name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Complex.cos_int_mul_two_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Int.cast",
"Real.pi",
"HMul.hMul",
"Complex.commRing",
"Complex.cos",
"Nat.instAtLeastTwoHAddOfNat",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Complex.instMul",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"instOfNatNat",
"Int",
"AddGroupWithOne.toIntCast",
"Complex.instNatCast",... | true |
CategoryTheory.typesCartesianMonoidalCategory._proof_4 | Mathlib.CategoryTheory.Monoidal.Types.Basic | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.Types.terminalLimitCone",
"CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts",
"CategoryTheory.SemiCartesianMonoidalCatego... | false |
_private.Mathlib.Algebra.Polynomial.Roots.0.Polynomial.eq_zero_of_forall_eval_zero_of_natDegree_lt_card._simp_1_1 | Mathlib.Algebra.Polynomial.Roots | [
"Preorder.toLT",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddLeftMono",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"ZeroLEOneClass",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"CharZero",
"AddMonoidWithOne.toOne",
"AddZero.toZero",
... | false |
Std.Time.instHAddOffsetOffset_6 | Std.Time.Date.Basic | [
"Rat.instOfNat",
"instHDiv",
"Rat",
"HDiv.hDiv",
"Std.Time.Millisecond.Offset.toNanoseconds",
"HAdd",
"Std.Time.Millisecond.Offset",
"Std.Time.Internal.UnitVal.add",
"Std.Time.Nanosecond.Offset",
"OfNat.ofNat",
"HAdd.mk",
"Rat.instDiv"
] | true |
AlgebraicGeometry.Scheme.Hom.appIso_inv_app_apply | Mathlib.AlgebraicGeometry.OpenImmersion | [
"AlgebraicGeometry.Scheme.Hom.opensFunctor",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Open... | true |
CategoryTheory.functorCategoryPreadditive._proof_13 | Mathlib.CategoryTheory.Preadditive.FunctorCategory | [
"CategoryTheory.Functor",
"instHSMul",
"CategoryTheory.functorCategoryPreadditive._proof_4",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.functorCategoryPreadditive._proof_12",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"AddCommGroup.toAddGroup",
"Int",
"CategoryTheory.NatTrans.... | false |
Std.IterM.mapWithPostcondition.eq_1 | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"Monad.toApplicative",
"MonadLiftT.monadLift",
"Std.IterM.InternalCombinators.map",
"MonadLiftT",
"Std.Iterator",
"Std.Iterators.Types.Map",
"Applicative.toFunctor",
"Std.Iterators.PostconditionT",
"Eq.refl",
"Std.IterM",
"Monad",
"Eq",
"Std.IterM.mapWithPostcondition"
] | true |
equivShrink_symm_bot | Mathlib.Order.Shrink | [
"instBotShrink",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"Equiv",
"Bot.bot",
"Bot",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Equiv.injective",
"Shrink",
"Equiv.symm",
"equivShrink",
"Eq",
"DFunLike.coe",
"Eq.trans",
"Small",
"EquivLike.toFunLike"
] | true |
Std.DTreeMap.Internal.Unit.RcoSliceData.noConfusionType | Std.Data.DTreeMap.Internal.Zipper | [
"Std.Rco",
"Ord",
"Std.DTreeMap.Internal.Unit.RcoSliceData",
"Unit",
"HEq",
"Std.DTreeMap.Internal.Unit.RcoSliceData.casesOn",
"Std.DTreeMap.Internal.Impl"
] | false |
MeasureTheory.Measure.ae_measure_lt_top | Mathlib.MeasureTheory.Measure.Prod | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"Preorder.toLT",
"MeasurableSet",
"congrArg",
"Filter.Eventually",
"PartialOrder.toPreorder",
"MeasureTheory.Measure.prod_apply",
"Eq.mp",
"Prod.mk",
"Ne",
"MeasurableSpace",
"MeasureTheory.SFinite",
"measurable_measure_prodMk_left",
"MeasureT... | true |
Function.isPeriodicPt_prodMap | Mathlib.Dynamics.PeriodicPts.Defs | [
"congrArg",
"Prod.map",
"Nat.iterate",
"Prod.fst",
"Function.IsPeriodicPt",
"iff_self",
"And",
"Iff",
"Function.isFixedPt_prodMap._simp_1",
"Nat",
"True",
"of_eq_true",
"congrFun'",
"Function.IsFixedPt",
"Prod",
"Prod.snd",
"Prod.map_iterate",
"Eq.trans"
] | true |
Algebra.traceForm_apply | Mathlib.RingTheory.Trace.Defs | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"Algebra",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"LinearM... | true |
Lean.Server.moduleFromDocumentUri | Lean.Server.Utils | [
"Pure.pure",
"Option.instBEq",
"bne",
"_private.Lean.Server.Utils.0.Lean.Server.externalUriToName",
"System.FilePath.extension",
"Monad.toApplicative",
"String",
"IO",
"Lean.SearchPath",
"Option.some",
"_private.Lean.Server.Utils.0.Lean.Server.documentUriFromModule?.match_4",
"instDecidableEqB... | true |
Std.DTreeMap.Internal.Impl.mem_alter!_self._simp_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.alter!",
"Std.DTreeMap.Internal.Impl.mem_alter!_self",
"Ord",
"Std.DTreeMap.Internal.Impl.get?",
"Std.TransOrd",
"Membership.mem",
"Std.DTreeMap.Internal.Impl.WF",
"Bool.true",
"propext",
"Bool",
"Option.isSome",
"Eq",
"Std.LawfulEqOrd",
"Std.DTreeMap.Internal.I... | false |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.ofArray_fold_fn.match_1.splitter | Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas | [
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.ofArray_fold_fn.match_1",
"Option.some",
"Prod.mk",
"Bool.true",
"Option.none",
"Unit",
"Nat",
"Bool",
"Bool.false",
"Std.Tactic.BVDecide.LRAT.Internal.PosFin",
"Std.Sat.Literal",
"Option"
] | true |
Lean.Elab.Term.SyntheticMVarDecl.mk | Lean.Elab.Term.TermElabM | [
"Lean.Syntax",
"Lean.Elab.Term.SyntheticMVarDecl.mk",
"Lean.Elab.Term.SyntheticMVarKind",
"Lean.Elab.Term.SyntheticMVarDecl"
] | true |
CategoryTheory.Monad.Algebra.Hom.recOn | Mathlib.CategoryTheory.Monad.Algebra | [
"CategoryTheory.Monad",
"CategoryTheory.Monad.Algebra.Hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Monad.Algebra.a",
"CategoryTheory.Monad.Algebra.Hom.rec",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"CategoryTheory.Monad.toFunctor",
"CategoryT... | false |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.ToExpr.0.Lean.Meta.Grind.Arith.Linear.ofLinExpr.match_1 | Lean.Meta.Tactic.Grind.Arith.Linear.ToExpr | [
"Lean.Grind.Linarith.Expr.zero",
"Lean.Grind.Linarith.Expr",
"Unit.unit",
"Lean.Grind.Linarith.Expr.neg",
"Lean.Grind.Linarith.Expr.intMul",
"Lean.Grind.Linarith.Expr.natMul",
"Lean.Grind.Linarith.Expr.sub",
"Int",
"Lean.Grind.Linarith.Var",
"Unit",
"Lean.Grind.Linarith.Expr.add",
"Nat",
"Le... | false |
_private.Mathlib.Analysis.Distribution.SchwartzSpace.Basic.0.SchwartzMap.evalCLM._simp_2 | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | [
"And",
"and_assoc",
"propext",
"Eq"
] | false |
AlgebraicIndependent.isEmpty_of_isAlgebraic | Mathlib.RingTheory.AlgebraicIndependent.Transcendental | [
"Algebra.IsAlgebraic.isAlgebraic",
"CommRing",
"AlgebraicIndependent",
"CommSemiring.toSemiring",
"False.elim",
"Algebra",
"isEmpty_or_nonempty",
"Algebra.IsAlgebraic",
"IsEmpty",
"Or.casesOn",
"CommRing.toCommSemiring",
"Nonempty.casesOn",
"AlgebraicIndependent.transcendental",
"Nonempty"... | true |
LinearMap.mk.congr_simp | Mathlib.Algebra.Module.Equiv.Basic | [
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddHom",
"AddMonoid.toAddZeroClass",
"RingHom",
"Eq.rec",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"RingHom.instFunLike",
"LinearMap.mk",
"Semiring.toMonoid",
"Eq.ndrec",
"Se... | true |
_private.Mathlib.Algebra.Algebra.Spectrum.Basic.0.spectrum.zero_mem_resolventSet_of_unit._simp_1_3 | Mathlib.Algebra.Algebra.Spectrum.Basic | [
"spectrum",
"CommSemiring.toSemiring",
"spectrum.zero_notMem_iff",
"IsUnit",
"Algebra",
"Membership.mem",
"CommSemiring",
"Semiring.toMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"Ring.toSemiring",
"Eq",
"Set.instMembership",
"Ring",
"Not",
"MulZeroClass.toZero",
"instMulZer... | false |
_private.Mathlib.Analysis.Meromorphic.FactorizedRational.0.Function.FactorizedRational.mulSupport_update._simp_1_1 | Mathlib.Analysis.Meromorphic.FactorizedRational | [
"One",
"Function.mem_mulSupport",
"Membership.mem",
"Ne",
"propext",
"Function.mulSupport",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Init.Data.Nat.Basic.0.Nat.le.dest.match_1_1 | Init.Data.Nat.Basic | [
"Exists",
"instHAdd",
"Exists.casesOn",
"HAdd.hAdd",
"Nat",
"Exists.intro",
"instAddNat",
"Eq"
] | false |
Fin.encodeFun.eq_def | Batteries.Data.Fin.Coding | [
"instPowNat",
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Nat.mul_succ",
"Trans.trans",
"HMul.hMul",
"Fin.succ",
"congrArg",
"Nat.succ_le_of_lt",
"HEq.refl",
"Fin.encodeFun._proof_1",
"Fin.isLt",
"_private.Batteries.Data.Fin.Coding.0.Fin.encodeFun.match_1.splitter",
"Nat.brecOn.go",
"Nat.rec",
"... | true |
CategoryTheory.GrothendieckTopology.instIsContinuousOverStarOver | Mathlib.CategoryTheory.Sites.Over | [
"CategoryTheory.Over",
"CategoryTheory.RepresentablyFlat.of_isRightAdjoint",
"CategoryTheory.compatiblePreservingOfFlat",
"CategoryTheory.Functor.isContinuous_of_coverPreserving",
"CategoryTheory.GrothendieckTopology.coverPreserving_over_star",
"CategoryTheory.Limits.HasBinaryProducts",
"CategoryTheory.... | true |
HahnSeries.finiteArchimedeanClassOrderHomInvLex._proof_3 | Mathlib.RingTheory.HahnSeries.Lex | [
"ZeroHom.funLike",
"Equiv.instEquivLike",
"HahnSeries.finiteArchimedeanClassOrderHomInvLex._proof_9",
"AddCommGroup.toAddCommMonoid",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Lex",
"LinearOrder",
"HahnSeries.finiteArchimedeanClassOrderHomInvLex.match_1",
"ArchimedeanClass.instLinearOrder",
"Parti... | false |
Representation.IntertwiningMap.comp_apply | Mathlib.RepresentationTheory.Intertwining | [
"Monoid",
"Representation",
"Representation.IntertwiningMap.comp",
"Representation.IntertwiningMap.instFunLike",
"AddCommMonoid",
"Semiring",
"Representation.IntertwiningMap",
"Module",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
Matrix.natCast_mulVec | Mathlib.Data.Matrix.Mul | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"instSMulOfMul",
"Matrix",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Function.hasSMul",
"Matrix.instNatCastOfZero",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Nat.cast",
"NonAssocSemiring",
"Fintype",
"... | true |
ULift.compactSpace | Mathlib.Topology.Compactness.Compact | [
"ULift.topologicalSpace",
"ULift",
"Topology.IsClosedEmbedding.compactSpace",
"CompactSpace",
"TopologicalSpace",
"ULift.down",
"Topology.IsClosedEmbedding.uliftDown"
] | true |
Filter.Tendsto.nhds | Mathlib.Topology.Filter | [
"Function.comp",
"nhds",
"Continuous.tendsto",
"TopologicalSpace",
"Filter.Tendsto",
"Filter.Tendsto.comp",
"Filter.continuous_nhds",
"Filter",
"Filter.instTopologicalSpace"
] | true |
Std.Http.RequestTarget.asteriskForm.elim | Std.Internal.Http.Data.URI.Basic | [
"Std.Http.RequestTarget.asteriskForm",
"PULift.up",
"Std.Http.RequestTarget.ctorIdx",
"Std.Http.RequestTarget",
"Nat",
"Std.Http.RequestTarget.ctorElim",
"Eq.symm",
"Eq"
] | false |
Polynomial.toFinsupp_injective | Mathlib.Algebra.Polynomial.Basic | [
"_private.Mathlib.Algebra.Polynomial.Basic.0.Polynomial.toFinsupp_injective.match_1_1",
"Polynomial.toFinsupp",
"Polynomial",
"congr_arg",
"Nat",
"Semiring",
"Function.Injective",
"AddMonoidAlgebra",
"Polynomial.ofFinsupp",
"Eq"
] | true |
instIsAlgebraicSubtypeMemSubalgebraAlgebraicClosure | Mathlib.RingTheory.Algebraic.Integral | [
"Subalgebra.instSetLike",
"IsDomain",
"CommRing",
"CommSemiring.toSemiring",
"Algebra",
"Membership.mem",
"id",
"Subtype",
"Algebra.IsAlgebraic",
"Subalgebra.toRing",
"CommRing.toCommSemiring",
"Subalgebra.IsAlgebraic",
"Subalgebra.algebra",
"Iff.mp",
"CommRing.toRing",
"Subalgebra.isA... | true |
RegularExpression.comp.elim | Mathlib.Computability.RegularExpressions | [
"PULift.up",
"RegularExpression",
"RegularExpression.comp",
"Nat",
"RegularExpression.ctorElim",
"Eq.symm",
"Eq",
"RegularExpression.ctorIdx"
] | false |
sup_congr_right | Mathlib.Order.Lattice | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le.antisymm",
"SemilatticeSup.toMax",
"le_sup_right",
"LE.le",
"Max.max",
"sup_le",
"SemilatticeSup.toPartialOrder",
"Eq",
"SemilatticeSup"
] | true |
_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.isColoop_iff_forall_mem_compl_isCircuit._simp_1_1 | Mathlib.Combinatorics.Matroid.Loop | [
"Matroid.E",
"Membership.mem",
"Matroid.isColoop_iff_forall_notMem_isCircuit._auto_1",
"autoParam",
"Matroid.IsColoop",
"Matroid.IsCircuit",
"propext",
"Eq",
"Set.instMembership",
"Matroid",
"Not",
"Matroid.isColoop_iff_forall_notMem_isCircuit",
"Set"
] | false |
ProbabilityTheory.«term_∥ₖ_» | Mathlib.Probability.Kernel.Composition.ParallelComp | [
"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 |
UInt8.left_le_or | Init.Data.UInt.Bitwise | [
"Eq.mpr",
"instHOrOfOrOp",
"congrArg",
"instOrOpUInt8",
"id",
"LE.le",
"instLENat",
"_private.Init.Data.UInt.Bitwise.0.UInt8.left_le_or._simp_1_1",
"HOr.hOr",
"UInt8.toNat_or",
"Nat",
"UInt8.toNat",
"UInt8",
"Eq",
"Nat.instOrOp",
"Nat.left_le_or",
"instLEUInt8",
"Eq.trans"
] | true |
Int.eq_zero_of_lcm_eq_zero | Init.Data.Int.Gcd | [
"Int.lcm_ne_zero",
"Int.lcm",
"Int.instDecidableEq",
"Ne",
"instOfNatNat",
"Int",
"_private.Init.Data.Int.Gcd.0.Int.eq_zero_of_lcm_eq_zero._proof_1_1",
"instOfNat",
"Nat",
"Decidable.byContradiction",
"Or",
"OfNat.ofNat",
"Eq",
"instDecidableOr",
"Not"
] | true |
Polynomial.UniversalCoprimeFactorizationRing.homEquiv._proof_11 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"IsUnit.mul_iff",
"Polynomial.MonicDegreeEq.monic",
"Nontrivial",
"Eq.mpr",
"AlgHom.coe_toRingHom",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"MulOne.toOne",
"Equiv.apply_symm_apply",
"CommRing",
"Equiv.instEquivLike",
"AlgHom.algHomClass",
... | false |
RCLike.complexLinearIsometryEquiv._proof_2 | Mathlib.Analysis.Complex.Basic | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingEquiv.toEquiv",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Mathlib.Tactic.Ring.Common.mul_congr",
"RCLike.toNormedAlgebra",
"HMul... | false |
CategoryTheory.«term_≫=_» | Mathlib.CategoryTheory.Category.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 |
AddSubmonoid.closure_empty | Mathlib.Algebra.Group.Submonoid.Basic | [
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"AddSubmonoid.instCompleteLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"AddSubmonoid",
"AddSubmonoid.gi",
"Bot.bot",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
... | true |
CategoryTheory.ShortComplex.Exact.op | Mathlib.Algebra.Homology.ShortComplex.Exact | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.Exact.mk",
"CategoryTheory.Limits.IsZero.op",
"Opposite",
"CategoryTheory.ShortComplex.HomologyData.iso",
"CategoryTheory.ShortComplex.HomologyData.op",
"CategoryTheory.ShortComplex",
"Exists",
"CategoryTheory.ShortComplex.RightH... | true |
emultiplicity_ne_of_multiplicity_ne | Mathlib.RingTheory.Multiplicity | [
"Monoid",
"ENat.instNatCast",
"mt",
"Ne",
"Nat.cast",
"multiplicity",
"Nat",
"ENat",
"Eq",
"emultiplicity",
"multiplicity_eq_of_emultiplicity_eq_some"
] | true |
Mathlib.Meta.NormNum.NormNums.casesOn | Mathlib.Tactic.NormNum.Core | [
"Mathlib.Meta.NormNum.NormNums.mk",
"Lean.PHashSet",
"Mathlib.Meta.NormNum.NormNums.rec",
"Mathlib.Meta.NormNum.NormNumExt",
"Lean.Meta.DiscrTree",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.instHashableName",
"Mathlib.Meta.NormNum.NormNums"
] | false |
Multiset.count_nsmul | Mathlib.Algebra.Order.Group.Multiset | [
"False",
"Nat.recAux",
"instHSMul",
"Multiset.notMem_zero._simp_1",
"HMul.hMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"Multiset.instAddCancelCommMonoid",
"Membership.mem",
"AddZeroClass.toAddZero",
"Multiset.count",
"Multiset",
"Multiset.count.congr_simp",
"instMu... | true |
CategoryTheory.SmallObject.SuccStruct.ofCocone._proof_6 | Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Set.Elem",
"DistribLattice.toLattice",
"Preorder.smallCategory",
"LE.le",
"CategoryTheory.Category.toCategoryStruct",
"Set.Ii... | false |
String.next_eq_posGT | Init.Data.String.Lemmas.FindPos | [
"String.Pos.next",
"congrArg",
"String",
"String.Pos.posGT_offset._proof_1",
"Ne",
"String.next_eq_posGT._proof_1",
"String.posGT",
"True",
"eq_self",
"String.endPos",
"String.Pos",
"of_eq_true",
"String.Pos.posGT_offset",
"Eq",
"String.Pos.offset",
"Eq.trans"
] | true |
_private.Mathlib.CategoryTheory.Sites.Over.0.CategoryTheory.instIsCocontinuousOverLeftIteratedSliceBackwardOver._proof_1 | Mathlib.CategoryTheory.Sites.Over | [
"CategoryTheory.Over",
"CategoryTheory.Functor.IsDenseSubsite.instIsCocontinuous",
"CategoryTheory.instCategoryOver",
"CategoryTheory.Over.iteratedSliceBackward",
"CategoryTheory.Over.left",
"CategoryTheory.Functor.IsCocontinuous",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.GrothendieckTop... | false |
_private.Init.Prelude.0.Lean.Syntax.getHeadInfo?.loop.match_1 | Init.Prelude | [
"Unit.unit",
"Lean.SourceInfo",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
AList.empty_union | Mathlib.Data.List.AList | [
"AList.instEmptyCollection",
"List",
"AList.ext",
"AList",
"AList.instUnion",
"Union.union",
"EmptyCollection.emptyCollection",
"Eq",
"Sigma",
"rfl",
"DecidableEq",
"AList.entries"
] | true |
List.Perm.swap' | Init.Data.List.Perm | [
"List.Perm.cons",
"List.Perm",
"List.Perm.swap",
"List.Perm.trans",
"List.cons",
"List"
] | true |
Metric.closure_eq_iInter_cthickening' | Mathlib.Topology.MetricSpace.Thickening | [
"Set.Subset.antisymm",
"Eq.mpr",
"Set.Ioc",
"Real",
"Set.Ioi",
"Preorder.toLT",
"Real.instZero",
"congrArg",
"Set.iInter",
"PartialOrder.toPreorder",
"Real.instLT",
"Classical.propDecidable",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Set.subset_iInter₂",
"Set.mem_Ioi",
"Metric.... | true |
Module.rank_def | Mathlib.LinearAlgebra.Dimension.Basic | [
"Eq.mpr",
"wrapped._@.Mathlib.LinearAlgebra.Dimension.Basic.3070247278._hygCtx._hyg.2",
"Cardinal",
"congrArg",
"iSup",
"Cardinal.mk",
"Set.Elem",
"id",
"Subtype",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"AddCommMonoid",
"Subtype.mk",
"Cardinal.instConditionallyCom... | true |
_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.comm_ring_aux₁._proof_11 | Mathlib.RingTheory.WittVector.Basic | [
"Nat.instMulZeroClass",
"Nat.Prime",
"_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun",
"AddMonoidAlgebra.commRing",
"CommSemiring.toSemiring",
"Rat",
"Rat.commSemiring",
"Fact",
"Pi.instPow",
"WittVector.hasNatPow",
"Finsupp.instAddCommMonoid",
"Monoid.toPow",
"CommRing.t... | false |
_private.Mathlib.Analysis.Complex.UpperHalfPlane.Exp.0._aux_Mathlib_Analysis_Complex_UpperHalfPlane_Exp___unexpand_Function_Periodic_qParam_1 | Mathlib.Analysis.Complex.UpperHalfPlane.Exp | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk... | false |
Mathlib.Linter.TextBased.initFn._@.Mathlib.Tactic.Linter.TextBased.3477620185._hygCtx._hyg.4 | Mathlib.Tactic.Linter.TextBased | [
"Lean.Option",
"Lean.Name.mkStr5",
"IO",
"Lean.Option.Decl.mk",
"Bool.true",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool",
"Lean.Name.mkStr2"
] | false |
_private.Lean.Elab.Deriving.ToExpr.0.Lean.Elab.Deriving.ToExpr.mkToExprInstanceHandler | Lean.Elab.Deriving.ToExpr | [
"Pure.pure",
"Lean.mkNullNode",
"Lean.Elab.Command.Scope.header",
"Lean.Elab.Command.liftTermElabM",
"Lean.Elab.Command.Scope.mk",
"Lean.Elab.Command.Scope.currNamespace",
"Lean.isInductive",
"Lean.Elab.Command.Scope.isMeta",
"Lean.Elab.Command.elabCommand",
"Lean.Option.set",
"Lean.Syntax",
"... | true |
GenContFract.convs_stable_of_terminated | Mathlib.Algebra.ContinuedFractions.TerminatedStable | [
"GenContFract.nums_stable_of_terminated",
"GenContFract.convs",
"GenContFract.dens",
"instHDiv",
"GenContFract.dens_stable_of_terminated",
"congrArg",
"DivisionRing.toDivInvMonoid",
"HDiv.hDiv",
"LE.le",
"GenContFract",
"instLENat",
"GenContFract.nums",
"Nat",
"congr",
"True",
"eq_self... | true |
Set.powersetCard.eq_empty_iff | Mathlib.Data.Set.PowersetCard | [
"Eq.mpr",
"Nat.choose",
"Nat.choose_eq_zero_iff",
"congrArg",
"Finset",
"Finite",
"Iff.rfl",
"Set.Elem",
"id",
"Nat.card",
"Nat.card_coe_set_eq",
"instOfNatNat",
"Set.ncard_eq_zero",
"Set.toFinite",
"Iff",
"Nat",
"LT.lt",
"propext",
"Set.instEmptyCollection",
"Set.powersetCard.... | true |
WeakPseudoEMetricSpace.ext_iff | Mathlib.Topology.EMetricSpace.Defs | [
"WeakPseudoEMetricSpace",
"WeakPseudoEMetricSpace.ext",
"HEq.refl",
"Eq.casesOn",
"TopologicalSpace",
"Iff",
"WeakPseudoEMetricSpace.toEDist",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"EDist",
"Eq.symm",
"Eq"
] | true |
Std.DTreeMap.Internal.Unit.RcoSliceData.mk | Std.Data.DTreeMap.Internal.Zipper | [
"Std.Rco",
"Ord",
"Std.DTreeMap.Internal.Unit.RcoSliceData",
"Unit",
"Std.DTreeMap.Internal.Unit.RcoSliceData.mk",
"Std.DTreeMap.Internal.Impl"
] | true |
GradedMonoid.fst_pow | Mathlib.Algebra.GradedMonoid | [
"instHSMul",
"AddMonoid.toNSMul",
"GradedMonoid.GMonoid.toMonoid",
"GradedMonoid.GMonoid",
"Sigma.fst",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"AddMonoid",
"GradedMonoid",
"HSMul.hSMul",
"instHPow",
"Eq",
"rfl"
] | true |
CategoryTheory.Join.inlCompFromSum_inv_app | Mathlib.CategoryTheory.Join.Sum | [
"CategoryTheory.Functor",
"CategoryTheory.Join.inlCompFromSum",
"CategoryTheory.sum",
"CategoryTheory.Join.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Jo... | true |
_private.Mathlib.MeasureTheory.Integral.Bochner.Basic.0.MeasureTheory.integral_eq_zero_iff_of_nonneg_ae._simp_1_3 | Mathlib.MeasureTheory.Integral.Bochner.Basic | [
"Real.instLE",
"Real",
"ENNReal.ofReal_eq_zero",
"Real.instZero",
"ENNReal.ofReal",
"LE.le",
"ENNReal",
"propext",
"Zero.toOfNat0",
"ENNReal.instZero",
"OfNat.ofNat",
"Eq"
] | false |
Interval.addCommMonoid.eq_1 | Mathlib.Algebra.Order.Interval.Basic | [
"Interval.addCommMonoid._proof_6",
"Interval.addZeroClass",
"Interval.addCommMonoid._proof_5",
"AddMonoid.mk",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"Interval",
"AddSemigroup.mk",
"AddCommMonoid",
"nsmulRecAuto",
"AddZero.toZero",
"Interval.addCommMonoid._proof_4",
"Interval.addCommMono... | true |
CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv_assoc | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.FormalCoproduct",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.FormalCoproduct.fromIncl_comp_coproductIsoSelf_inv",
"CategoryTheory.Discrete.fun... | true |
CategoryTheory.Limits.hasColimitsOfShape_of_initialSeg | Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape | [
"Iff.mpr",
"Eq.mpr",
"OrderIso.equivalence",
"Preorder.toLT",
"PrincipalSeg.mem_range_iff_rel",
"Order.succ",
"isWellOrder_lt",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Limits.HasIterationOfShape.hasColimitsOfShape",
"congrArg",
"PrincipalSeg.le_iff_le",
"LinearOrder",
"Fa... | true |
CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_inv_hom_id_app_eTruncLT_obj | Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | [
"WithBot.instPreorder",
"CategoryTheory.Triangulated.TStructure.eTruncLTLTIsoLT_inv_hom_id_app",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"WithTop.instPreorder",
"congrArg",
"CategoryTheory.Functor.Additive",
"PartialOrder.toPreorder",
"CategoryTheory.Funct... | true |
Lean.LocalDecl.cdecl | Lean.LocalContext | [
"Lean.LocalDecl.cdecl",
"Lean.LocalDeclKind",
"Lean.Expr",
"Lean.FVarId",
"Nat",
"Lean.Name",
"Lean.LocalDecl",
"Lean.BinderInfo"
] | true |
MeasureTheory.Measure.haar._proof_1 | Mathlib.MeasureTheory.Measure.Haar.Basic | [
"instWeaklyLocallyCompactSpaceOfLocallyCompactSpace",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"One.instNonempty",
"TopologicalSpace.PositiveCompacts.nonempty'",
"TopologicalSpace",
"Nonempty",
"LocallyCompactSpa... | false |
derivationToSquareZeroOfLift._proof_3 | Mathlib.RingTheory.Derivation.ToSquareZero | [
"Ideal.Quotient.isScalarTower",
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"derivationToSquareZeroOfLift._proof_1",
"Ideal",
"Submodule.Quotient.instSMul'",
"CommSemiring",
"HasQuotient.Quotient",
"CommRing.toCommSemiring",
"Id... | false |
List.Forall._f | Mathlib.Data.List.Defs | [
"List.cons",
"List",
"And",
"List.Forall.match_1",
"Unit",
"True",
"List.below",
"List.nil"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.Orthogonal.0.Submodule.map_orthogonal._simp_1_7 | Mathlib.Analysis.InnerProductSpace.Orthogonal | [
"Submodule",
"Membership.mem",
"Submodule.mem_inf",
"AddCommMonoid",
"And",
"Submodule.instMin",
"Submodule.setLike",
"propext",
"Semiring",
"Module",
"Eq",
"SetLike.instMembership",
"Min.min"
] | false |
Cardinal.lift_iSup_le_iff._simp_1 | Mathlib.SetTheory.Cardinal.Basic | [
"Cardinal",
"iSup",
"Cardinal.lift",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"BddAbove",
"Cardinal.instLE",
"Cardinal.instConditionallyCompleteLinearOrderBot",
"propext",
"ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder",
"ConditionallyC... | false |
OrderedFinpartition.extendMiddle._proof_2 | Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | [
"Fin.succ_lt_succ_iff._simp_1",
"dite_cond_eq_true",
"not_lt_zero._simp_1",
"Eq.mpr",
"of_eq_false",
"instNeZeroNatHAdd_1",
"False",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Function.update",
"StrictMono",
"eq_false",
"Fin.succ",
"congrArg",
"Fin.instNonUnitalCo... | false |
String.Slice.Subslice.extendLeft_self._proof_1 | Init.Data.String.Subslice | [
"String.Slice.Subslice",
"String.instLEPos_1",
"String.Slice.Pos.le_refl",
"String.Slice",
"LE.le",
"String.Slice.Subslice.startInclusive",
"String.Slice.Pos"
] | false |
String.validateUTF8 | Init.Data.String.Extra | [
"Bool",
"ByteArray.validateUTF8",
"ByteArray"
] | true |
_private.Lean.Elab.Util.0.Lean.Elab.liftMacroM.match_3 | Lean.Elab.Util | [
"String",
"Prod.mk",
"Lean.Name",
"Prod",
"Prod.casesOn"
] | false |
Complex.ofReal_cot | Mathlib.Analysis.Complex.Trigonometric | [
"Real",
"Complex.ofReal_cot_ofReal_re",
"Complex.ofReal",
"Complex.cot",
"Complex",
"Real.cot",
"Eq"
] | true |
CategoryTheory.Pseudofunctor.DescentData.Hom.ext_iff | Mathlib.CategoryTheory.Sites.Descent.DescentData | [
"Opposite",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Pseudofunctor.DescentData.Hom.hom",
"CategoryTheory.Pseudofunctor.DescentData.obj",
"CategoryTheory.Cat.str",
"Eq.casesOn... | true |
Std.Internal.List.getValueCast?._sunfold | Std.Data.Internal.List.Associative | [
"Std.Internal.List.getValueCast?._proof_1",
"Std.Internal.List.getValueCast?.match_1",
"Std.Internal.List.getValueCast?",
"Option.some",
"cast",
"LawfulBEq",
"instDecidableEqBool",
"dite",
"Bool.true",
"Option.none",
"List",
"BEq.beq",
"Unit",
"Bool",
"BEq",
"Eq",
"Not",
"Sigma",
... | false |
_private.Mathlib.LinearAlgebra.Lagrange.0.Lagrange.natDegree_basis.match_1_2 | Mathlib.LinearAlgebra.Lagrange | [
"Finset",
"Membership.mem",
"Ne",
"And.casesOn",
"And",
"Finset.instSetLike",
"And.intro",
"SetLike.instMembership"
] | false |
_private.Init.PropLemmas.0.nonempty_prop.match_1_1 | Init.PropLemmas | [
"Nonempty.intro",
"Nonempty.casesOn",
"Nonempty"
] | false |
DistribLattice.instIsModularLattice | Mathlib.Order.ModularLattice | [
"Iff.mpr",
"Eq.mpr",
"le_refl",
"Lattice.toSemilatticeSup",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"id",
"SemilatticeInf.toMin",
"LE.le",
"inf_sup_right",
"DistribLattice",
"Max.max",
... | true |
_private.Mathlib.Algebra.Polynomial.RuleOfSigns.0.Polynomial.signVariations_eraseLead_mul_X_sub_C._proof_1_4 | Mathlib.Algebra.Polynomial.RuleOfSigns | [
"Polynomial.C",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"congrArg",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"RingHom",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
"Nat.Linear.ExprCnstr.eq_of_... | false |
_private.Mathlib.ModelTheory.Encoding.0.FirstOrder.Language.BoundedFormula.listEncode.match_1.splitter | Mathlib.ModelTheory.Encoding | [
"FirstOrder.Language.BoundedFormula.imp",
"FirstOrder.Language.BoundedFormula.listEncode.match_1",
"FirstOrder.Language.Term",
"Sum",
"instOfNatNat",
"FirstOrder.Language.BoundedFormula.equal",
"FirstOrder.Language.BoundedFormula.falsum",
"instHAdd",
"HAdd.hAdd",
"Nat",
"FirstOrder.Language.Rela... | true |
String.splits_startPos_iff._simp_1 | Init.Data.String.Lemmas.Splits | [
"String.Pos.Splits",
"String",
"String.startPos",
"And",
"propext",
"String.splits_startPos_iff",
"Eq"
] | false |
_private.Init.Data.String.Lemmas.Order.0.String.Slice.Pos.sliceFrom_lt_sliceFrom_iff._simp_1_1 | Init.Data.String.Lemmas.Order | [
"String.instLTRaw",
"String.Slice.Pos.offset",
"String.Slice",
"String.Pos.Raw",
"LT.lt",
"String.instLTPos_1",
"propext",
"String.Slice.Pos",
"String.Slice.Pos.lt_iff",
"Eq"
] | false |
_private.Mathlib.Tactic.IntervalCases.0.Mathlib.Tactic.IntervalCases.natMethods.match_4 | Mathlib.Tactic.IntervalCases | [
"Lean.Expr.const",
"Prod.mk",
"Lean.Expr.sort",
"Lean.Level",
"Int",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Qq.Quoted.unsafeMk",
"Lean.Expr.app",
"Sigma.mk",
"Sigma.casesOn",
"Lean.Level.succ",
"Prod",
"Prod.casesOn",
"Lean.Name.mkStr1",
"Sigma",
"List.nil"
] | false |
Primrec.ofNat | Mathlib.Computability.Primrec.Basic | [
"Primcodable.ofDenumerable",
"id",
"Primrec",
"Nat",
"Iff.mp",
"Denumerable.nat",
"Denumerable",
"Primrec.ofNat_iff",
"Primrec.id",
"Denumerable.ofNat"
] | true |
_private.Lean.Meta.Tactic.Util.0.Lean.Meta.saturate.go.match_1 | Lean.Meta.Tactic.Util | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.MVarId",
"Option.none",
"List",
"Unit",
"Option"
] | false |
CategoryTheory.PreOneHypercover.toPullback_fst | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"Eq.mpr",
"CategoryTheory.Limits.pullback",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.Limits.pullback.lift",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.PreOneHypercover",
"CategoryTheory.PreOneHypercover.I₁",
"CategoryTheory.PreOneHypercover.toP... | true |
rpow_mul_exp_neg_mul_rpow_isLittleO_exp_neg | Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral | [
"NormedCommRing.toNormedRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"SeminormedRing.toNorm",
"Real.instPow",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedRing.toRing",
"HMul.hMul",
"Real.ins... | true |
DoResultPRBC.break.noConfusion | Init.Core | [
"id",
"DoResultPRBC.break",
"DoResultPRBC",
"heq_of_eq",
"DoResultPRBC.noConfusion",
"Eq.refl",
"HEq",
"Eq"
] | false |
CategoryTheory.NatTrans.CommShift | Mathlib.CategoryTheory.Shift.CommShift | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.NatTrans.CommShift.mk",
"AddMonoid",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.HasShift",
"CategoryTheory.Functor.CommShift",
"CategoryTheory.Categ... | true |
Monoid.PushoutI.NormalWord.Pair.mk._flat_ctor | Mathlib.GroupTheory.PushoutI | [
"Monoid.CoprodI.Word.fstIdx",
"MonoidHom",
"Monoid.toMulOneClass",
"Group",
"Monoid.CoprodI.Word.toList",
"Monoid.CoprodI.Word.Pair.mk",
"Option.some",
"Membership.mem",
"DivInvMonoid.toMonoid",
"Monoid.CoprodI.Word",
"Ne",
"Group.toDivInvMonoid",
"List",
"MulOneClass.toMulOne",
"List.in... | false |
Batteries.CodeAction.holeKindToHoleString | Batteries.CodeAction.Misc | [
"String",
"instAppendString",
"instHAppendOfAppend",
"Lean.Name",
"HAppend.hAppend",
"_private.Batteries.CodeAction.Misc.0.Batteries.CodeAction.holeKindToHoleString.match_1"
] | true |
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