name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
ne_zero_of_map | Mathlib.Algebra.Group.Hom.Defs | [
"Eq.mpr",
"congrArg",
"ZeroHomClass",
"map_zero",
"id",
"Ne",
"ne_of_apply_ne",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"FunLike",
"Zero"
] | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.ne_intMin_of_msb_eq_false._proof_1_3 | Init.Data.BitVec.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt"... | false |
_private.Mathlib.RingTheory.NonUnitalSubsemiring.Basic.0.NonUnitalSubsemiring.coe_closure_eq._simp_1_1 | Mathlib.RingTheory.NonUnitalSubsemiring.Basic | [
"AddMonoid.toAddZeroClass",
"AddSubmonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonUnitalSubsemiring.toAddSubmonoid",
"SetLike.coe",
"Distrib.toMul",
"Subsemigroup",
"AddSubmonoid.closure",
"NonUnitalNonAssocSemiring.toDistrib",
"AddCommMonoid.toAddMonoid",
"NonUnitalNonAssocSemiring",... | false |
Matrix.parabolicEigenvalue._proof_1 | Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
_private.Mathlib.Analysis.Calculus.Taylor.0.taylor_mean_remainder_cauchy._simp_1_7 | Mathlib.Analysis.Calculus.Taylor | [
"False",
"eq_false",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"CharZero",
"Nat.cast_add_one_ne_zero",
"AddMonoidWithOne.toOne",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat",
"On... | false |
USize.ofNatLT | Init.Prelude | [
"BitVec.ofNatLT",
"System.Platform.numBits",
"Nat",
"USize.ofBitVec",
"LT.lt",
"USize.size",
"instLTNat",
"USize"
] | true |
convexHull_eq_iInter | Mathlib.Analysis.Convex.Hull | [
"CompleteLattice.instOmegaCompletePartialOrder",
"Iff.of_eq",
"congrArg",
"DistribMulAction.toDistribSMul",
"Set.iInter",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddZeroClass.toAddZero",
"PartialOrder",
"Subtype",
"DistribSMul.toSMulZeroClass",
"HasSubset.Subset",
"ClosureOpe... | true |
SSet.horn.primitiveTriangle._proof_3 | Mathlib.AlgebraicTopology.SimplicialSet.Horn | [
"_private.Mathlib.AlgebraicTopology.SimplicialSet.Horn.0.SSet.horn.primitiveTriangle._proof_2",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat"
] | false |
Batteries.Random.MersenneTwister.State.mk.injEq | Batteries.Data.Random.MersenneTwister | [
"Vector",
"Eq.propIntro",
"Lean.injEq_helper",
"BitVec",
"Batteries.Random.MersenneTwister.State.mk",
"And",
"Batteries.Random.MersenneTwister.State",
"Batteries.Random.MersenneTwister.Config",
"Batteries.Random.MersenneTwister.State.mk.inj",
"Eq.ndrec",
"Eq.refl",
"Batteries.Random.MersenneTw... | true |
CategoryTheory.ihom.ev_coev_assoc | Mathlib.CategoryTheory.Monoidal.Closed.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ihom.coev",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Categ... | true |
_private.Mathlib.Data.Multiset.Bind.0.Multiset.nodup_bind._simp_1_1 | Mathlib.Data.Multiset.Bind | [
"List.Pairwise",
"Function.onFun",
"Membership.mem",
"List.Disjoint",
"List.nodup_flatMap",
"List.Nodup",
"List",
"And",
"List.instMembership",
"propext",
"Eq",
"List.flatMap"
] | false |
MeasureTheory.IsStoppingTime.measurableSpace.congr_simp | Mathlib.Probability.Martingale.OptionalSampling | [
"MeasureTheory.IsStoppingTime",
"Eq.rec",
"MeasureTheory.Filtration",
"MeasurableSpace",
"MeasureTheory.IsStoppingTime.measurableSpace",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Preorder",
"WithTop"
] | true |
CategoryTheory.Functor.PushoutObjObj.mapArrowRight_comp | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.IsPushout.inl_desc",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Functor.PushoutObjObj",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.C... | true |
_private.Mathlib.GroupTheory.ClassEquation.0.Group.nat_card_center_add_sum_card_noncenter_eq_card._simp_1_6 | Mathlib.GroupTheory.ClassEquation | [
"Set.not_nontrivial_iff",
"Set.Subsingleton",
"propext",
"Set.Nontrivial",
"Eq",
"Not",
"Set"
] | false |
cfc_le_one_iff | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"cfc_le_algebraMap_iff",
"RingHom.instRingHomClass",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"spectrum",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"congrArg",
"CommSemiring.toSemiring",
"cfc",
"ContinuousStar",
"P... | true |
Set.cast_ncard_sdiff | Mathlib.Data.Set.Card | [
"Eq.mpr",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Nat.cast_sub",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Set.Finite",
"id",
"AddMonoidWithOne.toNatCast",
"instSubNat",
"HasSubset.Subset",
"Set.Finite.subset",
"Nat.cast",
"SubNegMonoid.toSub",
"SDiff.sdiff",
"instHSub",
... | true |
Lean.Meta.Match.Pattern.applyFVarSubst._unsafe_rec | Lean.Meta.Match.Basic | [
"Lean.Meta.FVarSubst.apply",
"Lean.Meta.Match.Pattern.as",
"Lean.Meta.Match.Pattern.ctor",
"List.map",
"Lean.Meta.FVarSubst.find?",
"Lean.Meta.Match.Pattern.val",
"Lean.Expr",
"Lean.FVarId",
"Lean.Meta.Match.Pattern.var",
"Lean.Level",
"List",
"Unit",
"Lean.Meta.FVarSubst",
"Lean.Meta.Matc... | false |
Function.Injective.addAction.eq_1 | Mathlib.Algebra.Group.Action.Defs | [
"AddAction.mk",
"AddMonoid.toAddSemigroup",
"VAdd",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddSemigroupAction.mk",
"AddSemigroupAction.toVAdd",
"Function.Injective.addAction._proof_2",
"AddMonoid",
"instHVAdd",
"Eq.refl",
"Function.Injective.addAction._proof_3",
"Fu... | true |
Subring.toNonUnitalSubring | Mathlib.Algebra.Ring.Subring.Defs | [
"Subring.toSubsemiring",
"Subring.toNonUnitalSubring._proof_2",
"AddMonoid.toAddZeroClass",
"Submonoid.toSubsemigroup",
"Subring.neg_mem'",
"NonUnitalSubring",
"AddZeroClass.toAddZero",
"MulOne.toMul",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonUnitalSubsemiring.mk",
"NonAssocSemir... | true |
_private.Mathlib.Analysis.SpecialFunctions.BinaryEntropy.0.Real.deriv2_qaryEntropy._simp_1_3 | Mathlib.Analysis.SpecialFunctions.BinaryEntropy | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
Sym.cast._proof_1 | Mathlib.Data.Sym.Basic | [
"Function.LeftInverse",
"Multiset",
"Subtype.mk",
"Nat",
"Sym",
"Multiset.card",
"Eq.refl",
"Eq.symm",
"Subtype.val",
"Eq",
"Eq.trans",
"Subtype.property"
] | false |
Submodule.starProjection_inner_eq_zero | Mathlib.Analysis.InnerProductSpace.Projection.Basic | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"Submodule.orthogonalProjectionFn_inner_eq_zero",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Inner.inner",
"Submodule.starProjection",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"N... | true |
Std.DHashMap.diff | Std.Data.DHashMap.Basic | [
"Std.DHashMap.Raw",
"instOfNatNat",
"Subtype.mk",
"Std.DHashMap.inner",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Std.DHashMap.mk",
"Std.DHashMap.Internal.Raw₀.diff",
"Std.DHashMap.Internal.AssocList",
"Hashable",
"_private.Std.Data.DHashMap.Basic.0.Std.DHashMap.insert._proof_1",
"instLTN... | true |
Turing.TM1to0.trAux.eq_6 | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Prod.mk",
"Turing.TM1to0.Λ'",
"Turing.TM1to0.trAux",
"Option.none",
"Turing.TM1.Stmt.halt",
"Eq.refl",
"Prod",
"Eq",
"Turing.TM0.Stmt",
"Turing.TM1.Stmt",
"Turing.TM0.Stmt.write",
"Option"
] | true |
MonomialOrder.div_set | Mathlib.RingTheory.MvPolynomial.Groebner | [
"Finsupp.instFunLike",
"Finsupp.instLE",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Semiring.toModule",
"Finsupp.module",
"HMul.hMul",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"MonomialOrder.leadingCoeff",
"Finset",
"MonomialOrder.syn",
"AddMon... | true |
_private.Lean.Elab.DocString.Builtin.Keywords.0.Lean.Doc.kwImpl.makeHint.match_1 | Lean.Elab.DocString.Builtin.Keywords | [
"Lean.Syntax.Range",
"_private.Lean.Elab.DocString.Builtin.Keywords.0.Lean.Doc.containsAtom'.attempt._sparseCasesOn_1",
"Lean.Syntax.Range.mk",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"String.Pos.Raw",
"Lean.Syntax.Range.casesOn",
"Option"
] | false |
AdjoinRoot.instGroupWithZero._proof_8 | Mathlib.RingTheory.AdjoinRoot | [
"CommSemiring.toSemiring",
"Set.instSingletonSet",
"Ideal.IsTwoSided",
"Field.toSemifield",
"Polynomial",
"Ideal.instIsTwoSided_1",
"CommRing.toCommSemiring",
"Semifield.toDivisionSemiring",
"Polynomial.semiring",
"Polynomial.commRing",
"DivisionSemiring.toSemiring",
"Ideal.span",
"Euclidean... | false |
Lean.Widget.DiffTag.ctorElimType | Lean.Widget.InteractiveCode | [
"Lean.Widget.DiffTag.wasDeleted",
"cond",
"Nat.ble",
"Lean.Widget.DiffTag.willDelete",
"PULift",
"Lean.Widget.DiffTag.wasInserted",
"Lean.Widget.DiffTag.willInsert",
"Lean.Widget.DiffTag.wasChanged",
"Lean.Widget.DiffTag",
"Nat",
"Lean.Widget.DiffTag.willChange"
] | false |
sup_le_of_le_sdiff_left | Mathlib.Order.Heyting.Basic | [
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"GeneralizedCoheytingAlgebra",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"LE.le",
"sdiff_le",
"SDiff.sdiff",
"Max.max",
"sup_le",
"GeneralizedCoheytingAlgebra.toLattice",
"LE.le.trans",
"GeneralizedCohey... | true |
Lean.Grind.Linarith.Expr.denote | Init.Grind.Ordered.Linarith | [
"Lean.Grind.Linarith.Expr.zero",
"Lean.Grind.Linarith.Expr",
"Lean.Grind.Linarith.Expr.brecOn",
"Lean.Grind.Linarith.Expr.neg",
"instHSMul",
"Lean.Grind.Linarith.Expr.intMul",
"Lean.Grind.Linarith.Expr.natMul",
"Lean.Grind.Linarith.Context",
"Lean.Grind.IntModule.toNatModule",
"Lean.Grind.IntModul... | true |
CategoryTheory.Limits.isLimitConeUnopOfCocone_lift | Mathlib.CategoryTheory.Limits.Opposites | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.Cone",
"Opposite",
"CategoryTheory.Limits.coconeOfConeUnop",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.coneUnopOfCocone",
"Quiver.Hom.unop",
"CategoryTheory.Limits.IsColimit",
"C... | true |
Finset.card_neg_le | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Finset",
"LE.le",
"instLENat",
"Finset.card_image_le",
"Neg",
"Nat",
"Finset.card",
"Finset.neg",
"Neg.neg",
"DecidableEq"
] | true |
Lean.Server.lookupStatefulLspRequestHandler | Lean.Server.Requests | [
"Pure.pure",
"IO.instMonadLiftSTRealWorldBaseIO",
"Monad.toApplicative",
"String",
"instMonadLiftT",
"ST.Ref.get",
"IO.RealWorld",
"Applicative.toPure",
"instHashableString",
"instBEqOfDecidableEq",
"Lean.PersistentHashMap",
"Lean.Server.statefulRequestHandlers",
"instMonadBaseIO",
"ST",
... | true |
_private.Mathlib.Topology.MetricSpace.PiNat.0.PiNat.firstDiff_comm._simp_1_1 | Mathlib.Topology.MetricSpace.PiNat | [
"Ne",
"propext",
"ne_comm",
"Eq"
] | false |
Std.Do.SPred.bientails.eq_1 | Std.Do.SPred.Laws | [
"Std.Do.SPred.bientails",
"Iff",
"Std.Do.SPred",
"Eq.refl",
"Eq",
"ULift.down",
"List.nil"
] | true |
Lean.SerialMessage.casesOn | Lean.Message | [
"String",
"Lean.SerialMessage.mk",
"Lean.BaseMessage",
"Lean.SerialMessage.rec",
"Lean.SerialMessage",
"Lean.Name"
] | false |
_private.Mathlib.Data.List.TakeDrop.0.List.span.loop_eq_take_drop | Mathlib.Data.List.TakeDrop | [
"List.brecOn",
"List.append_assoc",
"congrArg",
"List.filter.match_1",
"List.span.loop",
"Prod.mk",
"List.append_nil",
"List.cons",
"Bool.true",
"List.reverse_cons",
"instHAppendOfAppend",
"List",
"Unit",
"Bool.casesOn",
"congr",
"True",
"eq_self",
"List.reverse",
"Bool",
"of_e... | true |
_private.Mathlib.Data.Finset.Filter.0.Finset.filter_nonempty_iff._simp_1_4 | Mathlib.Data.Finset.Filter | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
ContinuousMap.instCStarAlgebra._proof_1 | Mathlib.Analysis.CStarAlgebra.ContinuousMap | [
"CStarAlgebra.toNonUnitalCStarAlgebra",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"NormedRing.toRing",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"IsTopologicalSemiring",
"PseudoMetricSpace.toUniformSpace",
"CStarAlgebra.toNormedRing",
"NonUnitalNonAssocRing.toNonUnital... | false |
Stream'.WSeq.bind_assoc._simp_1 | Mathlib.Data.WSeq.Relation | [
"Stream'.WSeq.bind",
"True",
"Stream'.WSeq",
"eq_true",
"Stream'.WSeq.bind_assoc",
"Eq",
"Stream'.WSeq.Equiv"
] | false |
Function.End.mul_def | Mathlib.Algebra.Group.Action.End | [
"Function.End",
"HMul.hMul",
"Monoid.toMulOneClass",
"Function.comp",
"MulOne.toMul",
"MulOneClass.toMulOne",
"instMonoidEnd",
"Eq",
"rfl",
"instHMul"
] | true |
Aesop.CompleteMatch.mk.inj | Aesop.Forward.Match.Types | [
"Aesop.CompleteMatch.mk",
"Aesop.CompleteMatch.mk.noConfusion",
"Aesop.Match",
"Array",
"Aesop.CompleteMatch",
"Eq"
] | true |
Std.Time.ValidDate | Std.Time.Date.ValidDate | [
"Subtype",
"Std.Time.Month.Ordinal.Valid",
"Prod.fst",
"Std.Time.Day.Ordinal",
"Bool",
"Prod",
"Prod.snd",
"Std.Time.Month.Ordinal"
] | true |
IncidenceAlgebra.ext | Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | [
"Eq.mpr",
"congrArg",
"IncidenceAlgebra.apply_eq_zero_of_not_le",
"Classical.propDecidable",
"id",
"LE.le",
"LE",
"dite",
"funext₂",
"IncidenceAlgebra.instFunLike",
"Zero.toOfNat0",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"Not",
"IncidenceAlgebra",
"DFunLike.coe_injective'"... | true |
tensorKaehlerQuotKerSqEquiv._proof_4 | Mathlib.RingTheory.Smooth.Kaehler | [
"Ideal.Quotient.commSemiring",
"RingHom.instRingHomClass",
"Ideal.Algebra.kerSquareLift",
"CommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Algebra",
"RingHom",
"algebraMap",
"AddZeroClass.toAddZe... | false |
invOf_eq_left_inv | Mathlib.Algebra.Group.Invertible.Defs | [
"Monoid",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"Invertible.invOf",
"MulOne.toMul",
"mul_invOf_self",
"left_inv_eq_right_inv",
"MulOneClass.toMulOne",
"Invertible",
"One.toOfNat1",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"instHMul"
] | true |
CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_naturality_app | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax | [
"CategoryTheory.Cat.associator_hom_app",
"CategoryTheory.Oplax.StrongTrans.naturality",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Oplax.StrongTrans",
"CategoryTheory.Functor.comp",
"CategoryTheory.Cat.associator_inv_app",
"CategoryTheory.Cat.str",
"Categor... | true |
_private.Std.Time.Format.Basic.0.Std.Time.instReprText.repr.match_1 | Std.Time.Format.Basic | [
"Unit.unit",
"Std.Time.Text.full",
"Unit",
"Std.Time.Text.short",
"Std.Time.Text.casesOn",
"Std.Time.Text",
"Std.Time.Text.narrow"
] | false |
CategoryTheory.Comon.MonOpOpToComonObj | Mathlib.CategoryTheory.Monoidal.Comon_ | [
"Opposite",
"CategoryTheory.Comon.mk",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon",
"CategoryTheory.Comon.MonOpOpToComonObjComon",
"CategoryTheory.Mon.X",
"CategoryTheory.Category.opposite",
"CategoryTheory.Comon",
"Opposite.unop",
"CategoryTheory.Category",
"CategoryTheory.monoidalC... | true |
Std.ExtTreeSet.isSome_min?_of_isSome_min?_erase | Std.Data.ExtTreeSet.Lemmas | [
"Std.ExtTreeSet.min?",
"Std.ExtTreeSet.erase",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.ExtTreeMap.isSome_minKey?_of_isSome_minKey?_erase",
"Std.TransCmp",
"Bool.true",
"Unit",
"Std.ExtTreeSet",
"Bool",
"Option.isSome",
"Eq"
] | true |
TensorProduct.AlgebraTensorModule.map_tmul | Mathlib.LinearAlgebra.TensorProduct.Tower | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap",
"AddCommMonoid",
"CommSemiring"... | true |
Set.encard_le_encard_iff_encard_diff_le_encard_diff | Mathlib.Data.Set.Card | [
"Eq.mpr",
"Set.encard",
"Preorder.toLT",
"Nat.instIsOrderedAddMonoid",
"instTopENat",
"congrArg",
"IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT",
"instIsLeftCancelAddOfAddLeftReflectLE",
"covariant_swap_add_of_covariant_add",
"Iff.rfl",
"PartialOrder.toPreorder",
"instIsRightCancelA... | true |
Set.infs_subset_iff | Mathlib.Data.Set.Sups | [
"Membership.mem",
"HasSubset.Subset",
"HasInfs.infs",
"SemilatticeInf.toMin",
"Set.image2_subset_iff",
"SemilatticeInf",
"Iff",
"Set.hasInfs",
"Set.instMembership",
"Min.min",
"Set.instHasSubset",
"Set"
] | true |
_private.Mathlib.Geometry.Euclidean.Angle.Oriented.Basic.0.Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff._simp_1_3 | Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | [
"instHSMul",
"Finset.univ",
"Ring.toNonAssocRing",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"AddCommGroup.toAddGroup",
"Exists",
"AddZeroClass.toAddZero",
"AddCommGroup",
"NonUnitalNonAssocRing.toN... | false |
ContinuousAlgEquiv.image_symm_eq_preimage | Mathlib.Topology.Algebra.Algebra.Equiv | [
"Eq.mpr",
"congrArg",
"ContinuousAlgEquiv.symm",
"Algebra",
"ContinuousAlgEquiv.equivLike",
"id",
"ContinuousAlgEquiv.image_eq_preimage_symm",
"CommSemiring",
"TopologicalSpace",
"Set.preimage",
"Semiring",
"Eq.refl",
"Set.image",
"ContinuousAlgEquiv",
"ContinuousAlgEquiv.symm_symm",
"... | true |
DoubleCentralizer.instInhabited | Mathlib.Analysis.CStarAlgebra.Multiplier | [
"NormedSpace",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"DoubleCentralizer.instZero",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"NonUnitalNonAssocSemiring.toDistribSMul",
"NormedField.toField",
"NonUnitalRing.toNonUnitalNonAssocRing",
"AddZ... | true |
_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.ParamMap.Key.noConfusion | Lean.Compiler.LCNF.InferBorrow | [
"Lean.FVarId",
"_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.ParamMap.Key",
"_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.ParamMap.Key.noConfusionType",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq",
"_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.ParamMap.Key.... | false |
_private.Mathlib.RingTheory.Adjoin.Basic.0.Subalgebra.adjoin_eq_span_basis._simp_1_1 | Mathlib.RingTheory.Adjoin.Basic | [
"Set.range_comp",
"Function.comp",
"Set.image",
"Set.range",
"Eq.symm",
"Eq",
"Set"
] | false |
CategoryTheory.Cat.HasLimits.limitCone._proof_2 | Mathlib.CategoryTheory.Category.Cat.Limit | [
"CategoryTheory.Limits.limit.π",
"CategoryTheory.Cat.category",
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Bundled.str",
"CategoryTheory.Cat.HasLimits.homDiagram",
"CategoryTheory.Functor.comp",
"CategoryTheory.Category... | false |
_private.Init.Data.SInt.Bitwise.0.Int8.or_eq_zero_iff._simp_1_1 | Init.Data.SInt.Bitwise | [
"Int8",
"BitVec",
"Int8.toBitVec_inj",
"instOfNatNat",
"Nat",
"propext",
"Int8.toBitVec",
"OfNat.ofNat",
"Eq.symm",
"Eq"
] | false |
Std.DTreeMap.Internal.Impl.Const.alter._sunfold | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.Const.alter.match_3",
"Ord",
"Std.DTreeMap.Internal.Impl.Const.getThenInsertIfNew?.match_1",
"HSub.hSub",
"Std.DTreeMap.Internal.Impl.balance",
"Std.DTreeMap.Internal.Impl.Const.alter._proof_50",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.Const.alter... | false |
boolRingCatEquivBoolAlg | Mathlib.Algebra.Category.BoolRing | [
"BoolRing.carrier",
"RingEquiv.asBoolRingAsBoolAlg",
"OrderIso.asBoolAlgAsBoolRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"BoolAlg.hasForgetToBoolRing",
"instNonUnitalCommRingAsBoolRingOfGeneralizedBooleanAlgebra",
"CommRing.toNonUnitalCommRing",
"BoolAlg.carrier",
"CommSemiring.toSemiri... | true |
_private.Lean.Elab.Util.0.Lean.Elab.getBetterRef.match_1 | Lean.Elab.Util | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Lean.Elab.MacroStackElem",
"Option"
] | false |
Fin.div_val | Init.Data.Fin.Lemmas | [
"instHDiv",
"Fin.instDiv",
"HDiv.hDiv",
"Fin.val",
"Nat",
"Nat.instDiv",
"Fin",
"Eq",
"rfl"
] | true |
EuclideanSpace.inner_eq_star_dotProduct | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"Pi.instStarForall",
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"fact_one_le_two_ennreal",
"Inner.inner",
"dotProduct",
"Nat.instAtLeastTwoHAddOfNat",
"PseudoMetricSpace.toUniformSpace",
"instAddCommMonoidWithOneENNReal",
"NonUnitalNonAssocRing.toNonUni... | true |
AlgebraicGeometry.Scheme.fromSpecResidueField | Mathlib.AlgebraicGeometry.ResidueField | [
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommRingCat",
"AlgebraicGeometry.Spec.map",
"CommRingCat.instCategory",
"AlgebraicGeometry.Scheme.residueField",
"TopCat.Presheaf.stalk",
"A... | true |
_private.Mathlib.SetTheory.Ordinal.Veblen.0.Ordinal.cmp_veblenWith.match_1.eq_1 | Mathlib.SetTheory.Ordinal.Veblen | [
"Ordering.gt",
"Unit.unit",
"Ordinal.cmp_veblenWith.match_1",
"Ordering",
"Ordering.eq",
"Unit",
"Ordering.lt",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Analysis.Complex.PhragmenLindelof.0.PhragmenLindelof.eqOn_right_half_plane_of_superexponential_decay._simp_1_1 | Mathlib.Analysis.Complex.PhragmenLindelof | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
MvPowerSeries.support_truncFinset_subset | Mathlib.RingTheory.MvPowerSeries.Trunc | [
"Eq.mpr",
"Nat.instMulZeroClass",
"Semiring.toModule",
"Classical.not_not._simp_1",
"AddMonoidAlgebra.addAddCommMonoid",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"LinearMap.instFunLike",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"MvPowerSeries",
"Membership.mem",
"id",
"HasSubset... | true |
inf_le_inf | Mathlib.Order.Lattice | [
"PartialOrder.toPreorder",
"inf_le_of_right_le",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"inf_le_of_left_le",
"SemilatticeInf.toMin",
"LE.le",
"le_inf",
"SemilatticeInf",
"Min.min"
] | true |
_private.Mathlib.RingTheory.Norm.Transitivity.0.Algebra.Norm.Transitivity.auxMat_blockTriangular._simp_1_2 | Mathlib.RingTheory.Norm.Transitivity | [
"And",
"Classical.not_imp",
"propext",
"Eq",
"Not"
] | false |
IsCompact.isSigmaCompact | Mathlib.Topology.Compactness.SigmaCompact | [
"IsSigmaCompact",
"instInhabitedNat",
"Set.iUnion_const",
"TopologicalSpace",
"And",
"instNonemptyOfInhabited",
"Nat",
"And.intro",
"Exists.intro",
"Eq",
"Set.iUnion",
"IsCompact",
"Set"
] | true |
List.alternatingProd_cons_cons' | Mathlib.Algebra.BigOperators.Group.List.Basic | [
"One",
"Inv",
"HMul.hMul",
"Mul",
"List.alternatingProd",
"List.cons",
"List",
"Inv.inv",
"Eq",
"rfl",
"instHMul"
] | true |
AlgebraicGeometry.mono_pushoutSection_of_isCompact_of_flat_left_of_ringHomFlat | Mathlib.AlgebraicGeometry.Morphisms.Flat | [
"AlgebraicGeometry.Flat",
"Eq.mpr",
"RingHom.Flat",
"AlgebraicGeometry.mono_pushoutSection_of_iSup_eq",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"CategoryTheory.Limits.WalkingSpan",
"AlgebraicGeometry.Scheme",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CommR... | true |
HasFDerivWithinAt.of_insert | Mathlib.Analysis.Calculus.FDeriv.Basic | [
"AddCommGroup.toAddCommMonoid",
"HasFDerivWithinAt",
"NormedField.toField",
"AddCommGroup",
"Insert.insert",
"Field.toSemifield",
"ContinuousLinearMap",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"Set.instInsert",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"Nontrivial... | true |
_private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.Stepwise.imp_1eq._simp_1_3 | Init.Grind.Ring.CommSolver | [
"HSub.hSub",
"Lean.Grind.AddCommMonoid.toZero",
"instHSub",
"Lean.Grind.AddCommGroup.toSub",
"propext",
"Lean.Grind.AddCommGroup",
"Zero.toOfNat0",
"Lean.Grind.AddCommGroup.toAddCommMonoid",
"OfNat.ofNat",
"Eq",
"Lean.Grind.AddCommGroup.sub_eq_zero_iff"
] | false |
isCompact_setOf_finiteMeasure_le_of_isCompact | Mathlib.MeasureTheory.Measure.Prokhorov | [
"MeasureTheory.FiniteMeasure.instTopologicalSpace",
"MeasureTheory.FiniteMeasure.mass_map_le",
"Set.Subset.antisymm",
"MeasureTheory.FiniteMeasure.mass",
"MeasureTheory.FiniteMeasure",
"measurable_subtype_coe",
"Eq.mpr",
"MeasureTheory.Measure",
"isCompact_iff_compactSpace",
"MeasurableSet",
"co... | true |
Algebra.algebraMapSubmonoid_self | Mathlib.Algebra.Algebra.Basic | [
"CommSemiring.toSemiring",
"Algebra.id",
"Submonoid.map_id",
"NonAssocSemiring.toMulZeroOneClass",
"MulZeroOneClass.toMulOneClass",
"CommSemiring",
"Algebra.algebraMapSubmonoid",
"Semiring.toNonAssocSemiring",
"Eq",
"Submonoid"
] | true |
_private.Mathlib.CategoryTheory.Monoidal.Mon_.0.CategoryTheory.Functor.FullyFaithful.monObj._simp_1 | Mathlib.CategoryTheory.Monoidal.Mon_ | [
"CategoryTheory.Functor.OplaxMonoidal.δ_natural_left_assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.OplaxMonoidal.δ",
"CategoryTheory.Functor.map",
"CategoryTheory.MonoidalCategoryStruct.whiskerRight"... | false |
CategoryTheory.Abelian.SpectralObject.shortComplexMap._proof_26 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.SpectralObject.shortComplexMap._proof_21",
"instNeZeroNatHAdd_1",
"CategoryTheory.Abelian.SpectralObject.shortComplexMap._proof_13",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.shortComplexMap._proof_16",
"CategoryTheory.Abelian.... | false |
Lean.instInhabitedVersoDocString.default | Lean.DocString.Extension | [
"Inhabited.default",
"Lean.VersoDocString",
"Lean.Doc.Block",
"Array",
"Empty",
"Array.instInhabited",
"Lean.Doc.Part",
"Lean.ElabBlock",
"Lean.ElabInline",
"Lean.VersoDocString.mk"
] | true |
CategoryTheory.Limits.ImageFactorisation.mk | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.ImageFactorisation.mk",
"CategoryTheory.Limits.MonoFactorisation",
"CategoryTheory.Limits.ImageFactorisation",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.IsImage",
"CategoryTheory.Category"
] | true |
AddSubmonoid.pi | Mathlib.Algebra.Group.Submonoid.Operations | [
"AddSubmonoid.pi._proof_1",
"AddSubsemigroup.carrier",
"AddZeroClass.toAddZero",
"AddSubmonoid.toAddSubsemigroup",
"AddSubmonoid",
"AddSubmonoid.pi._proof_2",
"AddSubmonoid.mk",
"AddSubsemigroup.mk",
"AddZeroClass",
"Pi.addZeroClass",
"AddZero.toAdd",
"Set.pi",
"Set"
] | true |
_private.Mathlib.Algebra.Order.BigOperators.GroupWithZero.List.0.List.one_le_prod._simp_1_2 | Mathlib.Algebra.Order.BigOperators.GroupWithZero.List | [
"forall_eq_or_imp",
"And",
"propext",
"Or",
"Eq"
] | false |
Lean.Meta.Simp.NormCastConfig.beta._default | Init.MetaTypes | [
"id",
"Bool",
"Bool.false"
] | false |
DiscreteMeasurableSpace.toMeasurableSub | Mathlib.MeasureTheory.Group.Arithmetic | [
"Measurable.of_discrete",
"DiscreteMeasurableSpace",
"HSub.hSub",
"MeasurableSpace",
"MeasurableSub",
"instHSub",
"MeasurableSub.mk",
"Sub"
] | true |
FundamentalGroupoid.map_obj_as | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"ContinuousMap",
"FundamentalGroupoid.map",
"TopologicalSpace",
"FundamentalGroupoid",
"FundamentalGroupoid.as",
"Eq.refl",
"FundamentalGroupoid.instGroupoid",
"CategoryTheory.Groupoid.toCategory",
"Eq",
"ContinuousMap.instFunLike",
"DFunLike.coe",
"CategoryTheory.Functor.obj"
] | true |
ContinuousLinearMap.toNormedRing._proof_14 | Mathlib.Analysis.Normed.Operator.NormedSpace | [
"ContinuousLinearMap.toNormedAddCommGroup",
"SubNegMonoid.sub_eq_add_neg",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"Field.toSemifield",
"ContinuousLinearMap.toNormedRing.... | false |
Option.merge_eq_some_iff | Init.Data.Option.Lemmas | [
"False",
"Option.merge_none_right",
"and_true",
"Option.ctorIdx",
"congrArg",
"and_self",
"False.elim",
"Option.merge_none_left",
"Option.casesOn",
"false_and",
"noConfusion_of_Nat",
"Option.some.injEq",
"Option.some",
"Exists",
"exists_and_left._simp_1",
"exists_eq_left'._simp_1",
"... | true |
GrpWithZero.groupWithZeroConcreteCategory._proof_3 | Mathlib.Algebra.Category.GrpWithZero | [
"GroupWithZero.toMonoidWithZero",
"MonoidWithZeroHom.funLike",
"CategoryTheory.CategoryStruct.id",
"GrpWithZero.carrier",
"id",
"MonoidWithZeroHom",
"GrpWithZero.instLargeCategory",
"MonoidWithZero.toMulZeroOneClass",
"GrpWithZero",
"GrpWithZero.str",
"Eq.refl",
"CategoryTheory.Category.toCate... | false |
AlgebraicGeometry.PresheafedSpace.stalkMap.congr_hom | Mathlib.Geometry.RingedSpace.Stalks | [
"Eq.mpr",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"AlgebraicGeometry.PresheafedSpace.stalkMap.congr._proof_2",
"Quiver.Hom",
"AlgebraicGeometry.PresheafedSpace.Hom.stalkMap",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"C... | true |
MulAlgebraNorm.noConfusionType | Mathlib.Analysis.Normed.Unbundled.AlgebraNorm | [
"MulAlgebraNorm",
"Norm.norm",
"SeminormedRing.toNorm",
"Real",
"instHSMul",
"HMul.hMul",
"SeminormedCommRing",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"SeminormedCommRing.toCommRing",
"MulRingNorm.toMulRingSeminorm",
"Algebra",
"MulRingNorm",
"Algebra.toSMul",
"MulRingSemin... | false |
_private.Mathlib.Topology.EMetricSpace.Lipschitz.0.continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWith.match_1_1 | Mathlib.Topology.EMetricSpace.Lipschitz | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
AlgebraicGeometry.Scheme.map_basicOpen | Mathlib.AlgebraicGeometry.Restrict | [
"AlgebraicGeometry.Scheme.Hom.opensFunctor",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Lattice.toSemilatticeSup",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Complet... | true |
Nat.instTransLe | Init.Data.Nat.Basic | [
"LE.le",
"instLENat",
"Trans",
"Nat.le_trans",
"Nat",
"Trans.mk"
] | true |
SchwartzMap.fderivCLM._proof_7 | Mathlib.Analysis.Distribution.SchwartzSpace.Deriv | [
"AddMonoid.toAddSemigroup",
"PseudoMetricSpace.toUniformSpace",
"NormedAddGroup.toAddGroup",
"IsTopologicalAddGroup.toContinuousAdd",
"AddSemigroup.toAdd",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"NormedAddCommGroup.toNormedAddGroup",
"SubNegMonoid.toAddMonoid",
"C... | false |
CategoryTheory.Limits.isBilimitOfIsLimit._proof_1 | Mathlib.CategoryTheory.Preadditive.Biproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"dite_congr",
"Finset.univ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Finset",
"CategoryTheory.Limits.Bicone.toCone",
"CategoryTheory.eqToHom",... | false |
Nat.Prime.mem_primeFactors | Mathlib.Data.Nat.PrimeFin | [
"Iff.mpr",
"Nat.Prime",
"Dvd.dvd",
"Finset",
"Membership.mem",
"Ne",
"instOfNatNat",
"And",
"Nat.instDvd",
"Finset.instSetLike",
"Nat",
"And.intro",
"Nat.primeFactors",
"OfNat.ofNat",
"SetLike.instMembership",
"Nat.mem_primeFactors"
] | true |
trapezoidal_integral | Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule | [
"Real",
"instHDiv",
"trapezoidal_integral._proof_1",
"HMul.hMul",
"Real.instDivInvMonoid",
"Real.instSub",
"HSub.hSub",
"HDiv.hDiv",
"instSubNat",
"instOfNatNat",
"Nat.cast",
"Real.instAdd",
"Finset.range",
"Real.instOne",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"Real.instMul... | true |
Orientation.kahler_rotation_left' | Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | [
"instInnerProductSpaceRealComplex",
"LinearIsometryEquiv.instEquivLike",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"Orientation",
"Real.partialOrder",
"Real",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"Real.Angle",
"Complex.instNo... | true |
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