name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Vector.rec | Init.Data.Vector.Basic | [
"Vector",
"Array",
"Vector.mk",
"Nat",
"Eq",
"Array.size"
] | false |
Std.TreeMap.mem_of_mem_union_of_not_mem_right | Std.Data.TreeMap.Lemmas | [
"Std.DTreeMap.mem_of_mem_union_of_not_mem_right",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.instMembership",
"Union.union",
"Std.TreeMap.instUnion",
"Not",
"Std.TreeMap"
] | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.tdiv_one.match_1_1 | Init.Data.Int.DivMod.Lemmas | [
"Int.casesOn",
"Int.ofNat",
"Int",
"Nat",
"Int.negSucc"
] | false |
_private.Lean.Meta.GeneralizeTelescope.0.Lean.Meta.GeneralizeTelescope.generalizeTelescopeAux.match_1 | Lean.Meta.GeneralizeTelescope | [
"Lean.LocalDecl.cdecl",
"Lean.LocalDecl.ldecl",
"Lean.LocalDeclKind",
"Lean.Expr",
"Lean.FVarId",
"Nat",
"Bool",
"Lean.Name",
"Lean.LocalDecl.casesOn",
"Lean.LocalDecl",
"Lean.BinderInfo"
] | false |
TensorProduct.finsuppLeft_symm_apply_single | Mathlib.LinearAlgebra.DirectSum.Finsupp | [
"LinearEquiv.symm",
"TensorProduct.finsuppLeft._proof_5",
"Finsupp.module",
"Finsupp.smulCommClass",
"instAddCommMonoidDirectSum",
"DirectSum.instModule",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZe... | true |
CategoryTheory.SpectralSequence.Hom.mk.injEq | Mathlib.Algebra.Homology.SpectralSequence.Basic | [
"CategoryTheory.SpectralSequence.Hom.mk",
"CategoryTheory.SpectralSequence.Hom.mk.inj",
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Eq.propIntro",
"CategoryTheory.SpectralSequence.Hom.... | true |
CategoryTheory.EnrichedCat.bicategory._proof_6 | Mathlib.CategoryTheory.Enriched.EnrichedCat | [
"CategoryTheory.categoryForgetEnrichment",
"CategoryTheory.Functor",
"CategoryTheory.EnrichedCat.leftUnitor_hom_out_app",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ForgetEnrichment.of",
"CategoryTheory.EnrichedNatTrans.out",
"CategoryTheory.MonoidalCategory"... | false |
OpenSubgroup.hasCoeSubgroup.eq_1 | Mathlib.Topology.Algebra.OpenSubgroup | [
"OpenSubgroup",
"CoeTC",
"Group",
"Subgroup",
"OpenSubgroup.hasCoeSubgroup",
"TopologicalSpace",
"Eq.refl",
"Eq",
"CoeTC.mk",
"OpenSubgroup.toSubgroup"
] | true |
UniqueAdd.mt | Mathlib.Algebra.Group.UniqueProds.Basic | [
"Eq.mpr",
"Classical.not_not",
"congrArg",
"Mathlib.Tactic.Contrapose.contrapose₃",
"Finset",
"Membership.mem",
"id",
"Ne",
"not_or",
"instHAdd",
"And",
"Finset.instSetLike",
"HAdd.hAdd",
"UniqueAdd",
"implies_congr",
"congr",
"propext",
"Eq.refl",
"Or",
"Eq",
"Not",
"SetLi... | true |
Batteries.RBColor.black.elim | Batteries.Data.RBMap.Basic | [
"PULift.up",
"Batteries.RBColor.ctorIdx",
"Batteries.RBColor",
"Nat",
"Batteries.RBColor.ctorElim",
"Batteries.RBColor.black",
"Eq.symm",
"Eq"
] | false |
HomologicalComplex.Hom.comm | Mathlib.Algebra.Homology.HomologicalComplex | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.comp_zero",
"Classical.propDecidable",
"HomologicalComplex",
"id",
"ComplexShape",
"CategoryTheory.Limits.HasZeroMorphisms.... | true |
PiTensorProduct.constantBaseRingEquiv_symm | Mathlib.RingTheory.PiTensorProduct | [
"Semiring.toModule",
"PiTensorProduct.constantBaseRingEquiv",
"Algebra.algebraMap",
"AlgEquiv.symm",
"CommSemiring.toSemiring",
"RingHom",
"Algebra.id",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instFunLike",
"Fintype",
"AlgEquiv",
"NonAssocSemiring.toNonUnitalNon... | true |
Plausible.Shrinkable.shrink | Plausible.Shrinkable | [
"List",
"Plausible.Shrinkable"
] | true |
instAddCommMonoidPrimeMultiset._proof_3 | Mathlib.Data.PNat.Factors | [
"Add.mk",
"Multiset.add_assoc",
"Nat.Primes",
"instHAdd",
"HAdd.hAdd",
"Eq",
"instAddCommMonoidPrimeMultiset._aux_1",
"PrimeMultiset"
] | false |
AddSubgroup.comap_map_eq | Mathlib.Algebra.Group.Subgroup.Ker | [
"AddSubgroup.comap",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"AddSubgroup.instCompleteLattice",
"Lattice.toSemilatticeSup",
"AddMonoidHom.instAddMonoidHomClass",
"add_neg_cancel_left",
"CompleteLattice.toLattice",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddSubgroup.instPartialOrder",
"AddSu... | true |
instNonUnitalCStarAlgebraForall._proof_1 | Mathlib.Analysis.CStarAlgebra.Classes | [
"Pi.uniformSpace",
"CompleteSpace",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"SeminormedAddGroup.toPseudoMetricSpace",
"PseudoEMetricSpace.toUniformSpace",
"Pi.complete",
"NonUnitalSeminormedRing.toSeminormedAddCommGroup",
"NonUnitalCStarAlgebra.t... | false |
_aux_Mathlib_Algebra_Group_Hom_Defs___unexpand_MonoidHom_1 | Mathlib.Algebra.Group.Hom.Defs | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
WithBot.bot_mul_bot | Mathlib.Algebra.Order.Ring.WithTop | [
"WithBot",
"HMul.hMul",
"MulZeroClass.toMul",
"WithBot.instMulZeroClass",
"MulZeroClass",
"Bot.bot",
"Eq",
"WithBot.bot",
"rfl",
"instHMul",
"DecidableEq"
] | true |
_private.Mathlib.FieldTheory.IntermediateField.Adjoin.Basic.0.IntermediateField.adjoin_simple_isCompactElement._simp_1_2 | Mathlib.FieldTheory.IntermediateField.Adjoin.Basic | [
"IntermediateField.instPartialOrder",
"IntermediateField",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"Membership.mem",
"Set.instSingletonSet",
"LE.le",
"IntermediateField.adjoin_simple_le_iff",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"IntermediateField.adjoin",
"pro... | false |
_private.Mathlib.Data.Multiset.Filter.0.Multiset.filter_attach'._simp_1_2 | Mathlib.Data.Multiset.Filter | [
"Exists",
"exists_and_right",
"And",
"propext",
"Eq"
] | false |
Finsupp.DegLex.single_antitone | Mathlib.Data.Finsupp.MonomialOrder.DegLex | [
"Nat.instMulZeroClass",
"Equiv.instEquivLike",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Equiv",
"instOfNatNat",
"toDegLex",
"Finsupp.DegLex.instLinearOrderDegLexNat",
"Antitone",
"Nat",
"DegLex",
"OfNat.ofNat",
"DFunLike.coe"... | true |
_private.Mathlib.CategoryTheory.Monoidal.Preadditive.0.CategoryTheory.instPreservesFiniteBiproductsTensorLeft._simp_3 | Mathlib.CategoryTheory.Monoidal.Preadditive | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.id_tensorHom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.Monoida... | false |
_private.Batteries.Data.Array.Monadic.0.cond.match_1.splitter | Batteries.Data.Array.Monadic | [
"cond.match_1",
"Bool.true",
"Unit",
"Bool",
"Bool.false"
] | true |
Module.FaithfullyFlat.subsingleton_tensorProduct_iff_right | Mathlib.RingTheory.Flat.FaithfullyFlat.Basic | [
"CommRing",
"CommSemiring.toSemiring",
"Module.FaithfullyFlat.lTensor_reflects_triviality",
"AddCommGroup.toAddCommMonoid",
"inferInstance",
"AddCommGroup",
"Unique.instSubsingleton",
"CommRing.toCommSemiring",
"Iff",
"Iff.intro",
"Module.FaithfullyFlat",
"TensorProduct",
"Subsingleton",
"... | true |
Lean.Doc.State.openDecls | Lean.Elab.DocString | [
"List",
"Lean.Doc.State",
"Lean.OpenDecl"
] | true |
aeSeq.measurable | Mathlib.MeasureTheory.Function.AEMeasurableSequence | [
"MeasureTheory.Measure",
"AEMeasurable",
"Measurable",
"Classical.propDecidable",
"Membership.mem",
"aeSeq",
"AEMeasurable.mk",
"Measurable.ite",
"Nonempty.some",
"measurable_const'",
"aeSeq.aeSeqSet_measurableSet",
"MeasurableSpace",
"aeSeq._proof_1",
"aeSeqSet",
"Set.instMembership",
... | true |
Function.argmin._proof_1 | Mathlib.Order.WellFounded | [
"InvImage",
"WellFoundedLT",
"wellFounded_lt",
"LT.lt",
"InvImage.wf",
"WellFounded",
"LT"
] | false |
Finset.le_card_mul_mul_mulEnergy | Mathlib.Combinatorics.Additive.Energy | [
"Iff.mpr",
"Eq.mpr",
"Trans.trans",
"HMul.hMul",
"Monoid.toMulOneClass",
"SProd.sprod",
"congrArg",
"Finset.card_product",
"Finset",
"Nat.instMonoid",
"Finset.mulEnergy",
"Mul",
"Membership.mem",
"Eq.mp",
"Finset.mem_product._simp_1",
"id",
"MulOne.toMul",
"Prod.mk",
"instMulNat"... | true |
chartAt | Mathlib.Geometry.Manifold.ChartedSpace | [
"ChartedSpace.chartAt",
"TopologicalSpace",
"OpenPartialHomeomorph",
"ChartedSpace"
] | true |
RestrictedProduct.instMonoidCoeOfSubmonoidClass._proof_1 | Mathlib.Topology.Algebra.RestrictedProduct.Basic | [
"SetLike",
"Monoid",
"Monoid.toMulOneClass",
"MulMemClass",
"MulOne.toMul",
"MulOneClass.toMulOne",
"SubmonoidClass.toMulMemClass",
"SubmonoidClass"
] | false |
_private.Mathlib.MeasureTheory.Measure.Portmanteau.0.MeasureTheory.FiniteMeasure.limsup_measure_closed_le_of_tendsto._simp_1_1 | Mathlib.MeasureTheory.Measure.Portmanteau | [
"OrderBot.toBot",
"OrderBot",
"Bot.bot",
"LE.le",
"LE",
"True",
"eq_true",
"Eq",
"bot_le"
] | false |
AddUnits.continuousVAdd | Mathlib.Topology.Algebra.MulAction | [
"Topology.IsInducing.id",
"Topology.IsInducing.continuousVAdd",
"AddUnits.val",
"AddMonoid.toAddSemigroup",
"AddUnits.instTopologicalSpaceAddUnits",
"AddUnits.continuous_val",
"id",
"HVAdd.hVAdd",
"TopologicalSpace",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddSemigroupAction.toVAdd",
... | true |
FixedDetMatrices.instMulActionSpecialLinearGroupFixedDetMatrix._proof_3 | Mathlib.LinearAlgebra.Matrix.FixedDetMatrices | [
"Eq.mpr",
"MulOne.toOne",
"Subtype.mk.congr_simp",
"CommRing",
"instHSMul",
"Matrix.SpecialLinearGroup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"Matrix.instHMulOf... | false |
Lean.Elab.CheckTactic.elabCheckTactic | Lean.Elab.CheckTactic | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Command.CommandElab",
"Lean.NameMap",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.MetavarKind.natural",
"Bool... | true |
Subring.toAddSubgroup_strictMono | Mathlib.Algebra.Ring.Subring.Basic | [
"Preorder.toLT",
"StrictMono",
"AddGroupWithOne.toAddGroup",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"id",
"Subring.toAddSubgroup",
"NonAssocRing",
"AddSubgroup",
"NonAssocRing.toAddCommGroupWithOne",
"Subring",
"Subring.instPartialOrder",
"LT.lt",
"AddCommGroupWithOne.t... | true |
MeasureTheory.SimpleFunc.pow_apply | Mathlib.MeasureTheory.Function.SimpleFunc | [
"Monoid",
"MeasureTheory.SimpleFunc.hasNatPow",
"MeasureTheory.SimpleFunc",
"Monoid.toPow",
"MeasureTheory.SimpleFunc.instFunLike",
"MeasurableSpace",
"HPow.hPow",
"Nat",
"instHPow",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
continuousSMul_closedBall_ball | Mathlib.Analysis.Normed.Module.Ball.Action | [
"Continuous.comp'",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"SeminormedAddCommGroup",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"ContinuousSMul",
"continuous_subtype_val",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Continuous.snd",
"NormedSpace... | true |
Set.sUnion_sub | Mathlib.Algebra.Group.Pointwise.Set.Lattice | [
"HSub.hSub",
"Set.sUnion",
"Membership.mem",
"instHSub",
"Set.sub",
"Set.image2_sUnion_left",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Sub",
"Set"
] | true |
BitVec.getMsbD_rotateLeft | Init.Data.BitVec.Lemmas | [
"BitVec.rotateLeft_mod_eq_rotateLeft",
"Eq.mpr",
"Nat.mod_zero",
"False",
"Nat.zero_lt_succ._simp_1",
"BitVec.getMsbD",
"congrArg",
"Decidable.decide.congr_simp",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.getMsbD_rotateLeft._proof_1_1",
"BitVec",
"id",
"Bool.and",
"Nat.instMod",
"instHMod... | true |
CommSemiRingCat.Hom.hom | Mathlib.Algebra.Category.Ring.Basic | [
"CommSemiRingCat.instConcreteCategoryRingHomCarrier",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"CommSemiRingCat.carrier",
"RingHom",
"RingHom.instFunLike",
"CommSemiRingCat",
"CommSemiRingCat.commSemiring",
"Semiring.toNonAssocSemiring",
"CommSemiRingCat.instCategory",
"... | true |
Submodule.Quotient.equiv._proof_1 | Mathlib.LinearAlgebra.Quotient.Basic | [
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"LinearEquiv.symm",
"Submodule.mem_comap._simp_1",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.mem_map",
"LinearMap.instFunLike",
"Membership.mem",
"Exists",
"AddCommGroup",
"Eq.mp",
"LinearEquiv.symm_apply_apply",
"id",
"Linea... | false |
CategoryTheory.Limits.createsFiniteLimitsOfCreatesFiniteLimitsOfSize | Mathlib.CategoryTheory.Limits.Preserves.Creates.Finite | [
"CategoryTheory.Limits.CreatesFiniteLimits.mk",
"CategoryTheory.Functor",
"CategoryTheory.CreatesLimitsOfShape",
"ULift",
"CategoryTheory.ULiftHom",
"CategoryTheory.SmallCategory",
"CategoryTheory.ULiftHomULiftCategory.equiv",
"CategoryTheory.ULiftHom.category",
"CategoryTheory.finCategoryUlift",
... | true |
CategoryTheory.Equivalence.enoughProjectives_iff | Mathlib.CategoryTheory.Preadditive.Projective.Basic | [
"CategoryTheory.ProjectivePresentation",
"CategoryTheory.EnoughProjectives.presentation",
"CategoryTheory.Equivalence",
"Nonempty.some",
"CategoryTheory.Equivalence.functor",
"Nonempty.intro",
"Iff",
"CategoryTheory.Equivalence.projectivePresentationOfMapProjectivePresentation",
"Iff.intro",
"Cate... | true |
_private.Mathlib.CategoryTheory.Shift.ShiftedHomOpposite.0.CategoryTheory.ShiftedHom.opEquiv_symm_comp._proof_1 | Mathlib.CategoryTheory.Shift.ShiftedHomOpposite | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"Classical.byContradiction",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Int.instAddMonoid",
"Int.Linear.Poly.num",
"Int.instMul"... | false |
Nat.getElem_toArray_roc | Init.Data.Range.Polymorphic.NatLemmas | [
"Nat.getElem_toArray_rco",
"Std.Rco.toArray",
"congrArg",
"GetElem.getElem.congr_simp",
"Std.PRange.instIsAlwaysFiniteNat_1",
"instOfNatNat",
"instLENat",
"Array",
"GetElem.getElem",
"instHAdd",
"Nat.add_left_cancel_iff._simp_1",
"Array.instGetElemNatLtSize",
"HAdd.hAdd",
"Nat.toArray_roc_... | true |
Lean.Compiler.LCNF.instInhabitedSpecEntry | Lean.Compiler.LCNF.SpecInfo | [
"Inhabited",
"Lean.Compiler.LCNF.instInhabitedSpecEntry.default",
"Lean.Compiler.LCNF.SpecEntry",
"Inhabited.mk"
] | true |
_private.Mathlib.GroupTheory.DivisibleHull.0.«term↑ⁿ» | Mathlib.GroupTheory.DivisibleHull | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
Left.one_lt_mul | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"MulOne.toOne",
"Preorder.toLT",
"HMul.hMul",
"MulOne.toMul",
"MulLeftStrictMono",
"MulOneClass.toMulOne",
"LT.lt",
"One.toOfNat1",
"lt_mul_of_lt_of_one_lt",
"MulOneClass",
"OfNat.ofNat",
"Preorder",
"instHMul"
] | true |
_private.Init.Data.String.Basic.0.String.Slice.Pos.next_eq_nextFast._proof_1_7 | Init.Data.String.Basic | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"String.Slice.Pos.str",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"String.Slice.Pos.offset",
"String.Slice.Pos.str_ne_endPos",
"Int.add_one_le_of_lt",
"H... | false |
NormedField.toNormedSpace._proof_1 | Mathlib.Analysis.Normed.Module.Basic | [
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real.instLE",
"Real",
"HMul.hMul",
"NonUnitalRing.toNonUnitalNonAssocRing",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"LE.le",
"NormedField",
"NonUnitalSeminormedRing.toNorm",
"Distrib.toMul",
"NonUnitalSeminormedCommRing.toNonUni... | false |
USize.ofNatLT_sub | Init.Data.UInt.Lemmas | [
"instPowNat",
"congrArg",
"HSub.hSub",
"USize.ofNat",
"Nat.lt_of_le_of_lt",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instNatPowNat",
"System.Platform.numBits",
"instHSub",
"HPow.hPow",
"Nat",
"USize.ofNatLT",
"congr",
"LT.lt",
"True",
"eq_self",
"of_eq_true",
"USi... | true |
SimpleGraph.Subgraph.instDecidableRel_deleteVerts_adj._proof_1 | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"SimpleGraph.Subgraph",
"Membership.mem",
"Set.Elem",
"SimpleGraph.Subgraph.instTop",
"SimpleGraph",
"Top.top",
"Subtype.val",
"SimpleGraph.Subgraph.deleteVerts",
"Set.instMembership",
"SimpleGraph.Subgraph.verts",
"True.intro",
"Set"
] | false |
Lean.Grind.AC.SubseqResult.false.sizeOf_spec | Lean.Meta.Tactic.Grind.AC.Seq | [
"Lean.Grind.AC.SubseqResult.false",
"Lean.Grind.AC.SubseqResult",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Lean.Grind.AC.SubseqResult._sizeOf_inst",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
Homotopy.compLeft | Mathlib.Algebra.Homology.Homotopy | [
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Homotopy.hom",
"HomologicalComplex",
"Homotopy.compLeft._proof_2",
"Homotopy.mk",
"ComplexShape",
"CategoryTheory.Preadditive",
"Homotopy.compLeft._proof_1",
"CategoryTheory.... | true |
Sym2.inf | Mathlib.Data.Sym.Sym2.Order | [
"Equiv.instEquivLike",
"Sym2.lift",
"Equiv",
"Subtype",
"SemilatticeInf.toMin",
"inf_comm",
"Subtype.mk",
"SemilatticeInf",
"Eq",
"DFunLike.coe",
"Sym2",
"Min.min",
"EquivLike.toFunLike"
] | true |
Aesop.RuleTerm.const.elim | Aesop.RuleTac.RuleTerm | [
"Aesop.RuleTerm.ctorElim",
"PULift.up",
"Aesop.RuleTerm.const",
"Aesop.RuleTerm.ctorIdx",
"Nat",
"Lean.Name",
"Aesop.RuleTerm",
"Eq.symm",
"Eq"
] | false |
Algebra.SubmersivePresentation.jacobianRelationsOfHasCoeffs._proof_1 | Mathlib.RingTheory.Extension.Presentation.Core | [
"Iff.mpr",
"Finsupp.instAddZeroClass",
"Units.val",
"Nat.instMulZeroClass",
"CommRing",
"MvPolynomial.mem_range_map_iff_coeffs_subset",
"Subring.instSetLike",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Finset",
"IsScalarTower",
"Algebra.SubmersivePresentation.toPreSubmersivePresentation... | false |
Std.DHashMap.Internal.Raw₀.getKey?_insert_self | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Std.DHashMap.Raw.WF.insert₀",
"Std.DHashMap.Internal.Raw.WF.out",
"congrArg",
"Std.DHashMap.Internal.Raw₀.getKey?",
"Std.Internal.List.getKey?_insertEntry_self",
"Std.DHashMap.Raw",
"Option.some",
"Std.DHashMap.Internal.Raw₀.toL... | true |
Lean.Elab.Attribute.stx | Lean.Elab.Attributes | [
"Lean.Syntax",
"Lean.Elab.Attribute"
] | true |
CategoryTheory.Functor.splitEpiEquiv._proof_6 | Mathlib.CategoryTheory.Functor.EpiMono | [
"CategoryTheory.Functor.preimage",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.SplitEpi.section_",
"id",
"CategoryTheory.Functor.map",
"CategoryTheory.SplitEpi.mk",
"True",
"CategoryTheory.SplitEpi.ext",
"eq_self",
"of_eq_true... | false |
_private.Mathlib.MeasureTheory.Measure.Typeclasses.SFinite.0.MeasureTheory.Measure.countable_meas_pos_of_disjoint_iUnion₀._simp_1_4 | Mathlib.MeasureTheory.Measure.Typeclasses.SFinite | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"LE.le",
"IsBotZeroClass",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"nonpos_iff_eq_zero",
"Zero"
] | false |
_private.Init.TacticsExtra.0.Lean.Parser.Tactic._aux_Init_TacticsExtra___macroRules_Lean_Parser_Tactic_tacticRw_mod_cast____1.match_1 | Init.TacticsExtra | [
"Lean.TSyntax",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"List.cons",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr4",
"_private.Init.TacticsExtra.0.Lean.Parser.Tactic._aux_Init_TacticsExtra___macroRules_Lean_Parser_Tactic_tacticRw_mod_cast____1._sparseCasesOn_1",
"List.nil",
"Option"
] | false |
Cardinal.add_one_inj | Mathlib.SetTheory.Cardinal.Arithmetic | [
"Cardinal.one_lt_aleph0",
"Cardinal.instOne",
"Cardinal",
"Cardinal.add_right_inj_of_lt_aleph0",
"Cardinal.instAdd",
"instHAdd",
"Iff",
"HAdd.hAdd",
"One.toOfNat1",
"OfNat.ofNat",
"Eq"
] | true |
PowerSeries.IsWeierstrassDivision.unique | Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | [
"CommRing",
"MvPowerSeries.instZero",
"Semiring.toModule",
"IsAdicComplete.toIsHausdorff",
"CommSemiring.toSemiring",
"PowerSeries.weierstrassDiv",
"IsLocalRing.residue",
"IsLocalRing.maximalIdeal",
"RingHom",
"PowerSeries.IsWeierstrassDivision",
"PowerSeries.isWeierstrassDivision_weierstrassDiv... | true |
Ideal.add_eq_sup | Mathlib.RingTheory.Ideal.Operations | [
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"Submodule.completeLattice",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"HAdd.hAdd",
"Max.max",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Sub... | true |
_private.Mathlib.LinearAlgebra.TensorProduct.Map.0.LinearMap.rTensor_neg._simp_1_1 | Mathlib.LinearAlgebra.TensorProduct.Map | [
"CommSemiring.toSemiring",
"LinearMap.rTensorHom",
"TensorProduct.addCommMonoid",
"LinearMap.instFunLike",
"LinearMap.module",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"LinearMap.coe_rTensorHom",
"CommMonoid.toMonoid",
"TensorProduct.instSMul._proof_1",
"LinearMap.... | false |
IsRightRegular.mul_right_eq_self_iff | Mathlib.Algebra.Regular.Basic | [
"Monoid",
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Function.Injective.eq_iff",
"id",
"MulOne.toMul",
"IsRightRegular",
"MulOneClass.toMulOne",
"Iff",
"Iff.intro",
"propext",
"One.toOfNat1",
"Eq.refl",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"one_mul",... | true |
StrictAnti.strictAntiOn | Mathlib.Order.Monotone.Defs | [
"StrictAntiOn",
"Membership.mem",
"StrictAnti",
"Set.instMembership",
"Preorder",
"StrictAnti.imp",
"Set"
] | true |
NonUnitalStarRingHom.copy._proof_2 | Mathlib.Algebra.Star.StarRingHom | [
"AddMonoid.toAddZeroClass",
"NonUnitalStarRingHom.instFunLike",
"NonUnitalStarRingHom",
"Eq.rec",
"AddZeroClass.toAddZero",
"map_zero",
"NonUnitalStarRingHom.instNonUnitalRingHomClass",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"Star",
"Zero.toOfNat0",
"AddCommMonoid.toAdd... | false |
Lean.Elab.FixedParams.instToFormatInfo | Lean.Elab.PreDefinition.FixedParams | [
"Std.ToFormat",
"Lean.Elab.FixedParams.Info",
"Std.ToFormat.mk",
"Lean.Elab.FixedParams.Info.format"
] | true |
BitVec.ushiftRight_eq_extractLsb'_of_lt | Init.Data.BitVec.Lemmas | [
"BitVec.ushiftRight_eq_extractLsb'_of_lt._proof_2",
"BitVec.getElem_append._proof_2",
"Eq.mpr",
"Decidable.casesOn",
"dite_congr",
"BitVec.instHShiftRightNat",
"BitVec.extractLsb'",
"congrArg",
"BitVec.getLsbD_of_ge",
"BitVec.instHAppendHAddNat",
"HSub.hSub",
"Decidable",
"BitVec.getElem_app... | true |
HomologicalComplex.leftUnitor'_inv_comm_assoc | Mathlib.Algebra.Homology.Monoidal | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"HomologicalComplex.instHasTensorTensorUnit",
"HomologicalComplex.leftUnitor'_inv_comm",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.Additive",
"CategoryTheory.... | true |
FirstOrder.Field.FieldAxiom.toProp | Mathlib.ModelTheory.Algebra.Field.Basic | [
"One",
"HMul.hMul",
"FirstOrder.Field.FieldAxiom.toSentence.match_1",
"Mul",
"Exists",
"Ne",
"FirstOrder.Field.FieldAxiom",
"instHAdd",
"Neg",
"Unit",
"HAdd.hAdd",
"One.toOfNat1",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Neg.neg",
"Add",
"instHMul",
"Zero"
] | true |
_private.Mathlib.NumberTheory.Padics.PadicNumbers.0.PadicSeq.equiv_zero_of_val_eq_of_equiv_zero.match_1_1 | Mathlib.NumberTheory.Padics.PadicNumbers | [
"padicNorm.instIsAbsoluteValueRat",
"NormedCommRing.toNormedRing",
"Nat.Prime",
"Preorder.toLT",
"NormedRing.toRing",
"Rat",
"PartialOrder.toPreorder",
"HSub.hSub",
"Rat.linearOrder",
"Exists",
"SemilatticeInf.toPartialOrder",
"Fact",
"GE.ge",
"DistribLattice.toLattice",
"instLENat",
"... | false |
ProbabilityTheory.Kernel.isProper_iff_inter_eq_indicator_mul | Mathlib.Probability.Kernel.Proper | [
"Eq.mpr",
"instHSMul",
"Trans.trans",
"MeasureTheory.Measure",
"ProbabilityTheory.Kernel.restrict",
"MeasurableSpace.instLE",
"instSMulOfMul",
"HMul.hMul",
"IsScalarTower.right",
"MeasurableSet",
"congrArg",
"CommSemiring.toSemiring",
"Set.indicator",
"ProbabilityTheory.Kernel.restrict_app... | true |
Std.Net.instDecidableEqIPv6Addr.decEq | Std.Net.Addr | [
"Decidable.isTrue",
"instDecidableEqUInt16",
"Std.Net.IPv6Addr",
"Vector",
"Std.Net.instDecidableEqIPv6Addr.decEq._proof_1",
"Decidable",
"Std.Net.instDecidableEqIPv6Addr.decEq._proof_3",
"Std.Net.instDecidableEqIPv6Addr.decEq.match_1",
"Std.Net.IPv6Addr.mk",
"instOfNatNat",
"dite",
"UInt16",
... | true |
Algebra.WeaklyEtale.instTensorProduct | Mathlib.RingTheory.Etale.Weakly | [
"Eq.mpr",
"RingHom.Flat",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Algebra.WeaklyEtale.flat",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"RingHom.Flat.tensorProductMap",
"Function.bijective_id",
"Semiring.toModule",
"HMul.hMul",
"... | true |
IsCancelSMul.toIsLeftCancelSMul | Mathlib.Algebra.Group.Action.Defs | [
"SMul",
"IsCancelSMul",
"IsLeftCancelSMul"
] | true |
_private.Mathlib.Algebra.Homology.SpectralObject.SpectralSequence.0.CategoryTheory.Abelian.SpectralObject.SpectralSequence.homologyIso._proof_1 | Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Int.Linear.norm_le",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Int.not_le_eq",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
... | false |
«_aux_Init_Notation___macroRules_term_∘__1» | Init.Notation | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad"... | false |
DFinsupp.comapDomain'.congr_simp | Mathlib.Data.DFinsupp.Defs | [
"Function.LeftInverse",
"Eq.rec",
"Eq.ndrec",
"Eq.refl",
"DFinsupp",
"DFinsupp.comapDomain'",
"Eq",
"Zero"
] | true |
VectorField.mlieBracketWithin_congr_set | Mathlib.Geometry.Manifold.VectorField.LieBracket | [
"Filter.EventuallyEq.filter_mono",
"VectorField.mlieBracketWithin_congr_set'",
"NormedSpace",
"Compl.compl",
"Filter.instCompleteLatticeFilter",
"nhdsWithin",
"VectorField.mlieBracketWithin",
"nhds",
"CompleteLattice.toConditionallyCompleteLattice",
"Filter.EventuallyEq",
"Set.instSingletonSet",... | true |
Representation.isTrivial_def | Mathlib.RepresentationTheory.Basic | [
"LinearMap.id",
"Monoid",
"Representation",
"MonoidHom.instFunLike",
"Representation.IsTrivial",
"Monoid.toMulOneClass",
"Module.End.instSemiring",
"LinearMap",
"AddCommMonoid",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"MulOneClass.toMulOne",
"Semiring",
"Represent... | true |
Lean.Kernel.Environment.addDeclWithoutChecking | Lean.Environment | [
"Lean.Kernel.Exception",
"Classical.ofNonempty",
"Lean.Kernel.Environment",
"Lean.Declaration",
"_private.Lean.Environment.0.Lean.Kernel.Environment.addDeclCore._proof_1",
"Except"
] | true |
CategoryTheory.isNoetherianObject_iff_isEventuallyConstant | Mathlib.CategoryTheory.Subobject.NoetherianObject | [
"Eq.mpr",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"_private.Mathlib.CategoryTheory.Subobject.NoetherianObject.0.CategoryTheory.isNoetherianObject_iff_isEventuallyConstant._simp_1_2",
"CategoryTheory.IsFiltered.IsEventuallyConstant.mk",
"CategoryTheory.MonoOver.isIso_iff_subobjectMk_eq",
"Catego... | true |
_private.Lean.Shell.0.Lean.ShellOptions.process.liftIO | Lean.Shell | [
"Pure.pure",
"instMonadExceptOfMonadExceptOf",
"_private.Lean.Shell.0.Lean.ShellOptions.process.match_1",
"Monad.toApplicative",
"String",
"MonadExcept.throw",
"instMonadLiftT",
"IO",
"instMonadExceptOfEIO",
"IO.Error.instToString",
"EIO",
"liftM",
"instMonadEIO",
"Applicative.toPure",
"... | true |
MulAction.is_one_preprimitive_iff | Mathlib.GroupTheory.GroupAction.MultiplePrimitivity | [
"MulAction.isPreprimitive_of_fixingSubgroup_empty_iff",
"Iff.mpr",
"SubMulAction.instSetLike",
"Eq.mpr",
"IsAddRightRegular",
"False",
"Set.encard",
"instSMulOfMul",
"instAddMonoidWithOneENat",
"ENat.one_ne_top._simp_1",
"ENat.instNatCast",
"congrArg",
"CommSemiring.toSemiring",
"Set.encar... | true |
CategoryTheory.Functor.leftKanExtensionIsoFiberwiseColimit._proof_2 | Mathlib.CategoryTheory.Functor.KanExtension.Adjunction | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.ι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.hasColimit_map_comp_ι_comp_grothendieckProj",
"CategoryTheory.CostructuredArrow.grothendieckProj",
"CategoryTheory.Functor.comp",
... | false |
Lean.Server.Test.Runner.Client.WidgetInstance.mk.injEq | Lean.Server.Test.Runner | [
"Lean.Json",
"Eq.propIntro",
"Lean.Server.Test.Runner.Client.WidgetInstance.mk",
"UInt64",
"Lean.injEq_helper",
"Lean.Server.Test.Runner.Client.WidgetInstance",
"And",
"Lean.Server.Test.Runner.Client.WidgetInstance.mk.inj",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs.0.«_aux_Mathlib_Algebra_Order_GroupWithZero_Unbundled_Defs___macroRules__private_Mathlib_Algebra_Order_GroupWithZero_Unbundled_Defs_0_termα>0_1» | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Synta... | false |
_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1._arg_pusher | Mathlib.Data.Nat.Squarefree | [
"_private.Mathlib.Data.Nat.Squarefree.0.Nat.minSqFacAux.match_1.splitter",
"id",
"Nat.minSqFacAux.match_1",
"Nat",
"Eq.refl",
"Eq"
] | false |
CochainComplex.augmentTruncate_hom_f_succ | Mathlib.Algebra.Homology.Augment | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CochainComplex.truncate",
"CochainComplex.augmentTruncate",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.to... | true |
_private.Mathlib.Algebra.Lie.SemiDirect.0.LieAlgebra.SemiDirectSum.instLieRing._abel_1 | Mathlib.Algebra.Lie.SemiDirect | [
"LieHom",
"LieAlgebra.toModule",
"Mathlib.Tactic.Abel.const_add_termg",
"Mathlib.Tactic.Abel.term_atomg",
"NegZeroClass.toNeg",
"CommRing",
"LieDerivation",
"LieRing.toAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Bracket.bracket",
"HSub.hSub",
"lieAlgebraSelfMo... | false |
ArzelaAscoli.compactSpace_of_isClosedEmbedding | Mathlib.Topology.UniformSpace.Ascoli | [
"Topology.IsClosedEmbedding.isInducing",
"UniformSpace",
"Equiv.instEquivLike",
"ArzelaAscoli.compactSpace_of_closed_inducing'",
"Function.comp",
"Membership.mem",
"Exists",
"Equiv",
"UniformOnFun.topologicalSpace",
"CompactSpace",
"TopologicalSpace",
"And",
"EquicontinuousOn",
"UniformOnF... | true |
Lean.Level.quote | Lean.Level | [
"Lean.Syntax.Level",
"instOfNatNat",
"Lean.Level",
"Lean.Level.PP.toResult",
"Bool.true",
"Lean.Level.PP.Result.quote",
"Nat",
"Bool",
"optParam",
"OfNat.ofNat"
] | true |
Lean.Parser.Term.structInstField | Lean.Parser.Term.Basic | [
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.leadingNode",
"Lean.Parser.optional",
"instHAndThenOfAndThen",
"Lean.Parser.ppGroup",
"instOfNatNat",
"Lean.Parser.ppSpace",
"Lean.Parser.withAntiquot",
"Bool.true",
"Unit",
"Lean.Parser.Term.structInstFieldBinder",
"Nat",
"Lean.Parse... | true |
ModuleCat.restrictScalarsId | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | [
"CategoryTheory.Functor",
"ModuleCat",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso",
"ModuleCat.restrictScalars",
"ModuleCat.restrictScalarsId'",
"ModuleCat.moduleCategory",
"ModuleCat.restrictScalarsId._proof_1",
"RingHom.id",
"Semiring.toNonAssocSemiring... | true |
QuadraticModuleCat.toModuleCat_tensor | Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal | [
"CommRing",
"ModuleCat",
"CommSemiring.toSemiring",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"QuadraticModuleCat.toModuleCat",
"QuadraticModuleCat",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"ModuleCat.MonoidalCategory.instMonoidalCategoryStruct",
"instDistribOfSe... | true |
CategoryTheory.AddMon.equivLaxMonoidalFunctorPUnit_counitIso_inv_app_hom | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"PUnit.addCommGroup",
"CategoryTheory.Functor.comp",
"CategoryTheory.AddMon.instCategory",
"AddCommGroup.toAddGroup",
"CategoryTheory.AddMon.equiv... | true |
WithTop.mul_lt_mul | Mathlib.Algebra.Order.Ring.WithTop | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"WithTop.instPartialOrder",
"Preorder.toLT",
"CanonicallyOrderedAdd.mul_lt_mul_of_lt_of_lt",
"WithTop.coe_lt_top",
"HMul.hMul",
"WithTop.top_mul",
"MulZeroClass.toMul",
"CommSemiring.toNonUnitalCommSemiring",
"WithTop.instPreorder",
"congrAr... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.