name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Meta.Grind.Arith.Cutsat.ToIntThms.noConfusion | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Meta.Grind.Arith.Cutsat.ToIntThms.casesOn",
"Lean.Meta.Grind.Arith.Cutsat.ToIntThms.noConfusionType",
"Lean.Expr",
"Lean.Meta.Grind.Arith.Cutsat.ToIntThms",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Option"
] | false |
Lean.IR.Arg.erased.sizeOf_spec | Lean.Compiler.IR.Basic | [
"Lean.IR.Arg",
"Lean.IR.Arg.erased",
"instOfNatNat",
"Lean.IR.Arg._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
Lean.Compiler.LCNF.Simp.elimVar? | Lean.Compiler.LCNF.Simp.Main | [
"Pure.pure",
"Lean.Compiler.LCNF.Simp.DiscrM",
"Lean.Compiler.LCNF.LetValue",
"Option.some",
"ReaderT.instMonad",
"IO.RealWorld",
"Lean.FVarId",
"Applicative.toPure",
"Lean.Compiler.LCNF.Purity.pure",
"_private.Lean.Compiler.LCNF.Simp.Main.0.Lean.Compiler.LCNF.Simp.elimVar?.match_1",
"Lean.Compi... | true |
Std.Rio.isSome_succMany?_of_lt_size_toArray | Init.Data.Range.Polymorphic.Lemmas | [
"Option.isSome_filter",
"GetElem?.toGetElem",
"Std.PRange.UpwardEnumerable",
"congrArg",
"Option.any",
"Std.PRange.LawfulUpwardEnumerableLT",
"Std.PRange.LawfulUpwardEnumerableLeast?",
"Option.some",
"Std.Rio.upper",
"Eq.mp",
"Option.isSome_of_any",
"Nonempty.intro",
"Array",
"GetElem.getE... | true |
ClosedSubmodule.mem_bot._simp_1 | Mathlib.Topology.Algebra.Module.ClosedSubmodule | [
"ClosedSubmodule.mem_bot",
"OrderBot.toBot",
"AddMonoid.toAddZeroClass",
"ClosedSubmodule.instPartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"Bot.bot",
"AddCommMonoid",
"ClosedSubmodule.instSetLike",
"ClosedSubmodule",
"TopologicalSpace... | false |
Irrational.ne_rational | Mathlib.NumberTheory.Real.Irrational | [
"Int.cast",
"False",
"Rat.cast_intCast",
"Real.partialOrder",
"Real",
"instHDiv",
"DivisionRing.toRatCast",
"congrArg",
"Real.instDivInvMonoid",
"Real.instRatCast",
"Rat",
"DivisionRing.toDivInvMonoid",
"Rat.instIntCast",
"HDiv.hDiv",
"Rat.cast",
"Ne",
"DivisionRing.toRing",
"Int",... | true |
Polynomial.degree_comp | Mathlib.Algebra.Polynomial.Degree.Lemmas | [
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.C",
"Polynomial.eval",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"Nat.instMulZeroClass",
"WithBot",
"Preorder.toLT",
"Polynomial.degree_eq_natDegree",
"WithBot.instCommSemiring",
"HMul.hMul",
"eq_false... | true |
CategoryTheory.Functor.preservesBinaryCoproducts_of_preservesCokernels | Mathlib.CategoryTheory.Preadditive.LeftExact | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingPair.right",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheory.Limits.WalkingPair",
"C... | true |
CommRingCat.limitCommRing._proof_25 | Mathlib.Algebra.Category.Ring.Limits | [
"AddGroup.toSubtractionMonoid",
"Function.Injective.semiring._proof_4",
"CategoryTheory.Functor",
"Equiv.commRing._proof_7",
"Mul.mk",
"CommRingCat.limitCommRing._proof_10",
"Semigroup.toMul",
"Equiv.instEquivLike",
"One.mk",
"HMul.hMul",
"CategoryTheory.Limits.Types.Small.limitCone",
"CommRin... | false |
CategoryTheory.CoreHom.rec | Mathlib.CategoryTheory.Core | [
"CategoryTheory.Iso",
"CategoryTheory.CoreHom",
"CategoryTheory.Core.of",
"CategoryTheory.CoreHom.mk",
"CategoryTheory.Core",
"CategoryTheory.Category"
] | false |
exists_seq_tendsto_limsup | Mathlib.Topology.Order.LiminfLimsup | [
"OrderTopology",
"Filter.NeBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Filter.IsCoboundedUnder",
"Function.comp",
"Exists",
"nhds",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"autoParam",
"FirstCountableTopology",
"Filter.limsup",
"Filter.atTop",
"... | true |
QuaternionAlgebra.imI_zero | Mathlib.Algebra.Quaternion | [
"QuaternionAlgebra.imI",
"QuaternionAlgebra",
"QuaternionAlgebra.instZero",
"Zero.toOfNat0",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Zero"
] | true |
Set.OrdConnected.casesOn | Mathlib.Order.Interval.Set.Defs | [
"Set.OrdConnected.rec",
"Membership.mem",
"HasSubset.Subset",
"Set.Icc",
"Set.OrdConnected.mk",
"Set.OrdConnected",
"Set.instMembership",
"Preorder",
"Set.instHasSubset",
"Set"
] | false |
Std.DHashMap.Raw.Const.mem_toArray_iff_getKey?_eq_some_and_get?_eq_some | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.Const.toList",
"Std.DHashMap.Raw.WF",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.Const.toArray",
"Array.instMembership",
"Option.some",
"Membership.mem",
"List.mem_toArray._simp_1",
"Std.DHashMap.Raw.Const.mem_toList_iff_getKey?_eq_some_and_get?_eq_some._simp_1",
"Prod.m... | true |
Std.DTreeMap.Internal.RcoSliceData.recOn | Std.Data.DTreeMap.Internal.Zipper | [
"Std.Rco",
"Ord",
"Std.DTreeMap.Internal.RcoSliceData.mk",
"Std.DTreeMap.Internal.RcoSliceData",
"Std.DTreeMap.Internal.RcoSliceData.rec",
"Std.DTreeMap.Internal.Impl"
] | false |
ComplexShape.instHasNoLoopNatUp | Mathlib.Algebra.Homology.HasNoLoop | [
"False",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"Nat.instOne",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass",
"ComplexShape.HasNoLoop",
"AddCancelMonoid.toAddRightCancelMonoid",
"noConfusion_of_Nat",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"Nat.instAddCancelCommMonoid",
"A... | true |
Std.ExtTreeMap.minKey!_insert_le_self | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtTreeMap.minKey!",
"Std.ExtDTreeMap.minKey!_insert_le_self",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.ExtTreeMap",
"Std.ExtTreeMap.inner",
"Bool",
"Inhabited",
"Std.ExtTreeMap.insert",
"Ordering.isLE",
"Eq"
] | true |
_private.Mathlib.Algebra.Group.Subgroup.Ker.0.Subgroup.subgroupOf_map_powMonoidHom_eq_range._proof_1_2 | Mathlib.Algebra.Group.Subgroup.Ker | [
"Iff.mpr",
"Subgroup.instSubgroupClass",
"Iff.of_eq",
"Membership.mem",
"DivInvMonoid.toMonoid",
"Subgroup",
"CommGroup",
"SubgroupClass.toSubmonoidClass",
"Monoid.toPow",
"Group.toDivInvMonoid",
"HPow.hPow",
"Nat",
"pow_mem",
"Eq.refl",
"instHPow",
"CommGroup.toGroup",
"SetLike.inst... | false |
Int.Linear.Poly.isValidEq.eq_2 | Init.Data.Int.Linear | [
"Eq.mpr",
"False",
"congrArg",
"Int.Linear.Poly.isUnsatEq.match_1",
"Int.instDecidableEq",
"id",
"Int",
"Int.Linear.Poly.num",
"instBEqOfDecidableEq",
"BEq.beq",
"instOfNat",
"Bool",
"Eq.refl",
"congrFun'",
"Int.Linear.Poly.isValidEq",
"OfNat.ofNat",
"Bool.false",
"Eq",
"_private... | true |
Std.HashMap.size_unitOfList | Std.Data.HashMap.Lemmas | [
"List.Pairwise",
"Std.DHashMap.Const.size_unitOfList",
"LawfulHashable",
"List",
"BEq.beq",
"Unit",
"EquivBEq",
"Nat",
"Std.HashMap.unitOfList",
"Std.HashMap.size",
"Bool",
"Hashable",
"Bool.false",
"BEq",
"Eq",
"List.length"
] | true |
_private.Lean.Meta.Tactic.Grind.ForallProp.0.Lean.Meta.Grind.simpExists.match_3 | Lean.Meta.Tactic.Grind.ForallProp | [
"Lean.Expr",
"Nat.hasNotBit",
"_private.Lean.Meta.Tactic.Grind.ForallProp.0.Lean.Meta.Grind.simpExists._sparseCasesOn_3",
"Lean.Expr.lam",
"Lean.Name",
"Lean.BinderInfo",
"Lean.Expr.ctorIdx"
] | false |
CategoryTheory.Abelian.SpectralObject.rightHomologyDataShortComplex._proof_8 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.ShortComplex.Exact.gIsCokernel",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.Abelian.SpectralObject.H",
"CategoryTheory.Abelian.SpectralObject.cokernelSequenceOp... | false |
Algebra.FormallySmooth.iff_injective_lTensor_residueField | Mathlib.RingTheory.Smooth.Local | [
"LinearMap.id",
"Eq.mpr",
"RingHomSurjective.ids",
"Module.Finite.of_surjective",
"CommRing",
"Algebra.to_smulCommClass",
"Algebra.Extension.commRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Algebra.Extension.formallySmooth_iff_split_injection",
"Algebra.Extension... | true |
CategoryTheory.Limits.biprod.braiding | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.biprod.braiding._proof_4",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.biprod.braiding._proof_2",
"CategoryTheory.Iso",
"CategoryTheory.Iso.mk",
"CategoryTheory.Limits.biprod",
"CategoryTheory.Limits.biprod.snd",
"CategoryTheory.Limits.biprod.lift",
"Categ... | true |
Representation.IntertwiningMap.instSemiring._proof_3 | Mathlib.RepresentationTheory.Intertwining | [
"Monoid",
"Function.Injective.semiring._proof_4",
"Semigroup.toMul",
"instHSMul",
"Representation",
"Representation.IntertwiningMap.instAddCommMonoid",
"HMul.hMul",
"Representation.IntertwiningMap.toLinearMap_injective",
"CommSemiring.toSemiring",
"Representation.IntertwiningMap.instAdd",
"AddMo... | false |
AddEquiv.coe_toAddHom | Mathlib.Algebra.Group.Equiv.Defs | [
"AddHom",
"AddHom.funLike",
"AddEquiv",
"AddEquiv.instEquivLike",
"Eq",
"DFunLike.coe",
"Add",
"rfl",
"EquivLike.toFunLike",
"AddEquiv.toAddHom"
] | true |
WittVector.mul_coeff_zero | Mathlib.RingTheory.WittVector.Defs | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Nat.Prime",
"AlgHom.algHomClass",
"HMul.hMul",
"MvPolynomial.aeval_X",
"MvPolynomial.aeval",
"WittVector.peval",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoid.toAddZe... | true |
Nat.dfoldRev_zero._auto_1 | Init.Data.Nat.Fold | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.Comon.Hom.mk.congr_simp | Mathlib.CategoryTheory.Monoidal.Comon_ | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsComonHom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Comon.Hom",
"Eq.rec",
"Eq.ndrec",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Comon.Hom.mk",
"CategoryTheory.Comon.comon",
"Eq",
... | true |
Lean.Elab.GoalsAtResult.casesOn | Lean.Server.InfoUtils | [
"Lean.Elab.GoalsAtResult.rec",
"Lean.Elab.ContextInfo",
"Lean.Elab.GoalsAtResult.mk",
"Nat",
"Bool",
"Lean.Elab.GoalsAtResult",
"Lean.Elab.TacticInfo"
] | false |
CompHausLike.sigmaComparison | Mathlib.Topology.Category.CompHausLike.SigmaComparison | [
"CompHausLike.ofHom",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompHausLike.HasExplicitFiniteCoproducts",
"CategoryTheory.ConcreteCategory.hom",
"Quiver.Hom.op",
"ContinuousMap.mk",
"instCompactSpaceSigmaOfFinite",
"Finite",
"continuous_sig... | true |
NonUnitalSubring.instTop._proof_1 | Mathlib.RingTheory.NonUnitalSubring.Basic | [
"NonUnitalNonAssocRing",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddSubsemigroup.carrier",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid.toAddSubsemigroup",
"AddSubgroup",
"AddSubsemigroup.add_mem'",
"instHAdd",
"AddGroup.toSu... | false |
Order.IsSuccPrelimit.mid | Mathlib.Order.SuccPred.Limit | [
"Preorder.toLT",
"Order.IsSuccPrelimit",
"Classical.indefiniteDescription",
"Membership.mem",
"Set.Elem",
"LT.lt",
"Order.IsSuccPrelimit.mid._proof_1",
"Set.instMembership",
"Set.Ioo",
"Preorder",
"Set"
] | true |
DividedPowers.dpow | Mathlib.RingTheory.DividedPowers.Basic | [
"CommSemiring.toSemiring",
"Ideal",
"CommSemiring",
"Nat",
"DividedPowers"
] | true |
SkewMonoidAlgebra.coeff_erase_ne | Mathlib.Algebra.SkewMonoidAlgebra.Single | [
"False",
"eq_false",
"Finsupp.erase_ne",
"congrArg",
"AddMonoid.toAddZeroClass",
"SkewMonoidAlgebra.instAddMonoid",
"AddZeroClass.toAddZero",
"Ne",
"SkewMonoidAlgebra.toFinsupp",
"AddCommMonoid",
"AddZero.toZero",
"SkewMonoidAlgebra.erase",
"True",
"eq_self",
"SkewMonoidAlgebra",
"of_e... | true |
ChainComplex.single₀_map_f_zero | Mathlib.Algebra.Homology.Single | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid"... | true |
_private.Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree.0.Polynomial.isMonicOfDegree_two_iff'._simp_1_3 | Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree | [
"HMul.hMul",
"Mul",
"HasDistribNeg",
"neg_mul",
"HasDistribNeg.toInvolutiveNeg",
"InvolutiveNeg.toNeg",
"Eq.symm",
"Eq",
"Neg.neg",
"instHMul"
] | false |
Lean.instHashableFVarId | Lean.Expr | [
"Lean.FVarId",
"Hashable.mk",
"Lean.instHashableFVarId.hash",
"Hashable"
] | true |
Associates.mk_ne_zero | Mathlib.Algebra.GroupWithZero.Associated | [
"Associates.mk",
"Associates.instZero",
"Ne",
"Iff",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"Associates",
"Associates.mk_eq_zero",
"Zero.toOfNat0",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"not_congr",
"MonoidWithZero.toMonoid",
"MulZeroClass.toZero"
] | true |
Std.LawfulOrderInf.recOn | Init.Data.Order.Classes | [
"Std.LawfulOrderInf.mk",
"LE.le",
"LE",
"Min",
"Std.LawfulOrderInf.rec",
"And",
"Iff",
"Min.min",
"Std.LawfulOrderInf"
] | false |
Nat.factorization_ordCompl | Mathlib.Data.Nat.Factorization.Basic | [
"Finsupp.instFunLike",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"Finsupp.erase",
"Nat.instOrderedSub",
"Finsupp.erase_same",
"instHSMul",
"Nat.Prime",
"Dvd.dvd",
"instHDiv",
"Finsupp.ext",
"eq_false",
"Finsupp.erase_ne",
"Monoid.toMu... | true |
CategoryTheory.Limits.instFintypeWalkingParallelPairHom._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits | [
"Eq.mpr",
"False",
"CategoryTheory.Limits.WalkingParallelPairHom.ctorIdx",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.WalkingParallelPair.ctorIdx",
"congrArg",
"HEq.refl",
"Finset",
"CategoryTheory.Limits.WalkingParallelPairHom",
"False.elim",
"CategoryTheory.Limits.Walk... | false |
MeasureTheory.«_aux_Mathlib_MeasureTheory_Measure_MutuallySingular___macroRules_MeasureTheory_term_⟂ₘ__1» | Mathlib.MeasureTheory.Measure.MutuallySingular | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr3",... | false |
PseudoMetricSpace.ofPreNNDist._proof_4 | Mathlib.Topology.Metrizable.Uniformity | [
"Iff.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"List.zipWith",
"Real",
"ENNReal.ofNNReal",
"iInf",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"LE.le.trans_eq",
"Real.instZero",
"ENNReal.ofReal",
"NNReal.coe_eq_zero",
"List.sum",
"PartialOrder.toPreord... | false |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle.0.Real.Angle.sign_two_nsmul_eq_sign_iff._simp_1_7 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle | [
"Real",
"instHDiv",
"Real.pi",
"Real.lattice",
"Real.Angle",
"Real.instZero",
"abs",
"Real.instDivInvMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"Real.instLT",
"HDiv.hDiv",
"Real.instAddGroup",
"instOfNatNat",
"Nat.instNeZeroSucc",
"Nat",
"LT.lt",
"Real.Angle.cos_pos_iff_abs_toReal_lt_pi... | false |
MeasurableEmbedding.map_comap | Mathlib.MeasureTheory.Measure.Restrict | [
"Eq.mpr",
"MeasureTheory.Measure",
"MeasurableSet",
"congrArg",
"MeasureTheory.Measure.restrict_apply",
"MeasurableEmbedding.measurableSet_image'",
"MeasureTheory.Measure.restrict",
"id",
"MeasureTheory.Measure.comap_apply",
"Set.instInter",
"Set.image_preimage_eq_inter_range",
"Inter.inter",
... | true |
FinVec.Forall.eq_2 | Mathlib.Data.Fin.Tuple.Reflection | [
"FinVec.Forall",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Eq",
"Matrix.vecCons"
] | true |
List.splitWrtCompositionAux._f | Mathlib.Combinatorics.Enumerative.Composition | [
"List.splitWrtCompositionAux.match_1",
"List.cons",
"List",
"List.splitWrtCompositionAux.match_3",
"Nat",
"List.below",
"List.splitAt",
"Prod",
"List.nil"
] | false |
IsCompact.adherence_nhdset | Mathlib.Topology.Compactness.Compact | [
"Filter.instMembership",
"inter_mem_nhdsWithin",
"Filter.NeBot.ne",
"Compl.compl",
"Filter.instCompleteLatticeFilter",
"nhdsWithin",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"nhds",
"CompleteLattice.toConditionallyCompleteLattice",
"Eq.rec",
"inf_le_of_left_l... | true |
Submodule.reflectionLinearEquiv._proof_2 | Mathlib.Analysis.InnerProductSpace.Projection.Reflection | [
"NormedField.toField",
"Field.toSemifield",
"RingHomInvPair",
"RCLike.toDenselyNormedField",
"RCLike",
"Semifield.toDivisionSemiring",
"RingHomInvPair.ids",
"DivisionSemiring.toSemiring",
"DenselyNormedField.toNormedField",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
Polynomial.IsSplittingField.map | Mathlib.FieldTheory.SplittingField.IsSplittingField | [
"Subalgebra.instSetLike",
"Multiset.toFinset",
"Eq.mpr",
"Polynomial.roots",
"Lattice.toSemilatticeSup",
"eq_top_iff",
"Algebra.algebraMap",
"CompleteLattice.toLattice",
"congrArg",
"Polynomial.IsSplittingField.adjoin_rootSet",
"CommSemiring.toSemiring",
"Finset",
"IsScalarTower",
"Partial... | true |
Homeomorph.toEquiv_injective | Mathlib.Topology.Homeomorph.Defs | [
"Homeomorph.mk",
"Continuous",
"Homeomorph.toEquiv",
"Equiv",
"_private.Mathlib.Topology.Homeomorph.Defs.0.Homeomorph.toEquiv_injective.match_1_1",
"Equiv.toFun",
"TopologicalSpace",
"Homeomorph",
"Function.Injective",
"Eq",
"Equiv.invFun",
"rfl"
] | true |
DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem | Mathlib.Combinatorics.Tiling.Tile | [
"Eq.mpr",
"instHSMul",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"DiscreteTiling.PlacedTile.instMembership",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"_private.Mathlib.Combinatorics.Tiling.Tile.0.DiscreteTiling.PlacedTile.mem_smul_iff_smul_inv_mem... | true |
CompleteLattice.rec | Mathlib.Order.CompleteLattice.Defs | [
"Lattice",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"InfSet",
"SupSet",
"IsGLB",
"IsLUB",
"SemilatticeSup.toPartialOrder",
"BoundedOrder",
"CompleteLattice",
"CompleteLattice.mk",
"InfSet.sInf",
"SupSet.sSup",
"Set"
] | false |
CategoryTheory.FreeMonoidalCategory.projectObj.match_1 | Mathlib.CategoryTheory.Monoidal.Free.Basic | [
"Unit.unit",
"CategoryTheory.FreeMonoidalCategory.casesOn",
"CategoryTheory.FreeMonoidalCategory.of",
"Unit",
"CategoryTheory.FreeMonoidalCategory",
"CategoryTheory.FreeMonoidalCategory.unit",
"CategoryTheory.FreeMonoidalCategory.tensor"
] | false |
support_iteratedFDeriv_subset | Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | [
"NormedSpace",
"subset_closure",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap",
"NormedField.toField",
"HasSubset.Subset.trans",
"tsupport",
"Set.instIsTransSubset",
"HasSubset.Subset",
"SubtractionMonoid.toSubNegZeroMono... | true |
Lean.Compiler.LCNF.ToLCNF.State.toAny._default | Lean.Compiler.LCNF.ToLCNF | [
"id",
"Lean.instEmptyCollectionFVarIdSet",
"Lean.FVarIdSet",
"EmptyCollection.emptyCollection"
] | false |
Set.preimage_image_eq | Mathlib.Data.Set.Image | [
"Set.Subset.antisymm",
"_private.Mathlib.Data.Set.Image.0.Set.preimage_image_eq.match_1_1",
"Membership.mem",
"Eq.rec",
"Set.preimage",
"Set.image",
"Function.Injective",
"Eq",
"Set.instMembership",
"Set.subset_preimage_image",
"Set"
] | true |
Mathlib.Tactic.DepRewrite.depRwSeq | Mathlib.Tactic.DepRewrite | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.Parser.Tactic.location",
"Lean.Parser.Tactic.optConfig",
"instOfNatNat",
"Lean.Parser.Tactic.rwRuleSeq",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"OfNat.ofNat",
"Bool.false",
"Lean.Nam... | true |
String.append_assoc | Init.Data.String.Defs | [
"congrArg",
"String",
"_private.Init.Data.String.Defs.0.String.append_assoc._simp_1_1",
"String.toByteArray",
"instAppendString",
"instHAppendOfAppend",
"congr",
"True",
"eq_self",
"ByteArray.append_assoc",
"of_eq_true",
"String.toByteArray_append",
"congrFun'",
"ByteArray.instAppend",
"... | true |
Fin.val_ne_iff | Init.Data.Fin.Lemmas | [
"Ne",
"Fin.val",
"Iff",
"Nat",
"Fin",
"Eq",
"Fin.val_inj",
"not_congr"
] | true |
upperSemicontinuous_const | Mathlib.Topology.Semicontinuity.Defs | [
"Preorder.toLT",
"UpperSemicontinuous",
"TopologicalSpace",
"LT.lt",
"Semicontinuous.const",
"Preorder"
] | true |
ContinuousLinearMap.range_prod_eq | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd | [
"Submodule",
"RingHomSurjective.ids",
"Lattice.toSemilatticeSup",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"LinearMap.ker",
"instTopologicalSpaceProd",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"LinearMap.range",
"AddCommGroup",
"ContinuousLi... | true |
Std.DTreeMap.Internal.Impl.inter | Std.Data.DTreeMap.Internal.Operations | [
"Ord",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.filter",
"Std.DTreeMap.Internal.Impl.size",
"LE.le",
"instLENat",
"Std.DTreeMap.Internal.Impl.contains",
"Nat",
"Std.DTreeMap.Internal.Impl",
"Nat.decLe",
"Std.DTreeMap.Internal.Impl.BalancedTree.impl",
"Std.DTreeMap.Int... | true |
_private.Mathlib.LinearAlgebra.LinearIndependent.Defs.0.linearIndepOn_finset_iff._simp_1_2 | Mathlib.LinearAlgebra.LinearIndependent.Defs | [
"instHSMul",
"Finset.univ",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",... | false |
Std.TreeSet.Raw.maxD_erase_le_maxD | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.WF.out",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.TreeSet.Raw",
"Unit",
"Std.TreeMap.Raw.maxKeyD_erase_le_maxKeyD",
"Bool",
"Std.TreeSet.Raw.isEmpty",
"Std.TreeSet.Raw.erase",
"Ordering.isLE",
"Std.TreeSet.Raw.maxD",
"Bool.false",
"Std.TreeSet.Raw.inner",
"Eq",
"S... | true |
Besicovitch.TauPackage.index.eq_1 | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Real.instLE",
"Real",
"Preorder.toLT",
"Besicovitch.TauPackage",
"HMul.hMul",
"Classical.epsilon",
"Ordinal.partialOrder",
"iSup",
"Besicovitch.TauPackage.index",
"Besicovitch.TauPackage.τ",
"PartialOrder.toPreorder",
"Besicovitch.TauPackage.index.eq_def",
"Membership.mem",
"Real.instSupS... | true |
Polynomial.monomial_eq_zero_iff._simp_1 | Mathlib.Algebra.Polynomial.Basic | [
"Semiring.toModule",
"LinearMap.instFunLike",
"Polynomial.monomial_eq_zero_iff",
"Polynomial.monomial",
"LinearMap",
"Polynomial",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Polynomial.semiring",
"Nat",
"propext",
"Semiring",
"Zero.toOfNat0"... | false |
RelHom.instMonoid._proof_5 | Mathlib.Algebra.Order.Group.End | [
"Mul.mk",
"One.mk",
"HMul.hMul",
"RelHom",
"One.toOfNat1",
"RelHom.id",
"RelHom.comp",
"OfNat.ofNat",
"Eq",
"rfl",
"instHMul"
] | false |
AlgebraicGeometry.Scheme.LocalRepresentability.glueData_V | Mathlib.AlgebraicGeometry.Sites.Representability | [
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.Scheme.zariskiTopology",
"CategoryTheory.Functor.category",
"AlgebraicGeometry.Scheme.LocalRepresentability.glueData.match_1",
"CategoryTheory.yoneda",
"Cate... | true |
RootPairing.Equiv.mk.congr_simp | Mathlib.LinearAlgebra.RootSystem.Hom | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"RootPairing.Equiv.mk",
"LinearMap.instFunLike",
"Eq.rec",
"AddCommGroup",
"LinearMap",
"RootPairing.Hom",
"CommRing.toCommSemiring",
"Eq.ndrec",
"Function.Bijective",
"Eq.refl",
"RootPairing.Hom.weightMap",
"RootPair... | true |
RingCon.comapQuotientEquivOfSurj._proof_4 | Mathlib.RingTheory.Congruence.Hom | [
"RingCon.mk'_surjective",
"RingHom",
"Function.comp",
"RingCon",
"Distrib.toAdd",
"RingCon.Quotient",
"RingCon.mk'",
"NonAssocSemiring",
"RingHom.instFunLike",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Function.Surjective.comp",
"NonUnitalNonAssocSemiring.toDistrib",
... | false |
Algebra.SubmersivePresentation.sectionCotangent._proof_2 | Mathlib.RingTheory.Smooth.StandardSmoothCotangent | [
"CommRing",
"Algebra.to_smulCommClass",
"Algebra.Extension.commRing",
"instSMulOfMul",
"CommSemiring.toSemiring",
"Algebra.SubmersivePresentation.toPreSubmersivePresentation",
"Finite",
"Algebra",
"Algebra.toSMul",
"Algebra.PreSubmersivePresentation.toPresentation",
"Algebra.Extension.Ring",
"... | false |
C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum | Mathlib.RingTheory.WittVector.StructurePolynomial | [
"MvPolynomial.map_bind₁",
"wittPolynomial_zmod_self",
"AddGroup.toSubtractionMonoid",
"Finsupp.instAddZeroClass",
"Int.cast",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"dvd_sub_pow_of_dvd_sub",
"Int.cast_natCast",
"RingHom.instRingHomClass",
"MulOne.... | true |
Std.Time.PlainDateTime.mk.noConfusion | Std.Time.DateTime.PlainDateTime | [
"Std.Time.PlainTime",
"Std.Time.PlainDate",
"Std.Time.PlainDateTime.noConfusion",
"id",
"Std.Time.PlainDateTime",
"Std.Time.PlainDateTime.mk",
"Eq"
] | false |
Aesop.SimpTheorems.addSimpEntry | Aesop.Util.Basic | [
"Lean.Meta.SimpTheorems.registerDeclToUnfoldThms",
"Lean.PersistentHashSet.insert",
"Lean.Meta.SimpTheorems.post",
"Lean.Meta.instHashableOrigin",
"Lean.Meta.instBEqOrigin",
"Lean.Meta.SimpTheorems.lemmaNames",
"_private.Aesop.Util.Basic.0.Aesop.SimpTheorems.addSimpEntry.match_1",
"Lean.Meta.SimpTheor... | true |
instSMulCommClassMatrixFinOfNatNatProd | Mathlib.Topology.Compactification.OnePoint.ProjectiveLine | [
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"LinearEquiv.symm",
"Semiring.toModule",
"instSMulOfMul",
"Pi.addCommMonoid",
"DistribMulAction.toDistribSMul",
"Matrix",
"Prod.instAddZeroClass",
"AddMonoid.toAddZeroClass",
"instDecidableEqFin",
"LinearEquiv.finTwoArrow",
"Pr... | true |
EMetric.dense_iff | Mathlib.Topology.EMetricSpace.Defs | [
"Preorder.toLT",
"_private.Mathlib.Topology.EMetricSpace.Defs.0.EMetric.dense_iff._simp_1_4",
"congrArg",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"Dense",
"_private.Mathlib.Topology.EMetricSpace.Defs.0.EMetric.dense_iff._simp_1_2",
"_private.Mathlib.Topology.EMetricSpace.Defs.0.EMetri... | true |
Mathlib.Tactic.GCongr.addGCongrLemmaEntry | Mathlib.Tactic.GCongr.Core | [
"Mathlib.Tactic.GCongr.GCongrLemmas",
"Mathlib.Tactic.GCongr.instOrdGCongrKey",
"Std.TreeMap.alter",
"_private.Mathlib.Tactic.GCongr.Core.0.Mathlib.Tactic.GCongr.addGCongrLemmaEntry.insert",
"Option.some",
"Ord.compare",
"List.cons",
"List",
"Unit",
"Mathlib.Tactic.GCongr.GCongrLemma",
"_private... | true |
IsLocalExtrOn.isLocalExtr | Mathlib.Topology.Order.LocalExtr | [
"Filter.instMembership",
"IsLocalMinOn",
"IsLocalMinOn.isLocalMin",
"IsLocalExtr",
"IsLocalExtrOn",
"Membership.mem",
"nhds",
"IsLocalMaxOn",
"TopologicalSpace",
"IsMinFilter.isExtr",
"IsLocalMaxOn.isLocalMax",
"IsMaxFilter.isExtr",
"IsLocalExtrOn.elim",
"Filter",
"Preorder",
"Set"
] | true |
CompHaus.limitCone | Mathlib.Topology.Category.CompHaus.Basic | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"trivial",
"TopCat.instCategory",
"CategoryTheory.InducedCategory.homMk",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CompHaus.limitCone._proof_1",
"CategoryTheory.SmallCategory",
"Comp... | true |
CategoryTheory.Sieve.pushforward_le_bind_of_mem | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"CategoryTheory.Sieve.pushforward",
"PartialOrder.toPreorder",
"CategoryTheory.Sieve.bind",
"Preorder.toLE",
"Exists",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Sieve",
"LE.le",
"And.casesOn",
"CompleteLa... | true |
CategoryTheory.Limits.biproduct.lift_desc | Mathlib.CategoryTheory.Preadditive.Biproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasBiproduct",
"CategoryTheory.Limits.biproduct.ι_π_assoc",
"dite_congr",
"Finset.univ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.biproduct.lift",
"AddCommGroup.toAddCommMonoid",
"Finset",
... | true |
Std.DTreeMap.Internal.RocSliceData.rec | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"Std.DTreeMap.Internal.RocSliceData",
"Std.DTreeMap.Internal.RocSliceData.mk",
"Std.DTreeMap.Internal.Impl",
"Std.Roc"
] | false |
IterateAddAct.rec | Mathlib.GroupTheory.GroupAction.IterateAct | [
"IterateAddAct",
"Nat",
"IterateAddAct.mk"
] | false |
LawfulMonadStateOf.map_pure._inherited_default | Batteries.Control.LawfulMonadState | [
"Pure.pure",
"MonadStateOf",
"Monad.toApplicative",
"id",
"Applicative.toPure",
"semiOutParam",
"Applicative.toFunctor",
"Monad.toBind",
"Bind.bind",
"LawfulMonad._proof_1",
"Monad",
"Eq",
"Functor.map"
] | false |
Set.insert_def | Mathlib.Data.Set.Insert | [
"setOf",
"Membership.mem",
"Insert.insert",
"Set.instInsert",
"Or",
"Eq",
"Set.instMembership",
"rfl",
"Set"
] | true |
Vector.swap._proof_1 | Init.Data.Vector.Basic | [
"Array.swap",
"Vector",
"congrArg",
"Vector.set._proof_1",
"Nat",
"LT.lt",
"True",
"Vector.size_toArray",
"eq_self",
"of_eq_true",
"Array.size_swap",
"congrFun'",
"instLTNat",
"Eq",
"Array.size",
"Vector.toArray",
"Eq.trans"
] | false |
Fin.preimage_cast_Ioc | Mathlib.Order.Interval.Set.Fin | [
"Set.Ioc",
"PartialOrder.toPreorder",
"Fin.cast",
"Fin.instPartialOrder",
"Set.preimage",
"Nat",
"Eq.symm",
"Fin",
"Eq",
"rfl",
"Set"
] | true |
Matrix.det_eq_prod_roots_charpoly_of_splits | Mathlib.LinearAlgebra.Matrix.Charpoly.Eigs | [
"one_pow",
"Eq.mpr",
"NegZeroClass.toNeg",
"IsDomain",
"MulOne.toOne",
"Semigroup.toMul",
"CommRing",
"Polynomial.roots",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"pow_two",
"CommRing.toNonUnitalCommRing",
"pow_right_comm",
"neg_one_sq",
"Monoid.toMulOneClass",
"co... | true |
Nat.two_pow_add_eq_or_of_lt | Init.Data.Nat.Bitwise.Lemmas | [
"instPowNat",
"Eq.mpr",
"False",
"instHOrOfOrOp",
"Trans.trans",
"HMul.hMul",
"instDecidableTrue",
"Nat.testBit_two_pow_mul",
"eq_false",
"congrArg",
"Decidable.decide.congr_simp",
"HSub.hSub",
"GE.ge",
"id",
"Bool.and",
"Nat.instTransLtLe",
"decide_false",
"Nat.testBit_lt_two_pow"... | true |
_private.Init.Data.Fin.Iterate.0.Fin.hIterateFrom._unary.eq_def | Init.Data.Fin.Iterate | [
"Eq.mpr",
"congrArg",
"_private.Init.Data.Fin.Iterate.0.Fin.hIterateFrom._unary._proof_2",
"_private.Init.Data.Fin.Iterate.0.Fin.hIterateFrom._unary._proof_3",
"InvImage",
"HSub.hSub",
"WellFounded.Nat.fix",
"cast",
"WellFounded.Nat.fix_eq",
"Fin.mk",
"PSigma.casesOn",
"id",
"instSubNat",
... | false |
MulDistribMulActionHom.map_sub | Mathlib.GroupTheory.GroupAction.Hom | [
"Monoid",
"MonoidHom.instFunLike",
"instHDiv",
"MonoidHom",
"Monoid.toMulOneClass",
"MulDistribMulActionHom.instFunLike",
"Group",
"Group.toDivisionMonoid",
"HDiv.hDiv",
"MulDistribMulActionHom.instMulDistribMulActionSemiHomClassCoeMonoidHom",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
... | true |
uniformity_eq_comap_add_neg_nhds_zero_swapped | Mathlib.Topology.Algebra.IsUniformGroup.Defs | [
"AddGroup.toSubtractionMonoid",
"UniformSpace",
"Eq.mpr",
"NegZeroClass.toNeg",
"uniformity_eq_comap_add_neg_nhds_zero",
"congrArg",
"AddMonoid.toAddZeroClass",
"uniformity",
"Function.comp",
"nhds",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.... | true |
Lean.Compiler.LCNF.Param._sizeOf_inst | Lean.Compiler.LCNF.Basic | [
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Param._sizeOf_1",
"SizeOf.mk",
"Lean.Compiler.LCNF.Param",
"SizeOf"
] | false |
Std.DHashMap.Raw.contains_insert_self | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.contains_insert_self",
"Std.DHashMap.Raw.WF.insert₀",
"Std.DHashMap.Internal.Raw₀.contains",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.contains",
"id",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"Std.DHashMap.Int... | true |
LinearIndependent.fin_cons | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | [
"Submodule",
"LinearIndependent.finCons",
"AddCommGroup.toAddCommMonoid",
"Fin.cons",
"Membership.mem",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Submodule.setLike",
"LinearIndependent",
"Submodule.span",
"DivisionSemiring.toSemir... | true |
_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.filter_eq_self_iff._simp_1_3 | Mathlib.Data.Finsupp.Basic | [
"not_imp_comm",
"propext",
"Eq",
"Not"
] | false |
Equiv.completeDistribLattice._proof_9 | Mathlib.Order.CompleteBooleanAlgebra | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"Compl.compl",
"CompleteDistribLattice",
"Equiv",
"BiheytingAlgebra.toHeytingAlgebra",
"CompleteDistribLattice.toBiheytingAlgebra",
"Equiv.symm",
"Eq",
"HeytingAlgebra.toCompl",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
CategoryTheory.Abelian.SpectralObject.d._auto_5 | Mathlib.Algebra.Homology.SpectralObject.Differentials | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
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