name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Metric.instMetricSpaceInductiveLimit._proof_11 | Mathlib.Topology.MetricSpace.Gluing | [
"Set.univ",
"EMetricSpace.toPseudoEMetricSpace",
"Metric.InductiveLimit",
"instOfNatNat",
"instHAdd",
"MetricSpace",
"HAdd.hAdd",
"Metric.instMetricSpaceInductiveLimit._aux_9",
"PseudoEMetricSpace.toUniformSpace",
"Nat",
"instAddNat",
"instTopologicalSpaceSeparationQuotient._proof_3",
"Metri... | false |
UpperSet.coe_nonempty._simp_2 | Mathlib.Order.UpperLower.CompleteLattice | [
"UpperSet",
"UpperSet.instSetLike",
"Ne",
"LE",
"Set.Nonempty",
"SetLike.coe",
"UpperSet.coe_nonempty",
"propext",
"UpperSet.instTop",
"Top.top",
"Eq"
] | false |
_private.Mathlib.Order.Minimal.0.minimal_subtype._simp_1_2 | Mathlib.Order.Minimal | [
"Subtype",
"LE.le",
"LE",
"Subtype.mk",
"propext",
"Subtype.mk_le_mk",
"Eq",
"Subtype.instLE"
] | false |
Finset.card_mul_cast_divConst | Mathlib.Combinatorics.Additive.DoublingConst | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Finset.card_mul_divConst",
"instHDiv",
"HMul.hMul",
"congrArg",
"NNRat.instSemifield",
"Finset",
"Group",
"NNRat.cast_mul._simp_1",
"Semifield",
"id",
"HDiv.hDiv",
"NNRat",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMo... | true |
Lean.Elab.Term.MVarErrorKind | Lean.Elab.Term.TermElabM | [
"Lean.Elab.Term.MVarErrorKind.implicitArg",
"Lean.Elab.Term.MVarErrorKind.hole",
"Lean.Elab.Term.MVarErrorKind.custom"
] | true |
Rat.cast_inv._simp_1 | Mathlib.Data.Rat.Cast.CharZero | [
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"DivisionRing.toRatCast",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"DivisionSemiring.toGroupWithZero",
"DivisionMonoid.toDivInvOneMonoid",
"DivisionRing.toDivisionSemiring",
"Rat.cast",
"DivisionRing.toRing",
"CharZero",
"R... | false |
CategoryTheory.Pseudofunctor.Grothendieck.category._proof_5 | Mathlib.CategoryTheory.Bicategory.Grothendieck | [
"CategoryTheory.LocallyDiscrete.categoryStruct",
"CategoryTheory.Pseudofunctor.mapComp_assoc_right_hom_app_assoc",
"CategoryTheory.Category.assoc",
"CategoryTheory.Pseudofunctor.Grothendieck.Hom.ext",
"CategoryTheory.Functor",
"CategoryTheory.Cat.Hom₂.eqToHom_toNatTrans",
"CategoryTheory.LocallyDiscrete... | false |
FourierModule.casesOn | Mathlib.Analysis.Fourier.Notation | [
"FourierModule.mk",
"instHSMul",
"FourierTransform",
"SMul",
"FourierModule.rec",
"instHAdd",
"HAdd.hAdd",
"FourierTransform.fourier",
"HSMul.hSMul",
"Eq",
"FourierModule",
"Add"
] | false |
Projectivization.orthogonal._proof_1 | Mathlib.LinearAlgebra.Projectivization.Constructions | [
"Pi.Function.module",
"Units.instMulAction",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"dotProduct",
"AddCommGroup.toAddCommMonoid",
"Field.toDivisionRing",
"Units",
"DivisionRing.toDivisionSemiring",
"Subtype",
"NonUni... | false |
_private.Mathlib.NumberTheory.NumberField.Units.DirichletTheorem.0.NumberField.Units.dirichletUnitTheorem.logEmbedding_component_le._simp_1_2 | Mathlib.NumberTheory.NumberField.Units.DirichletTheorem | [
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"LE.le",
"Finset.instSetLike",
"propext",
"Finset.sup_le_iff",
"Finset.sup",
"SemilatticeSup.toPartialOrder",
"Eq",
"SemilatticeSup",
"SetLike.instMembership"
] | false |
Algebra.Extension.Hom.sub._simp_2 | Mathlib.RingTheory.Extension.Cotangent.Basic | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"LinearMap.instFunLike",
"Ideal.Cotangent",
"Membership.mem",
"Algebra.id",
"Subtype",
"Ideal.instAddCommGroupCotangent",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatN... | false |
RelSeries.append | Mathlib.Order.RelSeries | [
"SetRel",
"RelSeries.last",
"RelSeries.append._proof_2",
"Function.comp",
"Membership.mem",
"RelSeries.length",
"Prod.mk",
"instOfNatNat",
"RelSeries",
"RelSeries.append._proof_8",
"instHAdd",
"Fin.cast",
"HAdd.hAdd",
"Nat",
"RelSeries.toFun",
"instAddNat",
"RelSeries.head",
"Prod"... | true |
Padic.instNorm | Mathlib.NumberTheory.Padics.PadicNumbers | [
"Real",
"Nat.Prime",
"padicNormE",
"Real.instRatCast",
"Rat",
"Fact",
"Norm",
"Rat.cast",
"Field.toSemifield",
"instFieldPadic",
"Semifield.toDivisionSemiring",
"Nat",
"AbsoluteValue.funLike",
"Rat.instPartialOrder",
"DivisionSemiring.toSemiring",
"Padic",
"Norm.mk",
"DFunLike.coe"... | true |
TwoSidedIdeal.instSMulNatSubtypeMem._proof_1 | Mathlib.RingTheory.TwoSidedIdeal.Basic | [
"NonUnitalNonAssocRing",
"instHSMul",
"TwoSidedIdeal",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddMonoid.toNSMul",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Subtype",
"TwoSidedIdeal.nsmul_mem",
"AddGroup.toSubNegMonoid",
"TwoSidedIdeal.setLike",
"Nat",
"HSMul.hSMul",
"SubNegMonoid.toA... | false |
groupHomology.coe_mapCycles₁ | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"Submodule",
"Rep.V",
"CommRing",
"Finsupp.module",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"LinearMap.instFunLike"... | true |
CategoryTheory.Bicategory.whiskerRight_comp_symm_assoc | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.whiskerRight_comp_symm",
"congrArg",
"Eq.mp",
"CategoryTheory.Bicategory.whiskerRight",
"id",
"CategoryTheory.Bicategory.toCategoryStruct",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"C... | true |
RatFunc.CompletionAtInfty.instUniformSpace | Mathlib.FieldTheory.RatFunc.Valuation | [
"Int.instAddCommGroup",
"UniformSpace",
"Multiplicative.linearOrder",
"Int.instLinearOrder",
"Field.toDivisionRing",
"WithZero.instLinearOrderedCommGroupWithZero",
"DivisionRing.toRing",
"Int",
"RatFunc.inftyValuation._proof_2",
"Multiplicative.commGroup",
"Field.toCommRing",
"Multiplicative",... | true |
RingPreordering.coe_set_mk | Mathlib.Algebra.Order.Ring.Ordering.Defs | [
"NegZeroClass.toNeg",
"CommRing",
"Subsemiring.instSetLike",
"CommSemiring.toSemiring",
"Submonoid.toSubsemigroup",
"RingPreordering.mk",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"MulOne.toMul",
"SubtractionMonoid.toSubNegZeroMonoid",
"NonAssocSemiring.toMulZeroOneClass",
"RingP... | true |
Aesop.IndexMatchLocation.hyp | Aesop.Index.Basic | [
"Aesop.IndexMatchLocation.hyp",
"Lean.LocalDecl",
"Aesop.IndexMatchLocation"
] | true |
OrderDual.instNontrivial | Mathlib.Order.OrderDual | [
"Nontrivial",
"OrderDual"
] | true |
Lean.Compiler.LCNF.JoinPointFinder.FindCtx.mk | Lean.Compiler.LCNF.JoinPoints | [
"Lean.FVarIdMap",
"Lean.Compiler.LCNF.JoinPointFinder.FindCtx",
"Lean.FVarId",
"Nat",
"Lean.Compiler.LCNF.JoinPointFinder.FindCtx.mk",
"Option"
] | true |
_private.Mathlib.Analysis.Asymptotics.AsymptoticEquivalent.0.Asymptotics.IsEquivalent.smul._simp_1_6 | Mathlib.Analysis.Asymptotics.AsymptoticEquivalent | [
"False",
"HMul.hMul",
"eq_false",
"Mul",
"Ne",
"NoZeroDivisors",
"Zero.toOfNat0",
"mul_ne_zero",
"OfNat.ofNat",
"Eq",
"instHMul",
"Zero"
] | false |
Rack.act'_symm_apply | Mathlib.Algebra.Quandle | [
"Rack.act'",
"Equiv.instEquivLike",
"Rack",
"Equiv",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"rfl",
"Rack.invAct",
"EquivLike.toFunLike"
] | true |
FreeAddGroup.zero_ne_of | Mathlib.GroupTheory.FreeGroup.Reduce | [
"False",
"eq_false",
"congrArg",
"FreeAddGroup.toWord",
"FreeAddGroup.of",
"Prod.mk",
"Ne",
"FreeAddGroup.instZero",
"ne_of_apply_ne",
"List.cons",
"Bool.true",
"List",
"True",
"List.ne_cons_self",
"Bool",
"of_eq_true",
"Zero.toOfNat0",
"Prod",
"FreeAddGroup",
"OfNat.ofNat",
... | true |
Ordering.Compares.inj | Mathlib.Order.Compare | [
"Iff.mpr",
"Ordering.gt",
"Preorder.toLT",
"_private.Mathlib.Order.Compare.0.Ordering.Compares.inj.match_1_1",
"Ordering",
"Ordering.Compares.eq_lt",
"Ordering.eq",
"Ordering.Compares",
"Ordering.lt",
"LT.lt",
"Ordering.Compares.eq_gt",
"Eq",
"Ordering.Compares.eq_eq",
"Preorder"
] | true |
AddSubgroup.card_le_one_iff_eq_bot | Mathlib.Algebra.Group.Subgroup.Finite | [
"AddGroup.toSubtractionMonoid",
"AddSubgroup.instBot",
"instReflLe",
"congrArg",
"Std.le_refl",
"Finite",
"Membership.mem",
"Fintype.card",
"Subtype",
"Nat.card",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatNat",
"Bot.bot",
"LE.le",
"instLENat",
"SubNegZeroMonoid.toNegZeroClass",... | true |
ModuleCat.instPreservesFiniteLimitsLocalizationLocalizedModuleFunctor | Mathlib.Algebra.Category.ModuleCat.Localization | [
"CategoryTheory.Abelian.toPreadditive",
"CommRing",
"CategoryTheory.Limits.PreservesFiniteLimits",
"ModuleCat",
"CommSemiring.toSemiring",
"ModuleCat.localizedModuleFunctor",
"CategoryTheory.ShortComplex",
"List.instGetElem?NatLtLength",
"Localization",
"instOfNatNat",
"List.cons",
"MulZeroOne... | true |
_private.Lean.Compiler.LCNF.ElimDead.0.Lean.Compiler.LCNF.collectLocalDeclsLetValue.match_1 | Lean.Compiler.LCNF.ElimDead | [
"Lean.Compiler.LCNF.LetValue.reuse",
"Unit.unit",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.LetValue.pap",
"Lean.Compiler.LCNF.LitValue",
"Lean.Compiler.LCNF.LetValue.oproj",
"Lean.Compiler.LCNF.LetValue",
"Lean.Compiler.LCNF.LetValue.erased",
"Lean.Compiler.LCNF.LetValue.uproj",
"Lean.Expr",
... | false |
AddSubgroup.focalAddSubgroup.eq_1 | Mathlib.GroupTheory.Focal | [
"addCommutatorElement",
"Bracket.bracket",
"setOf",
"Membership.mem",
"Exists",
"AddSubgroup",
"And",
"AddGroup",
"AddSubgroup.instSetLike",
"Eq.refl",
"Eq",
"SetLike.instMembership",
"AddSubgroup.closure",
"AddSubgroup.focalAddSubgroup"
] | true |
CategoryTheory.Equalizer.Presieve.SecondObj._proof_1 | Mathlib.CategoryTheory.Sites.EqualizerSheafCondition | [
"CategoryTheory.Presieve.HasPairwisePullbacks",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"CategoryTheory.Limits.HasPullback",
"Subtype",
"Sigma.fst",
"Prod.fst",
"CategoryTheory.Presieve.HasPairwisePullbacks.has_pullbacks",
"CategoryTheory.Category.toCateg... | false |
Ring.instDirectLimit._proof_28 | Mathlib.Algebra.Colimit.Ring | [
"Mul.mk",
"CommRing",
"Ring.instDirectLimit._proof_17",
"Ring.instOneDirectLimit",
"HMul.hMul",
"FreeCommRing",
"AddMonoid.toAddSemigroup",
"AddGroupWithOne.toAddGroup",
"Ring.instDirectLimit._proof_10",
"CommSemiring.toSemiring",
"Neg.mk",
"AddMonoid.toZero",
"setOf",
"AddGroupWithOne.toA... | false |
Lean.Doc.Syntax.codeblock._regBuiltin.Lean.Doc.Syntax.codeblock.docString_1 | Lean.DocString.Syntax | [
"Lean.addBuiltinDocString",
"IO",
"Unit",
"Lean.Name.mkStr4"
] | false |
CategoryTheory.ComposableArrows.homMk₃._proof_3 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"CategoryTheory.ComposableArrows.map'._proof_8",
"instOfNatNat",
"_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._proof_299",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat"
] | false |
Nat.sum_div | Mathlib.Algebra.BigOperators.Ring.Finset | [
"Eq.mpr",
"Nat.div_mul_cancel",
"Dvd.dvd",
"instHDiv",
"HMul.hMul",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"HDiv.hDiv",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"instMulNat",
"instOfNatNat",
"Nat.instNonUnitalSemiring... | true |
AddSubmonoidClass.toAddMonoid._proof_2 | Mathlib.Algebra.Group.Submonoid.Defs | [
"SetLike",
"AddSubmonoidClass.toAddMemClass",
"AddMonoid.toAddSemigroup",
"AddSubmonoidClass.toAddZeroClass",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddSubmonoidClass",
"AddZeroClass.toAddZero",
"Subtype",
"ZeroMemClass.zero",
"Subtype.coe_injective",
"AddZero.toZero",
"instHAdd",
... | false |
Matrix.GeneralLinearGroup.continuous_det | Mathlib.Topology.Algebra.Group.Matrix | [
"Units.val",
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"CommRing",
"DivInvMonoid.toInv",
"Continuous",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"DivisionCommMonoid.toDivisionMonoid",
"Units.instTopologicalSpaceUnits",
"MonoidHom"... | true |
Lean.Elab.Tactic.Do.ProofMode.MGoal.assumption._unsafe_rec | Lean.Elab.Tactic.Do.ProofMode.Assumption | [
"guard",
"Pure.pure",
"OptionT.instMonad",
"instOrElseOfAlternative",
"OptionT",
"Lean.Elab.Tactic.Do.ProofMode.MGoal.mk",
"Lean.Elab.Tactic.Do.ProofMode.MGoal.hyps",
"Lean.Elab.Tactic.Do.ProofMode.parseHyp?",
"ReaderT",
"Lean.Elab.Tactic.Do.ProofMode.Hyp.p",
"String",
"Lean.Meta.State",
"Le... | false |
_private.Mathlib.MeasureTheory.PiSystem.0.mem_generatePiSystem_iUnion_elim'._simp_1_1 | Mathlib.MeasureTheory.PiSystem | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
Plausible.Configuration.numInst._default | Plausible.Testable | [
"id",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | false |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.StructInstState.optParamFields._default | Lean.Elab.StructInst | [
"Lean.Expr",
"id",
"List.toArray",
"Array",
"Bool",
"Lean.Name",
"Prod",
"List.nil"
] | false |
_private.Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory.0.CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverse._proof_6 | Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Comon.Hom",
"CategoryTheory.Functor.map",
"congr_arg",
"CategoryTheory.Comon.instCategory",
"CategoryTheory.NatTrans.naturality",
... | false |
CancelMonoidWithZero | Mathlib.Algebra.GroupWithZero.Defs | [
"CancelMonoidWithZero.mk"
] | true |
instModuleWeakBilin._proof_5 | Mathlib.Topology.Algebra.Module.Spaces.WeakBilin | [
"instHSMul",
"Semiring.toModule",
"CommSemiring.toSemiring",
"instModuleWeakBilin._proof_3",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"instModuleWeakBilin._proof_4",
"instModuleWeakBilin._aux_1",
"WeakBilin._proof_1",
"SemigroupAction.mk",
"LinearMap.module",
"LinearMap",
"AddCo... | false |
_private.Lean.Meta.Sym.ReplaceS.0.Lean.Meta.Sym.visitChild.match_1.eq_5 | Lean.Meta.Sym.ReplaceS | [
"Lean.Expr.const",
"Lean.Expr.mvar",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.fvar",
"List",
"_private.Lean.Meta.Sym.ReplaceS.0.Lean.Meta.Sym.visitChild.match_1",
"Nat",
"Lean.Name",
"Eq.refl",
"Eq",
"Lean... | true |
Lean.Lsp.SymbolKind.variable | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolKind.variable",
"Lean.Lsp.SymbolKind"
] | true |
_private.Mathlib.Topology.UniformSpace.Separation.0.t0Space_iff_ker_uniformity._simp_1_4 | Mathlib.Topology.UniformSpace.Separation | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.card_edgeFinset_turanGraph._proof_1_1 | Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | [
"instPowNat",
"Lean.RArray.leaf",
"False",
"instHDiv",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Lean.Grind.CommRing.Expr.var",
"Nat.instMonoid",
"Classical.byContradiction",
"HSub.hSub",
"Lean.Grind.CommSemiring.toSemiring",
"Lea... | false |
FirstOrder.Language.LHom._sizeOf_1 | Mathlib.ModelTheory.LanguageMap | [
"FirstOrder.Language.LHom.rec",
"instOfNatNat",
"Nat",
"FirstOrder.Language.Relations",
"FirstOrder.Language.Functions",
"FirstOrder.Language.LHom",
"FirstOrder.Language",
"OfNat.ofNat"
] | false |
IsMaxOn.dual | Mathlib.Order.Filter.Extr | [
"Iff.mpr",
"OrderDual.toDual",
"Equiv.instEquivLike",
"isMinOn_dual_iff",
"IsMaxOn",
"Function.comp",
"Equiv",
"IsMinOn",
"OrderDual",
"OrderDual.instPreorder",
"DFunLike.coe",
"Preorder",
"EquivLike.toFunLike",
"Set"
] | true |
SimplexCategory.Hom.ext_one_left._auto_3 | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.SplitEpi | Mathlib.CategoryTheory.EpiMono | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SplitEpi.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
_private.Mathlib.RingTheory.MvPolynomial.Symmetric.Defs.0.MvPolynomial.support_esymm''._simp_1_2 | Mathlib.RingTheory.MvPolynomial.Symmetric.Defs | [
"Finset.mem_singleton",
"Finset",
"Membership.mem",
"Finset.instSetLike",
"propext",
"Finset.instSingleton",
"Singleton.singleton",
"Eq",
"SetLike.instMembership"
] | false |
OpenPartialHomeomorph.pi._proof_4 | Mathlib.Topology.OpenPartialHomeomorph.Constructions | [
"Iff.mpr",
"Continuous.continuousOn",
"trivial",
"Pi.topologicalSpace",
"PartialEquiv.target",
"Membership.mem",
"OpenPartialHomeomorph.toFun'",
"ContinuousOn.comp",
"TopologicalSpace",
"PartialEquiv.pi",
"continuous_apply",
"ContinuousOn",
"PartialEquiv.invFun",
"OpenPartialHomeomorph.con... | false |
String.reduceGE._regBuiltin.String.reduceGE.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.String.2055768308._hygCtx._hyg.22 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.String | [
"IO",
"Sum.inl",
"String.reduceGE",
"Bool.true",
"Unit",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.addSimprocBuiltinAttr",
"Lean.Meta.Simp.Simproc"
] | false |
Lean.PrettyPrinter.Delaborator.appUnexpanderAttribute | Lean.PrettyPrinter.Delaborator.Basic | [
"Classical.ofNonempty",
"Lean.KeyedDeclsAttribute",
"Lean.instNonemptyKeyedDeclsAttribute",
"Lean.PrettyPrinter.Unexpander"
] | true |
MonoidAlgebra.mul_apply_left | Mathlib.Algebra.MonoidAlgebra.Defs | [
"Finsupp.instFunLike",
"Eq.mpr",
"instDecidableNot",
"HMul.hMul",
"ite_eq_right_iff._simp_1",
"DivInvOneMonoid.toInvOneClass",
"Finset.sum_ite_eq'",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Finsupp.mem_support_iff._simp_1",
"AddMonoid.toAddZeroClass",
"Finsupp.sum",
"Group",
"Class... | true |
TensorProduct.tensorQuotEquivQuotSMul_symm_mk | Mathlib.LinearAlgebra.TensorProduct.Quotient | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"LinearEquiv.symm",
"CommRing",
"instHSMul",
"Semiring.toModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.mk",
"TensorProduct.addCommMonoid",
"Submodule.hasQuotient",
"AddCommGroup",
"Submodule.instTop",
... | true |
Bornology.IsCobounded.superset | Mathlib.Topology.Bornology.Basic | [
"HasSubset.Subset",
"Bornology.cobounded",
"Bornology.IsCobounded",
"Bornology",
"Set.instHasSubset",
"Filter.mem_of_superset",
"Set"
] | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic.0.CStarAlgebra.spectralOrder._simp_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic | [
"IsSelfAdjoint",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"StarAddMonoid.toInvolutiveStar",
"AddZero.toZero",
"IsSelfAdjoint.zero",
"True",
"AddMonoid",
"eq_true",
"StarAddMonoid",
"Zero.toOfNat0",
"InvolutiveStar.toStar",
"OfNat.ofNat",
"Eq"
] | false |
Lean.Server.Watchdog.ModuleQueryMatch.noConfusion | Lean.Server.Watchdog | [
"String",
"Lean.Server.Watchdog.ModuleQueryMatchScore",
"Lean.Server.Watchdog.ModuleQueryMatch",
"Lean.Server.Watchdog.ModuleQueryMatch.noConfusionType",
"Lean.Server.Watchdog.ModuleQueryMatch.casesOn",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq"
] | false |
Sigma._sizeOf_inst._@.Mathlib.Util.CompileInductive.4222055393._hygCtx._hyg.9 | Mathlib.Util.CompileInductive | [
"Sigma._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Sigma"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.ToInt.0.Lean.Meta.Grind.Arith.Cutsat.normalizeBound | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToInt | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Sym.Context",
"Option.some",
"ReaderT.instMonad",
"Lean.Meta.Grind.Arith.evalInt?",
"Lean.Meta.Grind.Context",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.ToInt.0.Lean.Meta.Grind.Arith.Cutsat.normalizeBound.mat... | true |
CategoryTheory.Abelian.SpectralObject.dHomologyData._auto_1 | Mathlib.Algebra.Homology.SpectralObject.Homology | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.CategoryTheory.ObjectProperty.Basic.0.CategoryTheory.ObjectProperty.singleton_le_iff._simp_1_1 | Mathlib.CategoryTheory.ObjectProperty.Basic | [
"CategoryTheory.ObjectProperty.ofObj",
"Prop.le",
"CategoryTheory.ObjectProperty.ofObj_le_iff",
"LE.le",
"Pi.hasLe",
"propext",
"CategoryTheory.CategoryStruct",
"Eq",
"CategoryTheory.ObjectProperty"
] | false |
Multiset.sort_range | Mathlib.Data.Multiset.Sort | [
"List.mergeSort_eq_self",
"Nat.instAntisymmLe",
"List.SortedLE.pairwise",
"List.range",
"LE.le",
"instLENat",
"instIsTransLe",
"List",
"Nat.instPreorder",
"Nat",
"Multiset.sort",
"Multiset.range",
"Eq",
"Nat.decLe",
"List.SortedLT.sortedLE",
"List.sortedLT_range",
"LE.total",
"Nat.... | true |
Mathlib.Tactic.Translate.Config.tgt | Mathlib.Tactic.Translate.Core | [
"Lean.Name",
"Mathlib.Tactic.Translate.Config"
] | true |
_private.Mathlib.RingTheory.Coalgebra.TensorProduct.0.Coalgebra._aux_Mathlib_RingTheory_Coalgebra_TensorProduct___macroRules__private_Mathlib_RingTheory_Coalgebra_TensorProduct_0_Coalgebra_termμ_1 | Mathlib.RingTheory.Coalgebra.TensorProduct | [
"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.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr... | false |
Lean.Grind.CommRing.Poly.recOn | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly.rec",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.add",
"Int",
"Lean.Grind.CommRing.Mon",
"Lean.Grind.CommRing.Poly.num"
] | false |
Lean.Firefox.FrameTable.Entry.mk.inj | Lean.Util.Profiler | [
"Lean.Json",
"Int",
"Lean.Firefox.FrameTable.Entry.mk",
"And",
"Nat",
"And.intro",
"Lean.Firefox.FrameTable.Entry",
"Lean.Firefox.FrameTable.Entry.mk.noConfusion",
"Eq",
"Option"
] | true |
_private.Lean.Compiler.LCNF.MonoTypes.0.Lean.Compiler.LCNF.trivialStructureInfoExt | Lean.Compiler.LCNF.MonoTypes | [
"Inhabited.default",
"Lean.Compiler.LCNF.instInhabitedCacheExtension",
"Lean.Compiler.LCNF.TrivialStructureInfo",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.Compiler.LCNF.CacheExtension",
"Option",
"Lean.instHashableName"
] | true |
AlgebraicIndependent.option_iff_transcendental | Mathlib.RingTheory.AlgebraicIndependent.Transcendental | [
"Subalgebra.instSetLike",
"Finsupp.instAddZeroClass",
"Eq.mpr",
"AlgHom.coe_toRingHom",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"AlgebraicIndependent",
"AlgHom.algHomClass",
"AlgebraicIndependent.aeval_comp_mvPolynomialOptionEquivPolynomialAdjoin",
"MvPolynomial.aeval",
... | true |
mabs_div | Mathlib.Algebra.Order.Group.Abs | [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"IsOrderedMonoid",
"Monoid.toMulOneClass",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Group.toDivisionMonoid",
"mabs_mul_le",
"DivisionMonoid.toDivInvOneMonoid",
"Semila... | true |
MvPolynomial.sumToIter_iterToSum | Mathlib.Algebra.MvPolynomial.Equiv | [
"RingEquiv.apply_symm_apply",
"Finsupp.instAddZeroClass",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"MvPolynomial.iterToSum",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Finsupp.instAddMonoid",
"AddMonoidAlgebra.commSemiring",
"Nat.instAddMonoid",
"RingHom",
"Sum",
"Di... | true |
Lean.Omega.Int.ofNat_natAbs | Init.Omega.Int | [
"Eq.mpr",
"congrArg",
"Int.decLe",
"_private.Init.Omega.Int.0.Int.neg.match_1.splitter",
"id",
"Int.instNegInt",
"Int.ofNat",
"Int",
"LE.le",
"if_pos",
"Nat.cast",
"Int.negSucc_not_nonneg._simp_1",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"Nat",
"True",
"Int.natAbs",
"eq_self",
"o... | true |
CategoryTheory.LocalizerMorphism.RightResolution.unopFunctor._proof_3 | Mathlib.CategoryTheory.Localization.Resolution | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.LocalizerMorphism.RightResolution",
"Opposite",
"CategoryTheory.LocalizerMorphism.RightResolution.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op_inj",
"Quiver.Hom.unop",
"CategoryTheory.LocalizerMorphism.LeftResolutio... | false |
Opposite.unop_injective | Mathlib.Data.Opposite | [
"Opposite",
"congrArg",
"Opposite.op",
"Function.Injective",
"Eq",
"Opposite.unop"
] | true |
generatePiSystem.recOn | Mathlib.MeasureTheory.PiSystem | [
"generatePiSystem.base",
"Membership.mem",
"generatePiSystem.rec",
"Set.instInter",
"Inter.inter",
"Set.Nonempty",
"Set.instMembership",
"generatePiSystem",
"generatePiSystem.inter",
"Set"
] | false |
LinearIsometryEquiv.smul_apply | Mathlib.Analysis.RCLike.Basic | [
"LinearIsometryEquiv.instEquivLike",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddCommGroup",
"NormedSpace",
"Monoid.toMulOneClass",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"unitary",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"... | true |
MulArchimedean.rec | Mathlib.Algebra.Order.Archimedean.Defs | [
"MulOne.toOne",
"Preorder.toLT",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"PartialOrder",
"LE.le",
"Monoid.toPow",
"MulArchimedean",
"MulOneClass.toMulOne",
"HPow.hPow",
"CommMonoid.toMonoid",
"Nat",
"LT.lt",
"One.toOfNat1",
"instHPow",
"OfNat.o... | false |
Lean.Elab.Tactic.ElimTargetView.casesOn | Lean.Elab.Tactic.Induction | [
"Lean.Elab.Tactic.ElimTargetView",
"Lean.Syntax.Ident",
"Lean.Syntax",
"Lean.Elab.Tactic.ElimTargetView.mk",
"Lean.Elab.Tactic.ElimTargetView.rec",
"Option"
] | false |
AddOreLocalization.universalAddHom.eq_1 | Mathlib.GroupTheory.OreLocalization.Basic | [
"AddUnits.val",
"AddOreLocalization.instAddMonoid",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddMonoidHom.mk",
"AddOreLocalization.universalAddHom",
"Subtype",
"AddOreLocalization.liftExpand",
"AddSubmonoid",
"AddSubmonoid.toAddZeroClass",
"ZeroHom.mk",
"AddOr... | true |
ContinuousAddMonoidHom.toContinuousMap_toContinuousAddMonoidHom | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"ContinuousAddMonoidHom.toContinuousAddMonoidHom",
"ContinuousAddMonoidHom",
"ContinuousMap",
"AddMonoid.toAddZeroClass",
"ContinuousMapClass",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"ContinuousAddMonoidHom.instFunLike",
"toContinuousMap",
"TopologicalSpace",
"AddMonoid",
"Eq",
"Cont... | true |
MeasureTheory.Lp.instFourierPairInv | Mathlib.Analysis.Fourier.LpSpace | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"Real",
"CompleteSpace",
"measureSpaceOfInnerProductSpace",
"fact_one_le_two_ennreal",
"NormedSpace.toIsBoundedSMul",
"LinearIsometryEquiv.apply_symm_apply",
"Real.instRCLike",
"MeasureTheory.Lp.instModule",
"NormedSpace.toModule"... | true |
Lean.Elab.Tactic.Do.instInhabitedUses.default | Lean.Elab.Tactic.Do.LetElim | [
"Lean.Elab.Tactic.Do.Uses",
"Lean.Elab.Tactic.Do.Uses.zero"
] | true |
Filter.liminf_eq_sSup_sInf | Mathlib.Order.LiminfLimsup | [
"Filter.liminf",
"CompleteLattice.toConditionallyCompleteLattice",
"Filter.sets",
"OrderDual.instCompleteLattice",
"Set.image",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup",
"OrderDual",
"Filter.limsup_... | true |
Std.TreeSet.Raw.mem_of_mem_insertMany_list | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.WF.out",
"instForInOfForIn'",
"List.contains",
"Membership.mem",
"Ordering",
"inferInstance",
"Std.TreeSet.Raw.instMembership",
"Std.TransCmp",
"Id",
"Membership",
"List",
"Std.TreeSet.Raw",
"List.instMembership",
"Std.LawfulBEqCmp",
"Bool",
"Std.TreeMap.Raw.mem_of_mem... | true |
WeierstrassCurve.Affine.baseChange_equation | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic | [
"Eq.mpr",
"CommRing",
"AlgHom.algHomClass",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"RingHom.coe_coe",
"AlgHom.funLike",
"Iff.rfl",
"WeierstrassCurve.Affine.map",
"Algebra",
"RingHom",
"Algebra.toSMul",
"id",
"WeierstrassCurve.Affine.map_baseChange",
"CommRi... | true |
List.instLawfulBEqCmpCompareLex | Init.Data.Order.Ord | [
"Ordering.gt",
"List.compareLex_cons_cons",
"False",
"List.nil_beq_eq",
"congrArg",
"False.elim",
"noConfusion_of_Nat",
"Bool.false_eq_true",
"Ordering",
"Ordering.eq",
"Ordering.then_eq_eq._simp_1",
"Ordering.then",
"List.rec",
"Std.LawfulBEqCmp.mk",
"List.beq_nil_eq",
"List.cons",
... | true |
_private.Mathlib.LinearAlgebra.Matrix.Stochastic.0.Matrix.colStochastic._proof_1 | Mathlib.LinearAlgebra.Matrix.Stochastic | [
"mul_nonneg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"Finset.univ",
"eq_false",
"MulZeroClass.toMul",
"IsOrderedRing",
"Matrix",
"Finset",
"AddMonoid.toAddZeroClass",
"Classical.byContradiction",
... | false |
_private.Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral.0.MeasureTheory.HasFiniteIntegral.norm._simp_1_1 | Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral | [
"MeasureTheory.Measure",
"Preorder.toLT",
"PartialOrder.toPreorder",
"MeasurableSpace",
"ENorm.enorm",
"LT.lt",
"ENNReal",
"propext",
"ENorm",
"ENNReal.instPartialOrder",
"MeasureTheory.HasFiniteIntegral",
"ENNReal.instTop",
"Top.top",
"Eq",
"MeasureTheory.hasFiniteIntegral_iff_enorm",
... | false |
HahnSeries.toPowerSeries_symm_apply_coeff | Mathlib.RingTheory.HahnSeries.PowerSeries | [
"Semiring.toModule",
"RingEquiv.instEquivLike",
"LinearMap.instFunLike",
"MvPowerSeries.instMul",
"Distrib.toAdd",
"HahnSeries.toPowerSeries",
"PowerSeries.coeff",
"MvPowerSeries.instModule",
"HahnSeries.instAdd",
"LinearMap",
"MvPowerSeries.instAddCommMonoid",
"instDistribOfSemiring",
"MvPo... | true |
SimpleGraph.ConnectedComponent.lift | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"SimpleGraph.Walk",
"Quot.lift",
"SimpleGraph.ConnectedComponent",
"SimpleGraph.ConnectedComponent.lift._proof_1",
"SimpleGraph",
"SimpleGraph.Walk.IsPath",
"Eq",
"SimpleGraph.Reachable"
] | true |
CategoryTheory.Equivalence.symmEquivInverse_obj_inverse | Mathlib.CategoryTheory.Equivalence.Symmetry | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Equivalence",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.Equivalence.instCategory",
"CategoryTheory.Equivalence.symmEquivInverse",
"CategoryTheory.Category.opposite",
"Eq.refl",
"Eq",
"Opposite.unop",
"CategoryTheory.Functor.obj",
... | true |
LinearMap.toMatrix₂._proof_6 | Mathlib.LinearAlgebra.Matrix.SesquilinearForm | [
"CommSemiring.toSemiring",
"RingHom",
"RingHomCompTriple",
"CommSemiring",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
Set.symmDiff_subset_union | Mathlib.Data.Set.SymmDiff | [
"Lattice.toSemilatticeSup",
"Set.instUnion",
"SemilatticeSup.toMax",
"HasSubset.Subset",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"symmDiff_le_sup",
"Set.instBooleanAlgebra",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",
"GeneralizedCoheytingAlgebra.toLattice... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.MBTC.0.Lean.Meta.Grind.Arith.Linear.eqAssignment.match_1 | Lean.Meta.Tactic.Grind.Arith.Linear.MBTC | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Nat",
"_private.Lean.Meta.Tactic.Grind.Arith.Linear.MBTC.0.Lean.Meta.Grind.Arith.Linear.getAssignmentExt?._sparseCasesOn_1",
"Option"
] | false |
FreeSimplexQuiver.Hom._sizeOf_1 | Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | [
"FreeSimplexQuiver.Hom.rec",
"instOfNatNat",
"instHAdd",
"FreeSimplexQuiver",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"instSizeOfNat",
"Fin._sizeOf_inst",
"FreeSimplexQuiver.Hom",
"OfNat.ofNat",
"Fin"
] | false |
_private.Mathlib.Tactic.Linter.UnusedInstancesInType.0.Mathlib.Linter.UnusedInstancesInType.collectFVarsOutsideOfProofs._sparseCasesOn_1 | Mathlib.Tactic.Linter.UnusedInstancesInType | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
ProofWidgets.GetExprPresentationsParams.casesOn | ProofWidgets.Presentation.Expr | [
"Lean.Server.WithRpcRef",
"ProofWidgets.GetExprPresentationsParams.mk",
"ProofWidgets.GetExprPresentationsParams",
"ProofWidgets.GetExprPresentationsParams.rec",
"ProofWidgets.ExprWithCtx"
] | false |
UpperHemicontinuousWithinAt.of_forall_isOpen | Mathlib.Topology.Semicontinuity.Hemicontinuity | [
"Iff.mpr",
"upperHemicontinuousWithinAt_iff_forall_isOpen",
"nhdsWithin",
"Filter.Eventually",
"HasSubset.Subset",
"TopologicalSpace",
"UpperHemicontinuousWithinAt",
"IsOpen",
"Set.instHasSubset",
"Set"
] | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.