name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
BoundedContinuousFunction.instNSMul.eq_1 | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"instHSMul",
"PseudoMetricSpace.toBornology",
"ContinuousMap.mk",
"SMul",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"PseudoMetricSpace.toUniformSpace",
"AddZeroClass.toAddZero",
"BoundedAdd",
"BoundedContinuousFunction.instFunLike",
"BoundedContinuousFunction.instNSMul._proof_2",
"SMul.... | true |
Int16.ofIntTruncate_int8ToInt | Init.Data.SInt.Lemmas | [
"Eq.mpr",
"Int8.toInt_le",
"Int16.ofIntTruncate",
"Int16",
"of_decide_eq_true",
"Int8.toInt_toInt16",
"congrArg",
"Int8.toInt16",
"Int.decLe",
"Int8.minValue",
"Int8",
"Int8.toInt",
"id",
"Int",
"LE.le",
"Int8.minValue_le_toInt",
"Bool.true",
"Int16.toInt_ofIntTruncate",
"Int.le_... | true |
CategoryTheory.Limits.WidePullbackCone.reindex_pt | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.WidePullbackCone.reindex",
"CategoryTheory.Limits.WidePullbackShape.category",
"Equiv",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Limits.WidePullbac... | true |
Lean.Meta.Grind.AC.EqCnstrProof.superpose_head_idempotent.injEq | Lean.Meta.Tactic.Grind.AC.Types | [
"Lean.Meta.Grind.AC.EqCnstr",
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Meta.Grind.AC.EqCnstrProof.superpose_head_idempotent",
"Lean.Meta.Grind.AC.EqCnstrProof",
"And",
"Eq.ndrec",
"Eq.refl",
"Lean.Grind.AC.Var",
"Eq",
"Lean.Meta.Grind.AC.EqCnstrProof.superpose_head_idempotent.inj"
] | true |
CategoryTheory.CoreHom._sizeOf_1 | Mathlib.CategoryTheory.Core | [
"CategoryTheory.CoreHom.rec",
"CategoryTheory.Iso._sizeOf_inst",
"CategoryTheory.Iso",
"instOfNatNat",
"CategoryTheory.CoreHom",
"CategoryTheory.Core.of",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"SizeOf",
"CategoryTheory.Core",
"OfNat.ofNat",
"CategoryTheory.Catego... | false |
UInt64.casesOn | Init.Prelude | [
"UInt64",
"UInt64.ofBitVec",
"BitVec",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"UInt64.rec"
] | false |
ModelWithCorners.toFun' | Mathlib.Geometry.Manifold.IsManifold.Basic | [
"NormedSpace",
"ModelWithCorners.toPartialEquiv",
"TopologicalSpace",
"ModelWithCorners",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"PartialEquiv.toFun",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"NormedAddCommGroup"
] | true |
isFixedPt_of_tendsto_iterate | Mathlib.Dynamics.FixedPoints.Topology | [
"Eq.mpr",
"Nat.instLattice",
"Lattice.toSemilatticeSup",
"congrArg",
"ContinuousAt",
"Function.iterate_succ'",
"Filter.atTop_neBot",
"instInhabitedNat",
"Function.comp",
"nhds",
"id",
"instOfNatNat",
"Nat.iterate",
"Filter.atTop",
"TopologicalSpace",
"funext",
"instHAdd",
"Semilatt... | true |
MvPolynomial.eval₂Hom_X | Mathlib.Algebra.MvPolynomial.CommRing | [
"Finsupp.instAddZeroClass",
"MvPolynomial.hom_C",
"Int.cast",
"Eq.mpr",
"RingHom.instRingHomClass",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Finsupp.instAddMonoid",
"MvPolynomial.X",
... | true |
ENNReal.log.eq_1 | Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog | [
"LinearOrder.toDecidableEq",
"EReal",
"ENNReal.log",
"instTopEReal",
"Bot.bot",
"Real.log",
"ENNReal.toReal",
"ENNReal.instLinearOrder",
"ENNReal",
"Zero.toOfNat0",
"Eq.refl",
"ENNReal.instTop",
"ENNReal.instZero",
"Top.top",
"OfNat.ofNat",
"Eq",
"instBotEReal",
"Real.toEReal",
"... | true |
AddCommute.addSemiconjBy | Mathlib.Algebra.Group.Commute.Defs | [
"AddSemiconjBy",
"AddCommute",
"Add"
] | true |
Pi.inv_apply | Mathlib.Algebra.Notation.Pi.Defs | [
"Inv",
"Pi.instInv",
"Inv.inv",
"Eq",
"rfl"
] | true |
ZFSet.Definable.noConfusion | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet.Definable",
"ZFSet.Definable.casesOn",
"ZFSet",
"HEq.refl",
"ZFSet.Definable.mk_out._autoParam",
"ZFSet.mk",
"autoParam",
"PSet",
"Nat",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"ZFSet.Definable.noConfusionType",
"Fin",
"Eq"
] | false |
Lean.Compiler.LCNF.JoinPointFinder.FindState.mk.inj | Lean.Compiler.LCNF.JoinPoints | [
"Lean.instBEqFVarId",
"Lean.Compiler.LCNF.JoinPointFinder.FindState.mk",
"Lean.FVarId",
"Std.HashMap",
"Lean.Compiler.LCNF.JoinPointFinder.CandidateInfo",
"Lean.instHashableFVarId",
"Lean.Compiler.LCNF.JoinPointFinder.FindState",
"Eq",
"Lean.Compiler.LCNF.JoinPointFinder.FindState.mk.noConfusion"
] | true |
BialgHom.noConfusionType | Mathlib.RingTheory.Bialgebra.Hom | [
"CoalgebraStruct",
"MulOne.toOne",
"HMul.hMul",
"CoalgHom.toLinearMap",
"CommSemiring.toSemiring",
"CoalgHom",
"Algebra",
"Algebra.toModule",
"MulOne.toMul",
"LinearMap.toAddHom",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"BialgHom",
"NonUnitalNonA... | false |
Nat.toArray_roc_eq_nil_iff | Init.Data.Range.Polymorphic.NatLemmas | [
"Std.Rco.toArray",
"congrArg",
"Std.PRange.instIsAlwaysFiniteNat_1",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.add_le_add_iff_right._simp_1",
"List.toArray",
"Array",
"iff_self",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Nat.toArray_roc_eq_toArray_rco",
"Std.PRange.instUpwardEnumerableNat",
"N... | true |
Finset.le_piecewise_of_le_of_le | Mathlib.Data.Finset.Piecewise | [
"Finset",
"Decidable",
"Preorder.toLE",
"Membership.mem",
"Finset.piecewise",
"LE.le",
"Finset.piecewise_cases",
"Pi.hasLe",
"Finset.instSetLike",
"SetLike.instMembership",
"Preorder"
] | true |
CategoryTheory.Limits.piConstAdj | Mathlib.CategoryTheory.Limits.Shapes.Products | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Limits.HasProducts",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.yoneda",
"CategoryTheory.Functor.id",
"TypeCat.ofHom",
"Category... | true |
List.gt_of_range'_eq_append_cons | Std.Do.Triple.SpecLemmas | [
"_private.Std.Do.Triple.SpecLemmas.0.List.gt_of_range'_eq_append_cons._simp_1_1",
"List.range'_eq_append_iff",
"HMul.hMul",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"Exists",
"Eq.mp",
"List.range'_eq_cons_iff",
"instSubNat",
"instMulNat",
"instOfNatNat",
"Nat.mul_comm",
... | true |
Mathlib.Tactic.Ring.Common.instInhabitedBtℕ | Mathlib.Tactic.Ring.Common | [
"Rat.instOfNat",
"Lean.Expr.const",
"Rat",
"Lean.Expr",
"Lean.Expr.sort",
"Lean.Level",
"Option.none",
"Mathlib.Tactic.Ring.Common.btℕ",
"Mathlib.Tactic.Ring.RatCoeff.mk",
"Lean.Level.zero",
"Qq.Quoted.unsafeMk",
"Inhabited",
"Lean.Level.succ",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Inhab... | true |
Path.Homotopy.pathCast | Mathlib.Topology.Homotopy.Path | [
"Path.Homotopy",
"Path.cast",
"TopologicalSpace",
"Path",
"Eq"
] | true |
SkewMonoidAlgebra.instRing._proof_7 | Mathlib.Algebra.SkewMonoidAlgebra.Basic | [
"Monoid",
"HMul.hMul",
"NonUnitalNonAssocRing.toMul",
"AddMonoid.toZero",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NonUnitalNonAssocRing.zero_mul",
"NonAssocRing.toNonUnitalNonAssocRing",
"AddGroup.toSubNegMonoid",
"MulSemiringAction",
"SkewMonoidAlgebra",
"Zero.toOf... | false |
Lean.instBEqDataValue | Lean.Data.KVMap | [
"BEq.mk",
"Lean.instBEqDataValue.beq",
"Lean.DataValue",
"BEq"
] | true |
IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_nnnorm | Mathlib.Analysis.Normed.Group.Ultra | [
"IsUltrametricDist.isNonarchimedean_norm",
"Real",
"SeminormedAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"Iff",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"SeminormedAddCommGroup.toAddCommGroup",
... | true |
IsCyclotomicExtension.autEquivPow._proof_4 | Mathlib.NumberTheory.Cyclotomic.Gal | [
"IsDomain",
"MulOne.toOne",
"Nat.instMulZeroClass",
"CommRing",
"HMul.hMul",
"ZMod.commRing",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Algebra",
"Units",
"Set.instSingletonSet",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"IsCyclotomicExtension",
"Field.toSemifield",
"ZMod",
... | false |
GradedAlgHom.id._proof_1 | Mathlib.RingTheory.GradedAlgebra.AlgHom | [
"Submodule",
"GradedRingHom.map_mem",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Membership.mem",
"Algebra.toModule",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instFunLike",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Submodule.setLike",
"Semiring",
... | false |
Finset.subtractionCommMonoid._proof_6 | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"NegZeroClass.toNeg",
"instHSMul",
"Finset",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"Finset.zsmul",
"Int",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"SetLike.coe",
... | false |
SSet.isColimitCokernelCoforkChainComplexDOneZero._proof_2 | Mathlib.AlgebraicTopology.SimplicialSet.Homology.HomologyZero | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"TypeCat.ofHom",
"instOfNatNat",
"SSet",
"SSet.π₀",
"CategoryTheory.Limits.HasCoproducts",
"CategoryTheory.Functor.map",
"CategoryTheory.Limits.isColimitMapCoconeCof... | false |
GrpMax | Mathlib.Algebra.Category.Grp.Basic | [
"GrpCat"
] | true |
GrpCat.forget_createsLimit.eq_1 | Mathlib.Algebra.Category.Grp.Limits | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"GrpCat.hasForgetToMonCat",
"CategoryTheory.Functor",
"GrpCat",
"MonoidHom.instFunLike",
"MonoidHom",
"GrpCat.str",
"Monoid.toMulOneClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso.refl",
"MonCat",
"D... | true |
Ideal.powQuotSuccInclusion_injective | Mathlib.NumberTheory.RamificationInertia.Basic | [
"Ideal.Quotient.commSemiring",
"Eq.mpr",
"Submodule",
"CommRing",
"Semiring.toModule",
"IsScalarTower.right",
"Submodule.Quotient.addCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"AddCommGroup.toAddCommMonoid",
"LinearMap.ker_eq_bot",
"Submodule.addCommMonoid",
"I... | true |
Lean.Elab.WF.EqnInfo._sizeOf_inst | Lean.Elab.PreDefinition.WF.Eqns | [
"SizeOf.mk",
"Lean.Elab.WF.EqnInfo",
"SizeOf",
"Lean.Elab.WF.EqnInfo._sizeOf_1"
] | false |
Topology.IsScott.scottContinuousOn_iff_continuous | Mathlib.Topology.Order.ScottTopology | [
"Topology.IsScott.isUpperSet_of_isOpen",
"Iff.mpr",
"Eq.mpr",
"False",
"Continuous",
"_private.Mathlib.Topology.Order.ScottTopology.0.Topology.IsScott.scottContinuousOn_iff_continuous._simp_1_1",
"trivial",
"_private.Mathlib.Topology.Order.ScottTopology.0.Topology.IsScott.scottContinuousOn_iff_continu... | true |
Algebra.QuasiFinite.recOn | Mathlib.RingTheory.QuasiFinite.Basic | [
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"Algebra.QuasiFinite",
"AddCommGroup.toAddCommMonoid",
"Localization.AtPrime",
"TensorProduct.ad... | false |
lift_trdeg_le_of_surjective | Mathlib.RingTheory.AlgebraicIndependent.Basic | [
"Function.invFun",
"Nontrivial",
"Eq.mpr",
"CommRing",
"AlgebraicIndependent",
"Cardinal.instOne",
"AlgebraicIndepOn",
"Cardinal",
"instReflLe",
"congrArg",
"CommSemiring.toSemiring",
"iSup",
"HEq.refl",
"AlgHom",
"AlgHom.funLike",
"Cardinal.lift_iSup",
"PartialOrder.toPreorder",
"... | true |
Std.ExtDHashMap.getKey_diff | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.mem_diff_iff",
"Std.ExtDHashMap.inner",
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Quot.pliftOn._proof_2",
"Membership.mem",
"Std.DHashMap.diff",
"Std.ExtDHashMap.inductionOn",
"Std.ExtDHashMap.getKey",
"Std.ExtDHashMap.mk",
"_private.Std.Data.ExtDHashMap.Basic.0... | true |
Set.image_single_uIcc_left | Mathlib.Order.Interval.Set.Pi | [
"Lattice",
"Pi.instZero",
"Pi.single",
"Pi.instLattice",
"Set.image_update_uIcc_left",
"Zero.toOfNat0",
"Set.image",
"OfNat.ofNat",
"Eq",
"Set.uIcc",
"DecidableEq",
"Zero",
"Set"
] | true |
Std.DTreeMap.Internal.Impl.getD_insertMany_list_of_mem | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Std.Internal.List.insertList",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"List.Pairwise",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"instForInOfForIn'",
"Std.DTreeMap.Internal.Impl.get?_insertMany_list_of_mem._proof_1",
"Std.Internal.List.... | true |
Lean.Lsp.CompletionItemTag._sizeOf_inst | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.CompletionItemTag",
"Lean.Lsp.CompletionItemTag._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
ite_neg | Mathlib.Algebra.Notation.Lemmas | [
"Eq.mpr",
"Decidable.casesOn",
"congrArg",
"Decidable",
"id",
"if_pos",
"LT.lt",
"Zero.toOfNat0",
"congrFun'",
"OfNat.ofNat",
"Eq",
"if_neg",
"Not",
"LT",
"Zero",
"ite"
] | true |
CategoryTheory.SimplicialThickening.functorMap._proof_6 | Mathlib.AlgebraicTopology.SimplicialNerve | [
"CategoryTheory.SimplicialThickening",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"LinearOrder",
"PartialOrder.toPreorder",
"CategoryTheory.SimplicialThickening.Path.I",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"CategoryTheory.SimplicialThickening... | false |
CategoryTheory.injectiveResolutions._proof_3 | Mathlib.CategoryTheory.Abelian.Injective.Resolution | [
"IsRightCancelAdd",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"PartialOrder.toPreorder",
"instIsRightCancelAddOfAddRightReflectLE",
"Preorder.toLE",
"Nat.instAddCancelCommMonoid",
"contravariant_lt_of_covariant_le",
"AddLeftCancelMonoid.toAddLeftCancelSemigroup",
"i... | false |
Subfield.inf_relfinrank_left | Mathlib.FieldTheory.Relrank | [
"Subfield.inf_relrank_left",
"Nat.instMulZeroOneClass",
"Subfield.relrank",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Cardinal.commSemiring",
"Cardinal.toNat",
"MonoidWithZeroHom.funLike",
"Field.toDivisionRing",
"Subfield.instMin",
"id",
"instMulZeroOneClassOfSemiring",
"MonoidW... | true |
CategoryTheory.Bicategory.InducedBicategory.Hom₂._sizeOf_1 | Mathlib.CategoryTheory.Bicategory.InducedBicategory | [
"CategoryTheory.Bicategory.InducedBicategory.categoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"instSizeOfDefault",
"CategoryTheory.Bicategory.InducedBicategory.Hom₂.rec",
"CategoryTheory.Bicategory.toCategoryStruct",
"instOfNatNat",
"CategoryTheory.Bicategory.InducedBicategory.... | false |
Std.Internal.IO.Async.System.GroupId.noConfusion | Std.Internal.Async.System | [
"Std.Internal.IO.Async.System.GroupId.casesOn",
"Std.Internal.IO.Async.System.GroupId",
"Std.Internal.IO.Async.System.GroupId.noConfusionType",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | false |
Std.Internal.IO.Async.Async.instMonadAwaitPromise | Std.Internal.Async.Basic | [
"Std.Internal.IO.Async.MonadAwait",
"IO.Promise",
"Std.Internal.IO.Async.Async",
"Std.Internal.IO.Async.MonadAwait.mk",
"Std.Internal.IO.Async.Async.instMonadAwaitPromise._aux_1"
] | true |
Submodule.starProjection_apply | Mathlib.Analysis.InnerProductSpace.Projection.Basic | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"Submodule.starProjection",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"Submodule.addCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"Submodule.HasOrthogonalProje... | true |
CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.mk | Mathlib.AlgebraicTopology.ExtraDegeneracy | [
"CategoryTheory.Comma.right",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Fin.succ",
"CategoryTheory.SimplicialObject.const",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε._autoParam",
"... | true |
CategoryTheory.ShortComplex.SnakeInput.composableArrowsFunctor_map | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.ComposableArrows.homMk₅",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.SnakeInput.naturality_δ",
"CategoryTheory.ShortComplex.SnakeInput.L₃",
"CategoryTheory.ShortComplex.SnakeInput.composableArrowsFunctor._proof_5",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiv... | true |
CategoryTheory.Functor.const.opObjUnop._proof_1 | Mathlib.CategoryTheory.Functor.Const | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.opposite",
"Eq.refl",
"Categor... | false |
TopologicalSpace.OpenNhdsOf.comap | Mathlib.Topology.Sets.Opens | [
"TopologicalSpace.OpenNhdsOf.toOpens",
"FrameHom",
"Lattice.toSemilatticeSup",
"TopologicalSpace.Opens.instCompleteLattice",
"ContinuousMap",
"TopologicalSpace.OpenNhdsOf",
"TopologicalSpace.Opens",
"TopologicalSpace.OpenNhdsOf.mk",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"Topologica... | true |
Subarray.mkSlice_roc_eq_mkSlice_roo | Init.Data.Slice.Array.Lemmas | [
"Std.Rco",
"Std.instHasRcoIntersectionNat_1",
"Std.Rco.Sliceable.mkSlice",
"Subarray",
"congrArg",
"instSliceableArrayNatSubarray_1",
"Nat.max_eq_left",
"instSliceableSubarrayNat_3",
"Std.Roc.HasRcoIntersection.intersection",
"Std.Roo.lower",
"instOfNatNat",
"LE.le",
"Nat.le_add_left._simp_1... | true |
Ideal.isMaximal_of_isIntegral_of_isMaximal_comap | Mathlib.RingTheory.Ideal.GoingUp | [
"Iff.mpr",
"SetLike.lt_iff_le_and_exists",
"Algebra.IsIntegral.isIntegral",
"RingHom.instRingHomClass",
"CommRing",
"Preorder.toLT",
"Semiring.toModule",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Ideal.comap_eq_top_iff",
"Algebra",
"Preorder.toLE",
"RingH... | true |
uniformity_hasBasis_open | Mathlib.Topology.UniformSpace.Basic | [
"Filter.instMembership",
"Iff.mpr",
"UniformSpace",
"interior_subset",
"SetRel",
"isOpen_interior",
"uniformity",
"instTopologicalSpaceProd",
"Membership.mem",
"Exists",
"id",
"HasSubset.Subset",
"And",
"Filter.HasBasis",
"And.intro",
"interior",
"Exists.intro",
"Filter.hasBasis_se... | true |
IntermediateField.extendRight.instSMulSubtypeMem | Mathlib.FieldTheory.IntermediateField.ExtendRight | [
"CommRing",
"instHSMul",
"IntermediateField",
"IsScalarTower",
"SMul",
"IntermediateField.toField",
"Algebra",
"Algebra.toSMul",
"Membership.mem",
"Subtype",
"SMul.mk",
"Field.toSemifield",
"Subtype.mk",
"IntermediateField.extendRight",
"CommRing.toCommSemiring",
"Semifield.toDivisionS... | true |
TotallyBounded.exists_prodMk_finset_mem_hausdorffEntourage | Mathlib.Topology.UniformSpace.Closeds | [
"Filter.instMembership",
"UniformSpace",
"Eq.mpr",
"TotallyBounded",
"Finset.coe_filter",
"SetRel",
"congrArg",
"Finset",
"uniformity",
"setOf",
"Classical.propDecidable",
"Set.Finite",
"Membership.mem",
"Exists",
"id",
"Prod.mk",
"HasSubset.Subset",
"Set.mem_iUnion₂",
"Prod.fst"... | true |
RatFunc.definition._@.Mathlib.FieldTheory.RatFunc.Defs.2943445235._hygCtx._hyg.2 | Mathlib.FieldTheory.RatFunc.Defs | [
"CommRing",
"HMul.hMul",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"RatFunc.definition._proof_1._@.Mathlib.FieldTheory.RatFunc.Defs.2943445235._hygCtx._hyg.2",
"Membership.mem",
"nonZeroDivisors",
"Subtype",
"RatFunc.toFractionRing",
"Polynomial",
"MulZeroOneClass.toMulOneClass",
"Com... | false |
Lean.Lsp.instFromJsonRenameOptions.fromJson | Lean.Data.Lsp.LanguageFeatures | [
"Pure.pure",
"Lean.Json",
"Monad.toApplicative",
"String",
"Lean.Name.mkStr3",
"Lean.Json.getObjValAs?",
"Lean.instFromJsonBool",
"Applicative.toPure",
"ToString.toString",
"Except.instMonad",
"instAppendString",
"Except.mapError",
"instHAppendOfAppend",
"Lean.Name.instToString",
"Lean.L... | true |
Lean.Meta.SimpTheorems.isDeclToUnfold | Lean.Meta.Tactic.Simp.SimpTheorems | [
"Lean.PersistentHashSet.contains",
"Lean.Meta.SimpTheorems.toUnfold",
"Lean.Meta.SimpTheorems",
"Bool",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.instHashableName"
] | true |
Unitization.ind | Mathlib.Algebra.Algebra.Unitization | [
"Unitization.inl",
"Unitization.inr",
"Eq.rec",
"AddZeroClass.toAddZero",
"Unitization.instAdd",
"Prod.fst",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
"Unitization.toProd",
"AddZero.toAdd",
"Unitization",
"Eq",
"Prod.snd",
"Unitization.inl_fst_add_inr_snd_eq"
] | true |
Representation.tprod._proof_1 | Mathlib.RepresentationTheory.Basic | [
"Monoid",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"Representation",
"MonoidHom.instFunLike",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"Module.End.instSemiring",
"MonoidHomClass.toOneHomClass",
"Module.End.instOne",
"TensorProduct.m... | false |
Ordinal.omega_natCast_le_lift._simp_1 | Mathlib.SetTheory.Cardinal.Aleph | [
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ordinal.lift",
"AddMonoidWithOne.toNatCast",
"Ordinal.omega_natCast_le_lift",
"LE.le",
"Nat.cast",
"Ordinal.omega",
"Ordinal.addMonoidWithOne",
"Nat",
"propext",
"OrderEmbedding",
"Eq",
"DFunLike.coe",
"instFunLikeOrd... | false |
_private.Batteries.Data.Vector.Basic.0.Vector.scanlMFast.loop._proof_3 | Batteries.Data.Vector.Basic | [
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"USize.toNat",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"instAddUSize",
"Eq",
"_private.Batteries.Data.Vector.Basic.0.Vector.scanlMFast._proof_2",
"Not",
"Nat.decLe",
"USize... | false |
Complex.polarCoord_symm_apply | Mathlib.Analysis.SpecialFunctions.PolarCoord | [
"Distrib.leftDistribClass",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearEquiv.symm",
"Semigroup.toMul",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"Complex.cos",
"Real.cos",
"congrArg",
"NormedSpace.toModule",
"Complex.sin",
"mul_... | true |
Multiset.sum_map_sum_map | Mathlib.Algebra.BigOperators.Group.Multiset.Basic | [
"Multiset.sum",
"instHSMul",
"Multiset.map_cons",
"Multiset.map",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"Membership.mem",
"AddZeroClass.toAddZero",
"Multiset",
"nsmul_zero",
"Multiset.cons",
"Multiset.induction_on",
"AddCommMonoid",
"AddZero.toZero",
"Multiset.in... | true |
String.any_iff | Batteries.Data.String.Lemmas | [
"List.any_eq_true._simp_1",
"congrArg",
"String",
"Membership.mem",
"Exists",
"iff_self",
"Bool.true",
"List",
"And",
"Iff",
"List.instMembership",
"String.toList",
"True",
"Bool",
"of_eq_true",
"List.any",
"congrFun'",
"Char",
"String.Legacy.any",
"Eq",
"Eq.trans",
"String... | true |
Std.Do.SPred.or_intro_r' | Std.Do.SPred.DerivedLaws | [
"Std.Do.SPred.entails",
"Std.Do.SPred.entails.trans",
"Std.Do.SPred.or",
"Std.Do.SPred.or_intro_r",
"List",
"Std.Do.SPred"
] | true |
Subbimodule.toSubmodule' | Mathlib.Algebra.Module.Bimodule | [
"Submodule",
"Subbimodule.smul_mem'",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.Algebra.module",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"Algebra.toModule",
"DistribSMul.toSMulZeroClass",
"Subbimodu... | true |
CategoryTheory.Limits.pointwiseProductCompEvaluation._proof_2 | Mathlib.CategoryTheory.Limits.FilteredColimitCommutesProduct | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.piObjIso_hom_comp_π",
"congrArg",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Limits.Pi.functor._proof_1",
"Categor... | false |
Lean.Grind.LinarithConfig.instances._inherited_default | Init.Grind.Config | [
"id",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | false |
UInt8.ofFin_and | Init.Data.UInt.Bitwise | [
"UInt8.toFin",
"congrArg",
"UInt8.size",
"UInt8.ofFin",
"UInt8.toFin_ofFin",
"congr",
"True",
"eq_self",
"Iff.mp",
"of_eq_true",
"HAnd.hAnd",
"Fin.instAndOp",
"UInt8",
"Fin",
"Eq",
"instHAndOfAndOp",
"instAndOpUInt8",
"UInt8.toFin_inj",
"Eq.trans",
"UInt8.toFin_and"
] | true |
ZLattice.covolume.tendsto_card_le_div | Mathlib.Algebra.Module.ZLattice.Covolume | [
"instWeaklyLocallyCompactSpaceOfLocallyCompactSpace",
"IsModuleTopology.toContinuousSMul",
"Eq.mpr",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Submodule",
"frontier",
"locallyCompact_of_proper",
"Real.instLE",
"Real",
"Pi.t2Space",
"inst... | true |
Std.TreeMap.Raw.getEntryLT! | Std.Data.TreeMap.Raw.Basic | [
"Ordering",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Inhabited",
"Std.DTreeMap.Raw.Const.getEntryLT!",
"Prod"
] | true |
Complementeds.instMax._proof_1 | Mathlib.Order.Disjoint | [
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Complementeds",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"IsComplemented.sup",
"DistribLattice",
"Max.max",
"BoundedOrder",
"Subtype.val",
"Lattice.toSemilatticeInf",
"Subty... | false |
NonUnitalNormedRing.rec | Mathlib.Analysis.Normed.Ring.Basic | [
"Norm.norm",
"Real.instLE",
"Real",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toMul",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Norm",
"NonUnitalNormedRing",
"LE.le",
"instHAdd",
"AddSemigroup.toAdd",
... | false |
Aesop.EqualUpToIds.Unsafe.exprsEqualUpToIdsCore₂ | Aesop.Util.EqualUpToIds | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.instExceptToTraceResultBool",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.MonadCacheT.instAlternative",
"Bool.not",
"Aesop.EqualUpToIds.Unsafe.exprsEqualUpToIdsCore₃",
"Aesop.EqualUpToIds.GoalContext.lo... | true |
Rep.Tor._proof_3 | Mathlib.RepresentationTheory.Homological.GroupHomology.Basic | [
"CategoryTheory.Abelian.toPreadditive",
"CommRing",
"CommSemiring.toSemiring",
"Group",
"Rep.instCategory",
"DivInvMonoid.toMonoid",
"Rep.instEnoughProjectives",
"Group.toDivInvMonoid",
"CategoryTheory.HasProjectiveResolutions",
"Rep.instAbelian",
"CommRing.toCommSemiring",
"Rep",
"CategoryT... | false |
_private.Lean.Meta.FunInfo.0.Lean.Meta.collectDeps.visit._f | Lean.Meta.FunInfo | [
"Array.push",
"Lean.Expr.instBEq",
"Lean.Expr.letE",
"Function.comp",
"Lean.Expr",
"Lean.FVarId",
"instDecidableEqBool",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"instBEqOfDecidableEq",
"Array",
"Lean.Expr.forallE",
"Bool.true",
"Unit",
"Lean.MData",
"Lean.Expr.lam",
"Nat",
"_private.L... | false |
CoxeterSystem.getElem_alternatingWord._proof_1 | Mathlib.GroupTheory.Coxeter.Basic | [
"congrArg",
"CoxeterSystem.alternatingWord",
"Nat",
"LT.lt",
"True",
"eq_true",
"of_eq_true",
"instLTNat",
"List.length",
"CoxeterSystem.length_alternatingWord",
"Eq.trans"
] | false |
IsJordan.casesOn | Mathlib.Algebra.Jordan.Basic | [
"HMul.hMul",
"IsJordan.mk",
"Mul",
"IsJordan",
"IsJordan.rec",
"Eq",
"instHMul"
] | false |
Profinite.NobelingProof.iso_map._proof_3 | Mathlib.Topology.Category.Profinite.Nobeling.Basic | [
"Continuous",
"Pi.topologicalSpace",
"continuous_subtype_val",
"Continuous.comp",
"instTopologicalSpaceBool",
"Profinite.NobelingProof.π",
"Decidable",
"Membership.mem",
"continuous_pi",
"Set.Elem",
"Subtype",
"Profinite.NobelingProof.iso_map._proof_2",
"Continuous.subtype_mk",
"Subtype.mk... | false |
MaximalSpectrum.mk.injEq | Mathlib.RingTheory.Spectrum.Maximal.Defs | [
"MaximalSpectrum.mk.inj",
"Eq.propIntro",
"CommSemiring.toSemiring",
"MaximalSpectrum.mk",
"MaximalSpectrum",
"Ideal",
"CommSemiring",
"Ideal.IsMaximal",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
AffineIsometryEquiv.coe_one | Mathlib.Analysis.Normed.Affine.Isometry | [
"AffineIsometryEquiv.instEquivLike",
"SeminormedAddCommGroup",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"NormedSpace",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"id",
"AffineIsometryEquiv",
"NormedField",
"PseudoMetricSpace",
"One.toOfNat1",
"AffineIsometryEq... | true |
CategoryTheory.Limits.inr_pushoutZeroZeroIso_hom | Mathlib.CategoryTheory.Limits.Constructions.ZeroObjects | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Limits.colimit.isoColimitCocone",
"CategoryTheory.Limits.HasBinaryCoproduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasZeroObject.zeroIsInitial",
"congrArg",
"Categ... | true |
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice | Mathlib.Order.ConditionallyCompleteLattice.Defs | [
"ConditionallyCompleteLattice",
"ConditionallyCompleteLinearOrder"
] | true |
CategoryTheory.Functor.Fiber.homMk._proof_2 | Mathlib.CategoryTheory.FiberedCategory.Fiber | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.IsHomLift",
"CategoryTheory.IsHomLift.codomain_eq",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category... | false |
Int.dvd_ediv_iff_mul_dvd._simp_1 | Init.Data.Int.DivMod.Lemmas | [
"Int.instDiv",
"Dvd.dvd",
"instHDiv",
"HMul.hMul",
"Int.dvd_ediv_iff_mul_dvd",
"HDiv.hDiv",
"Int",
"Int.instDvd",
"Int.instMul",
"propext",
"Eq",
"instHMul"
] | false |
Lean.Elab.Tactic.Do.Context.rec | Lean.Elab.Tactic.Do.VCGen.Basic | [
"Lean.Elab.Tactic.Do.Context",
"Lean.FVarIdMap",
"Lean.Elab.Tactic.Do.SpecAttr.SpecTheorems",
"Lean.Elab.Tactic.Do.VCGen.Config",
"Nat",
"Lean.Meta.Simp.SimprocsArray",
"Lean.Elab.Tactic.Do.JumpSiteInfo",
"Lean.Meta.Simp.Context",
"Lean.Elab.Tactic.Do.Context.mk"
] | false |
Submonoid.decidableMemCentralizer | Mathlib.GroupTheory.Submonoid.Centralizer | [
"Monoid",
"Submonoid.centralizer",
"HMul.hMul",
"Monoid.toMulOneClass",
"Decidable",
"Membership.mem",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Submonoid.mem_centralizer_iff",
"decidable_of_iff'",
"Submonoid.instSetLike",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Submonoid",... | true |
CategoryTheory.Monad.ReflectsColimitOfIsSplitPair.recOn | Mathlib.CategoryTheory.Monad.Monadicity | [
"CategoryTheory.Monad.ReflectsColimitOfIsSplitPair.mk",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Monad.ReflectsColimitOfIsSplitPair",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryT... | false |
Localization.localRingHom_bijective_of_not_conductor_le | Mathlib.RingTheory.Conductor | [
"Localization.localRingHom_bijective_of_saturated_inf_eq_top._proof_1",
"Subalgebra.instSetLike",
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"CommRing",
"Semiring.toModule",
"HMul.hMul",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"Localization.AtPrime",
"Localization.localRingHom",... | true |
_private.Mathlib.Algebra.Star.Unitary.0.Unitary.smul_mem_of_mem._simp_1_1 | Mathlib.Algebra.Star.Unitary | [
"Monoid",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"unitary",
"StarMul",
"Membership.mem",
"MulOne.toMul",
"MulOneClass.toMulOne",
"And",
"StarMul.toInvolutiveStar",
"propext",
"One.toOfNat1",
"Unitary.mem_iff",
"InvolutiveStar.toStar",
"Submonoid.instSetLike",
"OfNat.ofN... | false |
Int32.or_eq_zero_iff._simp_1 | Init.Data.SInt.Bitwise | [
"instHOrOfOrOp",
"HOr.hOr",
"And",
"propext",
"instOrOpInt32",
"Int32.instOfNat",
"Int32.or_eq_zero_iff",
"OfNat.ofNat",
"Eq",
"Int32"
] | false |
Part.mk._flat_ctor | Mathlib.Data.Part | [
"Part",
"Part.mk"
] | false |
FirstOrder.Field.fieldOfModelACF | Mathlib.ModelTheory.Algebra.Field.IsAlgClosed | [
"FirstOrder.Field.modelField_of_modelACF",
"FirstOrder.Language.ring",
"FirstOrder.Language.Theory.ACF",
"FirstOrder.Language.Theory.Model",
"FirstOrder.Field.fieldOfModelField",
"FirstOrder.Language.Structure",
"Nat",
"FirstOrder.Language.Theory.field",
"Field"
] | true |
Algebra.SubmersivePresentation.basisKaehler.eq_1 | Mathlib.RingTheory.Smooth.StandardSmoothCotangent | [
"CommRing",
"Algebra.to_smulCommClass",
"instAddCommGroupKaehlerDifferential",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Compl.compl",
"Algebra.SubmersivePresentation.basisKaehlerOfIsCompl",
"Algebra.SubmersivePresentation.toPreSubmersivePresentation",
"Finite",
"Algebra",
"Mem... | true |
cfcₙ_tsub | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order | [
"NNReal.instTopologicalSpace",
"cfcₙ",
"Eq.mpr",
"NNReal.instCommSemiring",
"cfcₙ_tsub._auto_3",
"IsSelfAdjoint",
"Real.partialOrder",
"Real.instLE",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"instSMulOfMul",
"Continuous.continuousOn",
"cfcₙ_tsub._auto_7"... | true |
Lean.Elab.Term.ElabAppArgs.Context.mk | Lean.Elab.App | [
"Bool",
"Lean.Elab.Term.ElabAppArgs.Context.mk",
"Lean.Elab.Term.ElabAppArgs.Context"
] | true |
Int.clog_of_left_le_one | Mathlib.Data.Int.Log | [
"Int.instAddCommGroup",
"Eq.mpr",
"NegZeroClass.toNeg",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"LinearOrder",
"IsStrictOrderedRing",
"DivisionMonoid.toDivInvOneMonoid",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Semifield",
"id"... | true |
quasiconvexOn_iff_le_max | Mathlib.Analysis.Convex.Quasiconvex | [
"le_max_right",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Lattice.toSemilatticeSup",
"LinearOrder",
"SMul",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"PartialOrder",
"DistribLattice.toLatti... | true |
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