name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
mul_le_mul_of_nonpos_of_nonneg' | Mathlib.Algebra.Order.Ring.Unbundled.Basic | [
"mul_le_mul_of_nonpos_right",
"HMul.hMul",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Preorder.toLE",
"AddRightMono",
"Distrib.toAdd",
"LE.le",
"MulPosMono",
"ExistsAddOfLE",
"AddRightReflectLE",
"PosMulMono",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
... | true |
CategoryTheory.ShortComplex.Exact.isIso_imageToKernel | Mathlib.CategoryTheory.Abelian.Exact | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Limits.HasImages.has_image",
"CategoryTheory.Subobject.underlying",
"CategoryTheory.IsIso",
"CategoryTheory.Limits.imageSubobject",
"PartialOrder.toPreorder",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.exact_iff_isIso_imageToKern... | true |
Lean.KeyedDeclsAttribute.ExtensionState.declNames | Lean.KeyedDeclsAttribute | [
"Lean.KeyedDeclsAttribute.ExtensionState",
"Lean.PHashSet",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.instHashableName"
] | true |
LinearMap.mem_submoduleImage._simp_1 | Mathlib.Algebra.Module.Submodule.Range | [
"Submodule",
"Submodule.addCommMonoid",
"LinearMap.instFunLike",
"Membership.mem",
"Exists",
"Subtype",
"LinearMap.mem_submoduleImage",
"Submodule.module",
"LinearMap",
"AddCommMonoid",
"Subtype.mk",
"And",
"Submodule.setLike",
"propext",
"Semiring",
"Module",
"RingHom.id",
"Semiri... | false |
Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.isFinite | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo.0.Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval.isFinite.match_1",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicIntInterval",
"Bool.true",
"Unit",
"Lean.Meta.Grind.Arith.Cutsat.SymbolicBound",
"Bool",
"Bool.false"
] | true |
Lean.Server.Test.Runner.Client.InteractiveGoals.mk | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.InteractiveGoal",
"Array",
"Lean.Server.Test.Runner.Client.InteractiveGoals",
"Lean.Server.Test.Runner.Client.InteractiveGoals.mk"
] | true |
SimpleGraph.Walk.support_toPath_subset | Mathlib.Combinatorics.SimpleGraph.Paths | [
"List.instHasSubset",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"HasSubset.Subset",
"SimpleGraph.Walk.toPath",
"SimpleGraph",
"List",
"SimpleGraph.Walk.IsPath",
"SimpleGraph.Walk.support_bypass_subset",
"Subtype.val",
"DecidableEq"
] | true |
_private.Mathlib.LinearAlgebra.Pi.0.LinearMap.pi_eq_zero._simp_1_2 | Mathlib.LinearAlgebra.Pi | [
"funext_iff",
"propext",
"Eq"
] | false |
IdealFilter.isTorsion_def | Mathlib.RingTheory.IdealFilter.Basic | [
"Iff.rfl",
"AddCommMonoid",
"IdealFilter",
"Iff",
"IdealFilter.IsTorsionElem",
"IdealFilter.IsTorsion",
"Module",
"Ring.toSemiring",
"Ring"
] | true |
_private.Mathlib.Algebra.Homology.HomotopyCategory.HomComplex.0.CochainComplex.HomComplex.Cocycle.homOf._simp_1 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplex | [
"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 |
_private.Init.Data.String.Decode.0.ByteArray.utf8DecodeChar?.val_assemble₁_le._proof_1_1 | Init.Data.String.Decode | [
"Nat.lt_of_not_le",
"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.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",... | false |
Concept.instPartialOrder | Mathlib.Order.Concept | [
"PartialOrder",
"Concept.extent_injective",
"Concept.extent",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"Concept",
"CompleteBooleanAlgebra.toCompleteLattice",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"Set.instCompleteAtomicBooleanAlgebra",
... | true |
_private.Init.Data.List.Lemmas.0.List.length_pos_iff_exists_mem.match_1_1 | Init.Data.List.Lemmas | [
"Membership.mem",
"Exists",
"List",
"Exists.casesOn",
"List.instMembership",
"Exists.intro"
] | false |
_private.Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup.0.SubMulAction.fixingSubgroup_map_conj_eq._simp_1_2 | Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | [
"DivInvMonoid.toInv",
"zpow_neg_one",
"DivInvMonoid.toZPow",
"Int.instNegInt",
"Int",
"DivInvMonoid",
"Inv.inv",
"HPow.hPow",
"instOfNat",
"instHPow",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Neg.neg"
] | false |
Fin.dfoldrM.loop._unsafe_rec | Batteries.Data.Fin.Basic | [
"Pure.pure",
"instNeZeroNatHAdd_1",
"Fin.succ",
"Monad.toApplicative",
"Fin.mk",
"Fin.instOfNat",
"instOfNatNat",
"Applicative.toPure",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Fin.dfoldrM.loop.match_1",
"Nat",
"LT.lt",
"Fin.dfoldrM.loop._unsafe_rec",
"instAddNat",
"Monad.toBi... | false |
MeasureTheory.aecover_closedBall | Mathlib.MeasureTheory.Integral.IntegralEqImproper | [
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.AECover.mk",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"Set.Ici",
"congrArg",
"Filter.Eventually",
"Metric.isClosed_closedBall",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Preorder.toLE",
"Membership.mem",
"Filter.mp_mem",
"Eq.mp",
... | true |
CartanMatrix.isSimplyLaced_D | Mathlib.Data.Matrix.Cartan | [
"_private.Mathlib.Data.Matrix.Cartan.0.CartanMatrix.isSimplyLaced_D._proof_1_2",
"Matrix.IsSimplyLaced",
"id",
"Int.instNegInt",
"Ne",
"Int",
"instOfNat",
"Nat",
"Or",
"CartanMatrix.D",
"OfNat.ofNat",
"Fin",
"Eq",
"Neg.neg"
] | true |
BitVec.twoPow | Init.Data.BitVec.Basic | [
"HShiftLeft.hShiftLeft",
"BitVec",
"BitVec.instHShiftLeftNat",
"instOfNatNat",
"BitVec.ofNat",
"Nat",
"OfNat.ofNat"
] | true |
_private.Init.Data.Array.Monadic.0.Array.foldlM_filterMap.match_1.eq_1 | Init.Data.Array.Monadic | [
"Option.some",
"Option.none",
"Unit",
"Array.foldlM_filterMap.match_1",
"Eq.refl",
"Eq",
"Option"
] | true |
AddSubgroup.normalCore_le | Mathlib.Algebra.Group.Subgroup.Basic | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"SubNegZero... | true |
LocalSubring.noConfusion | Mathlib.RingTheory.LocalRing.LocalSubring | [
"CommRing",
"Subring.instSetLike",
"CommSemiring.toSemiring",
"HEq.refl",
"Membership.mem",
"Subring.instSubringClass",
"Subtype",
"IsLocalRing",
"CommRing.toNonAssocCommRing",
"LocalSubring.noConfusionType",
"CommRing.toCommSemiring",
"Subring",
"eq_of_heq",
"Eq.ndrec",
"LocalSubring",
... | false |
_private.Batteries.Data.String.Legacy.0.String.Legacy.posOfAux._proof_1 | Batteries.Data.String.Legacy | [
"String.instLTRaw",
"String",
"Nat.sub_lt_sub_left",
"HSub.hSub",
"instSubNat",
"String.Pos.Raw",
"instHSub",
"Nat",
"LT.lt",
"String.Pos.Raw.lt_next",
"instLTNat",
"String.Pos.Raw.next",
"String.Pos.Raw.byteIdx"
] | false |
_private.Mathlib.MeasureTheory.Function.SimpleFunc.0.MeasureTheory.SimpleFunc.support_eq._simp_1_1 | Mathlib.MeasureTheory.Function.SimpleFunc | [
"Membership.mem",
"Ne",
"Function.support",
"propext",
"Function.mem_support",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Set.instMembership",
"Zero",
"Set"
] | false |
List.pop_toArray | Init.Data.List.ToArray | [
"Array.ext'",
"List.dropLast",
"Array.pop",
"List.toArray",
"Array",
"List",
"eq_self",
"of_eq_true",
"Eq"
] | true |
_private.Lean.Util.Diff.0.Lean.Diff.diff.match_3 | Lean.Util.Diff | [
"Lean.Diff.Action",
"MProd.casesOn",
"MProd.mk",
"Array",
"Nat",
"MProd",
"Prod"
] | false |
CategoryTheory.Abelian.extFunctorObj._proof_1 | Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | [
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"Nat",
"AddZero.toAdd",
"Zero.toOfNat0",
"add_zero",
"OfNat.ofNat",
"Eq"
] | false |
_private.Mathlib.RingTheory.PolynomialAlgebra.0.PolyEquivTensor.left_inv._simp_1_3 | Mathlib.RingTheory.PolynomialAlgebra | [
"instHSMul",
"HMul.hMul",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.toSMul",
"algebraMap",
"CommSemiring",
"RingHom.instFunLike",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"NonUnitalNonAssocSemiring.toDistrib",
"HSMul.hSMul",
"Algebra.sm... | false |
Subgroup.toAddSubgroup._proof_2 | Mathlib.Algebra.Group.Subgroup.Lattice | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Monoid.toMulOneClass",
"Additive",
"AddSubgroup.casesOn",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Group",
"AddSubsemigroup.carrier",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subgroup.mk",
"Multiplic... | false |
EuclideanGeometry.orthogonalProjection.congr_simp | Mathlib.Geometry.Euclidean.Projection | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"Submodule",
"NormedRing.toRing",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Submodule.HasOrthogonalProjection",
"Subtype",
"ContinuousAffineMap",
"Submodule.mo... | true |
Tuple.comp_sort_eq_comp_iff_monotone | Mathlib.Data.Fin.Tuple.Sort | [
"Equiv.instEquivLike",
"LinearOrder",
"PartialOrder.toPreorder",
"Monotone",
"Tuple.unique_monotone",
"Function.comp",
"SemilatticeInf.toPartialOrder",
"Eq.rec",
"DistribLattice.toLattice",
"Iff",
"Fin.instPartialOrder",
"Equiv.Perm",
"Nat",
"Iff.intro",
"Eq.symm",
"Fin",
"Eq",
"DF... | true |
Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₁ | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.CooperSplit",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₁"
] | true |
_private.Std.Sync.Channel.0.Std.CloseableChannel.Bounded.State.casesOn | Std.Sync.Channel | [
"Vector",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Bounded.State",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Bounded.State.rec",
"Nat",
"LT.lt",
"IO.Promise",
"Bool",
"Std.Queue",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Bounded.Consumer",
"IO.Ref",
"instLTNat",
"_pri... | false |
_private.Mathlib.Data.List.OffDiag.0.List.Nodup.offDiag._proof_1_1 | Mathlib.Data.List.OffDiag | [
"Int.Linear.eq_of_core",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"eq_false",
"instLawfulBEq",
"Lean.G... | false |
_private.Mathlib.Topology.MetricSpace.Infsep.0.Set.Finite.infsep._simp_1_3 | Mathlib.Topology.MetricSpace.Infsep | [
"Finset",
"Set.Finite.mem_toFinset",
"Set.Finite",
"Membership.mem",
"Finset.instSetLike",
"Set.Finite.toFinset",
"propext",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
LinearMap.IsReflective.coroot._proof_1 | Mathlib.LinearAlgebra.RootSystem.OfBilinear | [
"LinearMap.IsReflective.regular",
"Distrib.leftDistribClass",
"Eq.mpr",
"Exists.choose_spec",
"Semigroup.toMul",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemirin... | false |
CompactlySupportedContinuousMap.noConfusionType | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"CompactlySupportedContinuousMap",
"ContinuousMap",
"CompactlySupportedContinuousMap.casesOn",
"TopologicalSpace",
"HEq",
"ContinuousMap.toFun",
"HasCompactSupport",
"Zero"
] | false |
Std.Broadcast.Sync.send | Std.Sync.Broadcast | [
"Task",
"instMonadLiftT",
"IO",
"Std.Broadcast.send",
"IO.ofExcept",
"IO.Error.instToString",
"EIO",
"liftM",
"instMonadEIO",
"Bind.bindLeft",
"Nat",
"Monad.toBind",
"Bind.bind",
"IO.Error",
"instMonadLiftTOfMonadLift",
"Except",
"Std.Broadcast.Sync",
"BaseIO",
"IO.wait",
"inst... | true |
_private.Mathlib.FieldTheory.Finite.Basic.0.FiniteField.exists_root_sum_quadratic._simp_1_2 | Mathlib.FieldTheory.Finite.Basic | [
"Finset.mem_image",
"Finset",
"Membership.mem",
"Exists",
"And",
"Finset.instSetLike",
"propext",
"Eq",
"Finset.image",
"SetLike.instMembership",
"DecidableEq"
] | false |
WeierstrassCurve.Projective.add | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point | [
"CommRing",
"WeierstrassCurve.Projective.dblXYZ",
"WeierstrassCurve.Projective.instSetoidForallFinOfNatNat",
"Classical.propDecidable",
"instOfNatNat",
"WeierstrassCurve.Projective",
"HasEquiv.Equiv",
"Nat",
"instHasEquivOfSetoid",
"WeierstrassCurve.Projective.addXYZ",
"OfNat.ofNat",
"Fin",
... | true |
Subring.unop_sup | Mathlib.Algebra.Ring.Subring.MulOpposite | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"MulOpposite",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"MulOpposite.instNonAssocRing",
"NonAssocRing",
"OrderIso.symm",
"Subring",
"Max.max",
"Subring.instPartialOrder",
"OrderIso.map_sup",
"Subring.unop",... | true |
List.lex_nil | Init.Data.List.Basic | [
"List.cons",
"List.lex",
"List",
"List.casesOn",
"eq_self",
"Bool",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"Eq.symm",
"Bool.false",
"BEq",
"Eq",
"List.nil"
] | true |
_private.Lean.Elab.DeclNameGen.0.Lean.Elab.Command.NameGen.MkNameState.mk.injEq | Lean.Elab.DeclNameGen | [
"_private.Lean.Elab.DeclNameGen.0.Lean.Elab.Command.NameGen.MkNameState.mk.inj",
"Eq.propIntro",
"Lean.NameSet",
"Lean.injEq_helper",
"Lean.ExprSet",
"_private.Lean.Elab.DeclNameGen.0.Lean.Elab.Command.NameGen.MkNameState.mk",
"And",
"Eq.ndrec",
"Eq.refl",
"_private.Lean.Elab.DeclNameGen.0.Lean.El... | true |
CategoryTheory.Lax.LaxTrans.recOn | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.rightUnitor",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.PrelaxFunctorStruct.map₂",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelax... | false |
Lean.PersistentEnvExtension.noConfusionType | Lean.Environment | [
"Lean.PersistentEnvExtensionState",
"Lean.PersistentEnvExtension.casesOn",
"Lean.PersistentEnvExtension",
"Array",
"Std.Format",
"Lean.Name",
"Lean.EnvExtension",
"HEq",
"Lean.OLeanLevel",
"Lean.ImportM",
"Eq",
"Lean.Environment"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.TwoDim.0.Orientation.termω | Mathlib.Analysis.InnerProductSpace.TwoDim | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
CategoryTheory.unop_whiskerLeft | Mathlib.CategoryTheory.Monoidal.Opposite | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"Quiver.Hom.unop",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.Category.opposite",
"CategoryTheory.M... | true |
SetRel.IsWellFounded.eq_1 | Mathlib.Order.RelSeries | [
"SetRel",
"SetRel.IsWellFounded",
"Membership.mem",
"Prod.mk",
"Eq.refl",
"Prod",
"WellFounded",
"Eq",
"Set.instMembership"
] | true |
CategoryTheory.ShortComplex.LeftHomologyMapData.zero_φK | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.ShortComplex.LeftHomologyMapData.zero",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.Limits.Ha... | true |
_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.MatcherKey.mk._flat_ctor | Lean.Meta.Match.Match | [
"_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.MatcherKey.mk",
"Lean.Expr",
"Bool",
"_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.MatcherKey"
] | false |
ContinuousLinearMap.restrictScalars_smul | Mathlib.Topology.Algebra.Module.LinearMap | [
"instHSMul",
"ContinuousLinearMap.restrictScalars",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"ContinuousConstSMul",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"AddZero.toZero",
"ContinuousLinearMap.i... | true |
Lean.Elab.TerminationHints.noConfusionType | Lean.Elab.PreDefinition.TerminationHint | [
"Lean.Elab.TerminationBy",
"Lean.Syntax",
"Lean.Elab.TerminationHints.casesOn",
"Lean.Elab.TerminationHints",
"Nat",
"Lean.Elab.PartialFixpoint",
"Eq",
"Lean.Elab.DecreasingBy",
"Option"
] | false |
instLinearOrderedCommGroupWithZeroMultiplicativeOrderDualOfLinearOrderedAddCommGroupWithTop._proof_3 | Mathlib.Algebra.Order.GroupWithZero.Canonical | [
"Semigroup.toMul",
"LinearOrderedAddCommGroupWithTop",
"HMul.hMul",
"DivInvMonoid.toMonoid",
"Int",
"DivInvMonoid.zpow",
"Nat.cast",
"LinearOrderedAddCommGroupWithTop.toSubNegMonoid",
"Multiplicative",
"Multiplicative.divInvMonoid",
"Nat",
"Monoid.toSemigroup",
"instNatCastInt",
"OrderDual... | false |
MeasurableSMul.mk | Mathlib.MeasureTheory.Group.Arithmetic | [
"MeasurableSMul.measurable_smul_const._autoParam",
"instHSMul",
"MeasurableSMul",
"SMul",
"Measurable",
"autoParam",
"MeasurableSpace",
"HSMul.hSMul",
"MeasurableConstSMul",
"MeasurableSMul.mk"
] | true |
List.flatMap | Init.Prelude | [
"List.map",
"List",
"List.flatten"
] | true |
PiNat.mem_cylinder_comm | Mathlib.Topology.MetricSpace.PiNat | [
"congrArg",
"PiNat.cylinder",
"_private.Mathlib.Topology.MetricSpace.PiNat.0.PiNat.mem_cylinder_comm._simp_1_1",
"Membership.mem",
"iff_self",
"Iff",
"PiNat.mem_cylinder_iff._simp_1",
"implies_congr",
"Nat",
"congr",
"LT.lt",
"True",
"of_eq_true",
"Eq.refl",
"instLTNat",
"Eq",
"Set.i... | true |
CategoryTheory.Limits.instPreservesColimitsOfShapeDiscreteOfFiniteOfPreservesFiniteCoproducts | Mathlib.CategoryTheory.Limits.Preserves.Finite | [
"CategoryTheory.Functor",
"Finite",
"Exists",
"Equiv",
"CategoryTheory.Discrete.equivalence",
"CategoryTheory.discreteCategory",
"CategoryTheory.Limits.preservesColimitsOfShape_of_equiv",
"Nat",
"Finite.exists_equiv_fin",
"Nonempty",
"CategoryTheory.Limits.PreservesColimitsOfShape",
"CategoryT... | true |
ContinuousAlgEquiv.coeCLE_apply | Mathlib.Topology.Algebra.Algebra.Equiv | [
"CommSemiring.toSemiring",
"ContinuousAlgEquiv.toContinuousLinearEquiv",
"Algebra",
"ContinuousAlgEquiv.equivLike",
"Algebra.toModule",
"ContinuousLinearEquiv.equivLike",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"TopologicalSpace",
"ContinuousLinearEquiv",
"NonAssocSemiring.t... | true |
_private.Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real.0.RealRMK.integral_riesz_aux._simp_1_7 | Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real | [
"add_assoc",
"AddSemigroup",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Eq.symm",
"Eq"
] | false |
NNRat.instContinuousSub | Mathlib.Topology.Instances.Rat | [
"Continuous.comp'",
"Rat.instOfNat",
"Rat.instSub",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"continuous_subtype_val",
"Continuous.snd",
"Rat",
"PartialOrder.toPreorder",
"continuous_const",
"HSub.hSub",
"Rat.instSemilatticeSup",
"Rat.linearOrder",
"... | true |
Std.TreeMap.getKeyD_diff_of_not_mem_right | Std.Data.TreeMap.Lemmas | [
"Std.DTreeMap.getKeyD_diff_of_not_mem_right",
"Std.TreeMap.instSDiff",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"SDiff.sdiff",
"Std.TreeMap.instMembership",
"Std.TreeMap.getKeyD",
"Eq",
"Not",
"Std.TreeMap"
] | true |
FinPartOrd.Iso.mk_inv | Mathlib.Order.Category.FinPartOrd | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartOrd.str",
"PartialOrder.toPreorder",
"Preorder.toLE",
"FinPartOrd.Iso.mk",
"FinPartOrd.isFintype",
"OrderIso",
"FinPartOrd.largeCategory",
"OrderIso.symm",
"instFunLikeOrderIso",
"FinPartOrd.toPartOrd",
"FinPartOrd.of",
"FinPartO... | true |
Std.TreeSet.Raw.min?_insert_le_self | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeMap.Raw.minKey?_insertIfNew_le_self",
"Unit.unit",
"Std.TreeSet.Raw.WF.out",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.TreeSet.Raw.isSome_min?_insert",
"Std.TreeSet.Raw.insert",
"Std.TreeSet.Raw",
"Unit",
"Option.get",
"Std.TreeSet.Raw.min?",
"Bool",
"Ordering.isLE",
"Std.Tr... | true |
ContinuousMap.casesOn | Mathlib.Topology.ContinuousMap.Defs | [
"Continuous",
"ContinuousMap.rec",
"ContinuousMap.mk",
"ContinuousMap",
"TopologicalSpace"
] | false |
_private.Mathlib.Topology.Instances.RatLemmas.0.«termℚ∞» | Mathlib.Topology.Instances.RatLemmas | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
_private.Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality.0.groupHomology.mapCycles₁_quotientGroupMk'_epi._simp_3 | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"DivInvOneMonoid.toInvOneClass",
"QuotientGroup.mk",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"QuotientGroup.instHasQuotientSubgroup",
"Subgroup",
"HasQuotient.Quotient",
"Inv.inv",
"QuotientGroup.mk_inv",
"InvOneClass.toInv",
"QuotientGroup.Quotient.group",
"Eq... | false |
ArithmeticFunction.instAlgebra | Mathlib.NumberTheory.ArithmeticFunction.Defs | [
"ArithmeticFunction.instSemiring",
"CommSemiring.toSemiring",
"Algebra",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"ArithmeticFunction.instModule",
"Algebra.toModule",
"ArithmeticFunction.instAlgebra._proof_3",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"ArithmeticFunction.inst... | true |
_private.Lean.Meta.Tactic.Grind.Internalize.0.Lean.Meta.Grind.isCongruentCheck.go._unsafe_rec | Lean.Meta.Tactic.Grind.Internalize | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Sym.isSameExpr",
"_private.Lean.Meta.Tactic.Grind.Internalize.0.Lean.Meta.Grind.isCongruentCheck.go._unsafe_rec",
"Lean.Meta.State",
"instMonadLiftT",
... | false |
EReal.neg_eq_top_iff | Mathlib.Data.EReal.Operations | [
"neg_injective",
"EReal.instNeg",
"EReal",
"instTopEReal",
"Function.Injective.eq_iff'",
"Bot.bot",
"Iff",
"InvolutiveNeg.toNeg",
"Top.top",
"Eq",
"instBotEReal",
"Neg.neg",
"rfl",
"EReal.instInvolutiveNeg"
] | true |
ModuleCat.CoextendScalars.obj' | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | [
"Semiring.toModule",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"LinearMap.addCommGroup",
"RingHom",
"ModuleCat.restrictScalars",
"LinearMap",
"ModuleCat.of",
"ModuleCat.isAddCommGroup",
"Ring.toAddCommGroup",
"ModuleCat.moduleCategory",
"ModuleCat.carrier",
"ModuleCat.CoextendScalars.isMo... | true |
_private.Mathlib.Tactic.Push.0.Mathlib.Tactic.Push.pushNegBuiltin._sparseCasesOn_2 | Mathlib.Tactic.Push | [
"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 |
_private.Mathlib.Order.Filter.Germ.Basic.0.Filter.Germ.IsConstant.match_1 | Mathlib.Order.Filter.Germ.Basic | [
"Exists",
"Filter.EventuallyEq",
"Exists.casesOn",
"Exists.intro",
"Filter"
] | false |
Matroid.isBasis_iff_isBasis'_subset_ground | Mathlib.Combinatorics.Matroid.Basic | [
"Matroid.IsBasis.subset_ground",
"Matroid.E",
"Matroid.IsBasis.isBasis'",
"Matroid.IsBasis'",
"HasSubset.Subset",
"And",
"Iff",
"And.right",
"And.left",
"Matroid.isBasis'_iff_isBasis",
"And.intro",
"Iff.intro",
"Iff.mp",
"Matroid.IsBasis",
"Matroid",
"Set.instHasSubset",
"Set"
] | true |
ContinuousAffineMap.coe_const | Mathlib.Topology.Algebra.ContinuousAffineMap | [
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ContinuousAffineMap",
"TopologicalSpace",
"AddTorsor",
"ContinuousAffineMap.const",
"Function.const",
"Module",
"ContinuousAffineMap.instFunLike",
"Ring.toSemiring",
"Eq",
"DFunLike.coe",
"Ring",
"rfl"
] | true |
Polynomial.cyclotomic.roots_eq_primitiveRoots_val | Mathlib.RingTheory.Polynomial.Cyclotomic.Roots | [
"Eq.mpr",
"IsDomain",
"CommRing",
"Polynomial.roots",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"AddGroupWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Polynomial.cyclotomic",
"... | true |
Subtype.mk.hinj | Mathlib.Data.Subtype | [
"Subtype",
"Subtype.mk",
"And",
"And.intro",
"HEq",
"Eq",
"Subtype.noConfusion"
] | true |
_private.Mathlib.Tactic.FBinop.0.FBinopElab.AnalyzeResult.maxS?._default | Mathlib.Tactic.FBinop | [
"id",
"FBinopElab.SRec",
"Option.none",
"Option"
] | false |
_private.Mathlib.RingTheory.Congruence.Hom.0.RingCon.mapGen_apply_apply_of_surjective.match_1_1 | Mathlib.RingTheory.Congruence.Hom | [
"RingCon.instFunLikeForallProp",
"RingHom",
"RingCon",
"Exists",
"Distrib.toAdd",
"And.casesOn",
"And",
"NonAssocSemiring",
"RingHom.instFunLike",
"Exists.casesOn",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"And.intro",
"Exists.intro",
"NonUnitalNonAssocSemiring.to... | false |
Module.FaithfullyFlat.iff_exact_iff_rTensor_exact | Mathlib.RingTheory.Flat.FaithfullyFlat.Basic | [
"Function.Exact",
"Iff.mpr",
"Eq.mpr",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"exists_const._simp_1",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"PUnit... | true |
Complex.addCommGroup._proof_11 | Mathlib.Data.Complex.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real",
"HMul.hMul",
"Nat.rawCast",
"Mathlib.Tactic.Ring.add_pf_add_gt",
"CommSemiring.toSemiring",
"Complex.im",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"id",
"Distrib.toAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Mathlib.Tactic.Ring.of_eq"... | false |
KummerDedekind.normalizedFactorsMapEquivNormalizedFactorsMinPolyMk._proof_2 | Mathlib.NumberTheory.KummerDedekind | [
"Submodule.Quotient.instZeroQuotient",
"CommRing",
"Semiring.toModule",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Ideal",
"NonAssocRing.toNonUnitalNonAssocRing",
"HasQuotient.Quotient",
"Ideal.Quotient.ring",
"Ideal.instIsTwoSided_1",... | false |
UpperSemicontinuous.inf | Mathlib.Topology.Semicontinuity.Basic | [
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"SemilatticeInf.toMin",
"LowerSemicontinuous.sup",
"UpperSemicontinuous",
"TopologicalSpace",
"OrderDual",
"OrderDual.instLinearOrder",
"instDistribLatticeOfLinearOrder",
"Min.min",
"Lattic... | true |
Equiv.Perm.sigmaCongrRight_refl | Mathlib.Logic.Equiv.Defs | [
"Equiv.Perm",
"Equiv.Perm.sigmaCongrRight",
"Equiv.refl",
"Eq",
"Sigma",
"rfl"
] | true |
UInt64.toUInt32_ofNatLT | Init.Data.UInt.Lemmas | [
"UInt64.size",
"UInt32.ofNat",
"UInt64.ofNatLT",
"UInt64.toUInt32",
"Nat",
"LT.lt",
"UInt32",
"instLTNat",
"Eq",
"rfl"
] | true |
_private.Lean.Compiler.IR.FreeVars.0.Lean.IR.MaxIndex.visitExpr | Lean.Compiler.IR.FreeVars | [
"Pure.pure",
"_private.Lean.Compiler.IR.FreeVars.0.Lean.IR.MaxIndex.visitVar",
"Unit.unit",
"Lean.IR.Expr",
"_private.Lean.Compiler.IR.FreeVars.0.Lean.IR.MaxIndex.visitArg",
"Monad.toApplicative",
"Lean.IR.Arg",
"Lean.IR.CtorInfo",
"instOfNatNat",
"Lean.IR.MaxIndex.State",
"Id",
"Applicative.t... | true |
ENNReal.toNNReal_zero | Mathlib.Data.ENNReal.Basic | [
"NNReal",
"ENNReal.toNNReal",
"instZeroENNReal",
"NNReal.instZero",
"ENNReal",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
_private.Mathlib.LinearAlgebra.Goursat.0.Submodule.goursat._simp_1_13 | Mathlib.LinearAlgebra.Goursat | [
"Subtype",
"Subtype.ext_iff",
"propext",
"Subtype.val",
"Eq"
] | false |
Aesop.PhaseSpec.safe.elim | Aesop.Builder.Basic | [
"PULift.up",
"Aesop.SafeRuleInfo",
"Aesop.PhaseSpec.ctorElim",
"Aesop.PhaseSpec.safe",
"Aesop.PhaseSpec.ctorIdx",
"Nat",
"Aesop.PhaseSpec",
"Eq.symm",
"Eq"
] | false |
Std.DTreeMap.Internal.Impl.toList_map | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"congrArg",
"List.map",
"Std.DTreeMap.Internal.Impl.toList",
"Std.DTreeMap.Internal.Impl.toList_eq_toListModel",
"Sigma.fst",
"List",
"Std.DTreeMap.Internal.Impl.toListModel_map",
"congr",
"True",
"eq_self",
"Std.DTreeMap.Internal.Impl.toListModel",
"of_eq_true",
"Sigma.mk",
"Sigm... | true |
ContinuousLinearMap.ratio_le_opNorm | Mathlib.Analysis.Normed.Operator.Basic | [
"div_le_of_le_mul₀",
"Norm.norm",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddCommGroup",
"NormedSpace",
"MulZeroClass.toMul",
"IsStrictOrderedRing.toMulPosStrictMono",
"ContinuousLinearMap.le_opNorm",
"AddCommGroup.t... | true |
Aesop.LocalRuleSet.mk.noConfusion | Aesop.RuleSet | [
"Aesop.LocalRuleSet.mk",
"id",
"instOfNatNat",
"Array",
"Aesop.LocalRuleSet",
"Aesop.LocalRuleSet.noConfusion",
"Lean.Meta.Simp.Simprocs",
"Nat",
"LT.lt",
"Aesop.LocalNormSimpRule",
"Lean.Meta.SimpTheorems",
"Lean.Name",
"instLTNat",
"Prod",
"OfNat.ofNat",
"Eq",
"Array.size",
"Aeso... | false |
Nonneg.nat_ceil_coe | Mathlib.Algebra.Order.Nonneg.Floor | [
"IsOrderedRing.toPosMulMono",
"IsOrderedRing.toZeroLEOneClass",
"IsOrderedRing",
"Nonneg.semiring",
"PartialOrder.toPreorder",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Preorder.toLE",
"PartialOrder",
"Nonneg.floorSemiring",
"Subtype",
"LE.le",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
... | true |
Std.DTreeMap.Internal.Impl.minKey?_insert!_le_minKey? | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"Std.DTreeMap.Internal.Impl.insert!",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.insert_eq_insert!",
"Std.DTreeMap.Internal.Impl.minKey?_insert_le_minKey?",
"Option.some",
"Eq.mp",
"Option.get.congr_simp",
"Std.DTreeMap.Int... | true |
Set.inclusion_inclusion | Mathlib.Data.Set.Inclusion | [
"HasSubset.Subset.trans",
"Set.Elem",
"Set.instIsTransSubset",
"HasSubset.Subset",
"Set.inclusion",
"Eq",
"rfl",
"Set.instHasSubset",
"Set"
] | true |
CategoryTheory.ShortComplex.SnakeInput.L₀'_exact | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.ShortComplex.SnakeInput.L₁_exact",
"CategoryTheory.Epi",
"CategoryTheory.Limits.pullback.lift",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
... | true |
Sym.coe_equivNatSumOfFintype_apply_apply | Mathlib.Data.Finsupp.Multiset | [
"Equiv.instEquivLike",
"Finset.univ",
"Multiset.count",
"Equiv",
"Subtype",
"Fintype",
"Nat",
"Sym",
"Sym.toMultiset",
"Sym.equivNatSumOfFintype",
"Nat.instAddCommMonoid",
"Subtype.val",
"Eq",
"DFunLike.coe",
"Finset.sum",
"rfl",
"EquivLike.toFunLike",
"DecidableEq"
] | true |
Aesop.Script.STactic.ctorIdx | Aesop.Script.Tactic | [
"Aesop.Script.STactic",
"Nat"
] | false |
SemiNormedGrp.explicitCokernel | Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"SemiNormedGrp.cokernelCocone",
"Zero.toOfNat0",
"SemiNormedGrp.instLargeCategory",
"CategoryTheory.Category.toCategoryStruct",
"SemiNormedGrp.... | true |
Lean.Grind.Linarith.le_lt_combine_cert | Init.Grind.Ordered.Linarith | [
"Lean.Grind.Linarith.Poly.combine",
"Bool.and",
"Int",
"Nat.cast",
"Int.instLTInt",
"GT.gt",
"BEq.beq",
"Lean.Grind.Linarith.Poly.mul",
"instOfNat",
"Nat",
"Int.natAbs",
"Bool",
"Lean.Grind.Linarith.Poly.leadCoeff",
"Int.decLt",
"instNatCastInt",
"Lean.Grind.Linarith.instBEqPoly",
"O... | true |
AddSubsemigroup.toSubsemigroup_closure | Mathlib.Algebra.Group.Subsemigroup.Operations | [
"Iff.mpr",
"Equiv.instEquivLike",
"AddSubsemigroup.instSetLike",
"PartialOrder.toPreorder",
"OrderIso.to_galoisConnection",
"Subsemigroup.instPartialOrder",
"Preorder.toLE",
"AddSubsemigroup.subset_closure",
"GaloisConnection.l_le",
"AddSubsemigroup.closure",
"Equiv",
"OrderIso",
"HasSubset.... | true |
Lean.Expr.containsFVar | Lean.Expr | [
"Lean.instBEqFVarId",
"Lean.Expr",
"Lean.FVarId",
"BEq.beq",
"Lean.Expr.hasAnyFVar",
"Bool"
] | true |
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