name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Std.Http.Status.httpVersionNotSupported.elim | Std.Internal.Http.Data.Status | [
"PULift.up",
"Std.Http.Status.ctorIdx",
"Std.Http.Status",
"Std.Http.Status.ctorElim",
"Nat",
"Std.Http.Status.httpVersionNotSupported",
"Eq.symm",
"Eq"
] | false |
instContinuousNegElemSphereOfNat | Mathlib.Analysis.Normed.Group.BallSphere | [
"NegZeroClass.toNeg",
"Real",
"SeminormedAddCommGroup",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Set.Elem",
"Subtype",
"IsTopologicalAddGroup.toContinuousNeg",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMo... | true |
Subalgebra.fg_iff_finiteType | Mathlib.RingTheory.FiniteType | [
"Subalgebra.instSetLike",
"Subalgebra.FG",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"Subtype",
"Algebra.FiniteType",
"CommSemiri... | true |
_private.Mathlib.Algebra.Homology.ExactSequenceFour.0.CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac._proof_8 | Mathlib.Algebra.Homology.ExactSequenceFour | [
"CategoryTheory.ComposableArrows.map'._proof_8",
"CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac._proof_4",
"instOfNatNat",
"LE.le",
"instLENat",
"autoParam",
"CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac._auto_1",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
... | false |
_private.Lean.Elab.Match.0.Lean.Elab.Term.getDiscrs | Lean.Elab.Match | [
"Lean.Syntax",
"instOfNatNat",
"Array",
"GetElem.getElem",
"Lean.Syntax.getSepArgs",
"Nat",
"True",
"OfNat.ofNat",
"Lean.Syntax.instGetElemNatTrue",
"True.intro"
] | true |
CategoryTheory.ShortComplex.instPreservesFiniteLimitsπ₂ | Mathlib.Algebra.Homology.ShortComplex.Limits | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.PreservesFiniteLimits",
"CategoryTheory.Limits.HasFiniteLimits",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.instCategory",
"inferInstance",
"CategoryTheory.Limits.PreservesFiniteLimits.mk",
"CategoryTheory.SmallCategory"... | true |
_private.Mathlib.Algebra.Lie.CartanExists.0.LieAlgebra.engel_isBot_of_isMin._proof_1_37 | Mathlib.Algebra.Lie.CartanExists | [
"LieHom",
"LieAlgebra.toModule",
"AddMemClass.toAddCommSemigroup",
"Module.End.instRing",
"LieSubalgebra.lieAlgebra",
"LieSubalgebra.instPartialOrder_1",
"Lean.RArray.leaf",
"False",
"LieSubmodule.Quotient.module",
"instHSMul",
"AddSubmonoidClass.toAddMemClass",
"Module.End.instMonoid",
"ins... | false |
lt_add_iff_lt_right_or_exists_lt | Mathlib.Algebra.Order.Monoid.Canonical.Basic | [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommMagma",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id",
"lt_add_iff_lt_left_or_exists_lt",
"CanonicallyOrderedAdd",
"add_comm",
"iff_self",
"funext",
... | true |
VectorPrebundle.trivializationOfMemPretrivializationAtlas.eq_1 | Mathlib.Topology.VectorBundle.Basic | [
"NormedSpace",
"FiberPrebundle.trivializationOfMemPretrivializationAtlas",
"VectorPrebundle.pretrivializationAtlas",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"Field.toSemifield",
"AddCommMonoid",
"Bundle.Pretrivialization",
"TopologicalSpace",
"Bundle.TotalSpa... | true |
_private.Mathlib.Topology.Order.0.continuous_Prop._simp_1_1 | Mathlib.Topology.Order | [
"Continuous",
"ContinuousAt",
"TopologicalSpace",
"propext",
"Eq",
"continuous_iff_continuousAt"
] | false |
AffineSubspace.vsub_mem_direction | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"Submodule",
"vsub_mem_vectorSpan",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"AddTorsor.toVSub",
"VSub.vsub",
"AffineSubspace.instSetLike",
"SetLike.coe",
"Submodule.setLike",
"AddTorsor",
"Module",
"Ring.toSemiring",
"AffineSubspace.di... | true |
_private.Mathlib.Algebra.Lie.Loop.0.LieAlgebra.LoopAlgebra.residuePairing._proof_1 | Mathlib.Algebra.Lie.Loop | [
"CommRing",
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommRing.toCommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
CategoryTheory.Pretriangulated.triangleMorphismId._proof_4 | Mathlib.CategoryTheory.Triangulated.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Pretriangulated.Triangle.obj₃",
"CategoryTheory.CategoryStruct.id",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Triangle",
"CategoryTheory.Category.comp_id",
"CategoryTheory.Pretriangulated.Triangle... | false |
DFinsupp.extendWith_some | Mathlib.Data.DFinsupp.Defs | [
"Option.some",
"DFinsupp.instDFunLike",
"Option.none",
"DFinsupp",
"Eq",
"DFunLike.coe",
"rfl",
"DFinsupp.extendWith",
"Option",
"Zero"
] | true |
Action.tensorUnitIso._proof_2 | Mathlib.CategoryTheory.Action.Monoidal | [
"Monoid",
"MonoidHom.instFunLike",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Iso",
"Action.instMonoidalCategory",
"CategoryTheory.End.monoid",
"CategoryTheory.Category.comp_id",
... | false |
Lean.Compiler.LCNF.LitValue.uint16.sizeOf_spec | Lean.Compiler.LCNF.Basic | [
"Lean.Compiler.LCNF.LitValue",
"Lean.Compiler.LCNF.LitValue._sizeOf_inst",
"instOfNatNat",
"Lean.Compiler.LCNF.LitValue.uint16",
"instHAdd",
"UInt16",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"UInt16._sizeOf_inst",
"OfNat.ofNat",
"Eq"
] | true |
IsStrictlyPositive.conjugate_of_isUnit_of_isSelfAdjoint._auto_1 | Mathlib.Algebra.Algebra.StrictPositivity | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Function.Coequalizer | Mathlib.Logic.Function.Coequalizer | [
"Function.Coequalizer.Rel",
"Quot"
] | true |
SeminormedCommRing.sub._inherited_default | Mathlib.Analysis.Normed.Ring.Basic | [
"Add.mk",
"Neg.mk",
"AddMonoid.mk",
"SubNegMonoid.sub'",
"id",
"instOfNatNat",
"AddSemigroup.mk",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Zero.mk",
"instAddNat",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
CategoryTheory.Limits.inhabitedCoconeMorphism | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.inhabitedCoconeMorphism._proof_2",
"CategoryTheory.Limits.CoconeMorphism.mk",
"Inhabited",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.CoconeMorphism",
"Categor... | true |
exists_lt_mem_inter_of_not_pairwise_disjoint | Mathlib.Data.Set.Pairwise.Basic | [
"Preorder.toLT",
"Function.onFun",
"congrArg",
"LinearOrder",
"Set.univ",
"PartialOrder.toPreorder",
"Set.pairwise_univ",
"Disjoint",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"DistribLattice.toLattice",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.t... | true |
LinearIsometryEquiv.toContinuousLinearEquiv._proof_3 | Mathlib.Analysis.Normed.Operator.LinearIsometry | [
"LinearIsometryEquiv.toHomeomorph",
"Continuous",
"SeminormedAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"Homeomorph.toEquiv",
"Homeomorph.continuous_toFun",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"Equiv.toFun",
"RingHomInvPair",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Semino... | false |
Std.IterStep.rec | Init.Data.Iterators.Basic | [
"Std.IterStep",
"Std.IterStep.skip",
"Std.IterStep.yield",
"Std.IterStep.done"
] | false |
Subgroup.comap_le_comap_of_le_range | Mathlib.Algebra.Group.Subgroup.Ker | [
"Iff.mpr",
"MonoidHom.range",
"Eq.ge",
"MonoidHom",
"Subgroup.map",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Function.comp",
"DivInvMonoid.toMonoid",
"Subgroup",
"LE.le",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Iff",
"Subgroup.map_comap_e... | true |
CategoryTheory.Limits.hasLimitsOfSize_opposite_iff | Mathlib.CategoryTheory.Limits.Opposites | [
"Opposite",
"CategoryTheory.Limits.HasColimitsOfSize",
"inferInstance",
"CategoryTheory.Limits.HasLimitsOfSize",
"Iff",
"CategoryTheory.Limits.hasLimits_op_of_hasColimits",
"Iff.intro",
"CategoryTheory.Category.opposite",
"CategoryTheory.Limits.hasColimits_of_hasLimits_op",
"CategoryTheory.Categor... | true |
CFC.continuous_abs | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs | [
"Continuous.comp'",
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"Continuous",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"instStarRingReal",
"instSMulOfMul",
"HMul.hMul",
"star_mul_self_nonneg._simp_1",
"NormedSpace",
"IsTopologicalRing.toIsTopologicalSemiring",
"C... | true |
Std.Time.TimeZone.TZif.TZifV2.toTZifV1 | Std.Time.Zoned.Database.TzIf | [
"Std.Time.TimeZone.TZif.TZifV2",
"Std.Time.TimeZone.TZif.TZifV1"
] | true |
CategoryTheory.NonPreadditiveAbelian.r._proof_2 | Mathlib.CategoryTheory.Abelian.NonPreadditive | [
"CategoryTheory.NonPreadditiveAbelian.r._proof_1",
"CategoryTheory.NonPreadditiveAbelian.has_cokernels",
"CategoryTheory.NonPreadditiveAbelian",
"CategoryTheory.Limits.HasCokernels.has_colimit",
"CategoryTheory.NonPreadditiveAbelian.toHasZeroMorphisms",
"CategoryTheory.Limits.HasCokernel",
"CategoryTheo... | false |
MatrixGroups.«_aux_Mathlib_LinearAlgebra_Matrix_GeneralLinearGroup_Projective___macroRules_MatrixGroups_termPGL(_,_)_1_1» | Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Projective | [
"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.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",... | false |
_private.Mathlib.Tactic.Linter.Style.0.Mathlib.Linter.Style.longLine.isImport | Mathlib.Tactic.Linter.Style | [
"String",
"String.startsWith",
"Bool",
"Bool.or",
"String.Slice.Pattern.ForwardSliceSearcher.instForwardPattern_1"
] | true |
Lean.DataValue.ofName | Lean.Data.KVMap | [
"Lean.Name",
"Lean.DataValue",
"Lean.DataValue.ofName"
] | true |
_private.Init.Data.Array.Extract.0.Array.extract_append._proof_1_3 | Init.Data.Array.Extract | [
"Array.instAppend",
"Lean.Omega.LinearCombo.coordinate_eval_6",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"Lean.Omega.Coeffs.get",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
... | false |
_private.Mathlib.NumberTheory.Divisors.0.Nat.properDivisors_eq_singleton_one_iff_prime.match_1_1 | Mathlib.NumberTheory.Divisors | [
"Finset",
"instOfNatNat",
"Nat.properDivisors",
"Nat",
"Nat.zero",
"Finset.instSingleton",
"Singleton.singleton",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Nat.casesOn"
] | false |
ValuationSubring.mem_pointwise_smul_iff_inv_smul_mem | Mathlib.RingTheory.Valuation.ValuationSubring | [
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Subring.toSubsemiring",
"instHSMul",
"DivInvOneMonoid.toInvOneClass",
"Ring.toNonAssocRing",
"Submonoid.toSubsemigroup",
"Group",
"DivisionSemiring.toGroupWithZero",
"Group.toDivisionMonoid",
"Membership.mem",
"Divis... | true |
LinearEquiv.congrRight₂_trans | Mathlib.LinearAlgebra.BilinearForm.Hom | [
"LinearEquiv.congrRight₂",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearMap.instSMulCommClass",
"LinearMap.BilinMap",
"LinearMap.module",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"CommMonoid.toMonoid",
"RingHomInvPair.ids",
"LinearMap.addComm... | true |
Lean.Lsp.ClientInfo | Lean.Data.Lsp.InitShutdown | [
"Lean.Lsp.ClientInfo.mk"
] | true |
_private.Mathlib.Analysis.Calculus.ContDiff.Defs.0.contDiffAt_infty._simp_1_1 | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"ContDiffAt",
"NormedSpace",
"contDiffWithinAt_univ",
"Set.univ",
"ENat",
"propext",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"ContDiffWithinAt",
"Eq.symm",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Eq",
"NormedAddCommGroup",
"WithTop"
] | false |
Std.ExtDHashMap.get!_empty | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.get!",
"Inhabited.default",
"Std.ExtDHashMap.instEmptyCollection",
"LawfulBEq",
"Std.DHashMap.get!_empty",
"Std.ExtDHashMap",
"Inhabited",
"Hashable",
"EmptyCollection.emptyCollection",
"BEq",
"Eq"
] | true |
Option.some_injective | Mathlib.Data.Option.Basic | [
"Option.some",
"Iff.mp",
"Function.Injective",
"Eq",
"Option.some_inj",
"Option"
] | true |
Fin.zero_ne_one | Init.Data.Fin.Lemmas | [
"instNeZeroNatHAdd_1",
"Fin.ne_of_lt",
"Fin.instOfNat",
"Ne",
"instOfNatNat",
"Fin.zero_lt_one",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Fin"
] | true |
mdifferentiable_of_mem_atlas | Mathlib.Geometry.Manifold.MFDeriv.Atlas | [
"instAddMonoidWithOneENat",
"chartedSpaceSelf",
"NormedSpace",
"PartialEquiv.target",
"Membership.mem",
"IsManifold",
"OpenPartialHomeomorph.toFun'",
"MDifferentiableOn",
"AddMonoidWithOne.toOne",
"TopologicalSpace",
"ModelWithCorners",
"mdifferentiableOn_atlas",
"ENat",
"And.intro",
"Op... | true |
Aesop.ForwardRuleMatches.update | Aesop.Tree.Data.ForwardRuleMatches | [
"Pure.pure",
"Lean.instBEqFVarId",
"Aesop.ForwardRuleMatch",
"Aesop.ForwardRuleMatches.eraseHyps",
"instForInOfForIn'",
"Monad.toApplicative",
"Std.HashSet",
"Array.instMembership",
"inferInstance",
"Lean.FVarId",
"ForIn.forIn",
"Id.run",
"Id",
"Applicative.toPure",
"Membership",
"ForI... | true |
BddAbove.isBounded | Mathlib.Topology.Order.Bornology | [
"Iff.mpr",
"Preorder.toLE",
"Bornology.IsBounded",
"BddAbove",
"And",
"And.intro",
"BddBelow",
"isBounded_iff_bddBelow_bddAbove",
"Bornology",
"Preorder",
"IsOrderBornology",
"Set"
] | true |
_private.Mathlib.RingTheory.Unramified.LocalStructure.0.Algebra.IsUnramifiedAt.exists_hasStandardEtaleSurjectionOn_of_exists_adjoin_singleton_eq_top_aux₁._simp_1_1 | Mathlib.RingTheory.Unramified.LocalStructure | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"Algebra",
"RingHom",
"Ideal.IsTwoSided",
"Ideal",
"CommSemiring",
"HasQuotient.Quotient",
"Ideal.Quotient.ring",
"RingHom.instFunLike",
"Ideal.Quotient.algebra",
"Ideal.instHasQuotient",
"Eq.symm",
"Semiring.toNonAsso... | false |
CochainComplex.ι_mapBifunctorShift₂Iso_hom_f | Mathlib.Algebra.Homology.BifunctorShift | [
"Int.instAddCommGroup",
"Eq.mpr",
"HomologicalComplex₂.totalShift₂Iso",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"instHSMul",
"ComplexShape.instTotalComplexShape",
"HMul.hMul",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"HomologicalC... | true |
SummableUniformlyOn.summable | Mathlib.Topology.Algebra.InfiniteSum.UniformOn | [
"UniformSpace",
"Exists.choose_spec",
"SummableUniformlyOn",
"HasSumUniformlyOn",
"Membership.mem",
"SummableUniformlyOn.exists",
"AddCommMonoid",
"HasSum.summable",
"Exists.choose",
"Summable",
"HasSumUniformlyOn.hasSum",
"UniformSpace.toTopologicalSpace",
"Set.instMembership",
"Summation... | true |
Real.BohrMollerup.f_nat_eq | Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | [
"Iff.mpr",
"Real.instIsOrderedRing",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Nat.instOrderedSub",
"Real",
"Preorder.toLT",
"Nat.cast_pos",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Nat.succ_pred_eq_of_pos",
"Real.instZero"... | true |
Num.of_nat_inj | Mathlib.Data.Num.Lemmas | [
"Function.LeftInverse.injective",
"Nat.instMulZeroClass",
"Nat.instOne",
"Num.to_of_nat",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"congr_arg",
"castNum",
"Num",
"Iff",
"Nat",
"Iff.intro",
"instAddNat",
"Eq",
"Num.addMonoidWithOne",
"MulZeroClass.toZero"
] | true |
AddCommute.nsmul_self | Mathlib.Algebra.Group.Commute.Defs | [
"instHSMul",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"AddZeroClass.toAddZero",
"AddCommute",
"AddCommute.refl",
"Nat",
"AddMonoid",
"AddZero.toAdd",
"HSMul.hSMul",
"AddCommute.nsmul_left"
] | true |
ContinuousAffineEquiv.coe_coe | Mathlib.Topology.Algebra.ContinuousAffineEquiv | [
"AddCommGroup.toAddCommMonoid",
"ContinuousAffineEquiv.instFunLike",
"AffineEquiv.equivLike",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ContinuousAffineEquiv",
"TopologicalSpace",
"AddTorsor",
"ContinuousAffineEquiv.toAffineEquiv",
"Module",
"AffineEquiv",
"Ring.toSemiring",
"Eq",
"DFunL... | true |
_private.Mathlib.Data.Sign.Defs.0.SignType.fin3Equiv.match_1.splitter | Mathlib.Data.Sign.Defs | [
"SignType.pos",
"SignType.neg",
"SignType.zero",
"Unit",
"SignType.fin3Equiv.match_1",
"SignType"
] | true |
Std.HashMap.getElem_modify_self | Std.Data.HashMap.Lemmas | [
"GetElem?.toGetElem",
"Membership.mem",
"Std.DHashMap.Const.get_modify_self",
"Std.HashMap",
"LawfulHashable",
"GetElem.getElem",
"EquivBEq",
"Iff.mp",
"Hashable",
"Std.HashMap.instGetElem?Mem",
"Std.HashMap.inner",
"BEq",
"Eq",
"Std.HashMap.instMembership",
"Std.HashMap.modify",
"Std.... | true |
Lean.Meta.Grind.Arith.Cutsat.DvdSolution | Lean.Meta.Tactic.Grind.Arith.Cutsat.Search | [
"Lean.Meta.Grind.Arith.Cutsat.DvdSolution.mk"
] | true |
CategoryTheory.CommSq.LiftStruct.unop._proof_1 | Mathlib.CategoryTheory.CommSq | [
"Eq.mpr",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CommSq",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.unop",
"CategoryTheory.CommSq.LiftStruct",
"id",
"CategoryTheory.unop_comp",
"CategoryTheory.CommSq.Lift... | false |
ProperConstVAdd.isProperMap_vadd | Mathlib.Topology.Algebra.ProperConstSMul | [
"ProperConstVAdd",
"VAdd",
"HVAdd.hVAdd",
"TopologicalSpace",
"instHVAdd",
"IsProperMap"
] | true |
Polynomial.signVariations_C_mul | Mathlib.Algebra.Polynomial.RuleOfSigns | [
"Left.neg_pos_iff._simp_1",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Polynomial.C",
"GroupWithZero.toMonoidWithZero",
"instDecidableNot",
"NegZeroClass.toNeg",
"RingHom.instRingHomClass",
"False",
"Polynomial.coeffList_C_mul",
"Preorder.toLT",
"RingHomClass.toAddMonoidHomClass",
"Polynomia... | true |
_private.Mathlib.Analysis.Fourier.Inversion.0.Real.tendsto_integral_gaussian_smul'._simp_1_1 | Mathlib.Analysis.Fourier.Inversion | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Sym.append.eq_1 | Mathlib.Data.Sym.Basic | [
"Multiset",
"Sym.append",
"Subtype.mk",
"instHAdd",
"HAdd.hAdd",
"Sym.append._proof_1",
"Nat",
"Sym",
"instAddNat",
"Multiset.card",
"Eq.refl",
"Subtype.val",
"Eq",
"Multiset.instAdd"
] | true |
Aesop.Goal.stats | Aesop.Tree.Stats | [
"Pure.pure",
"Aesop.Goal.id",
"Aesop.BaseM",
"Aesop.GoalKind.preNorm",
"Lean.Meta.SavedState",
"Aesop.GoalStats",
"Lean.MetavarContext.getDecl",
"ReaderT",
"Aesop.Goal.isNormal",
"Aesop.Goal",
"Lean.Meta.State.mctx",
"_private.Aesop.Tree.Stats.0.Aesop.Goal.stats.match_1",
"Lean.Meta.State",
... | true |
AlgebraicGeometry.IsPreimmersion.instIsZariskiLocalAtTarget | Mathlib.AlgebraicGeometry.Morphisms.Preimmersion | [
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.IsZariskiLocalAtTarget",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.SurjectiveOnStalks",
"AlgebraicGeometry.Scheme.instHasPullbacksPrecoverageOfHasPullbacks",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismPrope... | true |
Submonoid.smulCommClass_left | Mathlib.Algebra.Group.Submonoid.MulAction | [
"SMul",
"Membership.mem",
"inferInstance",
"Subtype",
"Submonoid.smul",
"Submonoid.instSetLike",
"MulOneClass",
"Submonoid.instSMulCommClassSubtypeMem",
"SetLike.instMembership",
"SMulCommClass",
"Submonoid"
] | true |
_private.Lean.Elab.Declaration.0.Lean.Elab.Command.findCommonPrefix.go._unsafe_rec | Lean.Elab.Declaration | [
"_private.Lean.Elab.Declaration.0.Lean.Elab.Command.findCommonPrefix.findCommon",
"_private.Lean.Elab.Declaration.0.Lean.Elab.Command.findCommonPrefix.go.match_1",
"_private.Lean.Elab.Declaration.0.Lean.Elab.Command.findCommonPrefix.go.match_3",
"Lean.Name.components",
"Lean.Name.anonymous",
"List",
"Un... | false |
hyperoperation_recursion | Mathlib.Data.Nat.Hyperoperation | [
"hyperoperation",
"instOfNatNat",
"instHAdd",
"_private.Mathlib.Data.Nat.Hyperoperation.0.hyperoperation_recursion._proof_1_1",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.hasCardinalLT_of_hasCardinalLT_arrow | Mathlib.CategoryTheory.Comma.CardinalArrow | [
"HasCardinalLT",
"Cardinal",
"HasCardinalLT.of_injective",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Comma",
"congr_arg",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Arrow",
"CategoryTheory.Arrow.mk",
"Eq",
"... | true |
ZeroAtInftyContinuousMap.instNonUnitalSeminormedRing | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"NonUnitalSeminormedRing",
"SeminormedAddCommGroup",
"ZeroAtInftyContinuousMap.instNonUnitalSeminormedRing._proof_1",
"PseudoMetricSpace.toUniformSpace",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"ZeroAtInftyContinuousMap.instNonUnitalSeminormedRing._proof_2",
"ZeroAtInftyContinuousMap.instSeminormedA... | true |
Lean.Meta.Grind.instHashableOrigin | Lean.Meta.Tactic.Grind.Theorems | [
"Hashable.mk",
"Lean.Meta.Grind.Origin",
"Hashable.hash",
"Lean.Name",
"Hashable",
"Lean.Meta.Grind.Origin.key",
"Lean.instHashableName"
] | true |
collapse_nonneg | Mathlib.Combinatorics.SetFamily.FourFunctions | [
"CommSemiring.toSemiring",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Pi.instZero",
"Finset.sum_nonneg",
"Finset.decidableEq",
"LE.le",
"Pi.hasLe",
"CommSemiri... | true |
Lean.Meta.NormCast.NormCastExtension.down | Lean.Meta.Tactic.NormCast | [
"Lean.Meta.NormCast.NormCastExtension",
"Lean.Meta.SimpExtension"
] | true |
_private.Init.Data.List.Impl.0.List.getLast?.match_1.eq_1 | Init.Data.List.Impl | [
"Unit.unit",
"List.cons",
"List",
"Unit",
"Eq.refl",
"Eq",
"List.getLast?.match_1",
"List.nil"
] | true |
Matrix.IsSimplyLaced | Mathlib.Data.Matrix.Cartan | [
"Matrix",
"Int.instNegInt",
"Int",
"instOfNat",
"Pairwise",
"Or",
"OfNat.ofNat",
"Eq",
"Neg.neg"
] | true |
Lean.Widget.RpcEncodablePacket.mk._flat_ctor._@.Lean.Server.FileWorker.WidgetRequests.2734021171._hygCtx._hyg.1 | Lean.Server.FileWorker.WidgetRequests | [
"Lean.Json",
"Lean.Widget.RpcEncodablePacket._@.Lean.Server.FileWorker.WidgetRequests.2734021171._hygCtx._hyg.1",
"Lean.Widget.RpcEncodablePacket.mk._@.Lean.Server.FileWorker.WidgetRequests.2734021171._hygCtx._hyg.1"
] | false |
RegularExpression.star.noConfusion | Mathlib.Computability.RegularExpressions | [
"RegularExpression",
"id",
"heq_of_eq",
"RegularExpression.star",
"Eq.refl",
"HEq",
"Eq",
"RegularExpression.noConfusion"
] | false |
AddMonoidAlgebra.isScalarTower_self | Mathlib.Algebra.MonoidAlgebra.Module | [
"AddMonoidAlgebra.mul_apply",
"Finsupp.instFunLike",
"Finsupp.smulZeroClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Finsupp.sum_smul_index'",
"instSMulOfMul",
"HMul.hMul",
"AddMonoidAlgebra.addAddCommMonoid",
"SMulZeroClass",
"congrArg",
"IsScalarTower",
"ite_self",
"Mul... | true |
ofMul_image_powers_eq_multiples_ofMul | Mathlib.Algebra.Group.Submonoid.Membership | [
"Set.ext",
"Monoid",
"Equiv.instEquivLike",
"Monoid.toMulOneClass",
"Additive",
"AddMonoid.toAddZeroClass",
"Equiv",
"AddSubmonoid",
"Additive.ofMul",
"SetLike.coe",
"congrFun",
"Set.mem_image_iff_of_inverse",
"AddSubmonoid.multiples",
"Submonoid.powers",
"Set.image",
"Additive.addMono... | true |
Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndFlattenState.mk.injEq | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndFlatten | [
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndHyp",
"Eq.propIntro",
"Lean.Expr.instBEq",
"Lean.injEq_helper",
"Std.HashSet",
"Lean.Expr",
"Lean.FVarId",
"Array",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndFlattenState.mk",
"And",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AndFlattenS... | true |
AddSubmonoid.closure_mul_closure | Mathlib.Algebra.Ring.Submonoid.Pointwise | [
"Iff.mpr",
"Eq.mpr",
"AddMonoidHom.instAddMonoidHomClass",
"HMul.hMul",
"congrArg",
"AddSubmonoid.mul",
"AddMonoidHom.mulRight_apply",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddSubmonoid.subset_closure",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero"... | true |
MvQPF.Pi.inst._proof_5 | Mathlib.Data.QPF.Multivariate.Constructions.Sigma | [
"Eq.mpr",
"MvPFunctor.Obj",
"MvQPF.Pi.instMvFunctor",
"congrArg",
"MvPFunctor.map",
"MvQPF.Pi.abs.match_1",
"id",
"MvPFunctor.A",
"MvQPF.Pi",
"MvQPF.toMvFunctor",
"funext",
"MvQPF.Pi.P",
"Nat",
"MvPFunctor.B",
"_private.Mathlib.Data.QPF.Multivariate.Constructions.Sigma.0.MvQPF.Sigma.inst... | false |
instSubsingletonProd | Init.Core | [
"Eq.rec",
"Prod.mk",
"Subsingleton.intro",
"_private.Init.Core.0.instSubsingletonProd.match_1",
"Subsingleton",
"Eq.refl",
"Prod",
"Subsingleton.elim",
"Eq"
] | true |
CategoryTheory.MarkovCategory.discard_natural | Mathlib.CategoryTheory.MarkovCategory.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.ComonObj.counit",
"CategoryTheory.CopyDiscardCategory.comonObj",
"CategoryTheory.MarkovCategory",
"CategoryTheory.MarkovCategory.toCopyDiscardCategory",
"CategoryTheory.CategoryStruct.comp",
"C... | true |
Representation.coinvariantsFinsuppLEquiv_apply | Mathlib.RepresentationTheory.Coinvariants | [
"CommRing",
"Representation",
"Finsupp.module",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Group",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DivInvMonoid.toMonoid",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoi... | true |
CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_hom | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.CokernelCofork",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Iso",
"Cat... | true |
_private.Init.Data.List.Sublist.0.List.singleton_suffix_append_singleton_iff._simp_1_1 | Init.Data.List.Sublist | [
"Exists",
"instHAppendOfAppend",
"List",
"List.suffix_iff_exists_eq_append",
"propext",
"List.IsSuffix",
"List.instAppend",
"Eq",
"HAppend.hAppend"
] | false |
_private.Mathlib.Geometry.Manifold.IntegralCurve.UniformTime.0.exists_isMIntegralCurve_iff_exists_isMIntegralCurveOn_Ioo.match_1_1 | Mathlib.Geometry.Manifold.IntegralCurve.UniformTime | [
"Real",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"IsMIntegralCurve",
"Exists",
"And.casesOn",
"TopologicalSpace",
"ModelWithCorners",
"And",
"Exists.casesOn",
"And.intro",
"TangentSpace",
"Exists.intro",
"Zero.toOfNat0",
"Real.normedField",
"DenselyNormedField.toNon... | false |
_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_14 | Mathlib.Data.List.TakeDrop | [
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_7",
"Lean.RArray.leaf",
"False",
"getElem?_neg",
"HMul.hMul",
"Int.Linear.norm_le",
"eq_false",
"List.getElem?_drop",
"Lean.Gr... | false |
Valuation.HasExtension.instAlgebra_valuationSubring | Mathlib.RingTheory.Valuation.Extension | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"outParam",
"CommSemiring.toSemiring",
"Algebra",
"Membership.mem",
"Valuation.HasExtension.instAlgebra_valuationSubring._proof_6",
"Field.toDivisionRing",
"Subtype",
"DivisionRing.toRing",
"SMul.mk",
"LinearOrderedCommGroupWith... | true |
ProbabilityTheory.truncation_nonneg | Mathlib.Probability.StrongLaw | [
"Set.Ioc",
"Real.instLE",
"Real",
"Real.instZero",
"Membership.mem",
"id",
"LE.le",
"Real.instNeg",
"Zero.toOfNat0",
"ProbabilityTheory.truncation",
"OfNat.ofNat",
"Set.instMembership",
"Set.indicator_apply_nonneg",
"Neg.neg",
"Real.instPreorder",
"Set"
] | true |
Lean.Elab.Term.MatchAltView.mk | Lean.Elab.MatchAltView | [
"Lean.TSyntax",
"Lean.Elab.Term.MatchAltView",
"Lean.Elab.Term.MatchAltView.mk",
"Lean.SyntaxNodeKinds",
"Lean.Syntax",
"Array"
] | true |
Real.arctan_sqrt_three | Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan | [
"Real.instIsOrderedRing",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst",
"Real.partialOrder",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NeZero.one",
"Real.... | true |
Set.MapsTo.inv | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Iff.mpr",
"InvolutiveInv.toInv",
"Set.inv_mem_inv",
"Pi.instInv",
"Membership.mem",
"InvolutiveInv",
"Inv.inv",
"Set.MapsTo",
"Set.inv",
"Set.instMembership",
"Set"
] | true |
Filter.HasBasis.vitaliFamily | Mathlib.MeasureTheory.Covering.VitaliFamily | [
"Eq.mpr",
"MeasureTheory.Measure",
"Filter.smallSets",
"congrArg",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Set.powerset",
"_private.Mathlib.MeasureTheory.Covering.VitaliFamily.0.Filter.HasBasis.vitaliFamily._simp_1_1",
"Membership.mem",
"nhds",
"id",
"HasSubset.Subset",
"Set.instInter"... | true |
Std.Http.Response.Builder.ctorIdx | Std.Internal.Http.Data.Response | [
"Nat",
"Std.Http.Response.Builder"
] | false |
List.dlookup_kunion_eq_some | Mathlib.Data.List.Sigma | [
"List.kunion",
"List.keys",
"List.mem_dlookup_kunion",
"Option.some",
"Membership.mem",
"List",
"And",
"Iff",
"List.instMembership",
"Or",
"Eq",
"List.dlookup",
"Not",
"Sigma",
"Option",
"DecidableEq"
] | true |
CategoryTheory.CommMon.forget | Mathlib.CategoryTheory.Monoidal.CommMon_ | [
"CategoryTheory.CommMon.instCategory",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.comp",
"CategoryTheory.BraidedCategory",
"CategoryTheory.CommMon.forget₂Mon",
"CategoryTheory.Mon.forget",
"CategoryTheory.Mon",
"CategoryTheory.Mon.instCategory",
"CategoryT... | true |
_private.Mathlib.RingTheory.DividedPowers.Basic.0.dividedPowersBot._proof_8 | Mathlib.RingTheory.DividedPowers.Basic | [
"Int.Linear.not_eq_norm_expr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Lean.RArray.leaf",
"False",
"eq_false",
"AddMonoid.toAddSemigroup",
"Lean.Grind.iff_eq",
"congrArg",
"CommSemiring.toSemiring",
"Int.Linear.le_unsat",
"Finset",
"AddMonoid.toAddZeroClass",
"Classical.byContradiction",... | false |
_private.Mathlib.Data.Finset.Sups.0.Finset.sups_eq_self._simp_1_1 | Mathlib.Data.Finset.Sups | [
"Finset",
"Finset.coe_inj",
"SetLike.coe",
"Finset.instSetLike",
"propext",
"Eq.symm",
"Eq",
"Set"
] | false |
CochainComplex.isStrictlyGE_iff | Mathlib.Algebra.Homology.Embedding.CochainComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"Nat.instOne",
"CochainComplex.truncLE._proof_2",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"CochainComplex.IsStrictlyGE",
"Eq.mp",
"HomologicalComplex.IsStrictlySu... | true |
PiTensorProduct.mapLIncl.eq_1 | Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm | [
"PiTensorProduct.instModule",
"Submodule.subtypeL",
"NormedCommRing.toNormedRing",
"PiTensorProduct.instSeminormedAddCommGroup",
"Submodule",
"SeminormedAddCommGroup",
"instSMulOfMul",
"NormedRing.toRing",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"NormedSpace.t... | true |
_private.Lean.Compiler.LCNF.Types.0.Lean.Compiler.LCNF.toLCNFType.visitForall.match_1 | Lean.Compiler.LCNF.Types | [
"_private.Lean.Compiler.LCNF.Types.0.Lean.Compiler.LCNF.toLCNFType.visitForall._sparseCasesOn_4",
"_private.Lean.Compiler.LCNF.Types.0.Lean.Compiler.LCNF.toLCNFType.visitForall._sparseCasesOn_2",
"String",
"Lean.Expr.const",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sor... | false |
_private.Mathlib.Data.List.Lookmap.0.List.lookmap_map_eq.match_1_1 | Mathlib.Data.List.Lookmap | [
"Unit.unit",
"List.cons",
"List",
"Unit",
"List.casesOn",
"List.nil"
] | false |
_private.Mathlib.Data.List.Cycle.0.List.prev_infix_of_mem_tail._proof_1_16 | Mathlib.Data.List.Cycle | [
"HSub.hSub",
"Lean.Grind.Nat.lt_eq",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"List",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"List.idxOf",
"List.length",
"DecidableEq"
] | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.