union",
"Std.TransCmp",
"Std.TreeMap.getKeyD",
"Inhabited",
"Union.union",
"Std.TreeMap.instUnion",
"Eq",
"Std.TreeMap"
] | true |
LinearMap.ker_eq_top._simp_1 | Mathlib.Algebra.Module.Submodule.Ker | [
"Submodule",
"LinearMap.ker_eq_top",
"LinearMap.ker",
"RingHom",
"Submodule.instTop",
"LinearMap",
"AddCommMonoid",
"propext",
"Semiring",
"Zero.toOfNat0",
"LinearMap.instZero",
"Module",
"Top.top",
"OfNat.ofNat",
"Semiring.toNonAssocSemiring",
"Eq"
] | false |
RegularWreathProduct.mk.injEq | Mathlib.GroupTheory.RegularWreathProduct | [
"Eq.propIntro",
"Lean.injEq_helper",
"RegularWreathProduct.mk",
"And",
"RegularWreathProduct",
"Eq.ndrec",
"Eq.refl",
"RegularWreathProduct.mk.inj",
"Eq"
] | true |
Field.Emb.Cardinal.leastExt.eq_1 | Mathlib.FieldTheory.CardinalEmb | [
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Cardinal",
"IntermediateField",
"PartialOrder.toPreorder",
"setOf",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"Fact",
"Algebra.toModule",
"Set.Elem... | true |
ContinuousAlgHom.coe_mk' | Mathlib.Topology.Algebra.Algebra | [
"MulOne.toOne",
"ContinuousAlgHom.instFunLike",
"Continuous",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"NonAssocSemiring.toMulZeroOneClass",
"MulZeroOneClass.toMulOneClass",
"CommSemiring",
"TopologicalSpace",
"MulOneClass.toMulOne",
"OneHom.toFun",
"AlgHom.toRingHom",
"ContinuousAlgHom.mk",... | true |
ProbabilityTheory.variance_id_gaussianReal | Mathlib.Probability.Distributions.Gaussian.Real | [
"ProbabilityTheory.variance_fun_id_gaussianReal",
"Real",
"ProbabilityTheory.gaussianReal",
"id",
"NNReal",
"ProbabilityTheory.variance",
"Real.measurableSpace",
"Eq",
"NNReal.toReal"
] | true |
Turing.PartrecToTM2.trStmts₁_supports' | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.trStmts₁",
"Iff.mpr",
"Turing.PartrecToTM2.Λ'.Supports",
"Finset.instUnion",
"Finset",
"Turing.PartrecToTM2.Λ'.instDecidableEq",
"Turing.PartrecToTM2.supports_union",
"Eq.mp",
"Turing.PartrecToTM2.Λ'",
"Turing.PartrecToTM2.Supports",
"HasSubset.Subset",
"Turing.PartrecToTM... | true |
Std.Time.Year.instSubOffset | Std.Time.Date.Unit.Year | [
"Std.Time.Year.instSubOffset._aux_1",
"Sub.mk",
"Std.Time.Year.Offset",
"Sub"
] | true |
Lean.Elab.MonadAutoImplicits.recOn | Lean.Elab.InfoTree.Types | [
"Lean.Elab.MonadAutoImplicits",
"Lean.Elab.MonadAutoImplicits.rec",
"Lean.Expr",
"Array",
"Lean.Elab.MonadAutoImplicits.mk"
] | false |
AlgebraicGeometry.Scheme.instCategoryAffineEtale._proof_8 | Mathlib.AlgebraicGeometry.Sites.AffineEtale | [
"CategoryTheory.MorphismProperty",
"Quiver.mk",
"AlgebraicGeometry.Scheme",
"Opposite",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.Category.comp_id._autoParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryT... | false |
Associated.mul_mul | Mathlib.Algebra.GroupWithZero.Associated | [
"HMul.hMul",
"Monoid.toMulOneClass",
"Associated.trans",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Associated",
"CommMonoid.toMonoid",
"Associated.mul_left",
"Associated.mul_right",
"CommMonoid",
"instHMul"
] | true |
Submodule.generators_card | Mathlib.Algebra.Module.SpanRank | [
"Submodule",
"Cardinal",
"Submodule.exists_span_set_card_eq_spanRank",
"Cardinal.mk",
"Submodule.generators",
"Set.Elem",
"AddCommMonoid",
"Classical.choose_spec",
"And",
"And.left",
"Submodule.span",
"Semiring",
"Classical.choose",
"Module",
"Eq",
"Submodule.spanRank",
"Set"
] | true |
Ordinal.cof_eq_zero._simp_1 | Mathlib.SetTheory.Cardinal.Cofinality.Ordinal | [
"Cardinal",
"Ordinal.zero",
"propext",
"Ordinal.cof",
"Zero.toOfNat0",
"Ordinal.cof_eq_zero",
"OfNat.ofNat",
"Eq",
"Cardinal.instZero",
"Ordinal"
] | false |
Polynomial.Splits.of_degree_eq_two | Mathlib.Algebra.Polynomial.Splits | [
"Polynomial.eval",
"WithBot",
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"Polynomial.degree",
"instNatCastNat",
"Polynomial.natDegree_eq_of_degree_eq_some",
"Field.toSemifield",
"Polynomial",
"Semifield.toDivisionSemiring",
"Nat.instNeZeroSucc",
"WithBot.natCast",
"Nat",
"DivisionSemir... | true |
Height.AdmissibleAbsValues.mk._flat_ctor | Mathlib.NumberTheory.Height.Basic | [
"Real.partialOrder",
"Real",
"HMul.hMul",
"Multiset.map",
"Multiset.prod",
"Height.AdmissibleAbsValues.mk",
"Membership.mem",
"Real.semiring",
"Multiset",
"Set.Elem",
"Height.AdmissibleAbsValues",
"Distrib.toAdd",
"Ne",
"Field.toSemifield",
"instDistribOfSemiring",
"Real.instOne",
"f... | false |
Plausible.GenError.ctorIdx | Plausible.Gen | [
"Nat",
"Plausible.GenError"
] | false |
Lean.Elab.Tactic.Grind.Cache._sizeOf_1 | Lean.Elab.Tactic.Grind.Basic | [
"Lean.Meta.Sym.BackwardRule._sizeOf_inst",
"Std.HashMap._sizeOf_inst",
"instHashableProd",
"Lean.Elab.Tactic.Grind.Cache.rec",
"Lean.Elab.Tactic.Grind.SimpCacheKey",
"Lean.PHashMap",
"Lean.Elab.Tactic.Grind.Cache",
"instOfNatNat",
"Std.HashMap",
"instHashableNat",
"Lean.Elab.Tactic.Grind.instBEq... | false |
Fact.mk | Mathlib.Logic.Basic | [
"Fact",
"Fact.mk"
] | true |
Lean.Expr.mapForallBinderNames._f | Mathlib.Lean.Expr.Basic | [
"_private.Mathlib.Lean.Expr.Basic.0.Lean.Expr.mapForallBinderNames.match_1",
"Lean.Expr",
"Lean.Expr.forallE",
"Lean.Name",
"Lean.BinderInfo",
"Lean.Expr.below"
] | false |
Set.chainHeight_coe_univ | Mathlib.Order.Height | [
"Set.chainHeight_eq_of_relEmbedding",
"Set.chainHeight",
"Set.image_univ",
"Subtype.relEmbedding",
"congrArg",
"Set.univ",
"setOf",
"Membership.mem",
"Eq.mp",
"Set.Elem",
"Subtype",
"Subtype.range_coe_subtype",
"funext",
"RelEmbedding",
"ENat",
"congr",
"Set.image_congr",
"eq_self"... | true |
Valuation.restrict_le_iff_le_embedding | Mathlib.RingTheory.Valuation.Basic | [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"ValuationClass.toMonoidWithZeroHomClass",
"Monoid.toMulOneClass",
"congrArg",
"MonoidWithZeroHomClass.toMonoidWithZeroHom",
"Iff.rfl",
"PartialOrder.toPreorder",
"Subtype.instLinearOrde... | true |
Lean.Lsp.FileChangeType.recOn | Lean.Data.Lsp.Workspace | [
"Lean.Lsp.FileChangeType.rec",
"Lean.Lsp.FileChangeType.Changed",
"Lean.Lsp.FileChangeType",
"Lean.Lsp.FileChangeType.Created",
"Lean.Lsp.FileChangeType.Deleted"
] | false |
BitVec.getLsbD_succ_last | Init.Data.BitVec.Lemmas | [
"instPowNat",
"BitVec",
"BitVec.getLsbD",
"instOfNatNat",
"BitVec.toNat",
"LE.le",
"instLENat",
"instNatPowNat",
"instHAdd",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"BitVec.getLsbD_last",
"Bool",
"instAddNat",
"instHPow",
"OfNat.ofNat",
"Decidable.decide",
"Eq",
"Nat.decLe"
] | true |
_private.Mathlib.ModelTheory.Encoding.0.FirstOrder.Language.BoundedFormula.listEncode.match_1.eq_2 | Mathlib.ModelTheory.Encoding | [
"FirstOrder.Language.BoundedFormula.imp",
"FirstOrder.Language.BoundedFormula.listEncode.match_1",
"FirstOrder.Language.Term",
"Sum",
"instOfNatNat",
"FirstOrder.Language.BoundedFormula.equal",
"FirstOrder.Language.BoundedFormula.falsum",
"instHAdd",
"HAdd.hAdd",
"Nat",
"FirstOrder.Language.Rela... | true |
CategoryTheory.Pseudofunctor.DescentData'.ofDescentData._proof_13 | Mathlib.CategoryTheory.Sites.Descent.DescentDataPrime | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Pseudofunctor.DescentData'.pullHom'",
"Opposite",
"CategoryTheory.Limits.ChosenPullback.isPullback",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"co... | false |
Composition.reverse_eq_ones | Mathlib.Combinatorics.Enumerative.Composition | [
"Function.Injective.eq_iff'",
"Composition",
"Iff",
"Nat",
"Composition.reverse_injective",
"Composition.ones",
"Composition.reverse",
"Eq",
"Composition.reverse_ones"
] | true |
Lean.Syntax.instForInTopDownOfMonad.match_1 | Lean.Syntax | [
"Lean.Syntax.node",
"Lean.Syntax.ctorIdx",
"Lean.SourceInfo",
"Lean.Syntax",
"Nat.hasNotBit",
"Array",
"Lean.SyntaxNodeKind",
"Lean.Syntax.instForInTopDownOfMonad._sparseCasesOn_1"
] | false |
Array.forIn'_eq_forIn' | Init.Data.Array.Basic | [
"Array.instMembership",
"Membership.mem",
"ForIn'.forIn'",
"ForInStep",
"Array",
"Array.instForIn'InferInstanceMembershipOfMonad",
"Monad",
"Eq",
"rfl",
"Array.forIn'"
] | true |
HahnSeries.embDomainRingHom._proof_4 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"RelEmbedding.mk",
"HahnSeries.embDomain",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Function.Embedding.mk",
"AddZeroClass.toAddZero",
"PartialOrder",
"LE.le",
"HahnSeries.instAdd",
"AddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",... | false |
CategoryTheory.rightAdjointMate_comp | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | [
"CategoryTheory.MonoidalCoherence.iso",
"Mathlib.Tactic.Monoidal.eval_whiskerLeft",
"Eq.mpr",
"CategoryTheory.HasRightDual.rightDual",
"CategoryTheory.MonoidalCategory.whisker_exchange",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Trans.trans",
"Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_con... | true |
_private.Batteries.Data.List.Lemmas.0.List.getElem_idxsOf_lt._proof_1_10 | Batteries.Data.List.Lemmas | [
"List.idxsOf",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"Lean.Grind.nestedProof",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.Order.le_of_eq_2_k",
"Std.IsLinearPreorder.toIsPreorder",
"Lean.Grind.Order.le_eq_true_of_le_k",
"Lean.Grind.instIsLinearOrd... | false |
_private.Mathlib.CategoryTheory.WithTerminal.Basic.0.CategoryTheory.WithTerminal.opEquiv.match_15.eq_2 | Mathlib.CategoryTheory.WithTerminal.Basic | [
"Unit.unit",
"Opposite",
"CategoryTheory.WithInitial.of",
"CategoryTheory.WithInitial",
"Unit",
"CategoryTheory.WithInitial.star",
"Eq.refl",
"CategoryTheory.WithTerminal.opEquiv.match_15",
"Eq"
] | true |
Std.ExtDTreeMap.getKey?_filterMap | Std.Data.ExtDTreeMap.Lemmas | [
"Option.pfilter",
"Std.ExtDTreeMap.getKey?",
"Std.DTreeMap",
"Std.ExtDTreeMap.mem_of_getKey?_eq_some",
"Option.some",
"Ordering",
"Std.ExtDTreeMap.get",
"Std.TransCmp",
"Std.ExtDTreeMap.filterMap",
"Std.LawfulEqCmp",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Std.DTreeMap.getKey?_fil... | true |
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