name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Diffeomorph.prodComm_symm | Mathlib.Geometry.Manifold.Diffeomorph | [
"Diffeomorph.symm",
"Prod.normedSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"instTopologicalSpaceProd",
"instTopologicalSpaceModelProd",
"Diffeomorph",
"TopologicalSpace",
"ModelWithCorners",
"ENat",
"Diffeomorph.prodComm",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedFi... | true |
_private.Mathlib.Logic.Nonempty.0.nonempty_pprod.match_1_3 | Mathlib.Logic.Nonempty | [
"Nonempty.intro",
"And.casesOn",
"And",
"Nonempty.casesOn",
"And.intro",
"Nonempty"
] | false |
_private.Init.Data.String.Termination.0.String.Pos.remainingBytes_inj._simp_1_1 | Init.Data.String.Termination | [
"String.toSlice",
"String",
"String.Pos.remainingBytes_toSlice",
"String.Pos.toSlice",
"Nat",
"String.Pos",
"Eq.symm",
"String.Pos.remainingBytes",
"Eq",
"String.Slice.Pos.remainingBytes"
] | false |
Lean.Meta.LibrarySearch.DeclMod.mp | Lean.Meta.Tactic.LibrarySearch | [
"Lean.Meta.LibrarySearch.DeclMod.mp",
"Lean.Meta.LibrarySearch.DeclMod"
] | true |
Lean.Widget.MsgEmbed.rec_2 | Lean.Widget.InteractiveDiagnostic | [
"Lean.Widget.StrictOrLazy",
"Lean.Widget.TaggedText.tag",
"Lean.Server.WithRpcRef",
"String",
"Lean.Widget.StrictOrLazy.lazy",
"Lean.Widget.MsgEmbed.trace",
"Lean.Widget.WidgetInstance",
"Lean.Widget.StrictOrLazy.strict",
"Lean.Widget.TaggedText",
"List.cons",
"Array",
"List",
"Lean.Widget.M... | false |
stdSimplex.map | Mathlib.Analysis.Convex.StdSimplex | [
"Pi.Function.module",
"stdSimplex.map._proof_1",
"Semiring.toModule",
"Pi.addCommMonoid",
"IsOrderedRing",
"LinearMap.instFunLike",
"Membership.mem",
"PartialOrder",
"Set.Elem",
"Finite.of_fintype",
"LinearMap",
"Subtype.mk",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"FunOnFinite.linear... | true |
_private.Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift.0.CochainComplex.HomComplex.Cochain.δ_rightShift._proof_1_3 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"congrArg",
"Int.Linear.eq_norm",
"Classical.byContradiction",
"HSub.hSub",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Int.Linear.Poly.num",
... | false |
TopCat.continuousFunctions.pullback._proof_4 | Mathlib.Topology.Sheaves.CommRingCat | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Continuous",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"TopCommRingCat.instConcreteCategorySubtypeRingHomαContinuousCoe",
"TopCat.instCategory",
"ContinuousMap",
"AddMonoid.toAddZe... | false |
Equiv.optionSubtypeNe_symm_apply | Mathlib.Logic.Equiv.Option | [
"Equiv.instEquivLike",
"Option.some",
"Equiv",
"Subtype",
"Ne",
"dite",
"Subtype.mk",
"Option.none",
"Eq.refl",
"Equiv.optionSubtypeNe",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"Not",
"EquivLike.toFunLike",
"Option",
"DecidableEq"
] | true |
Real.two_pi_pos | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"instNeZeroNatHAdd_1",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"Mathlib.Tactic.Ring.Common.neg_add",
"Real.pi"... | true |
Nat.sub_lt_right_of_lt_add | Init.Data.Nat.Basic | [
"HSub.hSub",
"Eq.rec",
"instSubNat",
"LE.le",
"instLENat",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"Eq",
"Nat.sub_lt_left_of_lt_add",
"Nat.add_comm"
] | true |
DirectSum.IsInternal.coeAlgEquiv | Mathlib.RingTheory.GradedAlgebra.Basic | [
"Submodule",
"DirectSum.coeAlgHom",
"Submodule.addSubmonoidClass",
"RingEquiv.toEquiv",
"DirectSum.IsInternal",
"AddMonoid.toAddSemigroup",
"CommSemiring.toSemiring",
"RingEquiv.ofBijective",
"DirectSum.IsInternal.coeAlgEquiv._proof_2",
"AlgHom",
"DirectSum.instNonUnitalNonAssocSemiring",
"Sub... | true |
CochainComplex.homotopyUnop._proof_9 | Mathlib.Algebra.Homology.CochainComplexOpposite | [
"HomologicalComplex.instCategory",
"Opposite",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"AddCommGroup.toAddCommMonoid",
"Quiver.Hom.op_inj",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAd... | false |
_private.Lean.Meta.HaveTelescope.0.Lean.Meta.simpHaveTelescopeAux.match_11 | Lean.Meta.HaveTelescope | [
"_private.Lean.Meta.HaveTelescope.0.Lean.Meta.simpHaveTelescopeAux._sparseCasesOn_11",
"Lean.Expr.const",
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Level",
"List",
"Lean.Name",
"Lean.Expr.ctorIdx"
] | false |
Std.ExtDHashMap.get_insertMany_list_of_contains_eq_false | Std.Data.ExtDHashMap.Lemmas | [
"Eq.mpr",
"Std.ExtDHashMap.inner",
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.ExtDHashMap.insertMany",
"Std.ExtDHashMap.get.congr_simp",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"instForInOfForIn'",
"List.map",
"Std.DHashMap.get_insertMany_list_of_contains_eq_false",
"L... | true |
Real.instAddRightCancelSemigroup | Mathlib.Data.Real.Basic | [
"Real",
"AddCancelMonoid.toAddRightCancelMonoid",
"inferInstance",
"Real.instAddGroup",
"AddRightCancelSemigroup",
"AddRightCancelMonoid.toAddRightCancelSemigroup",
"AddGroup.toAddCancelMonoid"
] | true |
Ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem | Mathlib.RingTheory.Ideal.GoingUp | [
"Eq.mpr",
"Polynomial.C",
"RingHom.instRingHomClass",
"False",
"CommRing",
"Semiring.toModule",
"HMul.hMul",
"eq_false",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"RingHom",
"Membership.mem",
"Exists",
"Eq.mp",
"Polynomia... | true |
Lean.Elab.Tactic.Do.Context.mk.injEq | Lean.Elab.Tactic.Do.VCGen.Basic | [
"Lean.Elab.Tactic.Do.Context",
"Eq.propIntro",
"Lean.FVarIdMap",
"Lean.injEq_helper",
"Lean.Elab.Tactic.Do.SpecAttr.SpecTheorems",
"Lean.Elab.Tactic.Do.VCGen.Config",
"And",
"Nat",
"Lean.Meta.Simp.SimprocsArray",
"Eq.ndrec",
"Lean.Elab.Tactic.Do.JumpSiteInfo",
"Lean.Meta.Simp.Context",
"Eq.r... | true |
groupCohomology.d₀₁._proof_2 | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | [
"Eq.mpr",
"Pi.Function.module",
"Rep.V",
"CommRing",
"instHSMul",
"Representation",
"MonoidHom.instFunLike",
"SemilinearMapClass.toMulActionSemiHomClass",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Rep.h... | false |
Fintype.univ_ofIsEmpty | Mathlib.Data.Fintype.OfMap | [
"Finset.univ",
"Finset",
"IsEmpty",
"Finset.instEmptyCollection",
"Fintype.ofIsEmpty",
"EmptyCollection.emptyCollection",
"Eq",
"rfl"
] | true |
UInt8.shiftLeft_add_of_toNat_lt | Init.Data.UInt.Bitwise | [
"Dvd.dvd",
"BitVec.instOfNat",
"congrArg",
"UInt8.toBitVec_add",
"HShiftLeft.hShiftLeft",
"BitVec.instAdd",
"_private.Init.Data.UInt.Bitwise.0.UInt8.shiftLeft_add_of_toNat_lt._simp_1_1",
"BitVec",
"Nat.instMod",
"instHMod",
"BitVec.instHShiftLeftNat",
"instOfNatNat",
"BitVec.toNat",
"BitVe... | true |
_private.Init.Data.ByteArray.Bootstrap.0.List.toByteArray.match_1.splitter | Init.Data.ByteArray.Bootstrap | [
"List.toByteArray.match_1",
"List.cons",
"List",
"ByteArray",
"UInt8",
"List.nil"
] | true |
CategoryTheory.AddMon.EquivLaxMonoidalFunctorPUnit.counitIso._proof_4 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"PUnit.addCommGroup",
"CategoryTheory.Functor.comp",
"CategoryTheory.AddMon.instCategory",
"AddCommGroup.toAddGroup",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryT... | false |
SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton | Mathlib.Combinatorics.SimpleGraph.Triangle.Basic | [
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"False",
"Finset.coe_singleton",
"SimpleGraph.IsNClique",
"eq_false",
"Sym2.mem_iff._simp_1",
"SimpleGraph.Adj.ne",
"Sym2.mk",
"congrArg",
"and_self",
"true_or",
"Finset",
"SimpleGraph.Adj",
"False.elim",
"setOf",
"forall_eq_or_imp._simp_1",
"_priv... | true |
SimpleGraph.Walk.isSubwalk_concat._simp_1 | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | [
"SimpleGraph.Adj",
"SimpleGraph.Walk.isSubwalk_concat",
"SimpleGraph.Walk",
"SimpleGraph.Walk.concat",
"SimpleGraph",
"SimpleGraph.Walk.IsSubwalk",
"True",
"eq_true",
"Eq"
] | false |
_private.Lean.Data.Json.Printer.0.Lean.Json.CompressWorkItemQueue.popObjectFieldKey! | Lean.Data.Json.Printer | [
"_private.Lean.Data.Json.Printer.0.Lean.Json.CompressWorkItemQueue.mk",
"String",
"HSub.hSub",
"_private.Lean.Data.Json.Printer.0.Lean.Json.CompressWorkItemQueue.kinds",
"Prod.mk",
"instSubNat",
"instOfNatNat",
"Array.pop",
"Array",
"_private.Lean.Data.Json.Printer.0.Lean.Json.CompressWorkItemQueu... | true |
CategoryTheory.NatTrans.naturality_app | Mathlib.CategoryTheory.Functor.Category | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.map",
"congr_arg",
"CategoryTheory.NatTrans.naturality",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"congr_fun",
"Ca... | true |
CategoryTheory.InjectiveResolution.instInjectiveXNatOfCocomplex | Mathlib.CategoryTheory.Abelian.Injective.Resolution | [
"PSigma.snd",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Injective",
"Nat.instOne",
"CochainComplex.mkAux",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Injective.injective_under",
"CategoryTheory.InjectiveResolution.ofCocomplex",
"CategoryTheory.ShortComple... | true |
instNonAssocSemiringWithConvMatrix._proof_1 | Mathlib.LinearAlgebra.Matrix.WithConv | [
"MulOne.toOne",
"One.mk",
"AddMonoid.toAddSemigroup",
"Zero.zero",
"Matrix",
"Add.mk",
"AddMonoid.toZero",
"instNonUnitalNonAssocSemiringWithConvMatrix",
"Add.add",
"NonAssocSemiring.toMulZeroOneClass",
"instOfNatNat",
"MulZeroOneClass.toMulOneClass",
"NonUnitalNonAssocSemiring.toAddCommMono... | false |
FiberBundle.prod_trivializationAt' | Mathlib.Topology.FiberBundle.Constructions | [
"FiberBundle",
"instTopologicalSpaceProd",
"TopologicalSpace",
"Bundle.TotalSpace.proj",
"FiberBundle.trivializationAt",
"Bundle.TotalSpace",
"Bundle.Trivialization",
"FiberBundle.prod",
"FiberBundle.trivializationAt'",
"Eq.refl",
"Bundle.Trivialization.prod",
"FiberBundle.Prod.topologicalSpac... | true |
Matroid.contract_spanning_iff | Mathlib.Combinatorics.Matroid.Minor.Contract | [
"Eq.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Matroid.E",
"Set.union_subset_iff",
"Set.subset_union_right",
"Matroid.contract_ground",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"Set.instUnion",
"Matroid.contract_... | true |
CategoryTheory.Functor.preservesProjectiveObjects_of_isEquivalence | Mathlib.CategoryTheory.Preadditive.Projective.Preserves | [
"CategoryTheory.Equivalence.isEquivalence_inverse",
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Limits.PreservesColimits.preservesFiniteColimits",
"CategoryTheory.Functor.PreservesProjectiveObjects",
"CategoryTheory.Functor.isLeftAdjoint_of_isEquivalence",
"CategoryThe... | true |
Valued.maximalIdeal._proof_2 | Mathlib.Topology.Algebra.Valued.ValuedField | [
"ValuationRing.isLocalRing",
"ValuationRing.toPreValuationRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Subring.instSetLike",
"outParam",
"Valued.integer",
"CommSemiring.toSemiring",
"Valued.v",
"Membership.mem",
"Field.toDivisionRing",
"Subtype",
"... | false |
Lean.Parser.Command.open._regBuiltin.Lean.Parser.Command.openOnly.formatter_21 | Lean.Parser.Command | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Unit",
"Lean.Parser.Command.openOnly.formatter",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
Topology.IsInducing.r1Space | Mathlib.Topology.Separation.Basic | [
"Topology.IsInducing.specializes_iff",
"R1Space.of_continuous_specializes_imp",
"Specializes",
"R1Space",
"Topology.IsInducing",
"TopologicalSpace",
"Iff.mp",
"Topology.IsInducing.continuous"
] | true |
omegaLimit_def | Mathlib.Dynamics.OmegaLimit | [
"Filter.instMembership",
"omegaLimit",
"Set.iInter",
"Membership.mem",
"TopologicalSpace",
"closure",
"Set.image2",
"Eq",
"Filter",
"rfl",
"Set"
] | true |
Submonoid.comap_iInf | Mathlib.Algebra.Group.Submonoid.Operations | [
"iInf",
"Submonoid.instInfSet",
"GaloisConnection.u_iInf",
"Submonoid.map",
"Submonoid.instCompleteLattice",
"MulOneClass.toMulOne",
"Submonoid.comap",
"Submonoid.gc_map_comap",
"MonoidHomClass",
"MulOneClass",
"Eq",
"Submonoid",
"FunLike"
] | true |
_private.Mathlib.Order.Filter.Ultrafilter.Basic.0.Filter.tendsto_iff_ultrafilter._simp_1_1 | Mathlib.Order.Filter.Ultrafilter.Basic | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Filter.tendsto_iff_comap",
"LE.le",
"Filter.Tendsto",
"propext",
"Eq",
"Filter",
"Filter.comap",
"Filter.instPartialOrder"
] | false |
Real.Angle.two_zsmul_toReal_eq_two_mul | Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle | [
"Eq.mpr",
"Set.Ioc",
"Real",
"instHSMul",
"instHDiv",
"Real.pi",
"HMul.hMul",
"Real.Angle",
"congrArg",
"Real.instDivInvMonoid",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"Nat.instAtLeastTwoHAddOfNat",
"AddMonoid.toNSMul",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAdd... | true |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.toArray_rco_eq_singleton_iff._proof_1_1 | Init.Data.Range.Polymorphic.NatLemmas | [
"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",
"Classical.propDecidable",... | false |
WithVal.instAlgebra._proof_4 | Mathlib.Topology.Algebra.Valued.WithVal | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"CommRing",
"HMul.hMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"LinearOrderedCommGroupWithZero",
"WithVal.equiv",
"NonUnitalRingHom.comp",
"MulHom.toFun",
"CommRing.toCommSemiring",
"Distrib.toMul",
"No... | false |
MeasureTheory.ae_le_toMeasurable | Mathlib.MeasureTheory.Measure.MeasureSpaceDef | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"Prop.le",
"HasSubset.Subset.eventuallyLE",
"MeasureTheory.subset_toMeasurable",
"MeasurableSpace",
"MeasureTheory.toMeasurable",
"Filter.EventuallyLE",
"MeasureTheory.Measure.instFunLike",
"MeasureTheory.Measure.instOuterMeasureClass",
"Set"
] | true |
_private.Mathlib.Probability.Decision.Risk.Basic.0.ProbabilityTheory.avgRisk_le_mul'._simp_1_1 | Mathlib.Probability.Decision.Risk.Basic | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Set.indicator_eq_zero._simp_1 | Mathlib.Algebra.Notation.Indicator | [
"Set.indicator",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.indicator_eq_zero",
"BooleanAlgebra.toBiheytingAlgebra",
"Function.support",
"Set.instBooleanAlgebra",
"propext",
"CoheytingAlgebra.toGeneralizedCoheytin... | false |
Std.ExtTreeMap.isEmpty_iff._simp_1 | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtTreeMap.isEmpty_iff",
"Std.ExtTreeMap.isEmpty",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.ExtTreeMap",
"propext",
"Bool",
"EmptyCollection.emptyCollection",
"Std.ExtTreeMap.instEmptyCollection",
"Eq"
] | false |
IsOfFinOrder.isUnit | Mathlib.GroupTheory.OrderOfElement | [
"Monoid",
"Units.val",
"IsUnit",
"Units",
"IsOfFinOrder.unit",
"Exists.intro",
"Eq",
"IsOfFinOrder",
"rfl"
] | true |
Std.Rcc.ctorIdx | Init.Data.Range.Polymorphic.PRange | [
"Nat",
"Std.Rcc"
] | false |
Mathlib.Tactic.TermCongr.unexpandCHole | Mathlib.Tactic.TermCongr | [
"Pure.pure",
"Lean.TSyntax",
"Unit.unit",
"instMonadExceptOfMonadExceptOf",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.TSyntax.raw",
"instDecidableEqBool",
"instOfNatNat",
"Applicative.toPure",
... | true |
instIsAtomisticSubmodule | Mathlib.LinearAlgebra.Basis.VectorSpace | [
"Iff.mpr",
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"AddMonoid.toAddZeroClass",
"Submodule.submodule_eq_sSup_le_nonzero_spans",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"CompleteLattice.toConditionallyCompleteLattice",
... | true |
AddOpposite.instNonUnitalSemiring | Mathlib.Algebra.Ring.Opposite | [
"SemigroupWithZero",
"AddOpposite",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalSemiring.toSemigroupWithZero",
"AddOpposite.instSemigroupWithZero",
"AddOpposite.instNonUnitalSemiring._proof_1",
"NonUnitalSemiring",
"NonUnitalSemiring.mk",
"NonUnitalNonAssocSemiring",
"AddOpposite.in... | true |
_private.Init.Data.UInt.Lemmas.0.UInt8.toUSize_le._simp_1_2 | Init.Data.UInt.Lemmas | [
"instLEUSize",
"USize.le_iff_toNat_le",
"LE.le",
"instLENat",
"USize.toNat",
"Nat",
"propext",
"Eq",
"USize"
] | false |
_private.Init.Data.String.Slice.0.String.Slice.SplitInclusiveIterator.toOption.match_1 | Init.Data.String.Slice | [
"Unit.unit",
"String.Slice.Pattern.SearchStep",
"String.Slice.SplitInclusiveIterator",
"String.Slice",
"String.Slice.Pattern.ToForwardSearcher",
"Unit",
"Std.Iter",
"String.Slice.SplitInclusiveIterator.operating",
"String.Slice.Pos",
"String.Slice.SplitInclusiveIterator.casesOn",
"String.Slice.S... | false |
Equiv.sigmaProdDistrib._proof_4 | Mathlib.Logic.Equiv.Prod | [
"_private.Mathlib.Logic.Equiv.Prod.0.Equiv.sigmaProdDistrib._proof_3",
"Prod.mk",
"Sigma.fst",
"Prod.fst",
"Function.RightInverse",
"Sigma.mk",
"Prod",
"Sigma.snd",
"Prod.snd",
"Sigma"
] | false |
Lean.StructureResolutionOrderConflict.ctorIdx | Lean.Structure | [
"Lean.StructureResolutionOrderConflict",
"Nat"
] | false |
SimpleGraph.cliqueSet_zero | Mathlib.Combinatorics.SimpleGraph.Clique | [
"Set.ext",
"SimpleGraph.IsNClique",
"congrArg",
"Finset",
"Membership.mem",
"SimpleGraph.isNClique_zero._simp_1",
"Set.instSingletonSet",
"instOfNatNat",
"Finset.instEmptyCollection",
"SimpleGraph",
"iff_self",
"SimpleGraph.mem_cliqueSet_iff._simp_1",
"Iff",
"Nat",
"congr",
"True",
"... | true |
CategoryTheory.PreZeroHypercover.I₀ | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover",
"CategoryTheory.Category"
] | true |
Cardinal.IsStrongLimit.isSuccLimit | Mathlib.SetTheory.Cardinal.Order | [
"Eq.mpr",
"Preorder.toLT",
"Order.IsSuccPrelimit",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Order.IsSuccLimit",
"id",
"Ne",
"And",
"Cardinal.partialOrder",
"Cardinal.IsStrongPrelimit.isSuccPrelimit",
"Cardinal.isSuccLimit_iff",
"Cardinal.IsStrongLimit.ne_zero",
"And.intro",
... | true |
CategoryTheory.GrpObj.lift_comp_inv_left | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.Category.assoc",
"CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unique",
"CategoryTheory.GrpObj.inv",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.GrpObj.toMonObj",
"Eq.mp",
"id",
"CategoryTheory.Car... | true |
instFaithfulSMulOfIsRightCancelMul | Mathlib.Algebra.Group.Action.Faithful | [
"instHSMul",
"instSMulOfMul",
"Mul",
"Eq.mp",
"FaithfulSMul",
"FaithfulSMul.mk",
"HSMul.hSMul",
"mul_left_inj._simp_2",
"Eq",
"IsRightCancelMul"
] | true |
_private.Mathlib.Analysis.Complex.CauchyIntegral.0.Complex.analyticOnNhd_univ_iff_differentiable._simp_1_1 | Mathlib.Analysis.Complex.CauchyIntegral | [
"Differentiable",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"differentiableOn_univ",
"NormedField.toField",
"AddCommGroup",
"Field.toSemifield",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"DifferentiableOn",
"propext",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"N... | false |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_356 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"List.countP",
"Finset.mem_singleton",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Equiv.instEquivLike",
"Lean.Grind.nestedProof",
"List.idxOfNth_lt_length_iff",
"eq_false",
"instLawfulBEq",
"List.Pairwise",
"Lean.Grind.... | false |
PosSMulStrictMono.nnrat_of_rat | Mathlib.Algebra.Order.Module.Rat | [
"Eq.mpr",
"instHSMul",
"Preorder.toLT",
"congrArg",
"NNRat.instSemifield",
"IsScalarTower",
"Rat",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"NNRat.smulDivisionSemiring",
"DistribLattice.toLattice",
"id",
"NNRat",
"Field.toSemifield",
"DivisionSemiring.toNNRatCast",
"... | true |
List.subperm_of_subset | Batteries.Data.List.Perm | [
"List.Pairwise",
"List.instHasSubset",
"Membership.mem",
"_private.Batteries.Data.List.Perm.0.List.subperm_of_subset.match_1_1",
"List.Perm",
"HasSubset.Subset",
"Ne",
"List.cons",
"List.Nodup",
"List",
"And",
"List.instMembership",
"List.Subperm",
"List.forall_mem_cons",
"And.intro",
... | true |
CategoryTheory.Limits.Cocone.equivStructuredArrow | Mathlib.CategoryTheory.Limits.ConeCategory | [
"CategoryTheory.Limits.Cocone.fromStructuredArrow",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.Cocone.equivStructuredArrow._proof_6",
"CategoryTheory.Limits.Cocone.eta",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp"... | true |
_private.Lean.Compiler.LCNF.Simp.Main.0.Lean.Compiler.LCNF.Simp.specializePartialApp.match_1 | Lean.Compiler.LCNF.Simp.Main | [
"Unit.unit",
"Lean.Compiler.LCNF.Arg",
"Subarray",
"Option.casesOn",
"Option.some",
"Prod.mk",
"Lean.Compiler.LCNF.Purity.pure",
"Option.none",
"Unit",
"Prod",
"Prod.casesOn",
"Option"
] | false |
Multiset.rel_map | Mathlib.Data.Multiset.MapFold | [
"Multiset.rel_map_left",
"Multiset.map",
"Multiset.rel_map_right",
"Multiset",
"Multiset.Rel",
"Iff",
"Iff.trans"
] | true |
Finset.lt_eq_subset | Mathlib.Data.Finset.Defs | [
"Preorder.toLT",
"Finset",
"PartialOrder.toPreorder",
"HasSSubset.SSubset",
"Finset.partialOrder",
"LT.lt",
"Finset.instHasSSubset",
"Eq",
"rfl"
] | true |
CategoryTheory.Prod.sectL_obj | Mathlib.CategoryTheory.Products.Basic | [
"Prod.mk",
"CategoryTheory.Prod.sectL",
"CategoryTheory.prod'",
"Eq.refl",
"Prod",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Hall.0.SimpleGraph.exists_bijective_of_forall_ncard_le._simp_1_1 | Mathlib.Combinatorics.SimpleGraph.Hall | [
"Finset",
"SetLike.coe",
"Finset.instSetLike",
"Nat",
"Finset.card",
"Set.ncard",
"Eq.symm",
"Eq",
"Set.ncard_coe_finset"
] | false |
SSet.Truncated.HomotopyCategory.isoTerminal._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal | [
"of_decide_eq_true",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"Bool.true",
"SimplexCategory.mk",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable.decide",
"Eq",
"Nat.decLe",
"SimplexCategory.len"
] | false |
IntermediateField.adjoin_toSubfield | Mathlib.FieldTheory.IntermediateField.Adjoin.Defs | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"Subfield.closure",
"RingHom",
"Field.toDivisionRing",
"Set.instUnion",
"Field.toSemifield",
"RingHom.instFunLike",
"Semifield.toDivisionSemiring",
"IntermediateField.adjoin",
"DivisionSemiring.toSemiring",
"IntermediateField.toSubf... | true |
CliffordAlgebra.instAlgebra' | Mathlib.LinearAlgebra.CliffordAlgebra.Basic | [
"CommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"QuadraticForm",
"Algebra",
"CliffordAlgebra.instAlgebra'._aux_1",
"AddCommGroup.toAddGroup",
"Algebra.toSMul",
"AddZeroCla... | true |
_private.Mathlib.Data.Set.Prod.0.Set.disjoint_prod._simp_1_3 | Mathlib.Data.Set.Prod | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne | [
"ENNReal.instCanonicallyOrderedAdd",
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"frontier",
"lt_of_le_of_lt",
"Real",
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"Preorder.toLT",
"Complex.borelSpace",
"measureSpaceOfInnerProductSpace",
"HMul.hMul",
... | true |
CategoryTheory.Limits.binaryCofanZeroRight | Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.BinaryCofan",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.Limits.BinaryCofan.mk",
"CategoryTheory.Limits.HasZeroObject",
"Ze... | true |
UniqueMDiffWithinAt.bundle_preimage' | Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential | [
"Prod.normedSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"FiberBundle",
"PseudoMetricSpace.toUniformSpace",
"UniqueMDiffWithinAt",
"Bundle.TotalSpace.mk",
"instTopologicalSpaceModelProd",
"FiberBundle.chartedSpace",
"TopologicalSpace",
"Bundle.TotalSpace.proj",
"ModelWithCorners",
"Semi... | true |
Lean.Elab.Term.LevelMVarErrorInfo.logError | Lean.Elab.Term.TermElabM | [
"Lean.instantiateMVars",
"Lean.MessageData",
"Lean.instMonadMCtxOfMonadLift",
"Lean.Elab.Term.LevelMVarErrorInfo",
"Lean.Elab.Term.LevelMVarErrorInfo.lctx",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"instMonadControlTOfPure",
"String",
"Lean.Meta.State",
"instMonadLiftT",
"Lean.LocalInst... | true |
Lean.Lsp.InitializationOptions.noConfusion | Lean.Data.Lsp.InitShutdown | [
"Lean.Lsp.InitializationOptions.casesOn",
"Lean.Lsp.InitializationOptions",
"Lean.Lsp.InitializationOptions.noConfusionType",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Lean.Lsp.LogConfig",
"Eq",
"Option"
] | false |
_private.Mathlib.AlgebraicGeometry.StructureSheaf.0.AlgebraicGeometry.StructureSheaf.toBasicOpenₗ._proof_3 | Mathlib.AlgebraicGeometry.StructureSheaf | [
"CategoryTheory.Functor",
"CommRing",
"instSMulOfMul",
"Opposite",
"PrimeSpectrum.basicOpen",
"Monoid.toMulOneClass",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.catego... | false |
CategoryTheory.WithTerminal.widePullbackShapeEquiv._proof_8 | Mathlib.CategoryTheory.WithTerminal.Basic | [
"Eq.mpr",
"CategoryTheory.WithTerminal.widePullbackShapeEquiv._proof_4",
"CategoryTheory.WithTerminal.widePullbackShapeEquiv._proof_5",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Limits.WidePullbackShape",
"C... | false |
_private.Init.Data.List.Pairwise.0.List.pairwise_flatten._simp_1_1 | Init.Data.List.Pairwise | [
"List.Pairwise",
"Membership.mem",
"List.pairwise_append",
"instHAppendOfAppend",
"List",
"And",
"List.instMembership",
"propext",
"List.instAppend",
"Eq",
"HAppend.hAppend"
] | false |
Mathlib.Meta.FunProp.LambdaTheoremArgs.const.elim | Mathlib.Tactic.FunProp.Theorems | [
"PULift.up",
"Mathlib.Meta.FunProp.LambdaTheoremArgs.ctorIdx",
"Nat",
"Mathlib.Meta.FunProp.LambdaTheoremArgs",
"Eq.symm",
"Eq",
"Mathlib.Meta.FunProp.LambdaTheoremArgs.const",
"Mathlib.Meta.FunProp.LambdaTheoremArgs.ctorElim"
] | false |
MulAction.noConfusion | Mathlib.Algebra.Group.Action.Defs | [
"Monoid",
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"HEq.refl",
"SemigroupAction",
"MulOneClass.toMulOne",
"MulAction.casesOn",
"MulAction",
"MulAction.noConfusionType",
"Monoid.toSemigroup",
"eq_of_heq",
"Eq.ndrec",
"One.toOfNat1",
"HEq",
"HSMul.hSMul",
"SemigroupAction.t... | false |
MonovaryOn.pow_right | Mathlib.Algebra.Order.Monovary | [
"Preorder.toLT",
"CommMonoid.toCommSemigroup",
"IsOrderedMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"MonovaryOn",
"Pi.instPow",
"DivInvMonoid.toMonoid",
"LE.le",
"CommGroup",
"Monoid.t... | true |
Int.gcd_pos_of_ne_zero_left | Init.Data.Int.Gcd | [
"Iff.mpr",
"Int.gcd",
"Int.natAbs_pos",
"Ne",
"instOfNatNat",
"Int",
"Nat.gcd_pos_of_pos_left",
"instOfNat",
"Nat",
"LT.lt",
"Int.natAbs",
"instLTNat",
"OfNat.ofNat"
] | true |
Lean.Elab.InlayHintKind.ctorElim | Lean.Elab.InfoTree.InlayHints | [
"Lean.Elab.InlayHintKind.type",
"Lean.Elab.InlayHintKind.ctorIdx",
"Lean.Elab.InlayHintKind",
"Lean.Elab.InlayHintKind.parameter",
"Nat",
"Lean.Elab.InlayHintKind.casesOn",
"Eq.ndrec",
"Lean.Elab.InlayHintKind.ctorElimType",
"PULift.down",
"Eq"
] | false |
Std.HashMap.Raw.Equiv.diff_left | Std.Data.HashMap.RawLemmas | [
"Std.HashMap.Raw.instSDiffOfBEqOfHashable",
"Std.HashMap.Raw.WF.out",
"Std.HashMap.Raw.WF",
"LawfulHashable",
"Std.HashMap.Raw",
"SDiff.sdiff",
"EquivBEq",
"Std.HashMap.Raw.inner",
"Hashable",
"Std.DHashMap.Raw.Equiv.diff_left",
"Std.HashMap.Raw.Equiv",
"Std.HashMap.Raw.Equiv.inner",
"BEq",
... | true |
Lean.Parser.AliasValue._sizeOf_inst | Lean.Parser.Extension | [
"Lean.Parser.AliasValue._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Parser.AliasValue"
] | false |
CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_leftAdd | Mathlib.CategoryTheory.Preadditive.OfBiproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.BinaryBicone.inl_fst",
"CategoryTheory.Limits.HasZeroMorphisms",
"Std.Identity.mk",
"CategoryTheory.Limits.BinaryBicone.inr_snd",
"CategoryTheory.Limits.biprod.lift_snd",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Ca... | true |
Fin.pos_iff_ne_zero | Init.Data.Fin.Lemmas | [
"Eq.mpr",
"congrArg",
"Nat.pos_iff_ne_zero",
"Iff.rfl",
"Zero.ofOfNat0",
"id",
"Fin.instOfNat",
"Ne",
"instOfNatNat",
"Fin.val_ne_iff",
"Fin.val",
"Fin.lt_def",
"Iff",
"Nat",
"LT.lt",
"instLTFin",
"propext",
"instLTNat",
"NeZero",
"OfNat.ofNat",
"Eq.symm",
"Fin",
"Eq",
... | true |
IsLocalization.mk'_spec | Mathlib.RingTheory.Localization.Defs | [
"HMul.hMul",
"IsLocalization",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Membership.mem",
"Subtype",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"IsLocalization.mk'",
"RingHom.instFunLike",
"Dist... | true |
CategoryTheory.Over.associator_inv_left_fst_snd_assoc | Mathlib.CategoryTheory.Monoidal.Cartesian.Over | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Over",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"Eq.mp",
... | true |
DedekindCut.principal_sInf_right | Mathlib.Order.Completion | [
"Set.ext",
"Eq.mpr",
"le_sInf_iff",
"lowerBounds",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"DedekindCut.principal",
"mem_lowerBounds",
"DedekindCut.left_principal",
"id",
"DedekindCut",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf",
... | true |
Set.Ico.coe_eq_zero | Mathlib.Algebra.Order.Interval.Set.Instances | [
"Nontrivial",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Set.Ico.instZero",
"IsOrderedRing",
"PartialOrder.toPreorder",
"Membership.mem",
"PartialOrder",
"Set.Elem",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Set.Ico",
"Subtype.ext_iff",
"AddMonoidWithOne.toOne",
"Iff",
"Semiring",
"On... | true |
_private.Init.Data.Range.Polymorphic.RangeIterator.0.Std.Rxc.Iterator.instIteratorAccess.match_1.splitter | Init.Data.Range.Polymorphic.RangeIterator | [
"Option.some",
"Std.Rxc.Iterator.instIteratorAccess.match_1",
"Option.none",
"Unit",
"Option"
] | true |
_private.Lean.Shell.0.Lean.ShellOptions.process.throwExpectedNumeric | Lean.Shell | [
"instMonadExceptOfMonadExceptOf",
"String",
"MonadExcept.throw",
"instMonadExceptOfEIO",
"EIO",
"instMonadEIO",
"ToString.toString",
"instAppendString",
"instHAppendOfAppend",
"Unit",
"Monad.toBind",
"UInt32",
"Bind.bind",
"_private.Lean.Shell.0.Lean.ShellOptions.process.eprint",
"OfNat.... | true |
Set.iUnion_iInter_of_antitone | Mathlib.Data.Set.Finite.Lattice | [
"IsCodirectedOrder",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Set.iInter",
"Finite",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"Antitone",
"CompleteDistribLattice.toFrame",
"CompleteBooleanAlgebra.t... | true |
Lean.Lsp.CodeActionTriggerKind.casesOn | Lean.Data.Lsp.CodeActions | [
"Lean.Lsp.CodeActionTriggerKind",
"Lean.Lsp.CodeActionTriggerKind.rec",
"Lean.Lsp.CodeActionTriggerKind.automatic",
"Lean.Lsp.CodeActionTriggerKind.invoked"
] | false |
Int16.ofIntTruncate_bitVecToInt | Init.Data.SInt.Lemmas | [
"Int16.ofIntTruncate",
"Int16",
"BitVec.ofInt_toInt",
"congrArg",
"Int16.ofBitVec",
"BitVec",
"BitVec.le_toInt",
"BitVec.ofInt",
"instOfNatNat",
"Int16.toBitVec_ofBitVec",
"Int16.toBitVec.inj",
"Nat",
"Int16.toBitVec",
"congr",
"True",
"eq_self",
"BitVec.toInt_le",
"of_eq_true",
... | true |
DirectSum.ring | Mathlib.Algebra.DirectSum.Ring | [
"Ring.mk",
"DirectSum.ring._proof_6",
"instAddCommMonoidDirectSum",
"DirectSum.ring._proof_3",
"AddCommGroup.toAddCommMonoid",
"DirectSum.ring._proof_1",
"DirectSum.GRing.toGSemiring",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"DirectSum.ring._proof_2",
"AddZeroClass.toAddZero",
"... | true |
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