name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
AsBoolAlg | Mathlib.Algebra.Ring.BooleanRing | [] | true |
_private.Mathlib.Topology.Sheaves.Flasque.0.TopCat.Sheaf.IsFlasque.epi_of_shortExact.match_1_7.eq_2 | Mathlib.Topology.Sheaves.Flasque | [
"Unit.unit",
"Fin.instOfNat",
"instOfNatNat",
"Unit",
"Nat.instNeZeroSucc",
"Nat",
"_private.Mathlib.Topology.Sheaves.Flasque.0.TopCat.Sheaf.IsFlasque.epi_of_shortExact.match_1_7",
"Eq.refl",
"OfNat.ofNat",
"Fin",
"Eq"
] | true |
_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.instHashablePurity.hash.match_1 | Lean.Compiler.LCNF.Basic | [
"Unit.unit",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Purity.pure",
"Unit",
"Lean.Compiler.LCNF.Purity.impure",
"Lean.Compiler.LCNF.Purity.casesOn"
] | false |
isClopen_range_inr | Mathlib.Topology.Clopen | [
"Sum",
"isOpen_range_inr",
"instTopologicalSpaceSum",
"IsClosed",
"TopologicalSpace",
"Sum.inr",
"isClosed_range_inr",
"And.intro",
"IsOpen",
"Set.range",
"IsClopen"
] | true |
Set.Nontrivial.not_subsingleton | Mathlib.Data.Set.Subsingleton | [
"Set.not_subsingleton_iff",
"Iff.mpr",
"Set.Subsingleton",
"Set.Nontrivial",
"Not",
"Set"
] | true |
Computation.Results.terminates | Mathlib.Data.Seq.Computation | [
"Computation.Terminates",
"Computation.Results",
"Computation",
"Nat",
"Computation.Results.mem",
"Computation.terminates_of_mem"
] | true |
_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.muFun._unsafe_rec | Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | [
"NegZeroClass.toNeg",
"Preorder.toLT",
"One",
"le_rfl",
"AddCommGroup.toAddCommMonoid",
"Finset",
"Preorder.toLE",
"Membership.mem",
"AddCommGroup",
"Finset.Ico",
"Subtype",
"LT.lt.le",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"Finset.Icc",
"SubNegZeroMonoid.toNegZeroClass",
... | false |
Finset.union_val_nd | Mathlib.Data.Finset.Lattice.Basic | [
"Finset.instUnion",
"Finset",
"Multiset",
"Finset.val",
"Union.union",
"Eq",
"Multiset.ndunion",
"rfl",
"DecidableEq"
] | true |
AddCommute.zsmul_add | Mathlib.Algebra.Group.Commute.Defs | [
"neg_add_rev",
"instHSMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"AddZeroClass.toAddZero",
"instOfNatNat",
"Int",
"SubtractionMonoid.toSubNegMonoid",
"AddCommute.nsmul_nsmul",
"Nat.cast",
"AddCommute",
"AddCommute.add_nsmul",
"instHAdd",
"negSucc_zsmul",
"HAdd.h... | true |
Lean.Compiler.LCNF.inScope | Lean.Compiler.LCNF.MonadScope | [
"Pure.pure",
"Lean.Compiler.LCNF.Scope",
"Lean.Compiler.LCNF.MonadScope",
"Monad.toApplicative",
"Lean.FVarId",
"Applicative.toPure",
"Std.TreeSet.contains",
"Bool",
"Monad.toBind",
"Bind.bind",
"Lean.Name.quickCmp",
"Monad",
"Lean.FVarId.name",
"Lean.Compiler.LCNF.MonadScope.getScope"
] | true |
HasStrictFDerivAt.cpow | Mathlib.Analysis.SpecialFunctions.Pow.Deriv | [
"NormedCommRing.toSeminormedCommRing",
"Complex.log",
"Algebra.to_smulCommClass",
"instHSMul",
"Prod.normedSpace",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"Prod.normedAddCommGroup",
"Complex.instNormedAddCommGroup",
"NormedSpace",
"CommSemiring.toSemi... | true |
TopCat.Presheaf.pushforwardEq_hom_app._proof_2 | Mathlib.Topology.Sheaves.Presheaf | [
"CategoryTheory.Functor.op",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.instCategory",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Preorder.smallCategory",
"TopCat.str",
"TopCat.carrier",
"Opposite.op",
"eq... | false |
PreconnectedSpace.rec | Mathlib.Topology.Connected.Basic | [
"Set.univ",
"PreconnectedSpace",
"PreconnectedSpace.mk",
"TopologicalSpace",
"IsPreconnected"
] | false |
Mathlib.Tactic.Sat.Clause.mk.injEq | Mathlib.Tactic.Sat.FromLRAT | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Expr",
"Int",
"Array",
"And",
"Mathlib.Tactic.Sat.Clause.mk.inj",
"Eq.ndrec",
"Eq.refl",
"Mathlib.Tactic.Sat.Clause.mk",
"Eq",
"Mathlib.Tactic.Sat.Clause"
] | true |
Function.Injective.isMulTorsionFree | Mathlib.Algebra.Group.Hom.Defs | [
"Monoid",
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"IsMulTorsionFree",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"IsMulTorsionFree.mk",
"Eq.mp",
"id",
"Ne",
"instOfNatNat",
"map_pow",
"Monoid.toPow",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat",
"congr",
"ins... | true |
HomogeneousLocalization.NumDenSameDeg.instNeg._proof_1 | Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization | [
"SetLike",
"HomogeneousLocalization.NumDenSameDeg.num",
"NegZeroClass.toNeg",
"CommRing",
"HomogeneousLocalization.NumDenSameDeg",
"CommSemiring.toSemiring",
"Membership.mem",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
... | false |
CategoryTheory.Adjunction.coconesIsoComponentInv._proof_1 | Mathlib.CategoryTheory.Adjunction.Limits | [
"Eq.mpr",
"CategoryTheory.Functor",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.cocones",
"id",
"Equiv",
"Categor... | false |
Function.RightInverse.filter_map | Mathlib.Order.Filter.Map | [
"Filter.map",
"Function.RightInverse",
"Filter",
"Function.LeftInverse.filter_map"
] | true |
GradedRingHom.coe_mul | Mathlib.RingTheory.GradedAlgebra.RingHom | [
"SetLike",
"HMul.hMul",
"GradedRingHom",
"Function.comp",
"GradedRingHom.instFunLike",
"GradedRingHom.instMul",
"Semiring",
"Eq",
"DFunLike.coe",
"rfl",
"instHMul"
] | true |
Submodule.toAddSubmonoid_injective | Mathlib.Algebra.Module.Submodule.Defs | [
"Iff.mpr",
"Submodule",
"Submodule.toAddSubmonoid",
"AddMonoid.toAddZeroClass",
"AddSubmonoid",
"AddCommMonoid",
"SetLike.coe",
"Submodule.setLike",
"Iff.mp",
"SetLike.ext'_iff",
"Semiring",
"AddCommMonoid.toAddMonoid",
"Function.Injective",
"Module",
"AddSubmonoid.instSetLike",
"Eq",
... | true |
CochainComplex.πTruncGE_naturality_assoc | Mathlib.Algebra.Homology.Embedding.CochainComplex | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CochainComplex.πTruncGE_naturality",
"CochainComplex.truncGEMap",
"HomologicalComplex.HasHomology",
"AddGroupWithOne.to... | true |
_private.Mathlib.Order.CompactlyGenerated.Basic.0.iSupIndep_iff_supIndep_of_injOn._simp_1_6 | Mathlib.Order.CompactlyGenerated.Basic | [
"Finset",
"Membership.mem",
"Finset.mem_preimage",
"SetLike.coe",
"Set.preimage",
"Finset.instSetLike",
"Finset.preimage",
"propext",
"Set.InjOn",
"Eq",
"SetLike.instMembership"
] | false |
List.sublists'.eq_1 | Mathlib.Data.List.Sublists | [
"List.sublists'",
"Array.push",
"instOfNatNat",
"Array.toList",
"List.toArray",
"Array.foldl",
"List.cons",
"Array",
"List",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"List.foldr",
"Eq",
"Array.size",
"List.nil"
] | true |
Measurable.sinh | Mathlib.MeasureTheory.Function.SpecialFunctions.Basic | [
"Real.measurable_sinh",
"Real",
"Measurable.comp",
"Measurable",
"Real.sinh",
"MeasurableSpace",
"Real.measurableSpace"
] | true |
fst_himp | Mathlib.Order.Heyting.Basic | [
"HImp",
"Prod.fst",
"Prod.instHImp",
"Prod",
"Eq",
"rfl",
"HImp.himp"
] | true |
NonemptyInterval.instPreorder._proof_3 | Mathlib.Order.Interval.Basic | [
"LT.mk",
"NonemptyInterval.toDualProd",
"Preorder.toLT",
"Prod.instLE_mathlib",
"Preorder.toLE",
"NonemptyInterval.le",
"inferInstance",
"Preorder.lt_iff_le_not_ge._autoParam",
"LE.le",
"Preorder.lift._proof_2",
"autoParam",
"LE",
"And",
"Iff",
"Preorder.lift._proof_1",
"LT.lt",
"LE.... | false |
_private.Lean.Data.Lsp.Internal.0.Lean.Lsp.instOrdRefIdent.ord.match_1 | Lean.Data.Lsp.Internal | [
"Lean.Lsp.RefIdent.casesOn",
"String",
"Nat.hasNotBit",
"Lean.Lsp.RefIdent.const",
"_private.Lean.Data.Lsp.Internal.0.Lean.Lsp.instBEqRefIdent.beq._sparseCasesOn_1",
"Lean.Lsp.RefIdent",
"Lean.Lsp.RefIdent.ctorIdx",
"Lean.Lsp.RefIdent.fvar"
] | false |
Nat.mod_four_ne_three_of_mem_primeFactors_of_isSquare_neg_one | Mathlib.NumberTheory.SumTwoSquares | [
"Nat.dvd_of_mem_primeFactors",
"Mathlib.Tactic.Ring.Common.neg_zero",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.Prime",
"NeZero.one",
"Mathlib.Tactic.Ring.Common.neg_add",
"HMul.hMul",
"Nat.rawCast",
"ZMod.commRing",
"Mathlib.Tactic.Ring.Common.single_pow",
"Monoid.... | true |
IsAddUnit.add_neg_cancel_left | Mathlib.Algebra.Group.Units.Defs | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"IsAddUnit",
"SubtractionMonoid.toSubNegMonoid",
"AddUnits.add_neg_cancel_left",
"instHAdd",
"HAdd.hAdd",
"SubtractionMonoid",
"SubNegMonoid.toNeg",
"AddZero.toAdd",
"IsAddUnit.addUnit'",
"SubNegMonoid.toAddMonoid",
"Eq",
"Neg.neg"
] | true |
IO.instReprTaskState.repr | Init.System.IO | [
"Std.Format.group",
"GE.ge",
"IO.TaskState",
"instOfNatNat",
"Int",
"instLENat",
"Unit",
"instOfNat",
"Nat",
"Std.Format",
"_private.Init.System.IO.0.IO.instReprTaskState.repr.match_1",
"Repr.addAppParen",
"OfNat.ofNat",
"Nat.decLe",
"Std.Format.nest",
"Std.Format.text",
"Std.Format.... | true |
Real.Angle.cos_eq_iff_eq_or_eq_neg | Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle | [
"NegZeroClass.toNeg",
"Real",
"Real.Angle.cos_eq_real_cos_iff_eq_or_eq_neg",
"Real.Angle",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Real.Angle.induction_on",
"Iff",
"NormedAddCommGroup.toAddCommGroup",
"Or",
"AddCo... | true |
_private.Lean.Elab.Tactic.Do.VCGen.0.Lean.Elab.Tactic.Do.VCGen.genVCs.assignMVars | Lean.Elab.Tactic.Do.VCGen | [
"Lean.Elab.Tactic.Do.Context",
"Inhabited.default",
"instInhabitedOfMonad",
"instInhabitedPUnit",
"Lean.MVarId",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Elab.Tactic.Do.State",
"List",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.instMonad",
"PUnit",
"Lean.Elab.Tactic.Do.VCGenM",
... | true |
BitVec.reverse_append._proof_2 | Init.Data.BitVec.Lemmas | [
"_private.Init.Data.BitVec.Lemmas.0.BitVec.reverse_append._proof_1",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Decidable.byContradiction",
"instAddNat",
"instDecidableEqNat",
"Eq",
"Not"
] | false |
Std.ExtDHashMap.mem_insert | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.DHashMap.mem_insert",
"Membership.mem",
"Std.ExtDHashMap.inductionOn",
"LawfulHashable",
"Bool.true",
"Std.ExtDHashMap.insert",
"BEq.beq",
"Iff",
"EquivBEq",
"Std.ExtDHashMap",
"Bool",
"Hashable",
"Or",
"BEq",
"Eq",
"St... | true |
AddValuation.comap_comp | Mathlib.RingTheory.Valuation.Basic | [
"RingHom",
"AddValuation.comap",
"Valuation.comap_comp",
"Multiplicative",
"AddValuation",
"RingHom.comp",
"LinearOrderedAddCommMonoidWithTop",
"OrderDual",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Eq",
"Ring",
"instLinearOrderedCommMonoidWithZeroMultiplicativeOrderDual"
] | true |
QuadraticAlgebra.imₗ._proof_2 | Mathlib.Algebra.QuadraticAlgebra.Defs | [
"instHSMul",
"Semiring.toModule",
"QuadraticAlgebra",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"QuadraticAl... | false |
_private.Init.Data.Range.Polymorphic.PRange.0.Std.instDecidableEqRoi.decEq._proof_2 | Init.Data.Range.Polymorphic.PRange | [
"False",
"Std.Roi.mk",
"Std.Roi.mk.noConfusion",
"eq_of_heq",
"HEq",
"Eq",
"Std.Roi",
"Not"
] | false |
_private.Mathlib.LinearAlgebra.UnitaryGroup.0.Matrix.kroneckerTMul_mem_unitary._simp_1_1 | Mathlib.LinearAlgebra.UnitaryGroup | [
"Monoid",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"unitary",
"StarMul",
"Membership.mem",
"MulOne.toMul",
"MulOneClass.toMulOne",
"And",
"StarMul.toInvolutiveStar",
"propext",
"One.toOfNat1",
"Unitary.mem_iff",
"InvolutiveStar.toStar",
"Submonoid.instSetLike",
"OfNat.ofN... | false |
BitVec.instOrOp | Init.Data.BitVec.Basic | [
"BitVec.or",
"BitVec",
"OrOp",
"Nat",
"OrOp.mk"
] | true |
Representation.IntertwiningMap.instSMulInt | Mathlib.RepresentationTheory.Intertwining | [
"Monoid",
"Representation.IntertwiningMap.instSMulInt._proof_1",
"instHSMul",
"Representation",
"AddCommGroup.toAddCommMonoid",
"LinearMap.addCommGroup",
"SMul",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"SMul.mk",
"Int",
"LinearMap",
"AddCommMonoid",
"AddGroup.toSubNegMonoid",
"Represe... | true |
Lean.Grind.AC.Seq.beq'_eq | Init.Grind.AC | [
"Lean.Grind.AC.Seq.casesOn",
"Eq.mpr",
"False",
"Bool.and'",
"congrArg",
"Bool.and'_eq_and",
"False.elim",
"Lean.Grind.AC.Seq.var.injEq",
"eq_iff_iff._simp_1",
"noConfusion_of_Nat",
"Bool.false_eq_true",
"Lean.Grind.AC.Seq.beq'",
"Nat.beq_eq",
"id",
"Bool.and",
"Nat.beq",
"and_congr_... | true |
UniqueMul.of_mulHom_image | Mathlib.Algebra.Group.UniqueProds.Basic | [
"MulHom",
"Eq.mpr",
"UniqueMul",
"HMul.hMul",
"_private.Mathlib.Algebra.Group.UniqueProds.Basic.0.UniqueMul.of_mulHom_image._simp_1_1",
"congrArg",
"Finset",
"Mul",
"Membership.mem",
"id",
"MulHom.mulHomClass",
"And",
"Finset.instSetLike",
"congr",
"True",
"eq_self",
"MulHom.funLike"... | true |
Std.Tactic.BVDecide.Frontend.Normalize.BitVec.add_left_inj | Std.Tactic.BVDecide.Normalize.Equal | [
"Eq.mpr",
"instLawfulBEq",
"congrArg",
"BitVec.instAdd",
"BitVec",
"Bool.eq_iff_iff",
"id",
"instBEqOfDecidableEq",
"instDecidableEqBitVec",
"iff_self",
"Bool.true",
"instHAdd",
"BEq.beq",
"Iff",
"HAdd.hAdd",
"Nat",
"congr",
"True",
"propext",
"Bool",
"of_eq_true",
"beq_iff... | true |
Std.DHashMap.Const.getKeyD_insertMany_list_of_mem | Std.Data.DHashMap.Lemmas | [
"List.Pairwise",
"instForInOfForIn'",
"List.map",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.Const.getKeyD_insertMany_list_of_mem",
"Membership.mem",
"inferInstance",
"Std.DHashMap.wf",
"instOfNatNat",
"Std.DHashMap.getKeyD",
"Id",
"Membership",
"LawfulHashable",
"Prod.fst",
"Subtyp... | true |
List.toList_mkSlice_roi | Init.Data.Slice.List.Lemmas | [
"Std.Slice.toList",
"Std.Rci.mk",
"Std.Iterators.Types.Take.instIterator",
"Std.Slice.Internal.ListSliceData",
"ListSlice.instToIterator",
"Std.Iterators.Types.ListIterator",
"congrArg",
"instSliceableListNatListSlice_5",
"Monad.toApplicative",
"Std.Iterators.Types.Take",
"instOfNatNat",
"Std.... | true |
_private.Mathlib.Control.Monad.Cont.0.ExceptT.run_bind.match_1.splitter | Mathlib.Control.Monad.Cont | [
"Except.ok",
"ExceptT.run_bind.match_1",
"Except.error",
"Except"
] | true |
Subgroup.widthInfty | Mathlib.NumberTheory.ModularForms.Cusps | [
"Real",
"Matrix",
"instDecidableEqFin",
"Subgroup.adjoinNegOne",
"Real.semiring",
"Subgroup",
"Real.instRing",
"instOfNatNat",
"Units.instGroup",
"Fin.fintype",
"Nat",
"Semiring.toMonoid",
"Matrix.GeneralLinearGroup",
"Matrix.semiring",
"OfNat.ofNat",
"Fin",
"Subgroup.strictWidthInft... | true |
Lean.Elab.WF.mkWfParam | Lean.Elab.PreDefinition.WF.Preprocess | [
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.mkAppM",
"List.toArray",
"List.cons",
"Lean.Name.mkStr1",
"List.nil"
] | true |
Char.minSurrogate | Batteries.Data.Char.Basic | [
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | true |
FGAlgCat.uliftFunctor._proof_3 | Mathlib.Algebra.Category.CommAlgCat.FiniteType | [
"CommRing",
"CommAlgCat.instCommRingObjForgetAlgHomCarrier",
"CommAlgCat.of",
"ULift.semiring",
"AlgEquiv.symm",
"CommSemiring.toSemiring",
"ULift",
"inferInstance",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"Algebra.FiniteType",
"CommAlgCat.instCategory",
"ULift.algebra",
"CommAl... | false |
AddSubmonoid.LocalizationMap.map_comp_map | Mathlib.GroupTheory.MonoidLocalization.Maps | [
"AddSubmonoid.LocalizationMap.add_neg_right",
"Eq.mpr",
"AddMonoidHom.restrict",
"AddSubmonoid.LocalizationMap.map",
"AddUnits.val",
"AddSubmonoid.LocalizationMap.map_add_right",
"AddSubmonoid.instAddSubmonoidClass",
"AddSubmonoid.LocalizationMap.lift._proof_2",
"AddMonoid.toAddSemigroup",
"AddSub... | true |
CategoryTheory.shiftFunctorZero_hom_app_shift | Mathlib.CategoryTheory.Shift.Basic | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.shiftFunctorComm",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",... | true |
Lean.Lsp.LeanDidOpenTextDocumentParams.toDidOpenTextDocumentParams | Lean.Data.Lsp.Extra | [
"Lean.Lsp.DidOpenTextDocumentParams",
"Lean.Lsp.LeanDidOpenTextDocumentParams"
] | true |
Finset.inl_mem_sumLift₂ | Mathlib.Data.Sum.Interval | [
"Eq.mpr",
"Finset.mem_sumLift₂",
"Sum.inl_ne_inr",
"False",
"congrArg",
"Finset",
"_private.Mathlib.Data.Sum.Interval.0.Finset.inl_mem_sumLift₂._simp_1_1",
"Membership.mem",
"Exists",
"Sum",
"id",
"Sum.inl",
"Sum.inl.injEq",
"_private.Mathlib.Data.Sum.Interval.0.Finset.inl_mem_sumLift₂._si... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.StructId.0.Lean.Meta.Grind.Arith.Linear.mkNatModuleInst? | Lean.Meta.Tactic.Grind.Arith.Linear.StructId | [
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Sym.synthInstance?",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.State",
"ReaderT",
"instMonadLiftT",
"Lean.Meta.Sym.Context",
"Lean.Name.mkStr3",
"Lean.Meta.Grind.Context",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"liftM",
"Lean.Level",
"ReaderT.... | true |
Set.subset_compl_iff_disjoint_right | Mathlib.Order.BooleanAlgebra.Set | [
"Compl.compl",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"BiheytingAlgebra.toHeytingAlgebra",
"HasSubset.Subset",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.instCompl",
"BooleanAlgebra.toBiheytingAlgebra",
"Iff",
"Set.instBooleanAlgebra",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",
"... | true |
GroupWithZero.div_eq_mul_inv | Mathlib.Algebra.GroupWithZero.Defs | [
"GroupWithZero.toMonoidWithZero",
"Semigroup.toMul",
"instHDiv",
"GroupWithZero.toInv",
"HMul.hMul",
"GroupWithZero",
"GroupWithZero.toDiv",
"HDiv.hDiv",
"Inv.inv",
"Monoid.toSemigroup",
"Eq",
"MonoidWithZero.toMonoid",
"instHMul"
] | true |
AlgebraicGeometry.Scheme.IsLocallyDirected.tAux._proof_2 | Mathlib.AlgebraicGeometry.Gluing | [
"CategoryTheory.Functor",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instCompleteLattice",
"CommRingCat",
"iSup",
"Alge... | false |
_private.Mathlib.NumberTheory.Divisors.0.Int.mem_divisors._simp_1_1 | Mathlib.NumberTheory.Divisors | [
"Int.divisors",
"Finset",
"Membership.mem",
"Int",
"Nat.divisors",
"Finset.instSetLike",
"Nat",
"Int.natAbs",
"propext",
"Int.mem_divisors_iff_natAbs_mem_divisors_natAbs",
"Eq",
"SetLike.instMembership"
] | false |
_private.Lean.Meta.Sym.Apply.0.Lean.Meta.Sym.BackwardRule.apply'.match_1 | Lean.Meta.Sym.Apply | [
"_private.Lean.Meta.Sym.Apply.0.Lean.Meta.Sym.BackwardRule.apply'._sparseCasesOn_1",
"Lean.Meta.Sym.ApplyResult.ctorIdx",
"Lean.MVarId",
"Nat.hasNotBit",
"List",
"Lean.Meta.Sym.ApplyResult",
"Lean.Meta.Sym.ApplyResult.goals"
] | false |
_private.Lean.Meta.FunInfo.0.Lean.Meta.FunInfoEnvCacheKey._sizeOf_inst | Lean.Meta.FunInfo | [
"SizeOf.mk",
"_private.Lean.Meta.FunInfo.0.Lean.Meta.FunInfoEnvCacheKey._sizeOf_1",
"SizeOf",
"_private.Lean.Meta.FunInfo.0.Lean.Meta.FunInfoEnvCacheKey"
] | false |
complEDS.eq_1 | Mathlib.NumberTheory.EllipticDivisibilitySequence | [
"Int.cast",
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"Int.sign",
"Int",
"AddGroupWithOne.toIntCast",
"complEDS'",
"instDistribOfSemiring",
"CommRing.toCommSemiring",
"Distrib.toMul",
"Int.natAbs",
"Eq.refl",
"CommRing.toRing",
"Eq",
"Ring.toAddGroupWithOne",
"complEDS",
... | true |
FrameHom.copy_eq | Mathlib.Order.Hom.CompleteLattice | [
"FrameHom",
"FrameHom.copy",
"FrameHom.instFunLike",
"DFunLike.ext'",
"CompleteLattice",
"Eq",
"DFunLike.coe"
] | true |
ONote.zero | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.zero",
"ONote"
] | true |
_private.Mathlib.Topology.UniformSpace.AbstractCompletion.0.AbstractCompletion.termι'_2 | Mathlib.Topology.UniformSpace.AbstractCompletion | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
Preorder.noConfusionType | Mathlib.Order.Defs.PartialOrder | [
"LE.le",
"LE",
"And",
"Iff",
"Preorder.casesOn",
"LT.lt",
"HEq",
"Not",
"Preorder",
"LT"
] | false |
Substring.Raw.ValidFor.startPos | Batteries.Data.String.Lemmas | [
"_private.Batteries.Data.String.Lemmas.0.Substring.Raw.ValidFor.startPos.match_1_1",
"Substring.Raw.mk",
"String.utf8Len",
"Substring.Raw.ValidFor",
"String.Pos.Raw",
"Substring.Raw",
"instHAppendOfAppend",
"List",
"instHAdd",
"Unit",
"String.Pos.Raw.mk",
"HAdd.hAdd",
"Nat",
"instAddNat",
... | true |
CategoryTheory.Functor.precomposeWhiskerLeftMapCocone_hom_hom | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.mapCocone",
"CategoryTheory.Limits.Cocone.precompose",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.CoconeMorphism.hom",
"CategoryTheory.Functor.comp... | true |
Topology.IsInducing.sumElim | Mathlib.Topology.Constructions.SumProd | [
"Filter.instMembership",
"Set.mem_range_self",
"Eq.mpr",
"Filter.Tendsto.le_comap",
"Topology.IsInducing.nhds_eq_comap",
"nhds_le_nhdsSet",
"Lattice.toSemilatticeSup",
"_private.Mathlib.Topology.Constructions.SumProd.0.Topology.IsInducing.sumElim._simp_1_2",
"and_true",
"Filter.disjoint_principal_... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_394 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.instEquivLike",
"Lean.Grind.Nat.lt_eq",
"List.getElem_filter_eq_getElem_getElem_findIdxs._proof_2",
"Equiv",
"instOfNatNat",
"LE.le",
"instLENat",
"List.findIdxNth",
"List.cons",
"List.findIdxs",
"instHAdd",
"HAdd.hAdd",
"Equiv.Perm",
"Nat",
"List.filter",
"LT.lt",
"Eq.substr"... | false |
CategoryTheory.Endofunctor.Coalgebra.isoMk_hom_f | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Coalgebra.instCategory",
"CategoryTheory.Endofunctor.Coalgebra.str",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Endofunctor.Coalgebra.isoMk._auto_1",
"CategoryTheory.Iso",
"CategoryTheory.Endofunctor.Coalgebra.V",
"Ca... | true |
CategoryTheory.ShortComplex.HomologyData.exact_iff_i_p_zero | Mathlib.Algebra.Homology.ShortComplex.Exact | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.HomologyData.iso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.instIsRegularMonoOfIsSplitMono",
"CategoryTheory.ShortComplex",
"CategoryTheory.Limits.comp_zero",
"CategoryTheory... | true |
Std.Http.URI.scheme | Std.Internal.Http.Data.URI.Basic | [
"Std.Http.URI",
"Std.Http.URI.Scheme"
] | true |
Std.Sat.AIG.instDecidableEqDecl.decEq._proof_3 | Std.Sat.AIG.Basic | [
"Std.Sat.AIG.Decl",
"False",
"False.elim",
"noConfusion_of_Nat",
"Std.Sat.AIG.Decl.atom",
"Std.Sat.AIG.Decl.false",
"Std.Sat.AIG.Decl.ctorIdx",
"Eq",
"Not"
] | false |
List.Ico.filter_le | Mathlib.Data.List.Intervals | [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"List.Ico.filter_le_of_le_bot",
"Preorder.toLE",
"id",
"max_eq_left",
"le_total",
"LE.le",
"instLENat",
"Or.casesOn",
"LinearOrder.toMax",
"max_eq_right",
"List",
"Max.max",
"Nat",
"List.filter",
"List.Ico.filter_le_of_le",
"Eq.ref... | true |
CategoryTheory.ChosenPullbacksAlong.mk | Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | [
"CategoryTheory.Over.map",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.ChosenPullbacksAlong",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.instCategoryOver",
"CategoryTheory.ChosenPullbacksAlong.mk",
"CategoryTheory.Category.toCategoryStruct",
"Categ... | true |
_private.Init.Data.String.Lemmas.Order.0.String.Slice.Pos.offset_lt_rawEndPos_iff._simp_1_2 | Init.Data.String.Lemmas.Order | [
"String.Slice.Pos.offset",
"String.Slice",
"String.Pos.Raw",
"propext",
"String.Slice.Pos",
"Eq",
"String.Slice.Pos.ext_iff"
] | false |
Equiv.Perm.Basis.ofPermHom._proof_7 | Mathlib.GroupTheory.Perm.Centralizer | [
"HMul.hMul",
"Monoid.toMulOneClass",
"Finset",
"Equiv.Perm.cycleFactorsFinset",
"Membership.mem",
"MulOne.toMul",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"Equiv.Perm.OnCycleFactors.range_toPermHom'",
"Group.toDivInvMonoid",
"Equiv.Perm.permGroup",
"MulOneClass.toMulOne",
"Inv.inv",... | false |
TopCat.Presheaf.algebra_section_stalk | Mathlib.Topology.Sheaves.CommRingCat | [
"CommRingCat.Hom.hom",
"Opposite",
"CommRingCat.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"CommRingCat",
"PartialOrder.toPreorder",
"Algebra",
"TopologicalSpace.Opens",
"Membership.mem",
"CommRingCat.instCategory",
"TopCat.Presheaf",
"Subtype",
"Preord... | true |
Representation.IntertwiningMap.instAddCommMonoid | Mathlib.RepresentationTheory.Intertwining | [
"Representation.IntertwiningMap.instAddCommMonoid._proof_6",
"Monoid",
"instHSMul",
"Representation",
"Representation.IntertwiningMap.instAdd",
"Representation.IntertwiningMap.instAddCommMonoid._proof_5",
"AddMonoid.toNSMul",
"AddMonoid.mk",
"Representation.IntertwiningMap.instAddCommMonoid._proof_3... | true |
Nat.eq_iff_prime_padicValNat_eq | Mathlib.Data.Nat.Factorization.Basic | [
"Finsupp.instFunLike",
"False",
"Nat.instMulZeroClass",
"Nat.Prime",
"eq_false",
"congrArg",
"padicValNat",
"Ne",
"instOfNatNat",
"dite",
"Nat.factorization_eq_zero_of_not_prime",
"Iff",
"implies_congr",
"Nat",
"congr",
"True",
"Iff.intro",
"eq_self",
"of_eq_true",
"Eq.ndrec",
... | true |
AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.quasiFiniteAt | Mathlib.AlgebraicGeometry.Morphisms.QuasiFinite | [
"Eq.mpr",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"CommRing",
"AlgHom.comp_algebraMap",
"AlgebraicGeometry.Scheme",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRingCat.Hom.hom",
"Opposite",
"le_rfl",
"AlgHom.algHomClass",
"CommRingCat.carrier",
"IsScalarT... | true |
Continuous.stronglyMeasurable | Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic | [
"TopologicalSpace.PseudoMetrizableSpace",
"Eq.mpr",
"Continuous",
"congrArg",
"SecondCountableTopology",
"Measurable.stronglyMeasurable",
"Measurable",
"TopologicalSpace.IsSeparable",
"id",
"borel",
"stronglyMeasurable_iff_measurable_separable",
"Or.casesOn",
"MeasurableSpace",
"Topologica... | true |
Std.ExtDHashMap.mem_filter | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"instLawfulHashableOfLawfulBEq",
"LawfulBEq",
"Membership.mem",
"Exists",
"Std.ExtDHashMap.inductionOn",
"Std.ExtDHashMap.get",
"Bool.true",
"Iff",
"Std.ExtDHashMap",
"Bool",
"Hashable",
"instEquivBEqOfLawfulBEq",
"BEq",
"Eq",
... | true |
isMulCommutative_iff_isLieAbelian | Mathlib.Algebra.Lie.Abelian | [
"AddGroup.toSubtractionMonoid",
"HMul.hMul",
"LieRing.toAddCommGroup",
"AddGroupWithOne.toAddGroup",
"congrArg",
"_private.Mathlib.Algebra.Lie.Abelian.0.isMulCommutative_iff_isLieAbelian._simp_1_1",
"Bracket.bracket",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"LieRingModule.toBracket",
... | true |
Rat.mul_def | Init.Data.Rat.Lemmas | [
"Nat.gcd",
"Iff.mpr",
"Nat.gcd_dvd_left",
"Eq.mpr",
"Nat.Coprime",
"Nat.div_mul_cancel",
"Rat.instMul",
"Rat.num",
"Dvd.dvd",
"instHDiv",
"Nat.mul_right_comm",
"HMul.hMul",
"Nat.mul_ne_zero",
"congrArg",
"Int.mul_assoc",
"Rat.mul._proof_1",
"Rat.mul._proof_3",
"Rat",
"Int.divExac... | true |
Subtype.orderBot.eq_1 | Mathlib.Order.BoundedOrder.Basic | [
"Subtype.orderBot",
"OrderBot.toBot",
"OrderBot",
"Subtype",
"Bot.bot",
"LE",
"Subtype.mk",
"OrderBot.mk",
"Eq.refl",
"Eq",
"Bot.mk",
"Subtype.orderBot._proof_1",
"Subtype.instLE"
] | true |
_private.Mathlib.Topology.NhdsWithin.0.eventually_mem_of_tendsto_nhdsWithin._simp_1_3 | Mathlib.Topology.NhdsWithin | [
"Set.mem_inter_iff",
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
MvPFunctor.liftP_iff | Mathlib.Data.PFunctor.Multivariate.Basic | [
"Eq.mpr",
"MvPFunctor.Obj",
"MvPFunctor",
"congrArg",
"Exists",
"id",
"Subtype",
"MvFunctor.LiftP",
"MvPFunctor.A",
"TypeVec.comp",
"MvPFunctor.map_eq",
"Subtype.mk",
"And.casesOn",
"And",
"Iff",
"Exists.casesOn",
"Nat",
"And.intro",
"Iff.intro",
"Exists.intro",
"MvPFunctor.B... | true |
AlgebraicGeometry.continuousMapPresheafEquivOfTotallyDisconnectedSpace._proof_2 | Mathlib.AlgebraicGeometry.Sites.ConstantSheaf | [
"ContinuousMap.continuous",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CommRingCat",
"ConnectedComponents.mk",
"ContinuousMap.mk",
"ContinuousMap",
"ContinuousMap.comp",
"Function.comp... | false |
Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.ci",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.co",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.io",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.ii"
] | true |
AlgebraicTopology.AlternatingFaceMapComplex.d_squared | Mathlib.AlgebraicTopology.AlternatingFaceMapComplex | [
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"instDecidableNot",
"NegZeroClass.toNeg",
"instNeZeroNatHAdd_1",
"lt_of_le_of_lt",
"Nat.instMulZeroClass",
"Finset.mem_filter._simp_1",
"instHSMul",
"Preorder.toLT",
"NonUnitalCommRing.toNonU... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.Proof.0.Lean.Meta.Grind.Arith.Linear.RingIneqCnstr.toExprProof.match_1 | Lean.Meta.Tactic.Grind.Arith.Linear.Proof | [
"Lean.Meta.Grind.Arith.Linear.RingIneqCnstrProof.cancelDen",
"Lean.Grind.CommRing.Expr",
"Lean.Meta.Grind.Arith.Linear.RingIneqCnstrProof.core",
"Lean.Expr",
"Int",
"Lean.Grind.Linarith.Var",
"Lean.Meta.Grind.Arith.Linear.RingIneqCnstrProof.notCore",
"Lean.Meta.Grind.Arith.Linear.RingIneqCnstr",
"Le... | false |
PrimeSpectrum.isHomeomorph_comap_tensorProductMap_of_isPurelyInseparable | Mathlib.RingTheory.Spectrum.Prime.Homeomorph | [
"Eq.mpr",
"AlgEquiv.instEquivLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"AlgHom.algHomClass",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"AlgEquiv.toAlg... | true |
Nat.mod_two_ne_zero | Init.Data.Nat.Lemmas | [
"Nat.instMod",
"instHMod",
"Ne",
"instOfNatNat",
"Nat.mod_two_not_eq_zero",
"HMod.hMod",
"Iff",
"Nat",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Topology.MetricSpace.Pseudo.Constructions.0.NNReal.nndist_eq._simp_1_3 | Mathlib.Topology.MetricSpace.Pseudo.Constructions | [
"abs",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"HSub.hSub",
"abs_sub_le_iff",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"LE.le",
"SubNegMonoid.toSub",
"And",
"instHSub",
"Ad... | false |
Zsqrtd.im | Mathlib.NumberTheory.Zsqrtd.Basic | [
"Int",
"Zsqrtd"
] | true |
SimpleGraph.reachable_iff_reflTransGen | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"SimpleGraph.Adj",
"SimpleGraph.Walk",
"Relation.ReflTransGen.refl",
"Relation.ReflTransGen.trans",
"SimpleGraph.Reachable.trans",
"Nonempty.intro",
"SimpleGraph",
"SimpleGraph.Walk.cons",
"Iff",
"Relation.ReflTransGen.single",
"SimpleGraph.Walk.nil",
"Nonempty.casesOn",
"SimpleGraph.Walk.re... | true |
Int16.ofInt_eq_ofNat | Init.Data.SInt.Lemmas | [
"Int16",
"congrArg",
"Int16.ofInt",
"BitVec",
"Int16.toBitVec_ofNat'",
"instOfNatNat",
"Int",
"BitVec.ofNat",
"Nat.cast",
"Int16.ofNat",
"Int16.toBitVec.inj",
"Nat",
"Int16.toBitVec",
"congr",
"True",
"eq_self",
"of_eq_true",
"Int16.toBitVec_ofInt",
"instNatCastInt",
"OfNat.ofN... | true |
_private.Lean.Server.Completion.CompletionCollectors.0.Lean.Server.Completion.bestLabelForDecl?.visitNamespaces | Lean.Server.Completion.CompletionCollectors | [
"_private.Lean.Server.Completion.CompletionCollectors.0.Lean.Server.Completion.bestLabelForDecl?.visitNamespaces._f",
"Lean.Name.brecOn",
"Unit",
"_private.Lean.Server.Completion.CompletionCollectors.0.Lean.Server.Completion.M",
"Lean.Name",
"StateT",
"Option"
] | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.