name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Analysis.Complex.Polynomial.GaussLucas.0.Polynomial.eq_centerMass_of_eval_derivative_eq_zero._simp_1_12 | Mathlib.Analysis.Complex.Polynomial.GaussLucas | [
"False",
"eq_false",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"CharZero",
"Nat.cast_add_one_ne_zero",
"AddMonoidWithOne.toOne",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat",
"On... | false |
CoassocSimps.symm_comp_rid_symm_assoc | Mathlib.RingTheory.Coalgebra.CoassocSimps | [
"LinearEquiv.symm",
"Semiring.toModule",
"TensorProduct.comm",
"TensorProduct.rid",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"LinearMap.comp",
"LinearEquiv.toLinearMap",
"NonAssocSemir... | true |
Set.powersetCard.addAction_faithful | Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | [
"Eq.mpr",
"_private.Mathlib.GroupTheory.GroupAction.SubMulAction.Combination.0.Set.powersetCard.addAction_faithful._simp_1_2",
"Equiv.instEquivLike",
"_private.Mathlib.GroupTheory.GroupAction.SubMulAction.Combination.0.Set.powersetCard.addAction_faithful._simp_1_5",
"Equiv.Perm.instOne",
"AddMonoid.toAddS... | true |
_private.Mathlib.RingTheory.MvPowerSeries.LinearTopology.0.MvPowerSeries.LinearTopology.isTopologicallyNilpotent_of_constantCoeff._simp_1_5 | Mathlib.RingTheory.MvPowerSeries.LinearTopology | [
"Nat.instMulZeroClass",
"Semiring.toModule",
"LinearMap.instFunLike",
"MvPowerSeries",
"RingHom",
"MvPowerSeries.map",
"MvPowerSeries.instModule",
"LinearMap",
"MvPowerSeries.instAddCommMonoid",
"MvPowerSeries.instSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instFunLike",
... | false |
Set.mapsTo_id | Mathlib.Data.Set.Function | [
"Membership.mem",
"id",
"Set.MapsTo",
"Set.instMembership",
"Set"
] | true |
AlgebraicGeometry.Scheme.Cover.ColimitGluingData.isColimitGluedCocone._proof_6 | Mathlib.AlgebraicGeometry.ColimitsOver | [
"AlgebraicGeometry.Scheme.Cover.ColimitGluingData.trans._proof_5",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.instIsStableUnderBaseChangeAlongOfIsStableUnderBaseChange",
"Alg... | false |
Std.Time.Week.Offset.toHours | Std.Time.Date.Unit.Week | [
"Rat.instOfNat",
"Int.cast",
"Rat.instMul",
"instHDiv",
"HMul.hMul",
"Std.Time.Hour.Offset",
"Rat",
"Rat.instIntCast",
"HDiv.hDiv",
"Int",
"_private.Std.Time.Date.Unit.Week.0.Std.Time.Week.Offset.toHours._proof_1",
"instOfNat",
"OfNat.ofNat",
"Std.Time.Internal.UnitVal.cast",
"Std.Time.W... | true |
CategoryTheory.Lax.LaxTrans.id | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.rightUnitor",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Lax.LaxTrans.id._proof_6",
"CategoryTheory.Lax.LaxTrans.id._proof_4",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrela... | true |
Lean.Elab.Modifiers.mk | Lean.Elab.DeclModifiers | [
"Lean.TSyntax",
"Lean.Elab.ComputeKind",
"Lean.Elab.RecKind",
"List.cons",
"Lean.Elab.Attribute",
"Array",
"Lean.Elab.Modifiers",
"Bool",
"Lean.Elab.Modifiers.mk",
"Lean.SyntaxNodeKind",
"Prod",
"Lean.Name.mkStr4",
"Lean.Elab.Visibility",
"List.nil",
"Option"
] | true |
TensorProduct.leftHasSMul | Mathlib.LinearAlgebra.TensorProduct.Defs | [
"Monoid",
"AddCon.addZeroClass",
"AddMonoid.toAddSemigroup",
"addConGen",
"TensorProduct.Eqv",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"TensorProduct.leftHasSMul._proof_2",
"AddCon.lift",
"SMul",
"AddMonoid.toAddZeroClass",
"FreeAddMonoid.instAddCancelMonoid",
"AddCancel... | true |
TestFunctionClass.noConfusionType | Mathlib.Analysis.Distribution.TestFunction | [
"Real",
"NormedSpace",
"outParam",
"Real.denselyNormedField",
"PseudoMetricSpace.toUniformSpace",
"TopologicalSpace.Opens",
"tsupport",
"ContDiff",
"HasSubset.Subset",
"SubtractionMonoid.toSubNegZeroMonoid",
"TestFunctionClass",
"DFunLike",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCo... | false |
_private.Lean.Meta.SynthInstance.0.Lean.Meta.PreprocessKind.mvarsOutputParams.sizeOf_spec | Lean.Meta.SynthInstance | [
"_private.Lean.Meta.SynthInstance.0.Lean.Meta.PreprocessKind._sizeOf_inst",
"_private.Lean.Meta.SynthInstance.0.Lean.Meta.PreprocessKind.mvarsOutputParams",
"instOfNatNat",
"_private.Lean.Meta.SynthInstance.0.Lean.Meta.PreprocessKind",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.ShortComplex.Homotopy.refl_h₁ | Mathlib.Algebra.Homology.ShortComplex.Preadditive | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.Preadditive",
"CategoryTheory.Preadditive.preadditiveHasZeroMorphisms",
... | true |
DirectLimit.instAddMonoid._proof_6 | Mathlib.Algebra.Colimit.DirectLimit | [
"instHSMul",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"LE.le",
"Nat",
"AddMonoid",
"HSMul.hSMul",
"map_nsmul",
"Eq",
"DFunLike.coe",
"Preorder",
"FunLike"
] | false |
Asymptotics.IsLittleO.sub | Mathlib.Analysis.Asymptotics.Defs | [
"Eq.mpr",
"NegZeroClass.toNeg",
"SeminormedAddCommGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"Norm",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"Asymptotics.IsLittleO.neg_left",
"SubNegZeroMonoid.to... | true |
Int.sub_lt_sub_right_iff._simp_1 | Init.Data.Int.Order | [
"HSub.hSub",
"Int",
"Int.instLTInt",
"Int.sub_lt_sub_right_iff",
"instHSub",
"LT.lt",
"propext",
"Int.instSub",
"Eq"
] | false |
Lean.Grind.NoopConfig.noConfusionType | Init.Grind.Config | [
"Lean.Grind.Config",
"Lean.Grind.NoopConfig",
"Eq",
"Lean.Grind.NoopConfig.casesOn"
] | false |
_private.Lean.Compiler.LCNF.Simp.DefaultAlt.0.Lean.Compiler.LCNF.Simp.addDefaultAlt.match_7 | Lean.Compiler.LCNF.Simp.DefaultAlt | [
"Prod.mk",
"Lean.Compiler.LCNF.Purity.pure",
"Nat",
"Prod",
"Prod.casesOn",
"Lean.Compiler.LCNF.Alt"
] | false |
_private.Lean.Meta.Tactic.Simp.Types.0.Lean.Meta.Simp.tryAutoCongrTheorem?._proof_1 | Lean.Meta.Tactic.Simp.Types | [
"Subarray",
"Lean.Meta.Simp.Config",
"Lean.Meta.Simp.Config.ground",
"Lean.Expr",
"Lean.Meta.Simp.Result",
"Prod.fst",
"Array",
"Bool.true",
"Lean.Meta.ParamInfo",
"Lean.Meta.CongrArgKind",
"And",
"Lean.Meta.FunInfo",
"And.right",
"Nat",
"LT.lt",
"Bool",
"instLTNat",
"Prod",
"Eq"... | false |
_private.Mathlib.Order.Defs.PartialOrder.0.le_antisymm_iff.match_1_1 | Mathlib.Order.Defs.PartialOrder | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"LE.le",
"And.casesOn",
"And",
"And.intro"
] | false |
Digraph.toSimpleGraphStrict._proof_1 | Mathlib.Combinatorics.Digraph.Orientation | [
"Digraph",
"Ne",
"Ne.symm",
"And",
"And.right",
"And.left",
"And.intro",
"Digraph.Adj",
"And.symm"
] | false |
_private.Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties.0.AlgebraicGeometry.affineLocally_iff_forall_isAffineOpen._simp_1_1 | Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"CommRing",
"AlgebraicGeometry.Scheme",
"CommRingCat.Hom.hom",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPa... | false |
Set.singleton_subset_singleton._gcongr_1 | Mathlib.Data.Set.Insert | [
"Iff.mpr",
"Set.singleton_subset_singleton",
"Set.instSingletonSet",
"HasSubset.Subset",
"Singleton.singleton",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
USize.toNat_ofFin | Init.Data.UInt.Lemmas | [
"USize.ofFin",
"Fin.val",
"USize.toNat",
"Nat",
"USize.size",
"Fin",
"Eq",
"rfl"
] | true |
_private.Mathlib.GroupTheory.GroupAction.Blocks.0.MulAction.IsBlock.of_subset._simp_1_3 | Mathlib.GroupTheory.GroupAction.Blocks | [
"DivInvMonoid.toInv",
"HMul.hMul",
"Monoid.toMulOneClass",
"DivisionMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"DivisionMonoid.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"mul_inv_rev",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Orientation.oangle_sign_sub_smul_left | Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"Orientation",
"Real.partialOrder",
"neg_smul",
"Real",
"instHSMul",
"Orientation.oangle",
"Real.instRCLike",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoi... | true |
_private.Batteries.Data.Random.MersenneTwister.0.Batteries.Random.MersenneTwister.Config.lMask | Batteries.Data.Random.MersenneTwister | [
"BitVec.instHShiftRightNat",
"HSub.hSub",
"BitVec.allOnes",
"BitVec",
"instSubNat",
"Fin.val",
"instHSub",
"HShiftRight.hShiftRight",
"Batteries.Random.MersenneTwister.Config",
"Nat",
"Batteries.Random.MersenneTwister.Config.wordSize",
"Batteries.Random.MersenneTwister.Config.maskBits"
] | true |
Lean.Environment.imports | Lean.Environment | [
"Lean.Environment.header",
"Lean.Import",
"Array",
"Lean.EnvironmentHeader.imports",
"Lean.Environment"
] | true |
Std.Internal.IO.Async.System.GroupInfo.groupName | Std.Internal.Async.System | [
"String",
"Std.Internal.IO.Async.System.GroupInfo"
] | true |
Std.Internal.List.maxKey!_insertEntryIfNew | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"instDecidableEqOrdering",
"Ord",
"Std.TransOrd",
"Std.Internal.List.minKey!_insertEntryIfNew",
"Std.OrientedOrd.opposite",
"Std.TransOrd.opposite",
"Std.Internal.List.insertEntryIfNew",
"Ordering",
"inferInstance",
"Ord.compare",
"List",
"Std.Internal.List.... | true |
_private.Lean.Compiler.LCNF.Simp.SimpValue.0.Lean.Compiler.LCNF.Simp.simpCtorDiscr?.match_6 | Lean.Compiler.LCNF.Simp.SimpValue | [
"Lean.Compiler.LCNF.Arg",
"HEq.refl",
"Lean.Compiler.LCNF.LetValue",
"Eq.casesOn",
"Nat.hasNotBit",
"Lean.Level",
"Lean.Compiler.LCNF.Purity",
"_private.Lean.Compiler.LCNF.Simp.SimpValue.0.Lean.Compiler.LCNF.Simp.simpCtorDiscr?._sparseCasesOn_6",
"Lean.Compiler.LCNF.Purity.pure",
"Array",
"List"... | false |
_private.Mathlib.Algebra.Ring.GeomSum.0.geom_sum₂_mul_of_le._simp_1_1 | Mathlib.Algebra.Ring.GeomSum | [
"Finset",
"Membership.mem",
"Finset.mem_range",
"Finset.range",
"Finset.instSetLike",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Eq",
"SetLike.instMembership"
] | false |
Mathlib.Tactic.FieldSimp.Sign.mul.match_1 | Mathlib.Tactic.FieldSimp.Lemmas | [
"Unit.unit",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"Mathlib.Tactic.FieldSimp.Sign.minus",
"List.cons",
"Mathlib.Tactic.FieldSimp.Sign.casesOn",
"Unit",
"Qq.Quoted",
"Mathlib.Tactic.FieldSimp.Sign.plus",
"Mathlib.Tactic.FieldSimp.Sign",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean... | false |
Std.DTreeMap.minKeyD_le_minKeyD_erase | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.isEmpty",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Bool.true",
"Std.DTreeMap.wf",
"Std.DTreeMap.Internal.Impl.minKeyD_le_minKeyD_erase",
"Bool",
"Ordering.isLE",
"Bool.false",
"Std.DTreeMap.minKeyD",
"Eq",
"Std.DTreeMap.erase"
] | true |
Std.DHashMap.Internal.Raw.WFImp.mk._flat_ctor | Std.Data.DHashMap.Internal.Defs | [
"Std.Internal.List.DistinctKeys",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw.WFImp",
"Std.DHashMap.Internal.Raw.WFImp.mk",
"Nat",
"Std.DHashMap.Raw.buckets",
"Std.DHashMap.Internal.toListModel",
"Hashable",
"Std.DHashMap.Raw.size",
"BEq",
"Eq",
"List.length",
"Std.DHashMap.Internal.IsHas... | false |
CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ._proof_6 | Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct | [
"_private.Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct.0.CategoryTheory.Limits.SequentialProduct.functorMap_commSq_succ._proof_5",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat"
] | false |
HasDerivWithinAt.clog | Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Complex.log",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"Complex.instNormedAddCommGroup",
"DivInvOneMonoid.toInvOneClass",
"IsTopologicalRing.toIsTopologi... | true |
LinearEquiv.symmEquiv_apply_symm_apply | Mathlib.Algebra.Module.Equiv.Defs | [
"LinearEquiv.symm",
"Equiv.instEquivLike",
"LinearEquiv.symmEquiv",
"RingHom",
"Equiv",
"AddCommMonoid",
"RingHomInvPair",
"LinearEquiv",
"Semiring",
"LinearEquiv.instEquivLike",
"Eq.refl",
"Module",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
List.alternatingProd._sunfold | Mathlib.Algebra.BigOperators.Group.List.Defs | [
"List.alternatingSum.match_1",
"One",
"Inv",
"HMul.hMul",
"Mul",
"List.alternatingProd",
"List",
"Unit",
"Inv.inv",
"One.toOfNat1",
"OfNat.ofNat",
"instHMul"
] | false |
QuotientAddGroup.induction_on | Mathlib.GroupTheory.Coset.Defs | [
"Quotient.inductionOn'",
"QuotientAddGroup.mk",
"AddSubgroup",
"HasQuotient.Quotient",
"AddGroup",
"QuotientAddGroup.instHasQuotientAddSubgroup",
"QuotientAddGroup.leftRel"
] | true |
ProbabilityTheory.Kernel.compProd_of_not_isSFiniteKernel_left | Mathlib.Probability.Kernel.Composition.CompProd | [
"MeasurableEquiv.instEquivLike",
"False",
"eq_false",
"congrArg",
"ProbabilityTheory.Kernel.comp",
"ProbabilityTheory.IsSFiniteKernel",
"ProbabilityTheory.Kernel.zero_comp",
"ProbabilityTheory.Kernel.comp_zero",
"MeasurableEquiv.symm",
"ProbabilityTheory.Kernel.deterministic",
"ProbabilityTheory... | true |
_private.Mathlib.Topology.Bornology.Absorbs.0.absorbs_inter._simp_1_1 | Mathlib.Topology.Bornology.Absorbs | [
"GroupWithZero.toMonoidWithZero",
"instHSMul",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Filter.Eventually",
"GroupWithZero",
"DivisionMonoid.toDivInvOneMonoid",
"absorbs_iff_eventually_cobounded_mapsTo",
"Inv.inv",
"Set.MapsTo",
"MulAction",
"propext",
"Monoid.toSe... | false |
_private.Mathlib.Algebra.BigOperators.Intervals.0.Finset.sum_Ico_Ico_comm._proof_1_4 | Mathlib.Algebra.BigOperators.Intervals | [
"Lean.RArray.leaf",
"False",
"Preorder.toLT",
"of_decide_eq_true",
"Lean.Grind.not_and",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Lean.Grind._simp_1",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"Preorder... | false |
_private.Lean.Meta.Tactic.Cbv.TheoremsLookup.0.Lean.Meta.Sym.Simp.Theorems.insertMany | Lean.Meta.Tactic.Cbv.TheoremsLookup | [
"Lean.Meta.Sym.Simp.Theorems",
"Lean.Meta.Sym.Simp.Theorem",
"instOfNatNat",
"Array.foldl",
"Array",
"Nat",
"OfNat.ofNat",
"Lean.Meta.Sym.Simp.Theorems.insert",
"Array.size"
] | true |
PFun.fixInduction'._proof_2 | Mathlib.Data.PFun | [
"Part",
"Eq.mpr",
"PFun",
"outParam",
"HEq.refl",
"Membership.mem",
"Sum",
"Eq.casesOn",
"Part.instMembership",
"Sum.inl",
"Membership",
"PFun.fix",
"PFun.fix_stop",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"Part.mem_unique"
] | false |
isOpen_interior._simp_1 | Mathlib.Topology.Closure | [
"isOpen_interior",
"TopologicalSpace",
"True",
"interior",
"eq_true",
"IsOpen",
"Eq",
"Set"
] | false |
Order.Ideal.instInfSet | Mathlib.Order.Ideal | [
"iInf",
"LowerSet.instInfSet",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"InfSet.mk",
"InfSet",
"Order.Ideal.instInfSet._proof_4",
"Order.Ideal.toLowerSet",
"SemilatticeSup.toPartialOrder",
"LowerSet",
"Order.Ideal.mk",
"Order.Ideal",
"SemilatticeSup",
"... | true |
String.Slice.Pattern.Model.ForwardSliceSearcher.matchesAt_iff_splits | Init.Data.String.Lemmas.Pattern.String.Basic | [
"Eq.mpr",
"congrArg",
"String",
"String.Slice.Pattern.Model.ForwardSliceSearcher.instPatternModel",
"String.Slice",
"Exists",
"_private.Init.Data.String.Lemmas.Pattern.String.Basic.0.String.Slice.Pattern.Model.ForwardSliceSearcher.matchesAt_iff_splits.match_1_2",
"id",
"String.Slice.Pattern.Model.Fo... | true |
Plausible.InjectiveFunction.shrink._proof_1 | Mathlib.Testing.Plausible.Functions | [
"List.map",
"List.Perm",
"Sigma.fst",
"List.Nodup",
"List",
"And",
"And.intro",
"Sigma.snd",
"Sigma"
] | false |
Lean.Parser.Tactic.case' | Init.Tactics | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.sepBy1",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"Lean.Parser.Tactic.caseArg",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1",
... | true |
CategoryTheory.Coverage.mk.noConfusion | Mathlib.CategoryTheory.Sites.Coverage | [
"CategoryTheory.Coverage",
"CategoryTheory.Precoverage",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"CategoryTheory.Presieve.FactorsThruAlong",
"HEq.refl",
"Membership.mem",
"Exists",
"id",
"And",
"heq_of_eq",
"CategoryTheory.Coverage.noConfusion",
"... | false |
ValuativeRel.instCommRingWithPreorder._proof_45 | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"Semiring.toNatCast",
"ValuativeRel.instCommRingWithPreorder._proof_22",
"ValuativeRel.instCommRingWithPreorder._proof_25",
"CommRing",
"ValuativeRel.instCommRingWithPreorder._proof_3",
"AddGroupWithOne.intCast_ofNat._autoParam",
"ValuativeRel.instCommRingWithPreorder._proof_11",
"AddMonoid.mk",
"In... | false |
CategoryTheory.instHasLiftingPropertySnd | Mathlib.CategoryTheory.LiftingProperties.Limits | [
"CategoryTheory.HasLiftingProperty",
"CategoryTheory.Limits.pullback",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.IsPullback.hasLiftingProperty",
"CategoryTheory.Limits.pullback.fst",
"CategoryThe... | true |
PresheafOfModules.instAddCommGroupModuleColimit._aux_14 | Mathlib.Algebra.Category.ModuleCat.Presheaf.ColimitFunctor | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"Opposite",
"AddCommGrpCat.instCategory",
"AddCommGroup.toAddGroup",
"CategoryTheory.Limits.IsColimit",
"Ab",
"AddCommGrpCat.carrier",
"RingCat",
"SubNegMonoid.toSub",
"PresheafOfModules",
"AddGroup.toSubNegMonoid",
"RingCat.instCateg... | false |
Subsemiring.unop_eq_bot._simp_1 | Mathlib.Algebra.Ring.Subsemiring.MulOpposite | [
"Subsemiring.instBot",
"MulOpposite",
"Bot.bot",
"Subsemiring",
"NonAssocSemiring",
"propext",
"Subsemiring.unop",
"Subsemiring.unop_eq_bot",
"Eq",
"MulOpposite.instNonAssocSemiring"
] | false |
MeasureTheory.Measure.addHaarScalarFactor_smul_congr | Mathlib.MeasureTheory.Measure.Haar.Unique | [
"MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts",
"Eq.mpr",
"DomMulAct",
"NNReal.instCommSemiring",
"instHSMul",
"MeasureTheory.Measure",
"HMul.hMul",
"MeasureTheory.Measure.IsAddHaarMeasure.domSMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"DistribMulAction.toDis... | true |
Aesop.ForwardRuleMatches.noConfusionType | Aesop.Tree.Data.ForwardRuleMatches | [
"Aesop.ForwardRuleMatch",
"Aesop.ForwardRuleMatches.casesOn",
"Lean.PHashSet",
"Aesop.instHashableForwardRuleMatch",
"Aesop.ForwardRuleMatches",
"Eq",
"Aesop.instBEqForwardRuleMatch"
] | false |
DFinsupp.instLocallyFiniteOrder | Mathlib.Data.DFinsupp.Interval | [
"DFinsupp.rangeIcc",
"instDecidableNot",
"Finset.instUnion",
"Finset",
"PartialOrder.toPreorder",
"PartialOrder",
"DFinsupp.instDFunLike",
"DFinsupp.support",
"DFinsupp.instPreorder",
"DFinsupp.instDecidableEq",
"DFinsupp.instLocallyFiniteOrder._proof_3",
"DFinsupp.instPartialOrder",
"Locall... | true |
NonemptyFinLinOrd.mk | Mathlib.Order.Category.NonemptyFinLinOrd | [
"NonemptyFinLinOrd.mk",
"LinOrd.carrier",
"LinOrd",
"Fintype",
"Nonempty",
"NonemptyFinLinOrd"
] | true |
_private.Init.Data.Format.Basic.0.Std.Format.WorkGroup | Init.Data.Format.Basic | [
"_private.Init.Data.Format.Basic.0.Std.Format.WorkGroup.mk"
] | true |
instMonoidWithConvMatrix._proof_4 | Mathlib.LinearAlgebra.Matrix.WithConv | [
"Monoid",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"Matrix",
"MulOneClass.mul_one",
"MulOne.toMul",
"MulOneClass.toMulOne",
"One.toOfNat1",
"WithConv",
"instMulOneClassWithConvMatrix",
"OfNat.ofNat",
"Eq",
"instHMul"
] | false |
Lean.Meta.DefEqCacheKind | Lean.Meta.ExprDefEq | [
"Lean.Meta.DefEqCacheKind.permanent",
"Lean.Meta.DefEqCacheKind.transient"
] | true |
Lean.Elab.Term.Quotation.MatchResult.noConfusion | Lean.Elab.Quotation | [
"Lean.Elab.Term.Quotation.MatchResult.casesOn",
"Lean.Elab.Term.Quotation.Alt",
"Lean.Elab.Term.Quotation.MatchResult.noConfusionType",
"Lean.Elab.Term.TermElabM",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Lean.Elab.Term.Quotation.MatchResult",
"Eq"
] | false |
Finset.instFintypeSubtypeMemSubgroupInvMulSubgroup._simp_2 | Mathlib.Combinatorics.Additive.VerySmallDoubling | [
"HMul.hMul",
"Finset",
"Mul",
"Finset.coe_mul",
"Finset.mul",
"SetLike.coe",
"Finset.instSetLike",
"Set.mul",
"Eq.symm",
"Eq",
"instHMul",
"DecidableEq",
"Set"
] | false |
MulRingSeminormClass.toMonoidHomClass | Mathlib.Algebra.Order.Hom.Basic | [
"outParam",
"PartialOrder",
"NonAssocSemiring.toMulZeroOneClass",
"NonAssocRing",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"MulOneClass.toMulOne",
"Semiring",
"MonoidHomClass",
"MulRingSeminormClass",
"NonAssocRing.toNonAssocSemiring",
"FunLike"
] | true |
_private.Lean.Elab.CheckTactic.0.Lean.Elab.CheckTactic.elabCheckTactic.match_8 | Lean.Elab.CheckTactic | [
"Lean.MVarId",
"Prod.mk",
"List",
"Lean.Elab.Term.State",
"Prod",
"Prod.casesOn"
] | false |
HomologicalComplex.Hom.isIso_of_components | Mathlib.Algebra.Homology.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.IsIso",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.Hom.isoOfComponents",
"congrArg",
"HomologicalComplex",
"ComplexShape",
"CategoryTheory.Iso... | true |
_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.NormalizePattern.Context.symPrios | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.NormalizePattern.Context",
"Lean.Meta.Grind.SymbolPriorities"
] | true |
exists_seq_strictAnti_strictMono_tendsto | Mathlib.Topology.Order.IsLUB | [
"zero_le",
"Nat.instMulZeroClass",
"OrderTopology",
"exists_seq_strictAnti_tendsto'",
"Preorder.toLT",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"StrictMono",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"... | true |
Asymptotics.IsLittleO.forall_isBigOWith | Mathlib.Analysis.Asymptotics.Defs | [
"Real",
"Asymptotics.IsBigOWith",
"Real.instZero",
"Real.instLT",
"Norm",
"LT.lt",
"Iff.mp",
"Zero.toOfNat0",
"Asymptotics.IsLittleO",
"OfNat.ofNat",
"Asymptotics.isLittleO_iff_forall_isBigOWith",
"Filter"
] | true |
MvPowerSeries.lexOrder_eq_top_iff_eq_zero._simp_1 | Mathlib.RingTheory.MvPowerSeries.LexOrder | [
"Nat.instMulZeroClass",
"Preorder.toLT",
"MvPowerSeries.instZero",
"Lex",
"LinearOrder",
"MvPowerSeries.lexOrder",
"WellFoundedGT",
"PartialOrder.toPreorder",
"MvPowerSeries",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"WithTop.top",
"Nat",
"MvPowerSeries.lexOrder_eq_top_... | false |
_private.Batteries.Data.Fin.Coding.0.Fin.encodeSigma.match_1.splitter | Batteries.Data.Fin.Coding | [
"Fin.succ",
"Zero.ofOfNat0",
"Fin.mk",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Fin.encodeSigma.match_1",
"instAddNat",
"instLTNat",
"Fin.sum",
"OfNat.ofNat",
"Fin"
] | true |
ContinuousMap.instNormedCommRing._proof_2 | Mathlib.Topology.ContinuousMap.Compact | [
"NormedCommRing.toSeminormedCommRing",
"NormedCommRing.toCommRing",
"Semigroup.toMul",
"CommRing",
"HMul.hMul",
"ContinuousMap.instNormedCommRing._proof_1",
"NormedCommRing",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"inferInstance",
"TopologicalSpace",
"ContinuousMap.instCommRingOf... | false |
SSet.Subcomplex.N.mk | Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplicesSubcomplex | [
"Opposite",
"SSet.nonDegenerate",
"Membership.mem",
"CategoryTheory.Subfunctor.obj",
"SSet.Subcomplex.N",
"SSet",
"SSet.N.mk'",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"CategoryTheory.types",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"SSet.Subcomplex.N.mk'",
"SSet.Subcom... | true |
em | Mathlib.Logic.Basic | [
"Classical.em",
"Or",
"Not"
] | true |
Mathlib.Tactic.Algebra.RingCompute.add | Mathlib.Tactic.Algebra.Basic | [
"Qq.QuotedDefEq",
"Pure.pure",
"_private.Mathlib.Tactic.Algebra.Basic.0.Mathlib.Tactic.Algebra.RingCompute.add.match_1",
"Mathlib.Tactic.Ring.Common.Result.mk",
"Mathlib.Tactic.Ring.Common.Cache",
"Mathlib.Tactic.Ring.RatCoeff",
"Lean.Meta.State",
"Lean.Expr.const",
"_private.Mathlib.Tactic.Algebra.... | true |
PolynomialLaw.instAddCommMonoid._proof_4 | Mathlib.RingTheory.PolynomialLaw.Basic | [
"PolynomialLaw.instSMul",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"PolynomialLaw",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Nat.cast",
... | false |
IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic | Mathlib.FieldTheory.LinearDisjoint | [
"Subalgebra.instSetLike",
"Module.FaithfullyFlat.instOfNontrivialOfFree",
"Set.ext",
"Eq.mpr",
"IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic",
"AlgEquiv.ofInjectiveField",
"SubsemiringClass.nontrivial",
"RingEquiv.subsemiringCongr",
"instHSMul",
"NonUnitalCommRing.toNonUn... | true |
TwoSidedIdeal.opOrderIso_apply | Mathlib.RingTheory.TwoSidedIdeal.Basic | [
"NonUnitalNonAssocRing",
"TwoSidedIdeal",
"MulOpposite",
"PartialOrder.toPreorder",
"Preorder.toLE",
"TwoSidedIdeal.op",
"LE.le",
"TwoSidedIdeal.opOrderIso",
"RelIso",
"RelIso.instFunLike",
"Eq.refl",
"MulOpposite.instNonUnitalNonAssocRing",
"Eq",
"DFunLike.coe",
"TwoSidedIdeal.instParti... | true |
_private.Mathlib.MeasureTheory.Measure.WithDensity.0.MeasureTheory.withDensity_apply_eq_zero'._simp_1_4 | Mathlib.MeasureTheory.Measure.WithDensity | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
Mathlib.Meta.NormNum.proveJacobiSym | Mathlib.Tactic.NormNum.LegendreSymbol | [
"Lean.Expr.natLit!",
"Lean.Expr.const",
"Lean.Name.mkStr5",
"Mathlib.Meta.NormNum.mkRawIntLit",
"instHMod",
"Lean.Expr.sort",
"Lean.Level",
"Int",
"Nat.cast",
"List.cons",
"HMod.hMod",
"Unit",
"Qq.Quoted",
"_private.Mathlib.Tactic.NormNum.LegendreSymbol.0.Mathlib.Meta.NormNum.proveJacobiSy... | true |
Std.ExtTreeSet.insertMany_nil | Std.Data.ExtTreeSet.Lemmas | [
"instForInOfForIn'",
"Ordering",
"inferInstance",
"Std.TransCmp",
"Id",
"Membership",
"List",
"List.instMembership",
"Std.ExtTreeSet",
"Id.instMonad",
"Std.ExtTreeSet.insertMany",
"Eq",
"rfl",
"List.nil",
"List.instForIn'InferInstanceMembershipOfMonad"
] | true |
Ideal.count_associates_eq | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"UniqueFactorizationMonoid.normalizedFactors",
"Prime.irreducible",
"Iff.mpr",
"Eq.mpr",
"Associates.mk",
"Submodule",
"IsDedekindDomain.toIsDomain",
"False",
"CommRing",
"IsDomain.to_noZeroDivisors",
"Dvd.dvd",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hM... | true |
CategoryTheory.Kleisli.Adjunction.adj._proof_4 | Mathlib.CategoryTheory.Monad.Kleisli | [
"CategoryTheory.Kleisli.Hom.of",
"CategoryTheory.Monad",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Kleisli.Adjunction.adj._proof_2",
"CategoryTheory.Kleisli",
"Equiv.mk",
"id",
"Equiv",
"CategoryTheory.Functor.map",
"CategoryTheory.Kleisli.A... | false |
Std.DHashMap.mem_of_mem_filter | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.Raw",
"Membership.mem",
"Std.DHashMap.instMembership",
"Std.DHashMap.wf",
"instOfNatNat",
"LawfulHashable",
"Subtype.mk",
"EquivBEq",
"Std.DHashMap.inner",
"Std.DHashMap.filter",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Bool",
"Std.DHashMap.Internal.AssocList",
"Hasha... | true |
Batteries.RBNode.forM._f | Batteries.Data.RBMap.Basic | [
"Pure.pure",
"Batteries.RBNode",
"Batteries.RBNode.fold.match_1",
"Batteries.RBNode.below",
"Monad.toApplicative",
"Batteries.RBNode.nil",
"Applicative.toPure",
"Unit",
"Batteries.RBColor",
"PUnit",
"Monad.toBind",
"Bind.bind",
"PUnit.unit",
"Monad",
"Batteries.RBNode.node"
] | false |
Std.DTreeMap.Raw.get?_alter | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.get?",
"instDecidableEqOrdering",
"congrArg",
"Std.LawfulEqCmp.compare_eq_iff_eq",
"Ord.mk",
"cast",
"Function.comp",
"Std.DTreeMap.Raw.alter",
"Ordering",
"Ordering.eq",
"Std.TransCmp",
"dite",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Internal.Impl.get?_alter!",
"Std.L... | true |
ULift.mulAction._proof_1 | Mathlib.Algebra.Module.ULift | [
"Monoid",
"Semigroup.toMul",
"instHSMul",
"HMul.hMul",
"ULift",
"MulAction",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq",
"ULift.down",
"SemigroupAction.mul_smul",
"instHMul"
] | false |
Std.DTreeMap.Internal.Impl.Const.getD_diff_of_contains_eq_false_right | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Bool.not",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"Std.DTreeMap.Internal.Impl.contains_eq_containsKey",
"beqOfOrd",
"List.map",
"Std.DTreeMap.Internal.Impl.Ordered.distinctKeys",
"Std.TransOrd",
"List.contains",
"Std.DTreeMap.Internal.Impl.Con... | true |
AddSubgroup.mk_le_mk._simp_1 | Mathlib.Algebra.Group.Subgroup.Defs | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"AddSubsemigroup.carrier",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid.toAddSubsemigroup",
"AddSubmonoid",
"SubtractionMon... | false |
EReal.induction₂_symm | Mathlib.Data.EReal.Basic | [
"Real",
"Real.instZero",
"EReal",
"Real.instLT",
"instTopEReal",
"Bot.bot",
"instZeroEReal",
"LT.lt",
"EReal.induction₂",
"Zero.toOfNat0",
"Top.top",
"OfNat.ofNat",
"instBotEReal",
"Real.toEReal"
] | true |
CategoryTheory.MonoidalCategory.Limits.pushout.associator_naturality_left_condition_assoc | Mathlib.CategoryTheory.Monoidal.Limits.Shapes.Pullback | [
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.MonoidalCategory.Limits.pushout.associator_naturality_left_condition",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver"... | true |
MDifferentiableOn.clm_bundle_apply₂ | Mathlib.Geometry.Manifold.VectorBundle.Hom | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedSpace._proof_1",
"ContinuousLinearMap.toNormedAddCommGroup",
"ContinuousLinearMap.continuousSMul",
"RingHomSurjective.ids",
"Prod.normedSpace",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"Un... | true |
LightProfinite.instInhabited._proof_3 | Mathlib.Topology.Category.LightProfinite.Basic | [
"TopologicalSpace.MetrizableSpace.toPseudoMetrizableSpace",
"CategoryTheory.instFinCategoryOfFiniteOfIsThin",
"SecondCountableTopology",
"CategoryTheory.CountableCategory.countableObj",
"PartialOrder.toPreorder",
"Countable.LindelofSpace",
"TopologicalSpace.instSecondCountableTopologyOfLindelofSpaceOfPs... | false |
List.erase_eq_eraseIdx | Init.Data.List.Erase | [
"Eq.mpr",
"Decidable.casesOn",
"_private.Init.Data.List.Erase.0.List.eraseP_eq_eraseIdx.match_1.splitter",
"List.eraseIdx",
"congrArg",
"Decidable",
"Option.some",
"id",
"List.idxOf?_cons",
"instDecidableEqBool",
"instOfNatNat",
"List.rec",
"if_pos",
"List.eraseP_eq_eraseIdx.match_1",
"L... | true |
Bool.or_eq_true_iff | Init.Data.Bool | [
"congrArg",
"iff_self",
"Bool.true",
"Bool.or_eq_true",
"Iff",
"True",
"Bool",
"of_eq_true",
"Bool.or",
"congrFun'",
"Or",
"implies_true",
"Eq",
"Eq.trans",
"forall_congr"
] | true |
ContinuousLinearEquiv.symm_comp_self | Mathlib.Topology.Algebra.Module.Equiv | [
"ContinuousLinearEquiv.symm",
"RingHom",
"Function.comp",
"id",
"ContinuousLinearEquiv.equivLike",
"AddCommMonoid",
"RingHomInvPair",
"TopologicalSpace",
"funext",
"ContinuousLinearEquiv",
"Semiring",
"ContinuousLinearEquiv.symm_apply_apply",
"Module",
"Semiring.toNonAssocSemiring",
"Eq"... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Equiv.getKeyD_eq._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
LocallyConstant.instNonAssocSemiring._proof_5 | Mathlib.Topology.LocallyConstant.Algebra | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"AddMonoid.toNSMul",
"LocallyConstant",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"TopologicalSpace",
"LocallyConstant.instAddMonoid",
"NonAssocSemiring",
"Nat",
"HSMul.hSMul",
"LocallyConstant.instFunLike",
"AddMonoidWithOne.toAddMonoid... | false |
_private.Init.Data.Option.Lemmas.0.Option.none_lt._simp_1_1 | Init.Data.Option.Lemmas | [
"Option.some",
"instLTOption",
"Option.none_lt_some",
"Option.none",
"LT.lt",
"True",
"eq_true",
"Eq",
"LT",
"Option"
] | false |
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