name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.LinearAlgebra.Matrix.Stochastic.0.Matrix.transpose_mem_colStochastic_iff_mem_rowStochastic._simp_1_2 | Mathlib.LinearAlgebra.Matrix.Stochastic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Finset.univ",
"IsOrderedRing",
"Matrix",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"PartialOrder",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"LE.le",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"Matrix.mem... | false |
MulAut.instGroup._proof_3 | Mathlib.Algebra.Group.End | [
"MulEquiv.refl",
"Mul.mk",
"instHDiv",
"One.mk",
"HMul.hMul",
"MulEquiv.trans",
"Semigroup.mk",
"Mul",
"MulAut",
"HDiv.hDiv",
"npowRecAuto",
"DivInvMonoid.div'",
"Monoid.mk",
"Div.mk",
"MulAut.instGroup._proof_2",
"Inv.mk",
"One.toOfNat1",
"Eq.refl",
"OfNat.ofNat",
"MulEquiv.sy... | false |
AlgebraNorm.isScalarTower_restriction._proof_4 | Mathlib.Analysis.Normed.Unbundled.AlgebraNorm | [
"AddGroup.toSubtractionMonoid",
"AlgebraNorm.instFunLikeReal",
"NegZeroClass.toNeg",
"RingHom.instRingHomClass",
"Real.partialOrder",
"Real",
"CommRing",
"RingHomClass.toAddMonoidHomClass",
"SeminormedCommRing",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"cong... | false |
_private.Mathlib.Data.DFinsupp.BigOperators.0.DFinsupp.sumAddHom._simp_1 | Mathlib.Data.DFinsupp.BigOperators | [
"Membership.mem",
"Multiset",
"Multiset.mem_add",
"Multiset.instMembership",
"instHAdd",
"HAdd.hAdd",
"propext",
"Or",
"Eq",
"Multiset.instAdd"
] | false |
Real.sigmoid_neg | Mathlib.Analysis.SpecialFunctions.Sigmoid | [
"add_mul",
"Real.instIsOrderedRing",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"add_neg_cancel",
"NegZeroClass.toNeg",
"Mathlib.Tactic.FieldSimp.subst_sub",
"Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst",
"Real.partialOrder",
"Real",
"instHDiv",
... | true |
PFun.core | Mathlib.Data.PFun | [
"PFun.graph'",
"PFun",
"SetRel.core",
"Set"
] | true |
SemiNormedGrp₁.instHasCokernels | Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels | [
"SemiNormedGrp₁.cokernelCocone",
"NormedAddGroupHom.ext",
"NormedAddGroupHom",
"NormedAddGroupHom.lift_mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.Limits.CokernelCofork",
"AddMonoid.toAddZeroClass",
"SemiNo... | true |
Metric.infEDist_closure_pos_iff_notMem_closure | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Membership.mem",
"id",
"Metric.infEDist",
"PseudoEMetricSpace",
"Iff",
"closure",
"PseudoEMetricSpace.toUniformSpace",
"LT.lt",
"ENNReal",
"propext",
"Metric.infEDist_closure",
"ENNReal.instPartialOrder",
... | true |
Lean.DefinitionSafety._sizeOf_inst | Lean.Declaration | [
"Lean.DefinitionSafety._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.DefinitionSafety"
] | false |
CategoryTheory.nerve.δ₂_two | Mathlib.AlgebraicTopology.SimplicialSet.Nerve | [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Opposite",
"CategoryTheory.ComposableArrows.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.eqToHom",
"CategoryTheory.ComposableArrows.map'._proof_8",
"PartialOrder.toPreorder",
... | true |
String.Pos.prev._proof_1 | Init.Data.String.FindPos | [
"String.toSlice",
"Eq.mpr",
"String.Pos.ofToSlice_toSlice",
"congrArg",
"String",
"String.startPos_toSlice",
"String.Pos.toSlice",
"id",
"String.startPos",
"Ne",
"String.Slice.startPos",
"String.Pos.ofToSlice",
"congr",
"String.Pos",
"String.Slice.Pos",
"Eq",
"Not",
"Eq.trans"
] | false |
Array.getElem?_map | Init.Data.Array.Lemmas | [
"dite_congr",
"Array.getElem_map",
"GetElem?.toGetElem",
"congrArg",
"Option.some",
"Array.map",
"Array.size_map",
"dite",
"Array",
"GetElem.getElem",
"Option.none",
"Option.map",
"Array.instGetElemNatLtSize",
"Array.instLawfulGetElemNatLtSize",
"Nat",
"congr",
"LT.lt",
"True",
"... | true |
TopologicalSpace.Opens.CompleteCopy.instMetricSpace._proof_4 | Mathlib.Topology.MetricSpace.Polish | [
"Filter.instMembership",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"gt_mem_nhds",
"Eq.mpr",
"Real",
"DivInvMonoid.toInv",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.lattice",
"CommRing.toNonUnitalCommRing",
"continuous_subtype_val",
"sub_self",
"... | false |
CategoryTheory.GradedObject.Monoidal.pentagon | Mathlib.CategoryTheory.GradedObject.Monoidal | [
"Eq.mpr",
"CategoryTheory.GradedObject.Monoidal.tensorHom",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.GradedObject.HasGoodTensor₁₂Tensor",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.GradedObject.Monoidal.tensorHom_com... | true |
_private.Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary.0.ModelWithCorners.isBoundaryPoint_iff_isBoundaryPoint_val._simp_1_1 | Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | [
"not_iff_not",
"Iff",
"propext",
"Eq",
"Not"
] | false |
_private.Mathlib.GroupTheory.DoubleCoset.0.DoubleCoset.iUnion_finset_rightRel_eq_univ_of_rightRel._simp_1_3 | Mathlib.GroupTheory.DoubleCoset | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Complex.ofReal_mul' | Mathlib.Data.Complex.Basic | [
"Real",
"HMul.hMul",
"Complex.im",
"Complex.instMul",
"Complex.ofReal",
"Complex.re",
"Real.instMul",
"Complex.ext",
"Complex.im_ofReal_mul",
"Complex",
"Eq",
"Complex.mk",
"instHMul",
"Complex.re_ofReal_mul"
] | true |
MvQPF.WEquiv.below.ind | Mathlib.Data.QPF.Multivariate.Constructions.Fix | [
"MvQPF.WEquiv.below.ind",
"PFunctor.B",
"instOfNatNat",
"MvPFunctor.A",
"MvQPF.WEquiv.below",
"instHAdd",
"HAdd.hAdd",
"Nat",
"MvQPF.WEquiv.ind",
"MvPFunctor.B",
"MvPFunctor.last",
"instAddNat",
"MvQPF",
"MvQPF.P",
"MvPFunctor.drop",
"OfNat.ofNat",
"MvPFunctor.wMk",
"TypeVec.Arrow"... | true |
Cardinal.ord_zero | Mathlib.SetTheory.Ordinal.Basic | [
"Ordinal.partialOrder",
"Cardinal",
"Ordinal.instOrderBot",
"PartialOrder.toPreorder",
"Cardinal.orderBot",
"Cardinal.ord",
"Ordinal.card",
"Cardinal.partialOrder",
"Cardinal.gc_ord_card",
"Ordinal.zero",
"GaloisConnection.l_bot",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Cardinal.instZero"... | true |
CategoryTheory.Grp.instMonoidalCategoryStruct.eq_1 | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.Grp.mk",
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Grp.instMonoidalCategoryStruct",
"CategoryTheory.GrpObj.instTensorUnit",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategoryStruct... | true |
_private.Init.Data.String.Lemmas.Order.0.String.Slice.Pos.le_ofSliceFrom_iff._simp_1_1 | Init.Data.String.Lemmas.Order | [
"Std.not_lt",
"LE.le",
"Std.LawfulOrderLT",
"LE",
"LT.lt",
"propext",
"Std.Total",
"Eq.symm",
"Eq",
"Not",
"LT"
] | false |
Lean.Lsp.instFromJsonVersionedTextDocumentIdentifier.fromJson | Lean.Data.Lsp.Basic | [
"Pure.pure",
"Lean.Json",
"Lean.instFromJsonNat",
"Lean.instFromJsonString",
"Monad.toApplicative",
"String",
"Lean.instFromJsonOption",
"Lean.Name.mkStr3",
"Lean.Json.getObjValAs?",
"Lean.Lsp.VersionedTextDocumentIdentifier.mk",
"Applicative.toPure",
"ToString.toString",
"Except.instMonad",... | true |
Module.AEval.instAddCommGroup._proof_6 | Mathlib.Algebra.Polynomial.Module.AEval | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Module.AEval",
"Algebra",
"AddCommGroup.toAddGroup",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"Module.A... | false |
Lean.Parser.Term.syntheticHole._regBuiltin.Lean.Parser.Term.syntheticHole.docString_3 | Lean.Parser.Term.Basic | [
"Lean.addBuiltinDocString",
"IO",
"Unit",
"Lean.Name.mkStr4"
] | false |
nhds_translation_mul_inv₀ | Mathlib.Topology.Algebra.GroupWithZero | [
"GroupWithZero.toMonoidWithZero",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"MulZeroClass.toMul",
"congrArg",
"GroupWithZero",
"DivisionMonoid.toDivInvOneMonoid",
"nhds",
"Homeomorph.mulRight₀",
"Ne",
"Homeomorph.comap_nhds_eq",
"M... | true |
Polynomial.IsDistinguishedAt.algEquivQuotient._proof_4 | Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | [
"CommRing",
"Semiring.toModule",
"IsAdicComplete.toIsHausdorff",
"CommSemiring.toSemiring",
"Polynomial.IsDistinguishedAt",
"Polynomial.IsDistinguishedAt.isWeierstrassDivisorAt'",
"Ideal",
"Polynomial",
"IsAdicComplete",
"CommRing.toCommSemiring",
"Ring.toAddCommGroup",
"Polynomial.toPowerSeri... | false |
Module.Relations.Solution.IsPresentationCore.noConfusion | Mathlib.Algebra.Module.Presentation.Basic | [
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"AddCommGroup",
"Module.Relations.Solution",
"Module.Relations.Solution.IsPresentationCore.noConfusionType",
"LinearMap",
"Module.Relations.Solution.IsPresentationCore",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Module.Relations",
"Module",
"Module.Relation... | false |
TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap | Mathlib.Algebra.Category.ModuleCat.Topology.Basic | [
"TopModuleCat.instCategory",
"TopModuleCat.instHasForget₂ContinuousLinearMapIdCarrierModuleCatLinearMap",
"CategoryTheory.Functor",
"TopModuleCat.indiscrete",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"LinearMap.instFunLike",
"ModuleCat.instConcreteCategoryLinearMap... | true |
IsMinFilter.min | Mathlib.Order.Filter.Extr | [
"Lattice.toSemilatticeSup",
"LinearOrder",
"PartialOrder.toPreorder",
"IsMinFilter",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"IsMinFilter.bicomp_mono",
"SemilatticeInf.toMin",
"LE.le",
"SemilatticeSup.toPartialOrder",
"instDistribLatticeOfLinearOrder",
"... | true |
Equiv.locallyFinite_comp_iff | Mathlib.Topology.LocallyFinite | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"Function.comp",
"Eq.mp",
"Equiv",
"LocallyFinite",
"TopologicalSpace",
"funext",
"Iff",
"Iff.intro",
"Equiv.injective",
"Equiv.symm",
"LocallyFinite.comp_injective",
"DFunLike.coe",
"EquivLike.toFunLike",
"Set"
] | true |
CategoryTheory.left_comp_retraction | Mathlib.CategoryTheory.Limits.Shapes.Reflexive | [
"Exists.choose_spec",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.IsCoreflexivePair",
"CategoryTheory.IsCoreflexivePair.common_retraction",
"And",
"CategoryTheory.commonRetraction",
"And.left",
"CategoryTheory.CategoryStruct.comp",
... | true |
CategoryTheory.Mat.instAddCommGroupHom._proof_10 | Mathlib.CategoryTheory.Preadditive.Mat | [
"AddMonoid.toAddSemigroup",
"Matrix",
"Finite",
"AddCommGroup.toAddGroup",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"instOfNatNat",
"Matrix.addSemigroup",
"autoParam",
"instHAdd",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"Ring.toAddCommGroup",
"Matrix.addMo... | false |
CategoryTheory.GrothendieckTopology.Subcanonical.recOn | Mathlib.CategoryTheory.Sites.Canonical | [
"CategoryTheory.GrothendieckTopology.Subcanonical",
"LE.le",
"CategoryTheory.GrothendieckTopology.Subcanonical.mk",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.GrothendieckTopology.Subcanonical.rec",
"CategoryTheory.Sheaf.canonicalTopology",
"CategoryTheory.GrothendieckTopology.instLEGrothend... | false |
Polynomial.smul_eq_C_mul | Mathlib.Algebra.Polynomial.Coeff | [
"Polynomial.C",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"HMul.hMul",
"congrArg",
"instDistribSMul",
"AddMonoid.toAddZeroClass",
"RingHom",
"Polynomial.coeff_C_mul",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Polynomial",
"Polynomial.coeff",
"... | true |
List.fst_mem_of_mem_zipIdx | Init.Data.List.Nat.Range | [
"List.map",
"Membership.mem",
"Eq.rec",
"Prod.fst",
"List",
"List.instMembership",
"Nat",
"List.zipIdx_map_fst",
"List.mem_map_of_mem",
"Prod",
"List.zipIdx",
"Eq"
] | true |
_private.Mathlib.RingTheory.Polynomial.GaussNorm.0.Polynomial.gaussNorm_mul_le._simp_1_4 | Mathlib.RingTheory.Polynomial.GaussNorm | [
"Ne",
"Polynomial",
"Nat",
"propext",
"Finset.Nonempty",
"Semiring",
"Zero.toOfNat0",
"Polynomial.instZero",
"OfNat.ofNat",
"Eq",
"Polynomial.support",
"Polynomial.support_nonempty"
] | false |
Turing.TM2.Stmt.pop.elim | Mathlib.Computability.TuringMachine.StackTuringMachine | [
"Turing.TM2.Stmt.ctorElim",
"PULift.up",
"Turing.TM2.Stmt.pop",
"Nat",
"Turing.TM2.Stmt.ctorIdx",
"Eq.symm",
"Eq",
"Turing.TM2.Stmt",
"Option"
] | false |
Subsemiring.gi | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"Subsemiring.closure_le",
"Subsemiring.instSetLike",
"Subsemiring.closure",
"PartialOrder.toPreorder",
"GaloisInsertion.mk",
"Preorder.toLE",
"Subsemiring.instPartialOrder",
"LE.le",
"Subsemiring",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"NonAssocSe... | true |
CategoryTheory.Limits.colimitQuotientCoproduct._proof_1 | Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.HasColimitsOfSize",
"CategoryTheory.Discrete.functor",
"CategoryTheory.SmallCategory",
"CategoryTheory.discreteCategory",
"CategoryTheory.Limits.HasColimit",
"CategoryTheory.Limits.hasColimitsOfSha... | false |
AffineSubspace.sOppSide_iff_exists_left | Mathlib.Analysis.Convex.Side | [
"Eq.mpr",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"Iff.rfl",
"IsStrictOrderedRing",
"AddCommGroup.toAddGroup",
"AffineSubspace.wOppSide_iff_exists_left",
"Membership.mem",
"Exists",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.... | true |
MvPolynomial.rename_expand | Mathlib.Algebra.MvPolynomial.Expand | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"DFunLike.congr_fun",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"Nat.instAddMonoid",
"MvPolynomial.rename_comp_expand",
"Algebra.id",
"CommSemiring",
"MvPolynomial.rename",
... | true |
MonovaryOn.subset | Mathlib.Order.Monotone.Monovary | [
"Membership.mem",
"MonovaryOn",
"HasSubset.Subset",
"Set.instMembership",
"Preorder",
"Set.instHasSubset",
"Set"
] | true |
HasProdUniformly.hasProdLocallyUniformly | Mathlib.Topology.Algebra.InfiniteSum.UniformOn | [
"UniformSpace",
"HasProdLocallyUniformly",
"Finset",
"PartialOrder.toPreorder",
"Eq.mp",
"id",
"_private.Mathlib.Topology.Algebra.InfiniteSum.UniformOn.0.HasProdUniformly.hasProdLocallyUniformly._simp_1_1",
"Finset.partialOrder",
"Finset.prod",
"Filter.atTop",
"TopologicalSpace",
"TendstoUnifo... | true |
gauge_gaugeRescale_le | Mathlib.Analysis.Convex.GaugeRescale | [
"GroupWithZero.toMonoidWithZero",
"Real.instLE",
"Real",
"instHSMul",
"instHDiv",
"gauge",
"gaugeRescale",
"Real.instZero",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"_private.Mathlib.Analysis.Convex.GaugeRescale.0.gauge_gaugeRescale_le._simp_1_2",
"Real.i... | true |
Lean.Meta.FoldDeclErrorRef | Mathlib.Lean.FoldEnvironment | [
"Lean.MessageData",
"List",
"IO.Ref"
] | true |
Module.Invertible.toSubmodule | Mathlib.RingTheory.PicardGroup | [
"Submodule",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"Algebra",
"Algebra.toModule",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"RingHomInvPair.i... | true |
Nat.instCommutativeHAdd | Init.Data.Nat.Basic | [
"Std.Commutative",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Std.Commutative.mk",
"Nat.add_comm"
] | true |
aeconst_of_dense_setOf_preimage_vadd_ae | Mathlib.Dynamics.Ergodic.Action.OfMinimal | [
"MeasureTheory.ae",
"ContinuousMap.continuous",
"MeasureTheory.Measure",
"ContinuousVAdd.continuous_vadd",
"R1Space",
"congrArg",
"ContinuousMap.curry",
"ContinuousMap.mk",
"ContinuousMap",
"MeasurableVAdd.toMeasurableConstVAdd",
"Set.univ",
"Set.eq_univ_iff_forall",
"ErgodicVAdd.toVAddInvar... | true |
CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq._proof_4 | Mathlib.CategoryTheory.Triangulated.Opposite.Basic | [
"AddMonoid.toAddSemigroup",
"Int",
"Int.instAddMonoid",
"autoParam",
"CategoryTheory.Pretriangulated.opShiftFunctorEquivalence_add_unitIso_hom_app_eq._auto_1",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"_private.Mathlib.CategoryTheory.Triangulated.Opposite.Basic.0.CategoryTheory.Pretriangulated... | false |
Lean.Meta.Simp.ConfigCtx.iota._inherited_default | Init.MetaTypes | [
"id",
"Bool.true",
"Bool"
] | false |
Std.TreeMap.getKey_maxKey! | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.getKey",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.DTreeMap.getKey_maxKey!",
"Std.TransCmp",
"Std.TreeMap.instMembership",
"Std.TreeMap.maxKey!",
"Inhabited",
"Eq",
"Std.TreeMap"
] | true |
AdjoinRoot.eval₂_root | Mathlib.RingTheory.AdjoinRoot | [
"Eq.mpr",
"CommRing",
"AdjoinRoot",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"AdjoinRoot.algebraMap_eq",
"RingHom",
"Algebra.id",
"id",
"Polynomial.eval₂",
"Polynomial.aeval_def",
"Polynomial",
"AdjoinRoot... | true |
IsDedekindDomain.HeightOneSpectrum.ofPrime | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"CommRing",
"IsDedekindDomain.HeightOneSpectrum.mk",
"CommSemiring.toSemiring",
"IsDedekindDomain.HeightOneSpectrum",
"Prime",
"CommSemiring.toCommMonoidWithZero",
"Ideal.instIdemCommSemiring",
"Ideal",
"CommRing.toCommSemiring",
"IsDedekindDomain.HeightOneSpectrum.ofPrime._proof_1",
"IsDedekind... | true |
_private.Mathlib.Algebra.BigOperators.Group.Finset.Gaps.0.Finset.prod_eq_prod_range_intervalGapsWithin._proof_1_3 | Mathlib.Algebra.BigOperators.Group.Finset.Gaps | [
"False",
"Set.mem_Iio",
"Preorder.toLT",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Classical.byContradiction",
"Lean.Grind.Nat.lt_eq",
"Membership.mem",
"Eq.mp",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Nat.instPreorder",
"Nat",
"LT.lt",
... | false |
Int.instLawfulOrderOrd | Init.Data.Int.Compare | [
"Std.LawfulOrderOrd",
"Std.LawfulOrderOrd.mk",
"Int",
"Int.isGE_compare",
"instOrdInt",
"Int.isLE_compare",
"Int.instLEInt"
] | true |
CategoryTheory.Limits.PreservesColimitsOfSize.preservesFiniteColimits | Mathlib.CategoryTheory.Limits.Preserves.Finite | [
"CategoryTheory.Limits.PreservesColimitsOfSize",
"CategoryTheory.Functor",
"CategoryTheory.FinCategory.categoryAsType",
"CategoryTheory.Limits.PreservesFiniteColimits.mk",
"CategoryTheory.FinCategory.fintypeObj",
"CategoryTheory.SmallCategory",
"CategoryTheory.Limits.PreservesColimitsOfSize.preservesCol... | true |
_private.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AC.0.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.VarStateM.computeCoefficients.go | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AC | [
"Lean.Expr.brecOn",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Op",
"_private.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AC.0.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.VarStateM.computeCoefficients.go._f",
"Lean.Expr",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.CoefficientsMap",
"Lean.Elab.Tact... | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.getMsbD_rotateLeft_of_lt._proof_1_1 | Init.Data.BitVec.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"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.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Om... | false |
Vector.find?.eq_1 | Init.Data.Vector.Lemmas | [
"Vector",
"Nat",
"Bool",
"Eq.refl",
"Vector.find?",
"Eq",
"Vector.toArray",
"Option",
"Array.find?"
] | true |
Filter.sup_limsup | Mathlib.Order.LiminfLimsup | [
"Filter.instMembership",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"iInf",
"CompleteLattice.toLattice",
"Iff.of_eq",
"congrArg",
"iSup",
"Filter.NeBot",
"Order.Coframe.toCompleteLattice",
"CompleteDistribLattice",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"Eq.rec",
... | true |
SSet.RelativeMorphism.HomotopyClass | Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | [
"SSet.Subcomplex.toSSet",
"SSet.RelativeMorphism",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"SSet.RelativeMorphism.Homotopy",
"SSet",
"CategoryTheory.types",
"SimplexCategory",
"Nonempty",
"CategoryTheory.Category.opposite",
"Cate... | true |
_private.Lean.Language.Basic.0.Lean.Language.SnapshotTree.forM.match_1 | Lean.Language.Basic | [
"Lean.Language.SnapshotTree",
"Lean.Language.SnapshotTask",
"Array",
"Lean.Language.Snapshot",
"Lean.Language.SnapshotTree.casesOn",
"Lean.Language.SnapshotTree.mk"
] | false |
MonCat.sectionsSubmonoid | Mathlib.Algebra.Category.MonCat.Limits | [
"CategoryTheory.Functor",
"MonoidHom.instFunLike",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"Subsemigroup.mk",
"CategoryTheory.Functor.comp",
"Membership.mem",
"MulOne.toMul",
"MonCat",
"MonCat.instCategory",
"MonCat.sectionsSubmonoid._proo... | true |
Set.fintypeProd | Mathlib.Data.Finite.Prod | [
"Set.instSProd",
"SProd.sprod",
"Finset",
"Set.fintypeProd._proof_1",
"Set.Elem",
"Fintype.ofFinset",
"Set.toFinset",
"Finset.instSProd",
"Fintype",
"Prod",
"Set"
] | true |
postcomp_compactConvergenceCLM_apply | Mathlib.Topology.Algebra.Module.Spaces.CompactConvergenceCLM | [
"ContinuousLinearMap.comp",
"UniformConvergenceCLM.instAddCommGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"UniformConvergenceCLM.instTopologicalSpace",
"setOf",
"AddCommGroup.toAddGroup",
"RingHom",
"NormedF... | true |
_private.Init.Data.UInt.Bitwise.0.UInt64.neg_one_shiftLeft_or_shiftLeft._simp_1_1 | Init.Data.UInt.Bitwise | [
"instHOrOfOrOp",
"UInt64",
"HShiftLeft.hShiftLeft",
"HOr.hOr",
"UInt64.shiftLeft_or",
"instOrOpUInt64",
"instShiftLeftUInt64",
"instHShiftLeftOfShiftLeft",
"Eq.symm",
"Eq"
] | false |
Nat.primesLE_card_eq_primeCounting | Mathlib.NumberTheory.PrimeCounting | [
"congrArg",
"Nat.primeCounting'",
"Nat.primesLE",
"instOfNatNat",
"Nat.primeCounting",
"instHAdd",
"HAdd.hAdd",
"Nat.primesBelow_card_eq_primeCounting'",
"Nat",
"True",
"eq_self",
"Finset.card",
"of_eq_true",
"instAddNat",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Eq.trans"
] | true |
CategoryTheory.Localization.induction_structuredArrow | Mathlib.CategoryTheory.Localization.StructuredArrow | [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HEq.refl",
"_private.Mathlib.CategoryTheory.Localization.StructuredArrow.0.CategoryTheory.Localization.induct... | true |
Lean.Elab.DefViewElabHeader.noConfusion | Lean.Elab.MutualDef | [
"Lean.Elab.BodyProcessedSnapshot",
"Lean.Elab.Tactic.TacticParsedSnapshot",
"Lean.Elab.DefViewElabHeader.noConfusionType",
"Lean.Elab.DefViewElabHeader.casesOn",
"Lean.Elab.DefViewElabHeaderData",
"Lean.Language.SnapshotBundle",
"Eq.ndrec",
"Eq.refl",
"Lean.Elab.DefViewElabHeader",
"Eq",
"Lean.E... | false |
pow_mulLeftLinearMap | Mathlib.Data.Matrix.Bilinear | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Module.End.instMonoid",
"instSMulOfMul",
"Matrix.module",
"DistribMulAction.toDistribSMul",
"Matrix",
"AddMonoid.toAddZeroClass",
"pow_mulLeftLinearMap._f",
"AddZeroClass.toAddZero",
"Nat.brecOn",
"DistribSMul.toSMulZeroClass",
"Matrix.addCommMonoid"... | true |
Lean.Compiler.CSimp.Entry.mk.noConfusion | Lean.Compiler.CSimpAttr | [
"Lean.Compiler.CSimp.Entry.mk",
"id",
"Lean.Name",
"Lean.Compiler.CSimp.Entry.noConfusion",
"Eq",
"Lean.Compiler.CSimp.Entry"
] | false |
FunLike.addCommGroup._proof_5 | Mathlib.Data.FunLike.Group | [
"instHSMul",
"IsSMulApply",
"SMul",
"FunLike.coe_smul'",
"AddMonoid.toNSMul",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"AddGroup.toSubNegMonoid",
"Nat",
"Pi.instSMul",
"HSMul.hSMul",
"SubNegMonoid.toAddMonoid",
"Eq",
"DFunLike.coe",
"FunLike"
] | false |
Lean.Meta.Simp.SimprocQ | Qq.Simp | [
"Lean.Expr.sort",
"Lean.Level",
"Lean.Meta.Simp.SimpM",
"Qq.Quoted",
"Lean.Meta.Simp.StepQ"
] | true |
DirectLimit.Ring.hom_ext | Mathlib.Algebra.Colimit.DirectLimit | [
"DirectLimit.setoid",
"congrArg",
"Preorder.toLE",
"RingHom",
"id",
"LE.le",
"DirectLimit",
"Quotient.mk",
"DirectLimit.Ring.of",
"RingHom.ext",
"DirectLimit.instNonAssocSemiringOfRingHomClass",
"RingHom.comp",
"NonAssocSemiring",
"RingHom.instFunLike",
"IsDirectedOrder",
"Nonempty",
... | true |
MeasureTheory.Submartingale.stoppedAbove | Mathlib.Probability.Martingale.BorelCantelli | [
"InnerProductSpace.toNormedSpace",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"Real.lattice",
"Real.instRCLike",
"instHasSolidNormReal",
"PartialOrder.toPreorder",
"instClosedIciTopology",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Submartingale",
"MeasureTheory.stoppedAbove",
"... | true |
CategoryTheory.MorphismProperty.HasPullbacksAlong.hasPullback | Mathlib.CategoryTheory.MorphismProperty.Limits | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.MorphismProperty.HasPullbacksAlong",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
_private.Lean.Elab.BuiltinTerm.0.Lean.Elab.Term.elabStrLit.match_1 | Lean.Elab.BuiltinTerm | [
"Unit.unit",
"String",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
_private.Lean.Elab.Structure.0.Lean.Elab.Command.Structure.withFields.go._sparseCasesOn_5 | Lean.Elab.Structure | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.one_ascFactorial.match_1_1 | Mathlib.Data.Nat.Factorial.Basic | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
CategoryTheory.InitiallySmall.instCategoryCofilteredInitialModel | Mathlib.CategoryTheory.Filtered.FinallySmall | [
"CategoryTheory.InitiallySmall",
"CategoryTheory.Functor",
"CategoryTheory.InitiallySmall.exists_of_isCofiltered",
"CategoryTheory.IsCofiltered",
"CategoryTheory.LocallySmall",
"CategoryTheory.Functor.Initial",
"Exists",
"CategoryTheory.InitiallySmall.instCategoryCofilteredInitialModel._proof_1",
"C... | true |
_private.Batteries.Data.Array.Lemmas.0.Array.extract_append_of_stop_le_size_left._proof_1_13 | Batteries.Data.Array.Lemmas | [
"Array.instAppend",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"HMul.hMul",
"Int.Linear.norm_le",
"eq_false",
"Lean.Grind.CommRing.Expr.var",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"Lean.Grind.Order.le_of_eq_2_k",
"Std.IsLinearPreorder.toIsPr... | false |
finSuccEquiv'_symm_coe_below | Mathlib.Logic.Equiv.Fin.Basic | [
"Equiv.instEquivLike",
"Option.some",
"Equiv",
"instOfNatNat",
"instHAdd",
"finSuccEquiv'_symm_some_below",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instLTFin",
"instAddNat",
"Equiv.symm",
"Fin.castSucc",
"OfNat.ofNat",
"Fin",
"Eq",
"DFunLike.coe",
"finSuccEquiv'",
"EquivLike.toFunLike",
... | true |
Algebra.Generators.H1Cotangent.δ | Mathlib.RingTheory.Kaehler.JacobiZariski | [
"LinearMap.baseChange",
"Algebra.Generators.toComp",
"CommRing",
"Algebra.to_smulCommClass",
"Algebra.Extension.commRing",
"Algebra.Generators.CotangentSpace.compEquiv._proof_6",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Algebra.Extension.instModuleCotangent",
"IsScala... | true |
Option.map_min | Init.Data.Option.Lemmas | [
"congrArg",
"Option.casesOn",
"Option.some",
"Option.instMin",
"Option.min_none_right",
"Min",
"Option.none",
"Option.map",
"congr",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"congrFun'",
"Eq.symm",
"Eq",
"Min.min",
"Eq.trans",
"Option.min_none_left",
"Option"
] | true |
Ideal.quotientMap.eq_1 | Mathlib.RingTheory.Ideal.Quotient.Operations | [
"Semiring.toModule",
"Ideal.Quotient.mk",
"RingHom.quotientKerEquivRange._proof_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RingHom",
"Membership.mem",
"Ideal.IsTwoSided",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"HasQuotient.Quotient"... | true |
TopHom.map_top' | Mathlib.Order.Hom.Bounded | [
"TopHom",
"TopHom.toFun",
"Top.top",
"Eq",
"Top"
] | true |
inf_lt_right | Mathlib.Order.Lattice | [
"Preorder.toLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"inf_le_right",
"SemilatticeInf.toPartialOrder",
"Ne",
"SemilatticeInf.toMin",
"LE.le",
"SemilatticeInf",
"Iff",
"LT.lt",
"Iff.trans",
"LE.le.lt_iff_ne'",
"Eq",
"Not",
"right_eq_inf",
"Min.min",
"not_congr"
] | true |
Mathlib.Tactic.RingNF.Config._sizeOf_inst | Mathlib.Tactic.Ring.RingNF | [
"SizeOf.mk",
"SizeOf",
"Mathlib.Tactic.RingNF.Config._sizeOf_1",
"Mathlib.Tactic.RingNF.Config"
] | false |
Action.forget_ε | Mathlib.CategoryTheory.Action.Monoidal | [
"Monoid",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.CategoryStruct.id",
"Action.instMonoidalForget",
"Action.instMonoidalCategory",
"Action.forget",
"CategoryTheory.Functor.Monoidal.toLaxMonoid... | true |
Representation.LinearizeMonoidal.η._proof_1 | Mathlib.RepresentationTheory.Action | [
"LinearMap.id",
"Monoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Representation",
"MonoidHom.instFunLike",
"Representation.linearize_single",
"Semiring.toModule",
"Finsupp.single_eq_same",
"LinearMap.comp.congr_simp",
"Finsupp.module",
"CategoryTheory.typesCartesianMonoidalCategory",
"Mon... | false |
Irrational.ne_one | Mathlib.NumberTheory.Real.Irrational | [
"Real",
"Irrational.ne_nat",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"Eq.mp",
"Ne",
"Real.instRing",
"instOfNatNat",
"Nat.cast",
"Real.instOne",
"AddMonoidWithOne.toOne",
"Irrational",
"Nat",
"One.toOfNat1",
"OfNat.ofNat",
"Nat.cast_one",
"Ring.toAddGroupWithOne",
"Real.i... | true |
forall_imp_iff_exists_imp | Mathlib.Logic.Basic | [
"False",
"not_forall_not",
"Classical.propDecidable",
"Exists",
"dite",
"And",
"Iff",
"And.left",
"Classical.not_imp",
"Iff.intro",
"Iff.mp",
"Nonempty",
"_private.Mathlib.Logic.Basic.0.forall_imp_iff_exists_imp.match_1_1",
"_private.Mathlib.Logic.Basic.0.forall_imp_iff_exists_imp.match_1_... | true |
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.minView.match_1.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Std.DTreeMap.Internal.Impl.Tree.mk",
"Std.DTreeMap.Internal.Impl.View",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.size",
"instHAdd",
"HAdd.hAdd",
"Std.DTreeMap.Internal.Impl.View.mk",
"Nat",
"instAddNat",
"Eq.refl",
"Std.DTreeMap.Internal.Impl.minView.match_1",
"Eq",
... | true |
PMF.support_uniformOfFintype | Mathlib.Probability.Distributions.Uniform | [
"Set.ext",
"False",
"congrArg",
"PMF",
"Set.mem_univ._simp_1",
"PMF.instFunLike",
"ENNReal.inv_eq_zero._simp_1",
"Membership.mem",
"PMF.support",
"Fintype.card",
"PMF.uniformOfFintype_apply",
"PMF.uniformOfFintype",
"AddMonoidWithOne.toNatCast",
"Ne",
"AddCommMonoidWithOne.toAddMonoidWit... | true |
Mathlib.Tactic.BicategoryLike.Mor₂Iso._sizeOf_inst | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.Mor₂Iso",
"SizeOf.mk",
"SizeOf",
"Mathlib.Tactic.BicategoryLike.Mor₂Iso._sizeOf_1"
] | false |
CommGrpCat.Forget₂.createsLimit.eq_1 | Mathlib.Algebra.Category.Grp.Limits | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"CategoryTheory.Limits.IsLimit.ofFaithful",
"MonCat.limitMonoid",
"CategoryTheory.Limits.Cone.π",
"GrpCat.hasForgetToMonCat",
"MulOne.toOne",
"CategoryTheory.Functor",
"GrpCat.limitConeIsLimit",
"CategoryTheory.Limits.Cone",
"CategoryTheory.LiftsToLim... | true |
CategoryTheory.NatTrans.PullbackShift.natIsoId.eq_1 | Mathlib.CategoryTheory.Shift.Pullback | [
"CategoryTheory.Functor",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"AddZeroClass.toAddZero",
"CategoryTheory.Iso.refl",
"CategoryTheory.Iso",
"CategoryTheory.PullbackShift",
"CategoryTheory.NatTrans.PullbackShift.natIsoId",
"AddMonoid",
"Eq.refl... | true |
NormedAddGroupHom.norm_id_le | Mathlib.Analysis.Normed.Group.Hom | [
"Norm.norm",
"Real.instLE",
"Real",
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"HMul.hMul",
"Real.instZero",
"Real.instZeroLEOneClass",
"instReflLe",
"congrArg",
"Std.le_refl._simp_1",
"NormedAddGroupHom.id",
"Real.semiring",
"LE.le",
"NormedAddGroupHom.opNorm_le_bound",
"zero_le_o... | true |
SimpleGraph.not_isDiag_of_mem_edgeSet | Mathlib.Combinatorics.SimpleGraph.Basic | [
"SimpleGraph.Adj.ne",
"Membership.mem",
"Prod.mk",
"Prod.fst",
"SimpleGraph.edgeSet",
"SimpleGraph",
"Sym2.ind",
"Set.instMembership",
"Prod.snd",
"Sym2",
"Not",
"Sym2.IsDiag",
"Set"
] | true |
Array.append_inj_left | Init.Data.Array.Lemmas | [
"Array.instAppend",
"Array",
"instHAppendOfAppend",
"And.left",
"Nat",
"Array.append_inj",
"Eq",
"Array.size",
"HAppend.hAppend"
] | true |
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