name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Init.Data.String.Lemmas.Pattern.String.Basic.0.String.Slice.Pattern.Model.ForwardSliceSearcher.isLongestMatchAt_iff_splits._simp_1_1 | Init.Data.String.Lemmas.Pattern.String.Basic | [
"String.Slice.slice",
"String.instLEPos_1",
"String",
"String.Slice",
"Exists",
"LE.le",
"String.Slice.copy",
"instAppendString",
"instHAppendOfAppend",
"And",
"propext",
"String.Slice.Pos",
"String.Slice.copy_slice_eq_iff_splits",
"Eq",
"HAppend.hAppend",
"String.Slice.Pos.Splits"
] | false |
MultilinearMap.mkContinuous_norm_le | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"Norm.norm",
"Real.instLE",
"Real",
"SeminormedAddCommGroup",
"HMul.hMul",
"Finset.univ",
"NormedSpace",
"Real.instZero",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap.hasOpNorm",
"ContinuousMultilinearMap",
"NormedFie... | true |
_private.Lean.Elab.Tactic.BuiltinTactic.0.Lean.Elab.Tactic.evalReplace.match_1 | Lean.Elab.Tactic.BuiltinTactic | [
"Option.ctorIdx",
"_private.Lean.Elab.Tactic.BuiltinTactic.0.Lean.Elab.Tactic.evalSepTactics._sparseCasesOn_1",
"Option.some",
"Nat.hasNotBit",
"Lean.LocalDecl",
"Option"
] | false |
CategoryTheory.ComposableArrows.sc'._auto_1 | Mathlib.Algebra.Homology.ExactSequence | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
QuadraticModuleCat.instMonoidalCategory | Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CategoryTheory.Monoidal.InducingFunctorData.mk",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"ModuleCat",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.MonoidalCategory",
"QuadraticModuleCat.instMon... | true |
Subgroup.mem_goursatSnd | Mathlib.GroupTheory.Goursat | [
"MulOne.toOne",
"MonoidHom.instFunLike",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"and_true",
"MonoidHom",
"Iff.of_eq",
"Subgroup.map",
"Monoid.toMulOneClass",
"congrArg",
"Subgroup.subtype",
"Group",
"Prod.exists._simp_1",
"Group.toDivisionMonoid",
"Prod.instMulOneClass",
... | true |
groupCohomology.H1IsoOfIsTrivial.congr_simp | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | [
"Rep.V",
"CommRing",
"ModuleCat",
"Rep.IsTrivial",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"groupCohomology.H1IsoOfIsTrivial",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Additive",
"AddMonoid.toAddZeroClass",
"Group",
"Rep.hV1",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZ... | true |
Std.DHashMap.Raw.getKeyD_insertIfNew | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Internal.Raw₀.getKeyD_insertIfNew",
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Eq.mpr",
"instDecidableNot",
"Std.DHashMap.Internal.Raw₀.contains",
"congrArg",
"Std.DHashMap.Internal.Raw.insertIfNew_eq",
"Std.DHashMap.Raw",
"_private.Std.Data.DHashMap.Ra... | true |
AddMonoidAlgebra.singleZeroAlgHom.eq_1 | Mathlib.Algebra.MonoidAlgebra.Basic | [
"AddMonoidAlgebra.semiring",
"AlgHom",
"AddMonoidAlgebra.singleZeroAlgHom._proof_1",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.algebra",
"Algebra",
"AddMonoidAlgebra.singleZeroAlgHom",
"AddMonoidAlgebra.singleZeroRingHom",
"CommSemiring",
"AddMonoid",
"AlgHom.mk",
"Semiring",
"Eq.refl",
... | true |
CategoryTheory.HasDetector.recOn | Mathlib.CategoryTheory.Generator.Basic | [
"CategoryTheory.HasDetector.mk",
"Exists",
"CategoryTheory.HasDetector.rec",
"CategoryTheory.HasDetector",
"CategoryTheory.IsDetector",
"CategoryTheory.Category"
] | false |
Ideal.hasBasis_nhds_zero_adic | Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | [
"Filter.instMembership",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Submodule",
"CommRing",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"trivial",
"AddGroupFilterBasis.topology",
"IsScalarTower.right",
"Filter.HasBasis.mem_iff",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemir... | true |
Std.DTreeMap.Raw.Const.unitOfList_equiv_foldl | Std.Data.DTreeMap.Raw.Lemmas | [
"Eq.mpr",
"Unit.unit",
"congrArg",
"instForInOfForIn'",
"Std.DTreeMap.Raw.Const.unitOfList",
"Std.DTreeMap.Raw.Const.unitOfList_eq_insertManyIfNewUnit_empty",
"Ordering",
"inferInstance",
"id",
"Std.DTreeMap.Raw.Equiv",
"Std.DTreeMap.Raw.Const.insertManyIfNewUnit",
"List.foldl",
"Id",
"Mem... | true |
AddCommGroup.primaryComponent._proof_3 | Mathlib.GroupTheory.Torsion | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"instHSMul",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"neg_nsmul",
"AddMonoid.toNSMul",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"id",
"Subtraction... | false |
Unitization.inrNonUnitalAlgHom_toFun | Mathlib.Algebra.Algebra.Unitization | [
"Semiring.toModule",
"CommSemiring.toSemiring",
"Unitization.instDistribMulAction",
"Unitization.inr",
"Unitization.inrNonUnitalAlgHom",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalAlgHom",
"NonUnitalAlgHom.instFunLike",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemirin... | true |
AbsoluteValue.map_units_intCast | Mathlib.Data.Int.AbsoluteValue | [
"Nontrivial",
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"Units.val",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Monoid.toMulOneClass",
"AddGro... | true |
CategoryTheory.CommGrp.forget₂Grp_obj_X | Mathlib.CategoryTheory.Monoidal.CommGrp_ | [
"CategoryTheory.CommGrp.instCategory",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CommGrp.forget₂Grp",
"CategoryTheory.CommGrp.X",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.CommGrp",
"CategoryTheory.BraidedCat... | true |
ContDiffBump.noConfusionType | Mathlib.Analysis.Calculus.BumpFunction.Basic | [
"Real",
"Real.instZero",
"Real.instLT",
"ContDiffBump",
"LT.lt",
"ContDiffBump.casesOn",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
List.foldrM_map | Init.Data.List.Monadic | [
"Pure.pure",
"List.foldrM_cons",
"congrArg",
"Monad.toApplicative",
"List.map",
"List.foldrM",
"LawfulMonad",
"List.rec",
"Applicative.toPure",
"List.cons",
"List",
"congr",
"True",
"eq_self",
"of_eq_true",
"Monad.toBind",
"Bind.bind",
"congrFun'",
"Monad",
"Eq",
"Eq.trans"
] | true |
CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose_map_app_fst_app | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.snd",
"CategoryTheory.Functor",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precompose._proof_4",
"Cat... | true |
AddConstMap.«term_→+c[_,_]_» | Mathlib.Algebra.AddConstMap.Basic | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
_private.Mathlib.Computability.TuringMachine.Config.0.Turing.ToPartrec.Code.exists_code._simp_1_17 | Mathlib.Computability.TuringMachine.Config | [
"Part",
"Part.some",
"Part.mem_some_iff",
"Membership.mem",
"Part.instMembership",
"propext",
"Eq"
] | false |
_private.Init.Data.List.Nat.Modify.0.List.eraseIdx_modify_of_lt._proof_1_1 | Init.Data.List.Nat.Modify | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"List.eraseIdx",
"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.Omeg... | false |
MeasureTheory.IsSigmaSubadditiveSetFun | Mathlib.MeasureTheory.Measure.PreVariation | [
"ChainCompletePartialOrder.instOfCompleteLattice",
"MeasurableSet",
"Function.onFun",
"ENNReal.instAddCommMonoid",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Disjoint",
"Function.comp",
"Subtype",
"LE.le",
"ChainCompletePartialOrder.toPartialOrder",
"MeasurableSpace",
"tsum",
"Nat",... | true |
_private.Init.Data.String.Lemmas.Iterate.0.String.Slice.mem_toList_copy_iff_exists_get._simp_1_1 | Init.Data.String.Lemmas.Iterate | [
"String.Slice.Model.map_get_positionsFrom_startPos",
"String.Slice.Model.positionsFrom",
"List.map",
"String.Slice",
"Subtype",
"Ne",
"String.Slice.startPos",
"String.Slice.copy",
"List",
"String.Slice.endPos",
"String.toList",
"String.Slice.Pos.get",
"String.Slice.Pos",
"Char",
"Eq.symm... | false |
List.foldr_flip_eq_foldl | Mathlib.Data.List.Fold | [
"congrArg",
"List.foldl_cons_eq_apply_foldl",
"flip",
"List.rec",
"List.foldl",
"List.cons",
"List",
"congr",
"True",
"eq_self",
"of_eq_true",
"RightCommutative",
"congrFun'",
"List.foldr",
"Eq",
"Eq.trans"
] | true |
Lean.Elab.Tactic.evalSplit._regBuiltin.Lean.Elab.Tactic.evalSplit_1 | Lean.Elab.Tactic.Split | [
"Lean.Elab.Tactic.tacticElabAttribute",
"IO",
"Lean.Elab.Tactic.evalSplit",
"Unit",
"Lean.Elab.Tactic.Tactic",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
PowerSeries.WithPiTopology.multipliable_one_add_of_tendsto_order_atTop_nhds_top | Mathlib.RingTheory.PowerSeries.PiTopology | [
"instTopENat",
"MvPowerSeries.instCommSemiring",
"CommSemiring.toSemiring",
"LinearOrder",
"PartialOrder.toPreorder",
"PowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top",
"SemilatticeInf.toPartialOrder",
"nhds",
"LocallyFiniteOrderBot",
"DistribLattice.toLattice",
"Distrib... | true |
Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing | Mathlib.RingTheory.Valuation.Integers | [
"_private.Mathlib.RingTheory.Valuation.Integers.0.Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing._simp_1_6",
"Set.mem_range_self",
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"NonAssocSe... | true |
LinearMap.extendScalarsOfIsLocalizationEquiv_apply | Mathlib.RingTheory.Localization.Module | [
"IsLocalization",
"CommSemiring.toSemiring",
"LinearMap.extendScalarsOfIsLocalization",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.module",
"LinearMap",
"smulC... | true |
Lean.Meta.Grind.Arith.CommRing.NonCommSemiringM.Context.semiringId | Lean.Meta.Tactic.Grind.Arith.CommRing.NonCommSemiringM | [
"Nat",
"Lean.Meta.Grind.Arith.CommRing.NonCommSemiringM.Context"
] | true |
TopCat.GlueData.MkCore.t'._proof_7 | Mathlib.Topology.Gluing | [
"Continuous.comp'",
"Continuous",
"continuous_subtype_val",
"TopologicalSpace.Opens.instPartialOrder",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"ContinuousMap",
"TopCat.GlueData.MkCore.t",
"PartialOrder.toPreorder",
"instTopologicalSpaceProd",
"Subtype.casesOn",
"Topologic... | false |
Subalgebra.unop_iSup | Mathlib.Algebra.Algebra.Subalgebra.MulOpposite | [
"Subalgebra.unop",
"iSup",
"MulOpposite.instAlgebra",
"OrderIso.map_iSup",
"MulOpposite",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Preorder.toLE",
"Subalgebra.opEquiv",
"CompleteLattice.toConditionallyCompleteLattice",
"OrderIso.symm",
"CommSemiring",
... | true |
List.max_le_of_forall_le | Mathlib.Data.List.MinMax | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"congrArg",
"LinearOrder",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"List.mem_cons_of_mem",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"id",
"List.rec",
"B... | true |
sSupHom.mk.noConfusion | Mathlib.Order.Hom.CompleteLattice | [
"HEq.refl",
"id",
"SupSet",
"heq_of_eq",
"sSupHom.noConfusion",
"sSupHom",
"Eq.refl",
"Set.image",
"HEq",
"Eq",
"sSupHom.mk",
"SupSet.sSup",
"Set"
] | false |
Prod.snd_bot | Mathlib.Order.BoundedOrder.Basic | [
"Bot.bot",
"Bot",
"Prod.instBot",
"Prod",
"Eq",
"Prod.snd",
"rfl"
] | true |
_private.Mathlib.Data.Ordmap.Invariants.0.Ordnode.Bounded.weak_right.match_1_1 | Mathlib.Data.Ordmap.Invariants | [
"WithBot.some",
"WithBot",
"Ordnode",
"Ordnode.node",
"WithTop.some",
"And.casesOn",
"Ordnode.casesOn",
"Nat",
"And.intro",
"Ordnode.nil",
"Ordnode.Bounded",
"Preorder",
"WithTop"
] | false |
AList.erase.eq_1 | Mathlib.Data.Finmap | [
"AList.mk",
"AList.erase._proof_1",
"List.kerase",
"AList.erase",
"AList",
"Eq.refl",
"Eq",
"DecidableEq",
"AList.entries"
] | true |
RingEquiv.map_neg_one | Mathlib.Algebra.Ring.Equiv | [
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingEquiv.map_neg",
"RingEquiv.instEquivLike",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"RingEquiv.map_one",
"Eq.rec",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Sub... | true |
Std.ExtTreeMap.get_union_of_not_mem_left | Std.Data.ExtTreeMap.Lemmas | [
"Membership.mem",
"Ordering",
"Std.ExtTreeMap.mem_of_mem_union_of_not_mem_left",
"Std.TransCmp",
"Std.ExtTreeMap",
"Std.ExtTreeMap.instUnionOfTransCmp",
"Std.ExtTreeMap.inner",
"Std.ExtTreeMap.instMembershipOfTransCmp",
"Union.union",
"Eq",
"Std.ExtTreeMap.get",
"Not",
"Std.ExtDTreeMap.Const... | true |
CategoryTheory.LaxMonoidalFunctor.hom_ext | Mathlib.CategoryTheory.Monoidal.NaturalTransformation | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.LaxMonoidalFunctor.Hom.hom",
"CategoryTheory.LaxMonoidalFunctor.toFunctor",
"CategoryTheory.LaxMonoidalFunctor.Hom.mk",
"CategoryThe... | true |
Multiset.sum_map_sub | Mathlib.Algebra.BigOperators.Group.Multiset.Basic | [
"Multiset.sum",
"Multiset.map",
"sub_zero",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"Multiset.sum_hom₂",
"AddZeroClass.toAddZero",
"Multiset",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubtractionCommMonoid.toSubtractionMonoid",
"SubtractionCommMonoid.toAddC... | true |
Std.DTreeMap.Internal.RxcIterator.mk.noConfusion | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"HEq.refl",
"Std.DTreeMap.Internal.RxcIterator",
"id",
"Std.DTreeMap.Internal.Zipper",
"Std.DTreeMap.Internal.RxcIterator.noConfusion",
"heq_of_eq",
"Std.DTreeMap.Internal.RxcIterator.mk",
"Eq.refl",
"HEq",
"Eq"
] | false |
_private.Mathlib.RingTheory.Valuation.Discrete.Basic.0.Valuation.Uniformizer.is_generator._simp_1_2 | Mathlib.RingTheory.Valuation.Discrete.Basic | [
"False",
"True",
"propext",
"not_true",
"Eq",
"Not"
] | false |
Order.pred_le_iff_eq_or_le | Mathlib.Order.SuccPred.Basic | [
"Eq.mpr",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"congrArg",
"LinearOrder",
"Iff.rfl",
"PartialOrder.toPreorder",
"ge_of_eq",
"Classical.propDecidable",
"Preorder.toLE",
"DistribLattice.toLattice",
"id",
"LE.le",
"dite",
"Iff",
"le_iff_eq_or_lt'",
"Order.pred",
"LT.lt",
"pr... | true |
Rat.instEncodable._proof_1 | Mathlib.Data.Rat.Encodable | [
"Nat.Coprime",
"Ne",
"instOfNatNat",
"Int",
"And",
"Nat.pos_of_ne_zero",
"Nat",
"And.intro",
"LT.lt",
"Int.natAbs",
"instLTNat",
"OfNat.ofNat"
] | false |
HomologicalComplex.mapBifunctor₂₃.d₁_eq | Mathlib.Algebra.Homology.BifunctorAssociator | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"instHSMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"Units.instSMul",
"AddCommGroup.toAddGroup",
"HomologicalComplex",
"Units",
"Prod.mk",
... | true |
_private.Mathlib.Geometry.Manifold.Notation.0.Manifold.Elab.findModelInner.fromCLM.match_1 | Mathlib.Geometry.Manifold.Notation | [
"Lean.Expr",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
USize.pow._f | Init.Data.UInt.Basic | [
"USize.mul",
"instOfNatNat",
"Nat.below",
"Unit",
"Nat",
"UInt8.pow.match_1",
"OfNat.ofNat",
"Nat.succ",
"USize",
"USize.instOfNat"
] | false |
_private.Mathlib.Analysis.Meromorphic.Divisor.0.MeromorphicOn.divisor._simp_12 | Mathlib.Analysis.Meromorphic.Divisor | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
ProofWidgets.RpcEncodablePacket._@.ProofWidgets.Presentation.Expr.4196812879._hygCtx._hyg.1 | ProofWidgets.Presentation.Expr | [
"ProofWidgets.RpcEncodablePacket.mk._@.ProofWidgets.Presentation.Expr.4196812879._hygCtx._hyg.1"
] | false |
_private.Mathlib.Geometry.Euclidean.Sphere.SecondInter.0.EuclideanGeometry.Sphere.secondInter_map._simp_1_2 | Mathlib.Geometry.Euclidean.Sphere.SecondInter | [
"LinearIsometry",
"SeminormedAddCommGroup",
"NormedSpace",
"AffineIsometry.linearIsometry",
"NormedSpace.toModule",
"LinearIsometry.instFunLike",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"AffineIsometry.map_vsub",
"Field.toSemifield",
"AddTorsor.toVSub",
"NormedField",
"VSub.vsub",
... | false |
Lean.PrettyPrinter.Parenthesizer.State.rec | Lean.PrettyPrinter.Parenthesizer | [
"Lean.Syntax.Traverser",
"Nat",
"Bool",
"Lean.Name",
"Lean.PrettyPrinter.Parenthesizer.State.mk",
"Lean.PrettyPrinter.Parenthesizer.State",
"Option"
] | false |
instSigmaCompactSpaceForallOfFinite | Mathlib.Topology.Compactness.SigmaCompact | [
"Eq.mpr",
"compactCovering",
"Pi.topologicalSpace",
"congrArg",
"Set.univ",
"Finite",
"iUnion_compactCovering",
"instInhabitedNat",
"id",
"isCompact_univ_pi",
"SigmaCompactSpace.mk",
"isCompact_compactCovering",
"TopologicalSpace",
"funext",
"And",
"instNonemptyOfInhabited",
"Nat",
... | true |
AlgebraicGeometry.Scheme.Hom.image_le_image_iff | Mathlib.AlgebraicGeometry.OpenImmersion | [
"AlgebraicGeometry.Scheme.Hom.opensFunctor",
"Eq.mpr",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"con... | true |
SignType | Mathlib.Data.Sign.Defs | [
"SignType.pos",
"SignType.neg",
"SignType.zero"
] | true |
normedAddCommGroupTangentSpaceVectorSpace._aux_8 | Mathlib.Geometry.Manifold.Riemannian.Basic | [
"Real",
"chartedSpaceSelf",
"NormedSpace",
"Real.denselyNormedField",
"NormedAddCommGroup.toMetricSpace",
"PseudoMetricSpace.toUniformSpace",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"TangentSpace",
"MetricSpace.toPseudoMetricSpace",
"Real.normedField",
"DenselyNormedField.toNontriviallyNor... | false |
Int8.toISize_lt._simp_1 | Init.Data.SInt.Lemmas | [
"instLTISize",
"Int8.toISize",
"Int8",
"LT.lt",
"propext",
"instLTInt8",
"Int8.toISize_lt",
"ISize",
"Eq"
] | false |
Multiset.fold_cons_left | Mathlib.Data.Multiset.Fold | [
"Std.Commutative",
"Multiset",
"Multiset.cons",
"Multiset.foldr_cons",
"Eq",
"Multiset.fold",
"instLeftCommutativeOfCommutativeOfAssociative",
"Std.Associative"
] | true |
Lean.Elab.Tactic.Do.ProofMode.elabMExists._regBuiltin.Lean.Elab.Tactic.Do.ProofMode.elabMExists_1 | Lean.Elab.Tactic.Do.ProofMode.Refine | [
"Lean.Elab.Tactic.tacticElabAttribute",
"IO",
"Lean.Elab.Tactic.Do.ProofMode.elabMExists",
"Unit",
"Lean.Elab.Tactic.Tactic",
"Lean.Name.mkStr6",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
UInt64.sub_eq_iff_eq_add | Init.Data.UInt.Lemmas | [
"Eq.mpr",
"UInt64.toBitVec_add",
"instAddUInt64",
"congrArg",
"UInt64",
"HSub.hSub",
"BitVec.instAdd",
"UInt64.toBitVec_sub",
"BitVec",
"BitVec.sub_eq_iff_eq_add",
"UInt64.eq_iff_toBitVec_eq._simp_1",
"id",
"instOfNatNat",
"instHAdd",
"BitVec.instSub",
"Iff",
"instHSub",
"HAdd.hAdd... | true |
VectorFourier.fderiv_fourierIntegral | Mathlib.Analysis.Fourier.FourierTransformDeriv | [
"VectorFourier.fourierSMulRight",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"Real",
"Algebra.to_smulCommClass",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedSpace.toIsBoundedSMul",
"HMu... | true |
CategoryTheory.Functor.CorepresentableBy.equivOfIsoObj_symm_apply | Mathlib.CategoryTheory.Yoneda | [
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.Functor.CorepresentableBy",
"CategoryTheory.Functor.CorepresentableBy.ofIsoObj",
"Equiv",
"CategoryTheory.Iso",
"CategoryTheory.types",
"CategoryTheory.Iso.symm",
"Eq.refl",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"CategoryTheory.F... | true |
_private.Mathlib.Tactic.Cases.0.Mathlib.Tactic._aux_Mathlib_Tactic_Cases___elabRules_Mathlib_Tactic_induction'_1.match_4 | Mathlib.Tactic.Cases | [
"Lean.Syntax.Ident",
"Lean.Expr",
"Lean.FVarId",
"Prod.mk",
"Array",
"Prod",
"Prod.casesOn"
] | false |
CategoryTheory.SmallObject.SuccStruct.arrowι._proof_1 | Mathlib.CategoryTheory.SmallObject.Iteration.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"LinearOrder",
"PartialOrder.toPreorder",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Set.Elem",
"DistribLattice.toLattice",
"Order.IsSuccLimit",
"Preorder.smallCategory",
"CategoryTheory.Limits.HasColimit"... | false |
_private.Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex.0.Finset.image_subset_iff._simp_1 | Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | [
"Finset",
"Membership.mem",
"HasSubset.Subset",
"Finset.image_subset_iff",
"Finset.instSetLike",
"propext",
"Finset.instHasSubset",
"Eq",
"Finset.image",
"SetLike.instMembership",
"DecidableEq"
] | false |
HasFDerivWithinAt.congr' | Mathlib.Analysis.Calculus.FDeriv.Congr | [
"AddCommGroup.toAddCommMonoid",
"Membership.mem",
"HasFDerivWithinAt",
"NormedField.toField",
"AddCommGroup",
"Set.EqOn",
"Field.toSemifield",
"ContinuousLinearMap",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"NontriviallyNor... | true |
monovary_id_iff._simp_1 | Mathlib.Order.Monotone.Monovary | [
"Monovary",
"PartialOrder.toPreorder",
"Monotone",
"PartialOrder",
"id",
"monovary_id_iff",
"propext",
"Eq",
"Preorder"
] | false |
gaugeSeminormFamily_ball | Mathlib.Analysis.LocallyConvex.AbsConvexOpen | [
"gaugeSeminormFamily._proof_1",
"gauge_lt_one_eq_self_of_isOpen",
"NormedCommRing.toNormedRing",
"Real.instIsOrderedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"IsOrderedModule.toPosSMulMono",
"Real.partialOrder",
"Real",
"Algebra.to_smulCommClass",
"gaugeSeminorm",
"instStarRingRe... | true |
InfHom.coe_mk | Mathlib.Order.Hom.Lattice | [
"InfHom",
"Min",
"InfHom.mk",
"InfHom.instFunLike",
"Eq",
"DFunLike.coe",
"Min.min",
"rfl"
] | true |
TopPair.Homotopy.trans._proof_2 | Mathlib.Topology.Category.TopPair | [
"not_le",
"Iff.mpr",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"TopPair.map",
"Real.partialOrder",
"Decidable.casesOn",
"Real.instLE",
"Real",
"DivInvMonoid.toInv",
"dite_congr",
"Preorder.toLT",
"instHDiv",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Cat... | false |
List.lawfulBEq_iff | Init.Data.List.Lemmas | [
"Eq.mpr",
"List.singleton_inj",
"congrArg",
"Bool.and_true",
"LawfulBEq",
"inferInstance",
"id",
"Bool.and",
"List.reflBEq_iff",
"List.cons",
"Bool.true",
"List",
"EquivBEq.toReflBEq",
"BEq.beq",
"Iff",
"ReflBEq",
"LawfulBEq.mk",
"Iff.intro",
"Iff.mp",
"Bool",
"List.instBEq",... | true |
Set.uIoc_injective_left | Mathlib.Order.Interval.Set.UnorderedInterval | [
"congrArg",
"LinearOrder",
"Set.uIoc",
"Set.uIoc_comm",
"Eq.mp",
"Set.uIoc_injective_right",
"funext",
"Function.Injective",
"Set"
] | true |
_private.Batteries.Data.List.Lemmas.0.List.getElem_idxOf_eq_idxOfNth_add._proof_1_2 | Batteries.Data.List.Lemmas | [
"List.idxsOf",
"List.getElem_getElem_idxsOf_sub._proof_4",
"HSub.hSub",
"Lean.Grind.Nat.lt_eq",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"GetElem.getElem",
"List",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"instAddNat",
"_private.Batteries.Data.Li... | false |
Finset.sum_smul | Mathlib.Algebra.Module.BigOperators | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"AddMonoidHom.instAddMonoidHomClass",
"DistribMulAction.toDistribSMul",
"Finset",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddMonoidHom.instAddCommMonoid",
"AddCommMonoidWithOne.toAddMonoidWithOne"... | true |
_private.Mathlib.RingTheory.RingHom.Integral.0.RingHom.isIntegral_ofLocalizationSpan._simp_1_7 | Mathlib.RingTheory.RingHom.Integral | [
"Monoid",
"Monoid.toMulOneClass",
"map_pow",
"Monoid.toPow",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat",
"MonoidHomClass",
"instHPow",
"Eq.symm",
"Eq",
"DFunLike.coe",
"FunLike"
] | false |
_private.Mathlib.Order.RelSeries.0.LTSeries.apply_add_index_le_apply_add_index_int._proof_1_7 | Mathlib.Order.RelSeries | [
"Lean.RArray.leaf",
"False",
"Preorder.toLT",
"of_decide_eq_true",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"setOf",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"FiniteDimensiona... | false |
SuccAddOrder.toSuccOrder | Mathlib.Algebra.Order.SuccPred | [
"One",
"SuccAddOrder",
"SuccOrder",
"Add",
"Preorder"
] | true |
IsOfFinAddOrder.prod_iff | Mathlib.GroupTheory.OrderOfElement | [
"IsOfFinAddOrder.snd",
"IsOfFinAddOrder.prod_mk",
"Prod.fst",
"IsOfFinAddOrder.fst",
"IsOfFinAddOrder",
"And",
"Iff",
"And.right",
"And.left",
"And.intro",
"Iff.intro",
"AddMonoid",
"Prod.instAddMonoid",
"Prod",
"Prod.snd"
] | true |
Std.Tactic.BVDecide.LRAT.Internal.Clause.isUnit_iff | Std.Tactic.BVDecide.LRAT.Internal.Clause | [
"Std.Tactic.BVDecide.LRAT.Internal.Clause.toList",
"outParam",
"Option.some",
"Std.Tactic.BVDecide.LRAT.Internal.Clause.isUnit",
"List.cons",
"Iff",
"Std.Tactic.BVDecide.LRAT.Internal.Clause",
"Std.Sat.CNF.Clause",
"Std.Sat.Literal",
"Eq",
"List.nil",
"Option"
] | true |
RingEquiv.toSemiRingCatIso._proof_3 | Mathlib.Algebra.Category.Ring.Basic | [
"RingEquiv.instEquivLike",
"RingEquiv.instRingEquivClass",
"Distrib.toAdd",
"instDistribOfSemiring",
"Distrib.toMul",
"Semiring",
"RingEquiv",
"RingEquivClass.toRingHomClass",
"Semiring.toNonAssocSemiring",
"EquivLike.toFunLike",
"RingHomClass"
] | false |
Profinite.NobelingProof.continuous_CC'₁ | Mathlib.Topology.Category.Profinite.Nobeling.Successor | [
"Preorder.toLT",
"Continuous",
"Order.succ",
"isWellOrder_lt",
"Pi.topologicalSpace",
"Ordinal.partialOrder",
"continuous_subtype_val",
"Profinite.NobelingProof.CC'₁._proof_2",
"LinearOrder",
"WellFoundedLT",
"Continuous.comp",
"PartialOrder.toPreorder",
"instTopologicalSpaceBool",
"Functi... | true |
Equiv.eq_conj | Mathlib.Logic.Equiv.Basic | [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"Iff.rfl",
"Function.comp",
"Equiv.symm_comp_eq",
"id",
"Equiv",
"Iff",
"propext",
"Equiv.comp_symm_eq",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"Function.comp_assoc"
] | true |
MvPowerSeries.substAlgHom_coe | Mathlib.RingTheory.MvPowerSeries.Substitution | [
"UniformSpace",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"MvPolynomial.aeval",
"MvPowerSeries.substAlgHom._proof_5",
"MvPowerSeries.instCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"MvPowerSeries.substAl... | true |
_private.Lean.Meta.Match.MatchEqs.0.Lean.Meta.Match.initFn._@.Lean.Meta.Match.MatchEqs.3248161880._hygCtx._hyg.2 | Lean.Meta.Match.MatchEqs | [
"Lean.Name.mkNum",
"IO",
"Lean.Name.mkStr3",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.registerTraceClass",
"Lean.Name.anonymous",
"Unit",
"Nat",
"OfNat.ofNat",
"Bool.false"
] | false |
EuclideanDomain.mul_div_cancel' | Mathlib.Algebra.EuclideanDomain.Basic | [
"Eq.mpr",
"Dvd.dvd",
"instHDiv",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"MulZeroClass.toMul",
"congrArg",
"CommSemiring.toSemiring",
"semigroupDvd",
"CommSemiring.toCommMonoidWithZero",
"SemigroupWithZero.toSemigroup",
"mul_div_cancel_left₀",
"id",
"HDiv.hDiv",
"Ne",
"CommMonoidW... | true |
Turing.Dir.left.sizeOf_spec | Mathlib.Computability.TuringMachine.Tape | [
"Turing.Dir._sizeOf_inst",
"Turing.Dir.left",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Turing.Dir"
] | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_40 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"List.idxOfNth",
"instHAdd",
"HAdd.hAdd",
"Nat",
"List.filter",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Decidable.decide",
"Eq",
"List.length",
"List.nil",
"DecidableE... | false |
_private.Mathlib.Data.Set.Card.0.Set.Finite.exists_injOn_of_encard_le._simp_1_12 | Mathlib.Data.Set.Card | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
Associates | Mathlib.Algebra.GroupWithZero.Associated | [
"Monoid",
"Associated.setoid",
"Quotient"
] | true |
Lean.ParametricAttribute.mk._flat_ctor | Lean.Attributes | [
"Lean.NameMap",
"Lean.AttributeImpl",
"Lean.PersistentEnvExtension",
"List",
"Lean.ParametricAttribute",
"Bool",
"Lean.Name",
"Prod",
"Lean.ParametricAttribute.mk"
] | false |
SimpleGraph.ConnectedComponent.even_card_of_isPerfectMatching | Mathlib.Combinatorics.SimpleGraph.Matching | [
"SimpleGraph.Subgraph.IsPerfectMatching.induce_connectedComponent_isMatching",
"congrArg",
"SimpleGraph.Subgraph",
"SimpleGraph.Adj",
"DecidableRel",
"Membership.mem",
"Subtype.fintype",
"Eq.mp",
"Set.Elem",
"Fintype.card",
"SimpleGraph.ConnectedComponent",
"Set.toFinset_card",
"Set.toFinset... | true |
MulOpposite.instInvolutiveNeg | Mathlib.Algebra.Opposites | [
"MulOpposite",
"MulOpposite.instNeg",
"InvolutiveNeg",
"InvolutiveNeg.mk",
"MulOpposite.instInvolutiveNeg._proof_1",
"InvolutiveNeg.toNeg"
] | true |
IsPowMul.restriction | Mathlib.Analysis.Normed.Ring.Basic | [
"Subalgebra.instSetLike",
"Real",
"CommRing",
"SubmonoidClass.instPow",
"Algebra",
"Membership.mem",
"id",
"Subtype",
"instOfNatNat",
"LE.le",
"instLENat",
"Monoid.toPow",
"Real.instMonoid",
"CommRing.toCommSemiring",
"HPow.hPow",
"Nat",
"Semiring.toMonoid",
"Subalgebra.instSubsemi... | true |
FiniteDimensional.basisSingleton._proof_6 | Mathlib.LinearAlgebra.FiniteDimensional.Basic | [
"DivisionRing.toDivisionSemiring",
"RingHomInvPair",
"RingHomInvPair.ids",
"DivisionSemiring.toSemiring",
"DivisionRing",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
AlgebraicGeometry.Scheme.Hom.map_appLE'_assoc | Mathlib.AlgebraicGeometry.Scheme | [
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"congrArg",
... | true |
Aesop.runTacticMAsElabM | Aesop.RuleTac.ElabRuleTerm | [
"instMonadReaderOfReaderTOfMonad",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"instMonadLiftT",
"MonadReader.read",
"Lean.Meta.MetaM",
"IO.RealWorld",
"liftM",
"Aesop.runTacticMAsTermElabM",
"ReaderT.instMonadLift",
"Aesop.ElabM.Context",
"instMonadReaderOfMonadReaderOf",
"Aesop.ElabM.C... | true |
Filter.Germ.instDivisionSemiring._proof_6 | Mathlib.Order.Filter.FilterProduct | [
"Nontrivial",
"Filter.Germ.instGroupWithZero",
"DivisionSemiring.toGroupWithZero",
"DivisionSemiring",
"Filter.Germ",
"Ultrafilter",
"GroupWithZero.toNontrivial",
"Ultrafilter.toFilter"
] | false |
Cardinal.mul_natCast_le_mul_natCast._simp_1 | Mathlib.SetTheory.Cardinal.Arithmetic | [
"HMul.hMul",
"Cardinal",
"Cardinal.mul_natCast_le_mul_natCast",
"Cardinal.instMul",
"Ne",
"instOfNatNat",
"LE.le",
"Nat.cast",
"Cardinal.instLE",
"Nat",
"propext",
"OfNat.ofNat",
"Eq",
"Cardinal.instNatCast",
"instHMul"
] | false |
Mathlib.Tactic.Choose.ElimStatus.ctorIdx | Mathlib.Tactic.Choose | [
"Lean.Expr",
"List",
"Nat",
"Mathlib.Tactic.Choose.ElimStatus.casesOn",
"Mathlib.Tactic.Choose.ElimStatus"
] | false |
List.toList_mkSlice_roc | Init.Data.Slice.List.Lemmas | [
"Std.Slice.toList",
"Std.Iterators.Types.Take.instIterator",
"Std.Slice.Internal.ListSliceData",
"Std.Rco.Sliceable.mkSlice",
"ListSlice.instToIterator",
"Std.Iterators.Types.ListIterator",
"congrArg",
"Monad.toApplicative",
"Std.Iterators.Types.Take",
"instOfNatNat",
"Id",
"Applicative.toPure... | true |
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