name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Data.Nat.Cast.NeZero.0.NeZero.one_le._proof_1_1 | Mathlib.Data.Nat.Cast.NeZero | [
"False",
"of_decide_eq_true",
"eq_false",
"Classical.byContradiction",
"Zero.ofOfNat0",
"HSub.hSub",
"Nat.not_le_eq",
"Eq.mp",
"id",
"instSubNat",
"Ne",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Simproc.add_le_le",
"Bool.true",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat.le_zero... | false |
CategoryTheory.Preadditive.toCommGrp_obj_grp | Mathlib.CategoryTheory.Preadditive.CommGrp_ | [
"CategoryTheory.CommGrp.instCategory",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.CommGrp",
"CategoryTheory.BraidedCategory",
"CategoryTheory.Preadditive",
"CategoryTheory.Preadditive.toCommGrp",
"CategoryTheory.GrpObj... | true |
Plausible.Gen.oneOfWithDefault | Plausible.Gen | [
"ReaderT",
"ULift",
"HSub.hSub",
"List.getD",
"ReaderT.instMonad",
"_private.Plausible.Gen.0.Plausible.Gen.oneOfWithDefault.match_1",
"_private.Plausible.Gen.0.Plausible.Gen.oneOfWithDefault._proof_1",
"Subtype",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Id",
"Except.instMonad",... | true |
CategoryTheory.FinCategory.objAsTypeToAsType | Mathlib.CategoryTheory.FinCategory.AsType | [
"CategoryTheory.Functor",
"CategoryTheory.FinCategory.categoryAsType",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.FinCategory.objAsTypeToAsType._proof_1",
"CategoryTheory.Functor.mk",
"CategoryTheory.FinCategory.ObjAsType",
"Fintype.card",
"id",
... | true |
CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv._proof_4 | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | [
"CategoryTheory.Limits.FormalCoproduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.FormalCoproduct.Hom",
"Subtype",
"Prod.mk",
"CategoryTheory.Limits.FormalCoproduct.Hom.f",
"Prod.fst",
"Subtype.mk",
"_private.Mathlib.CategoryTheory.Limits.FormalC... | false |
Lean.Server.FileWorker.WorkerState.importCachingTask? | Lean.Server.FileWorker | [
"Lean.Server.FileWorker.AvailableImportsCache",
"Lean.Server.ServerTask",
"IO.Error",
"Except",
"Lean.Server.FileWorker.WorkerState",
"Option"
] | true |
_private.Mathlib.Tactic.Ring.Common.0.Mathlib.Tactic.Ring.Common.ExBase.toProd.match_1 | Mathlib.Tactic.Ring.Common | [
"Mathlib.Tactic.Ring.Common.Result.mk",
"Lean.Expr.const",
"Mathlib.Tactic.Ring.Common.Result",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Lean.Literal.natVal",
"Qq.Quoted",
"Mathlib.Tactic.Ring.Common.Result.casesOn",
"Qq.Quoted.unsafeMk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level... | false |
LinearOrder.mkOfAddGroupCone.eq_1 | Mathlib.Algebra.Order.Group.Cone | [
"SetLike",
"NegZeroClass.toNeg",
"Preorder.toLT",
"LinearOrder.mkOfAddGroupCone._proof_1",
"Max.mk",
"LinearOrder",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"Ord.mk",
"AddCommGroup.toAddGroup",
"Min.mk",
"Membership.mem",
"decidableEqOfDecidableLE",
"AddCommGroup",
"Lin... | true |
PEquiv.trans_assoc | Mathlib.Data.PEquiv | [
"PEquiv.instFunLikeOption",
"Option.bind_assoc",
"PEquiv",
"Eq",
"DFunLike.coe",
"PEquiv.ext",
"Option",
"PEquiv.trans"
] | true |
Path.Homotopic.proj.eq_1 | Mathlib.Topology.Homotopy.Product | [
"Pi.topologicalSpace",
"ContinuousMap.mk",
"Path.Homotopic.Quotient.map",
"Path.Homotopic.Quotient",
"TopologicalSpace",
"continuous_apply",
"Path.Homotopic.proj",
"Eq.refl",
"Eq"
] | true |
UInt16.ofInt_one | Init.Data.UInt.Lemmas | [
"UInt16.ofInt",
"Int",
"UInt16",
"instOfNat",
"OfNat.ofNat",
"Eq",
"UInt16.instOfNat",
"rfl"
] | true |
FormalMultilinearSeries.id._proof_4 | Mathlib.Analysis.Analytic.Composition | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"IsBoundedSMul.toUniformContinuousConstSMul"... | false |
Equiv.Perm.Basis.toCentralizer_apply | Mathlib.GroupTheory.Perm.Centralizer | [
"MonoidHom.instFunLike",
"Equiv.instEquivLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Finset",
"Subgroup.centralizer",
"Equiv.Perm.cycleFactorsFinset",
"Membership.mem",
"Set.instSingletonSet",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"Equiv.Perm.OnCycleFactors.range_toPermHom'",
"G... | true |
GaloisCoinsertion.liftCompleteLattice.eq_1 | Mathlib.Order.GaloisConnection.Basic | [
"GaloisCoinsertion.choice",
"GaloisCoinsertion.liftCompleteLattice",
"GaloisCoinsertion.liftCompleteLattice._proof_3",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"GaloisCoinsertion.liftCompleteLattice._proof_2",
"GaloisCoinsertion.liftCompleteLattice._proof_1",
"InfSet.mk",
"CompleteLat... | true |
_private.Lean.Meta.InferType.0.Lean.Meta.isProofQuickApp | Lean.Meta.InferType | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.instInhabitedMetaM",
"Nat",
"Lean.LBool"
] | true |
ClopenUpperSet.ext_iff | Mathlib.Topology.Sets.Order | [
"HEq.refl",
"Eq.casesOn",
"LE",
"TopologicalSpace",
"Iff",
"SetLike.coe",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"ClopenUpperSet.ext",
"ClopenUpperSet",
"Eq.symm",
"Eq",
"ClopenUpperSet.instSetLike",
"Set"
] | true |
Equiv.ext_iff | Mathlib.Logic.Equiv.Defs | [
"Equiv.instEquivLike",
"HEq.refl",
"Eq.casesOn",
"Equiv",
"Equiv.ext",
"Iff",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
_private.Mathlib.Algebra.Polynomial.Derivative.0.Polynomial.iterate_derivative_prod_X_sub_C.match_1_4 | Mathlib.Algebra.Polynomial.Derivative | [
"SProd.sprod",
"Finset",
"HSub.hSub",
"Classical.propDecidable",
"Membership.mem",
"Prod.mk",
"instSubNat",
"_private.Mathlib.Algebra.Polynomial.Derivative.0.Polynomial.iterate_derivative_prod_X_sub_C.match_1_1",
"Prod.fst",
"Finset.instSProd",
"instHSub",
"Finset.instSetLike",
"Finset.power... | false |
Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.blast | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Mul | [
"Std.Sat.AIG.RefVec.get",
"Std.Sat.AIG.Decl",
"BitVec.instOfNat",
"Std.Sat.AIG.RefVecEntry.vec",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastMul._proof_2",
"BitVec",
"Eq.rec",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastMul.blast._proof_2",
"instOfNatNat",
"Std.Sat.AIG.BinaryRefVec",
"LE.le",
"ins... | true |
Std.Internal.List.Const.getKeyD_modifyKey_self | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"BEq.rfl",
"congrArg",
"Std.Internal.List.getKeyD",
"instDecidableEqBool",
"ite_cond_eq_true",
"Std.Internal.List.Const.modifyKey",
"Bool.true",
"List",
"EquivBEq.toReflBEq",
"Std.Internal.List.containsKey",
"BEq.beq",
"EquivBEq",
"True",
"eq_self",
"S... | true |
String.Slice.Pattern.ForwardSliceSearcher.instToForwardSearcher | Init.Data.String.Pattern.String | [
"String.Slice",
"String.Slice.Pattern.ForwardSliceSearcher.iter",
"String.Slice.Pattern.ToForwardSearcher",
"String.Slice.Pattern.ToForwardSearcher.mk",
"String.Slice.Pattern.ForwardSliceSearcher"
] | true |
TopCat.GlueData.MkCore.cocycle | Mathlib.Topology.Gluing | [
"TopologicalSpace.Opens.instPartialOrder",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"ContinuousMap",
"TopCat.GlueData.MkCore.t",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Membership.mem",
"Subtype",
"Preorder.smallCategory",
"TopCat.GlueData.MkCore.J",
"Topolog... | true |
MonCat.Colimits.monoidColimitType._proof_2 | Mathlib.Algebra.Category.MonCat.Colimits | [
"MonCat.Colimits.Relation.mul_2",
"CategoryTheory.Functor",
"Mul.mk",
"One.mk",
"HMul.hMul",
"MonCat.Colimits.colimitSetoid",
"MonCat.Colimits.Prequotient",
"Semigroup.mk",
"Quotient.map₂",
"MonCat",
"npowRecAuto",
"instOfNatNat",
"Quotient.ind₂",
"Quotient.ind",
"MonCat.instCategory",
... | false |
_private.Mathlib.Data.Countable.Defs.0.Finite.to_countable.match_1 | Mathlib.Data.Countable.Defs | [
"Exists",
"Equiv",
"Nonempty.intro",
"Exists.casesOn",
"Nat",
"Nonempty.casesOn",
"Exists.intro",
"Nonempty",
"Fin"
] | false |
LocallyConstant.instAddGroup._proof_6 | Mathlib.Topology.LocallyConstant.Algebra | [
"LocallyConstant.smul",
"instHSMul",
"LocallyConstant",
"Int",
"TopologicalSpace",
"AddGroup",
"AddGroup.toSubNegMonoid",
"HSMul.hSMul",
"LocallyConstant.instFunLike",
"Eq",
"DFunLike.coe",
"rfl",
"SubNegMonoid.toZSMul"
] | false |
NormedAddGroupHom.toAddMonoidHomClass | Mathlib.Analysis.Normed.Group.Hom | [
"AddMonoidHom.map_zero",
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"NormedAddGroupHom.map_add'",
"NormedAddGroupHom.funLike",
"ZeroHomClass.mk",
"AddZero.toZero",
"AddMonoidHomClass.mk",
... | true |
WType.instEncodable | Mathlib.Data.W.Basic | [
"Nat.encodable",
"WType",
"Nat.rec",
"WType.instEncodable._proof_2",
"Sigma.fst",
"WType.instEncodable._proof_1",
"LE.le",
"instLENat",
"Subtype.mk",
"Fintype",
"Encodable.ofLeftInverse",
"Nat",
"_private.Mathlib.Data.W.Basic.0.WType.WType'",
"Sigma.mk",
"_private.Mathlib.Data.W.Basic.0.... | true |
PredOrder.ofPredLeIff | Mathlib.Order.SuccPred.Basic | [
"Preorder.toLT",
"PredOrder.ofPredLeIff._proof_1",
"PredOrder.ofPredLeIff._proof_2",
"Preorder.toLE",
"PredOrder.mk",
"LE.le",
"Iff",
"LT.lt",
"PredOrder.ofPredLeIff._proof_3",
"PredOrder",
"Preorder"
] | true |
Module.supportDim_le_of_surjective | Mathlib.RingTheory.KrullDimension.Module | [
"WithBot.instPreorder",
"CommRing",
"WithBot",
"Preorder.toLT",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"LinearMap.instFunLike",
"Preorder.toLE",
"Membership.mem",
"AddCommGroup",
"Set.Elem",
"instPreorderENat",
"LE.le",
"LinearMap",
"Subty... | true |
Matroid.cRk_map_eq | Mathlib.Combinatorics.Matroid.Rank.Cardinal | [
"Eq.mpr",
"Matroid.cRk_inter_ground",
"Matroid.map_ground",
"Cardinal",
"Set.inter_subset_right._simp_1",
"congrArg",
"Matroid.E",
"Set.image_preimage_inter",
"id",
"HasSubset.Subset",
"Set.instInter",
"Matroid.cRk_map_image",
"Inter.inter",
"Set.preimage",
"Matroid.cRk",
"of_eq_true",... | true |
Subarray.size_le_array_size | Init.Data.Array.Subarray | [
"Eq.mpr",
"Subarray",
"_private.Init.Data.Array.Subarray.0.Subarray.size_le_array_size._simp_1_3",
"congrArg",
"HSub.hSub",
"Nat.sub_le",
"id",
"Std.Slice.Internal.SubarrayData.mk",
"instSubNat",
"LE.le",
"Subarray.stop",
"instLENat",
"Array",
"instHSub",
"Nat.le_trans",
"Std.Slice.mk"... | true |
_private.Batteries.Data.Array.Scan.0.Array.scanrM.loop_toList._proof_1_4 | Batteries.Data.Array.Scan | [
"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'",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"... | false |
Equiv.sumSigmaDistrib_symm_apply | Mathlib.Logic.Equiv.Sum | [
"Equiv.instEquivLike",
"Sum",
"Equiv",
"Sigma.fst",
"Sum.inl",
"Equiv.sumSigmaDistrib",
"Sum.inr",
"Eq.refl",
"Sigma.mk",
"Equiv.symm",
"Sigma.snd",
"Eq",
"DFunLike.coe",
"Sigma",
"EquivLike.toFunLike",
"Sum.elim"
] | true |
MonoidWithZeroHom.ValueGroup₀.instIsOrderedMonoid | Mathlib.Algebra.Order.GroupWithZero.Range | [
"CommMonoidWithZero.toCommMonoid",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"IsOrderedMonoid",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"Subtype.instLinearOrder",
"LinearOrderedCommMonoidWithZero.toLinearOrder",
"MonoidWithZeroHo... | true |
_private.Mathlib.Order.Atoms.0.IsAtomic.Set.Iic.isAtomic.match_1 | Mathlib.Order.Atoms | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Exists",
"PartialOrder",
"LE.le",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"IsAtom"
] | false |
Lean.Elab.Tactic.BVDecide.Frontend.TacticContext.ctorIdx | Lean.Elab.Tactic.BVDecide.Frontend.LRAT | [
"Lean.Elab.Tactic.BVDecide.Frontend.TacticContext",
"Nat"
] | false |
Lean.Widget.RpcEncodablePacket.«_@».Lean.Widget.InteractiveGoal.562241082._hygCtx._hyg.1.rec | Lean.Widget.InteractiveGoal | [
"Lean.Json",
"Lean.Widget.RpcEncodablePacket._@.Lean.Widget.InteractiveGoal.562241082._hygCtx._hyg.1",
"Lean.Widget.RpcEncodablePacket.mk._@.Lean.Widget.InteractiveGoal.562241082._hygCtx._hyg.1",
"Option"
] | false |
Int.sub_lt_self | Init.Data.Int.Order | [
"Eq.mpr",
"Trans.trans",
"congrArg",
"HSub.hSub",
"Int.neg_neg_of_pos",
"id",
"Int.instNegInt",
"Int",
"instTransEq",
"Int.add_lt_add_left",
"Int.instLTInt",
"instHAdd",
"instHSub",
"instOfNat",
"HAdd.hAdd",
"LT.lt",
"Int.instAdd",
"Eq.refl",
"Int.instSub",
"instTransEq_1",
"... | true |
Commute.eq | Mathlib.Algebra.Group.Commute.Defs | [
"HMul.hMul",
"Mul",
"Commute",
"Eq",
"instHMul"
] | true |
TopologicalSpace.Opens.frameMinimalAxioms._proof_4 | Mathlib.Topology.Sets.Opens | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"TopologicalSpace.Opens.instCompleteLattice",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Preorder.toLE",
"LE.le",
"TopologicalSpace",
"Lattice.le_inf",
"Lattice.inf",
"SemilatticeSup.toPartialOrder"
] | false |
AddSubmonoid.addUnitsEquivAddUnitsType._proof_3 | Mathlib.Algebra.Group.Submonoid.Units | [
"AddGroup.toSubtractionMonoid",
"AddSubmonoid.coe_val_add_coe_neg_val",
"NegZeroClass.toNeg",
"AddUnits.val",
"Function.LeftInverse",
"AddSubmonoid.addUnitsEquivAddUnitsType.match_1",
"AddSubmonoid.toAddMonoid",
"AddMonoid.toAddZeroClass",
"AddSubmonoid.addUnits._proof_1",
"Membership.mem",
"Add... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.get?_eq_some_iff._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
_private.Batteries.Data.List.Lemmas.0.List.getElem_filter_eq_getElem_getElem_findIdxs_sub._proof_1_30 | Batteries.Data.List.Lemmas | [
"List.countP",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"HMul.hMul",
"Int.Linear.norm_le",
"Lean.Grind.CommRing.Expr.var",
"Int.Linear.Expr.eq_of_norm_eq",
"Lean.Grind.Order.eq_of_le_of_le_0",
"congrArg",
"Lean.Grind.Semiring.mul_one",
"List.leng... | false |
TensorProduct.smul_tmul | Mathlib.LinearAlgebra.TensorProduct.Defs | [
"Monoid",
"TensorProduct.CompatibleSMul",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"TensorProduct.CompatibleSMul.smul_tmul",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
... | true |
_private.Mathlib.RingTheory.Polynomial.Resultant.Basic.0.Polynomial.resultant_add_mul_monomial_right._proof_1_25 | Mathlib.RingTheory.Polynomial.Resultant.Basic | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Preorder.toLT",
"HMul.hMul",
"Lean.Grind.not_and",
"Int.Linear.Expr.eq_of_norm_eq",
"Lean.Grind.ToInt.toInt",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Int.Linear.le_neg",
"Int... | false |
Mathlib.Tactic.Translate.TranslationInfo.recOn | Mathlib.Tactic.Translate.Core | [
"Mathlib.Tactic.Translate.TranslationInfo.mk",
"Mathlib.Tactic.Translate.TranslationInfo.rec",
"Mathlib.Tactic.Translate.Reorder",
"Mathlib.Tactic.Translate.RelevantArg",
"Mathlib.Tactic.Translate.TranslationInfo",
"Lean.Name"
] | false |
MeasurableSet.mem | Mathlib.MeasureTheory.MeasurableSpace.Constructions | [
"Iff.mpr",
"MeasurableSet",
"measurable_mem",
"Measurable",
"Membership.mem",
"MeasurableSpace",
"Prop.instMeasurableSpace",
"Set.instMembership",
"Set"
] | true |
dist_pi_const_le | Mathlib.Topology.MetricSpace.Pseudo.Pi | [
"Iff.mpr",
"Real.instLE",
"Real",
"pseudoMetricSpacePi",
"le_rfl",
"dist_nonneg",
"dist_pi_le_iff",
"LE.le",
"PseudoMetricSpace",
"Fintype",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Real.instPreorder"
] | true |
_private.Mathlib.Topology.Algebra.Polynomial.0.Polynomial.coeff_le_of_roots_le._simp_1_1 | Mathlib.Topology.Algebra.Polynomial | [
"Multiset.map",
"Multiset.mem_map",
"Membership.mem",
"Exists",
"Multiset",
"Multiset.instMembership",
"And",
"propext",
"Eq"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.Defs.0.InnerProductSpace.Core.«_aux_Mathlib_Analysis_InnerProductSpace_Defs___macroRules__private_Mathlib_Analysis_InnerProductSpace_Defs_0_InnerProductSpace_Core_term_†_1» | Mathlib.Analysis.InnerProductSpace.Defs | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.... | false |
Real.sign_eq_zero_iff._simp_1 | Mathlib.Data.Real.Sign | [
"Real",
"Real.instZero",
"Real.sign",
"Real.sign_eq_zero_iff",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
minimal_nonempty_open_eq_singleton | Mathlib.Topology.Separation.Basic | [
"Iff.mpr",
"Exists",
"Set.instSingletonSet",
"HasSubset.Subset",
"minimal_nonempty_open_subsingleton",
"TopologicalSpace",
"And",
"Set.Nonempty",
"Set.exists_eq_singleton_iff_nonempty_subsingleton",
"And.intro",
"Set.Subsingleton",
"IsOpen",
"T0Space",
"Singleton.singleton",
"Eq",
"Set... | true |
left_iff_dite_iff | Init.PropLemmas | [
"Eq.mpr",
"False",
"_private.Init.PropLemmas.0.Decidable.imp_iff_left_iff._simp_1",
"Decidable.casesOn",
"instDecidableTrue",
"eq_false",
"congrArg",
"true_or",
"Decidable",
"not_true_eq_false",
"dif_pos",
"id",
"dif_neg",
"dite",
"iff_self",
"forall_prop_domain_congr",
"forall_false... | true |
GradedMonoid.list_prod_map_eq_dProd | Mathlib.Algebra.GradedMonoid | [
"Eq.mpr",
"GradedMonoid.mk_list_dProd",
"AddMonoid.toAddSemigroup",
"GradedMonoid.mk.eq_1",
"List.dProdIndex",
"GradedMonoid.GOne.toOne",
"congrArg",
"Sigma.eta",
"List.map",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"GradedMonoid.GMonoid",
"id",
"Sigma.fst",
"GradedMonoid.GM... | true |
CategoryTheory.IsPullback.of_hasPullback | Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Defs | [
"CategoryTheory.Limits.pullback",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.IsPullback",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.limit.cone",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.Is... | true |
ProbabilityTheory.Kernel.IndepFun.comp | Mathlib.Probability.Independence.Kernel.IndepFun | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"MeasurableSpace.comap",
"HMul.hMul",
"MeasurableSet",
"CommSemiring.toSemiring",
"Filter.Eventually",
"Measurable",
"setOf",
"Function.comp",
"Membership.mem",
"ProbabilityTheory.Kernel.instFunLike",
"Set.preimage_comp",
"ENNReal.instCommSemiri... | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.getKey_eraseKey._simp_1_1 | Std.Data.Internal.List.Associative | [
"Option.some",
"Bool.true",
"Std.Internal.List.getKey",
"List",
"Std.Internal.List.containsKey",
"Bool",
"Std.Internal.List.getKey?_eq_some_getKey",
"Std.Internal.List.getKey?",
"Eq.symm",
"BEq",
"Eq",
"Sigma",
"Option"
] | false |
CategoryTheory.Under.pushout_obj | Mathlib.CategoryTheory.Comma.Over.Pullback | [
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Under.pushout._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasPushoutsAlong",
"CategoryTheory.Under.mk",
"CategoryTheory.Under.hom",
"CategoryTheory.Under.pushout",
"CategoryTheory.Under.right",
"Categ... | true |
Order.height_toDual | Mathlib.Order.KrullDimension | [
"OrderDual.toDual",
"Equiv.instEquivLike",
"Equiv",
"ENat",
"OrderDual",
"Order.height",
"OrderDual.instPreorder",
"Eq",
"DFunLike.coe",
"rfl",
"Preorder",
"EquivLike.toFunLike",
"Order.coheight"
] | true |
AddLocalization.ind | Mathlib.GroupTheory.MonoidLocalization.Basic | [
"AddCon.instFunLikeForallProp",
"Iff.mpr",
"AddCon",
"Prod.instAdd",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"AddSubmonoid.add",
"Prod.mk",
"AddSubmonoid",
"Prod.fst",
"AddCommMonoid",
"AddLocalization.mk_eq_mk_iff",
"AddLocalization.rec",
"Eq... | true |
ProbabilityTheory.Kernel.partialTraj_comp_partialTraj | Mathlib.Probability.Kernel.IonescuTulcea.PartialTraj | [
"Eq.mpr",
"ProbabilityTheory.Kernel.comp_assoc",
"congrArg",
"ProbabilityTheory.Kernel.comp",
"Finset",
"Nat.instLocallyFiniteOrder",
"Membership.mem",
"LocallyFiniteOrder.toLocallyFiniteOrderBot",
"ProbabilityTheory.Kernel.partialTraj_succ_eq_comp",
"id",
"Subtype",
"instOfNatNat",
"LE.le",... | true |
Ordinal.bsup_le | Mathlib.SetTheory.Ordinal.Family | [
"Iff.mpr",
"Preorder.toLT",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ordinal.bsup",
"LE.le",
"Ordinal.bsup_le_iff",
"LT.lt",
"Ordinal"
] | true |
_private.Mathlib.RingTheory.Coalgebra.CoassocSimps.0.CoassocSimps.coassoc_left._simp_1_1 | Mathlib.RingTheory.Coalgebra.CoassocSimps | [
"LinearMap.id",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"LinearMap.lTensor",
"TensorProduct.map",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"TensorProduct",
"Module",
"Eq.symm",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"LinearMap.lTensor_def",
"TensorPro... | false |
Lean.Elab.TacticInfo.goalsBefore | Lean.Elab.InfoTree.Types | [
"Lean.MVarId",
"List",
"Lean.Elab.TacticInfo"
] | true |
RingOfIntegers.exponent | Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind | [
"Nat.instMulZeroOneClass",
"Ideal.absNorm",
"NumberField.instCommRingRingOfIntegers",
"CommSemiring.toSemiring",
"RingOfIntegers.exponent._proof_2",
"Int.instNontrivial",
"MonoidWithZeroHom.funLike",
"Algebra.id",
"Int",
"Ideal",
"instMulZeroOneClassOfSemiring",
"CommRing.toCommSemiring",
"M... | true |
WeierstrassCurve.Projective.map_a₆ | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | [
"CommRing",
"CommSemiring.toSemiring",
"RingHom",
"WeierstrassCurve.Projective",
"WeierstrassCurve.Projective.map",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"WeierstrassCurve.a₆",
"Eq.refl",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe"
] | true |
ContMDiff.piecewise | Mathlib.Geometry.Manifold.ContMDiff.Basic | [
"Eq.mpr",
"frontier",
"Set.piecewise_eq_of_notMem",
"interior_subset",
"NormedSpace",
"Classical.not_not._simp_1",
"IsClosed.isOpen_compl",
"congrArg",
"subset_closure",
"Mathlib.Tactic.Contrapose.contrapose₃",
"Compl.compl",
"ContMDiff",
"ite_self",
"isOpen_interior",
"setOf",
"Classi... | true |
FirstOrder.Language.mk.injEq | Mathlib.ModelTheory.Basic | [
"Eq.propIntro",
"FirstOrder.Language.mk",
"Lean.injEq_helper",
"And",
"Nat",
"FirstOrder.Language.mk.inj",
"Eq.ndrec",
"Eq.refl",
"FirstOrder.Language",
"Eq"
] | true |
Mathlib.Tactic.Linarith.LinarithConfig.splitHypotheses._default | Mathlib.Tactic.Linarith.Frontend | [
"id",
"Bool.true",
"Bool"
] | false |
TopologicalAddGroup.IsSES.pushforward_def | Mathlib.MeasureTheory.Measure.Haar.Extension | [
"Function.invFun",
"AddGroup.toSubtractionMonoid",
"Real",
"MeasureTheory.Measure",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"CompactlySupportedContinuousM... | true |
LLVM.Visibility._sizeOf_1 | Lean.Compiler.IR.LLVMBindings | [
"LLVM.Visibility.rec",
"UInt64",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"UInt64._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"LLVM.Visibility",
"OfNat.ofNat"
] | false |
NonUnitalCommRing.toNonUnitalCommSemiring._proof_2 | Mathlib.Algebra.Ring.Defs | [
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toMul",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"NonUnitalCommRing",
"instHAdd",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"NonUnitalNonAssocR... | false |
Lean.removeRoot | Lean.Data.OpenDecl | [
"Lean.Name.replacePrefix",
"Lean.Name.anonymous",
"Lean.rootNamespace",
"Lean.Name"
] | true |
_private.Std.Data.DHashMap.Internal.AssocList.Lemmas.0.Std.DHashMap.Internal.AssocList.Const.alter.match_1.eq_1 | Std.Data.DHashMap.Internal.AssocList.Lemmas | [
"Unit.unit",
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.Const.alter.match_1",
"Option.some",
"Option.none",
"Unit",
"Eq.refl",
"Eq",
"Option"
] | true |
_private.Mathlib.Algebra.Homology.ExactSequenceFour.0.CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac._proof_15 | Mathlib.Algebra.Homology.ExactSequenceFour | [
"CategoryTheory.ComposableArrows.map'._proof_8",
"instOfNatNat",
"LE.le",
"instLENat",
"autoParam",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac._proof_13",
"CategoryTheory.ComposableArro... | false |
CategoryTheory.inclusion | Mathlib.CategoryTheory.ConnectedComponents | [
"CategoryTheory.Functor",
"CategoryTheory.ConnectedComponents.Component",
"CategoryTheory.Sigma.incl",
"CategoryTheory.ConnectedComponents",
"CategoryTheory.Sigma.sigma",
"CategoryTheory.Decomposed",
"CategoryTheory.ObjectProperty.FullSubcategory.category",
"CategoryTheory.ConnectedComponents.objectPr... | true |
ContDiffMapSupportedInClass.casesOn | Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | [
"Real",
"NormedSpace",
"outParam",
"Real.denselyNormedField",
"ContDiffMapSupportedInClass",
"Compl.compl",
"PseudoMetricSpace.toUniformSpace",
"Pi.instZero",
"ContDiff",
"SubtractionMonoid.toSubNegZeroMonoid",
"Set.EqOn",
"DFunLike",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMono... | false |
Lean.Meta.Cache._sizeOf_1 | Lean.Meta.Basic | [
"Lean.Meta.InferTypeCache",
"Lean.Meta.instBEqInfoCacheKey",
"Lean.Meta.instHashableDefEqCacheKey",
"Option._sizeOf_inst",
"Lean.Meta.AbstractMVarsResult._sizeOf_inst",
"Lean.Meta.instBEqDefEqCacheKey",
"Lean.Meta.InfoCacheKey",
"Lean.Meta.DefEqCacheKey._sizeOf_inst",
"Lean.Meta.AbstractMVarsResult"... | false |
_private.Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary.0.DifferentiableAt.mem_interior_convex_of_surjective_fderiv.match_1_1 | Mathlib.Geometry.Manifold.IsManifold.InteriorBoundary | [
"Real",
"Semiring.toModule",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"Membership.mem",
"Exists",
"Real.semiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Exists.casesOn",
... | false |
GradedRingHom.instOne | Mathlib.RingTheory.GradedAlgebra.RingHom | [
"SetLike",
"One",
"One.mk",
"GradedRingHom",
"Semiring",
"GradedRingHom.id"
] | true |
ExteriorAlgebra.lift_symm_apply | Mathlib.LinearAlgebra.ExteriorAlgebra.Basic | [
"AlgHom.toLinearMap",
"CliffordAlgebra.ι",
"CommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"CliffordAlgebra.ι._proof_2",
"HMul.hMul",
"QuadraticMap.instZero",
"Algebra.algebraMap",
"ExteriorAlgebra",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"Alg... | true |
Mathlib.Tactic.IntervalCases.Methods.bisect._unsafe_rec | Mathlib.Tactic.IntervalCases | [
"Pure.pure",
"Lean.MVarId.withContext",
"Subarray",
"instHDiv",
"Lean.MetavarKind.syntheticOpaque",
"ReaderT",
"instMonadControlTOfPure",
"Lean.MVarId.assign",
"Lean.Meta.State",
"Mathlib.Tactic.IntervalCases.Methods.roundUp",
"instMonadLiftT",
"Array.toSubarray",
"Lean.Expr.mvar",
"Mathli... | false |
_private.Mathlib.NumberTheory.FermatPsp.0.Nat.exists_infinite_pseudoprimes._proof_1_6 | Mathlib.NumberTheory.FermatPsp | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"of_decide_eq_true",
"congrArg",
"Classical.byContradiction",
"Lean.Grind.Nat.lt_eq",
"Nat.Linear.Expr.mulL",
"id",
"False.casesOn",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Linear.Expr.num",
"Bool.true",
"instHAdd",
"Nat.Li... | false |
Mathlib.Tactic.RingNF.RingMode.ctorElimType | Mathlib.Tactic.Ring.RingNF | [
"cond",
"Nat.ble",
"Mathlib.Tactic.RingNF.RingMode.raw",
"PULift",
"Nat",
"Mathlib.Tactic.RingNF.RingMode.SOP",
"Mathlib.Tactic.RingNF.RingMode"
] | false |
Complex.lim_re | Mathlib.Analysis.Complex.Norm | [
"Norm.norm",
"Eq.mpr",
"Complex.instIsComplete",
"Real",
"Complex.mul_re",
"HMul.hMul",
"Real.lattice",
"sub_self",
"Real.instZero",
"Real.instAddMonoid",
"abs",
"congrArg",
"Complex.im",
"Real.instSub",
"IsAbsoluteValue.abs_isAbsoluteValue",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
... | true |
enorm_prod_le_of_le | Mathlib.Analysis.Normed.Group.Basic | [
"ESeminormedMonoid.toContinuousENorm",
"enorm_prod_le",
"ENNReal.instAddCommMonoid",
"ESeminormedCommMonoid.toESeminormedMonoid",
"Finset",
"PartialOrder.toPreorder",
"ESeminormedCommMonoid.toCommMonoid",
"Membership.mem",
"ESeminormedCommMonoid",
"LE.le",
"Finset.prod",
"TopologicalSpace",
... | true |
_private.Mathlib.Analysis.Hofer.0._aux_Mathlib_Analysis_Hofer___macroRules__private_Mathlib_Analysis_Hofer_0_termD_1 | Mathlib.Analysis.Hofer | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr... | false |
_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.Ico_pow_dvd_eq_Ico_of_lt._simp_1_3 | Mathlib.Data.Nat.Factorization.Basic | [
"And",
"Iff",
"and_congr_left_iff",
"propext",
"Eq"
] | false |
Lean.Elab.Term.ToDepElimPattern.State | Lean.Elab.Match | [
"Lean.Elab.Term.ToDepElimPattern.State.mk"
] | true |
_private.Mathlib.Order.Directed.0.directedOn_iff_directed._simp_1_5 | Mathlib.Order.Directed | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
MonoidHom.CompTriple.IsId.eq_id | Mathlib.Algebra.Group.Hom.CompTypeclasses | [
"Monoid",
"MonoidHom",
"Monoid.toMulOneClass",
"MulOneClass.toMulOne",
"MonoidHom.id",
"MonoidHom.CompTriple.IsId",
"Eq"
] | true |
Equiv.prodPiEquivSumPi_apply | Mathlib.Logic.Equiv.Prod | [
"Equiv.instEquivLike",
"Equiv.prodPiEquivSumPi",
"Sum",
"Equiv",
"Sum.inl",
"Equiv.sumPiEquivProdPi",
"Sum.inr",
"Eq.refl",
"Equiv.symm",
"Prod",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"Sum.elim"
] | true |
CategoryTheory.Functor.descOfIsLeftKanExtension_fac_app | Mathlib.CategoryTheory.Functor.KanExtension.Basic | [
"CategoryTheory.Functor.descOfIsLeftKanExtension",
"CategoryTheory.Functor",
"CategoryTheory.Functor.IsLeftKanExtension",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.whiskerLeft",
"CategoryTheory.Na... | true |
CategoryTheory.ShortComplex.LeftHomologyData.copy._proof_5 | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.ShortComplex.LeftHomologyData.copy._proof_2... | false |
Lean.Grind.CommRing.Poly.insert.go.induct_unfolding | Init.Grind.Ring.CommSolver | [
"cond",
"Ordering.gt",
"Eq.mpr",
"Lean.Grind.CommRing.Poly",
"Bool.cond_neg",
"Lean.Grind.CommRing.Poly.add",
"congrArg",
"Lean.Grind.CommRing.Poly.denote.match_1.congr_eq_1",
"Ordering",
"Int.instDecidableEq",
"Ordering.eq",
"id",
"Lean.Grind.CommRing.Poly.below",
"Lean.Grind.CommRing.Pol... | true |
_private.Mathlib.LinearAlgebra.LinearPMap.0.LinearPMap.graph_map_fst_eq_domain._simp_1_6 | Mathlib.LinearAlgebra.LinearPMap | [
"Exists",
"exists_and_right",
"And",
"propext",
"Eq"
] | false |
MeasureTheory.exp_neg_llr | Mathlib.MeasureTheory.Measure.LogLikelihoodRatio | [
"MeasureTheory.ae",
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"Pi.instNeg",
"MeasureTheory.exp_llr_of_ac'",
"congrArg",
"MeasureTheory.SigmaFinite",
"setOf",
"MeasureTheory.Measure.rnDeriv",
"MeasureTheory.llr",
"Membership.mem",
"Filter.mp_mem",
"MeasureTheory.Measure.AbsolutelyContinuou... | true |
Lean.Compiler.LCNF.CtorFieldInfo.object.injEq | Lean.Compiler.LCNF.ToImpureType | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Compiler.LCNF.CtorFieldInfo.object",
"Lean.Expr",
"Lean.Compiler.LCNF.CtorFieldInfo.object.inj",
"And",
"Lean.Compiler.LCNF.CtorFieldInfo",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
ContDiff.fourierPowSMulRight | Mathlib.Analysis.Fourier.FourierTransformDeriv | [
"ContinuousMultilinearMap.instDistribMulAction",
"Iff.mpr",
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"Real",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Sem... | true |
CategoryTheory.Limits.sigmaConstCokernelCofork_pt | Mathlib.CategoryTheory.Limits.Preserves.SigmaConst | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"Compl.compl",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"Set.Elem",
"CategoryTheory.Limits.HasCoproduct",
... | true |
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