name
stringlengths
2
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module
stringlengths
6
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type
stringlengths
1
5.67M
allowCompletion
bool
2 classes
himp_top
Mathlib.Order.Heyting.Basic
∀ {α : Type u_2} [inst : GeneralizedHeytingAlgebra α] {a : α}, a ⇨ ⊤ = ⊤
true
csInf_Ioi
Mathlib.Order.ConditionallyCompleteLattice.Basic
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {a : α} [NoMaxOrder α] [DenselyOrdered α], sInf (Set.Ioi a) = a
true
_private.Mathlib.Dynamics.OmegaLimit.0.mem_omegaLimit_iff_frequently._simp_1_1
Mathlib.Dynamics.OmegaLimit
∀ {α : Type u} {f : Filter α} {P : α → Prop}, (∃ᶠ (x : α) in f, P x) = ∀ {U : Set α}, U ∈ f → ∃ x ∈ U, P x
false
Rep.ofMulActionSubsingletonIsoTrivial
Mathlib.RepresentationTheory.Rep.Basic
(k : Type u) → (G : Type v) → [inst : Ring k] → [inst_1 : Monoid G] → (H : Type u) → [Subsingleton H] → [MulOneClass H] → [inst_4 : MulAction G H] → Rep.ofMulAction k G H ≅ Rep.trivial k G k
true
Finset.ordConnected_range_val
Mathlib.Data.Finset.Grade
∀ {α : Type u_1}, (Set.range Finset.val).OrdConnected
true
ringHomEquivModuleIsScalarTower._proof_4
Mathlib.Algebra.Module.RingHom
∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (x : { _inst // IsScalarTower R S S }), ⟨Module.compHom S (match x with | ⟨val, property⟩ => RingHom.smulOneHom), ⋯⟩ = x
false
NonemptyInterval.subtractionCommMonoid._proof_11
Mathlib.Algebra.Order.Interval.Basic
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [inst_2 : IsOrderedAddMonoid α] (a b : NonemptyInterval α), a + b = b + a
false
Lean.PrettyPrinter.Delaborator.TopDownAnalyze.App.Context.f
Lean.PrettyPrinter.Delaborator.TopDownAnalyze
Lean.PrettyPrinter.Delaborator.TopDownAnalyze.App.Context → Lean.Expr
true
Ideal.quotientInfRingEquivPiQuotient._proof_2
Mathlib.RingTheory.Ideal.Quotient.Operations
∀ {R : Type u_1} [inst : CommRing R] {ι : Type u_2} (f : ι → Ideal R) (i : ι), (f i).IsTwoSided
false
AlgEquiv.equivCongr_symm
Mathlib.Algebra.Algebra.Equiv
∀ {R : Type uR} {A₁ : Type uA₁} {A₂ : Type uA₂} {A₁' : Type uA₁'} {A₂' : Type uA₂'} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Semiring A₂] [inst_3 : Semiring A₁'] [inst_4 : Semiring A₂'] [inst_5 : Algebra R A₁] [inst_6 : Algebra R A₂] [inst_7 : Algebra R A₁'] [inst_8 : Algebra R A₂'] (e : A₁ ≃ₐ[R] A₂) (e' : A₁' ≃ₐ[R] A₂'), (e.equivCongr e').symm = e.symm.equivCongr e'.symm
true
_private.Mathlib.LinearAlgebra.AffineSpace.Combination.0.Finset.weightedVSub_eq_linear_combination._simp_1_1
Mathlib.LinearAlgebra.AffineSpace.Combination
∀ {ι : Type u_1} {R : Type u_5} {M : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {f : ι → R} {s : Finset ι} {x : M}, ∑ i ∈ s, f i • x = (∑ i ∈ s, f i) • x
false
CategoryTheory.Limits.HasZeroMorphisms.instSubsingleton
Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C], Subsingleton (CategoryTheory.Limits.HasZeroMorphisms C)
true
CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape_le_transfiniteCompositions
Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (W : CategoryTheory.MorphismProperty C) (J : Type w) [inst_1 : LinearOrder J] [inst_2 : SuccOrder J] [inst_3 : OrderBot J] [inst_4 : WellFoundedLT J], W.transfiniteCompositionsOfShape J ≤ CategoryTheory.MorphismProperty.transfiniteCompositions.{w, v, u} W
true
Subfield.relrank_mul_relrank_eq_inf_relrank
Mathlib.FieldTheory.Relrank
∀ {E : Type v} [inst : Field E] (A : Subfield E) {B C : Subfield E}, B ≤ C → A.relrank B * B.relrank C = (A ⊓ B).relrank C
true
IsContDiffImplicitAt.ne_zero
Mathlib.Analysis.Calculus.ImplicitContDiff
∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E₁ : Type u_2} [inst_1 : NormedAddCommGroup E₁] [inst_2 : NormedSpace 𝕜 E₁] {E₂ : Type u_3} [inst_3 : NormedAddCommGroup E₂] [inst_4 : NormedSpace 𝕜 E₂] {F : Type u_4} [inst_5 : NormedAddCommGroup F] [inst_6 : NormedSpace 𝕜 F] {n : WithTop ℕ∞} {f : E₁ × E₂ → F} {f' : E₁ × E₂ →L[𝕜] F} {u : E₁ × E₂}, IsContDiffImplicitAt n f f' u → n ≠ 0
true
Finset.insert_inter_of_notMem
Mathlib.Data.Finset.Lattice.Lemmas
∀ {α : Type u_1} [inst : DecidableEq α] {s₁ s₂ : Finset α} {a : α}, a ∉ s₂ → insert a s₁ ∩ s₂ = s₁ ∩ s₂
true
_private.Lean.Meta.Sym.Offset.0.Lean.Meta.Sym.isOffset.match_1
Lean.Meta.Sym.Offset
(motive : Lean.Expr → Sort u_1) → (n : Lean.Expr) → ((val : ℕ) → motive (Lean.Expr.lit (Lean.Literal.natVal val))) → ((x : Lean.Expr) → motive x) → motive n
false
Topology.RelCWComplex.FiniteDimensional.mk._flat_ctor
Mathlib.Topology.CWComplex.Classical.Finite
∀ {X : Type u} [inst : TopologicalSpace X] {C D : Set X} [inst_1 : Topology.RelCWComplex C D], (∀ᶠ (n : ℕ) in Filter.atTop, IsEmpty (Topology.RelCWComplex.cell C n)) → Topology.RelCWComplex.FiniteDimensional C
false
AddCon.toSetoid_bot
Mathlib.GroupTheory.Congruence.Defs
∀ {M : Type u_1} [inst : Add M], ⊥.toSetoid = ⊥
true
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_579
Mathlib.GroupTheory.Perm.Cycle.Type
∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w : α), ¬[g a, g (g a)].Nodup → ∀ (w_1 : α), 2 ≤ List.count w_1 [g a, g (g a)] → List.idxOfNth w_1 [g (g a)] [g (g a)].length < (List.filter (fun x => decide (x = w_1)) [g a, g (g a)]).length
false
_private.Lean.Elab.Tactic.Conv.Congr.0.Lean.Elab.Tactic.Conv.congrImplies.match_1
Lean.Elab.Tactic.Conv.Congr
(motive : List Lean.MVarId → Sort u_1) → (__discr : List Lean.MVarId) → ((mvarId₁ mvarId₂ head head_1 : Lean.MVarId) → motive [mvarId₁, mvarId₂, head, head_1]) → ((x : List Lean.MVarId) → motive x) → motive __discr
false
CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT_hom_app_fac'_assoc
Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] [inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.HasShift C ℤ] [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C] (t : CategoryTheory.Triangulated.TStructure C) [inst_6 : CategoryTheory.IsTriangulated C] (a b : EInt) (X : C) {Z : C} (h : (t.eTruncGE.obj a).obj X ⟶ Z), CategoryTheory.CategoryStruct.comp ((t.eTruncLTGEIsoGELT a b).hom.app X) (CategoryTheory.CategoryStruct.comp ((t.eTruncGE.obj a).map ((t.eTruncLTι b).app X)) h) = CategoryTheory.CategoryStruct.comp ((t.eTruncLTι b).app ((t.eTruncGE.obj a).obj X)) h
true
CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation._sizeOf_1
Mathlib.CategoryTheory.Sites.Grothendieck
{C : Type u} → {inst : CategoryTheory.Category.{v, u} C} → {X : C} → {J : CategoryTheory.GrothendieckTopology C} → {S : J.Cover X} → {I₁ I₂ : S.Arrow} → [SizeOf C] → I₁.Relation I₂ → ℕ
false
Lean.Firefox.SampleUnits._sizeOf_1
Lean.Util.Profiler
Lean.Firefox.SampleUnits → ℕ
false
MeasureTheory.AEFinStronglyMeasurable.mul
Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace β] {f g : α → β} [inst_1 : MulZeroClass β] [ContinuousMul β], MeasureTheory.AEFinStronglyMeasurable f μ → MeasureTheory.AEFinStronglyMeasurable g μ → MeasureTheory.AEFinStronglyMeasurable (f * g) μ
true
Subgroup.card_le_card_group
Mathlib.Algebra.Group.Subgroup.Finite
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [Finite G], Nat.card ↥H ≤ Nat.card G
true
CommRingCat.hasLimitsOfSize
Mathlib.Algebra.Category.Ring.Limits
∀ [UnivLE.{v, u}], CategoryTheory.Limits.HasLimitsOfSize.{w, v, u, u + 1} CommRingCat
true
Lean.Parser.manyIndent.formatter
Lean.Parser.Extra
Lean.PrettyPrinter.Formatter → Lean.PrettyPrinter.Formatter
true
MeasureTheory.AEEqFun.le_inf
Mathlib.MeasureTheory.Function.AEEqFun
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace β] [inst_2 : SemilatticeInf β] [inst_3 : ContinuousInf β] (f' f g : α →ₘ[μ] β), f' ≤ f → f' ≤ g → f' ≤ f ⊓ g
true
instDecidableIff._proof_3
Init.Core
∀ {p q : Prop}, ¬p → q → (p ↔ q) → False
false
Std.Tactic.BVDecide.Normalize.Int16.toBitVec_ite
Std.Tactic.BVDecide.Normalize.BitVec
∀ {c : Prop} {t e : Int16} [inst : Decidable c], (if c then t else e).toBitVec = if c then t.toBitVec else e.toBitVec
true
Std.HashSet.size_le_size_insertMany_list
Std.Data.HashSet.Lemmas
∀ {α : Type u} {x : BEq α} {x_1 : Hashable α} {m : Std.HashSet α} [EquivBEq α] [LawfulHashable α] {l : List α}, m.size ≤ (m.insertMany l).size
true
_private.Lean.Elab.Do.Legacy.0.Lean.Elab.Term.Do.ToTerm.toTerm.go.match_1
Lean.Elab.Do.Legacy
(motive : Lean.Elab.Term.Do.Code → Sort u_1) → (c : Lean.Elab.Term.Do.Code) → ((ref val : Lean.Syntax) → motive (Lean.Elab.Term.Do.Code.return ref val)) → ((ref : Lean.Syntax) → motive (Lean.Elab.Term.Do.Code.continue ref)) → ((ref : Lean.Syntax) → motive (Lean.Elab.Term.Do.Code.break ref)) → ((e : Lean.Syntax) → motive (Lean.Elab.Term.Do.Code.action e)) → ((j : Lean.Name) → (ps : Array (Lean.Elab.Term.Do.Var × Bool)) → (b k : Lean.Elab.Term.Do.Code) → motive (Lean.Elab.Term.Do.Code.joinpoint j ps b k)) → ((ref : Lean.Syntax) → (j : Lean.Name) → (args : Array Lean.Syntax) → motive (Lean.Elab.Term.Do.Code.jmp ref j args)) → ((xs : Array Lean.Elab.Term.Do.Var) → (stx : Lean.Syntax) → (k : Lean.Elab.Term.Do.Code) → motive (Lean.Elab.Term.Do.Code.decl xs stx k)) → ((xs : Array Lean.Elab.Term.Do.Var) → (stx : Lean.Syntax) → (k : Lean.Elab.Term.Do.Code) → motive (Lean.Elab.Term.Do.Code.reassign xs stx k)) → ((stx : Lean.Syntax) → (k : Lean.Elab.Term.Do.Code) → motive (Lean.Elab.Term.Do.Code.seq stx k)) → ((ref : Lean.Syntax) → (h? : Option Lean.Elab.Term.Do.Var) → (o c : Lean.Syntax) → (t e : Lean.Elab.Term.Do.Code) → motive (Lean.Elab.Term.Do.Code.ite ref h? o c t e)) → ((ref genParam discrs optMotive : Lean.Syntax) → (alts : Array (Lean.Elab.Term.Do.Alt Lean.Elab.Term.Do.Code)) → motive (Lean.Elab.Term.Do.Code.match ref genParam discrs optMotive alts)) → ((ref : Lean.Syntax) → («meta» : Bool) → (d : Lean.Syntax) → (alts : Array (Lean.Elab.Term.Do.AltExpr Lean.Elab.Term.Do.Code)) → (elseBranch : Lean.Elab.Term.Do.Code) → motive (Lean.Elab.Term.Do.Code.matchExpr ref «meta» d alts elseBranch)) → motive c
false
Lean.Widget.MsgEmbed.expr
Lean.Widget.InteractiveDiagnostic
Lean.Widget.CodeWithInfos → Lean.Widget.MsgEmbed
true
CategoryTheory.ShortComplex.unopFunctor_obj
Mathlib.Algebra.Homology.ShortComplex.Basic
∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] (S : CategoryTheory.ShortComplex Cᵒᵖ), (CategoryTheory.ShortComplex.unopFunctor C).obj S = Opposite.op S.unop
true
Field.toEuclideanDomain.match_3
Mathlib.Algebra.EuclideanDomain.Field
∀ {K : Type u_1} [inst : Field K] (x x_1 : K) (motive : x * x_1 = 0 ∧ x ≠ 0 → Prop) (x_2 : x * x_1 = 0 ∧ x ≠ 0), (∀ (hab : x * x_1 = 0) (hna : x ≠ 0), motive ⋯) → motive x_2
false
Lean.Omega.LinearCombo.neg_eval
Init.Omega.LinearCombo
∀ (lc : Lean.Omega.LinearCombo) (v : Lean.Omega.Coeffs), (-lc).eval v = -lc.eval v
true
MvPolynomial.degreeOf_rename_of_injective
Mathlib.Algebra.MvPolynomial.Degrees
∀ {R : Type u} {σ : Type u_1} {τ : Type u_2} [inst : CommSemiring R] {p : MvPolynomial σ R} {f : σ → τ}, Function.Injective f → ∀ (i : σ), MvPolynomial.degreeOf (f i) ((MvPolynomial.rename f) p) = MvPolynomial.degreeOf i p
true
CategoryTheory.Idempotents.app_p_comm
Mathlib.CategoryTheory.Idempotents.FunctorCategories
∀ {J : Type u_1} {C : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} J] [inst_1 : CategoryTheory.Category.{v_2, u_2} C] {P Q : CategoryTheory.Idempotents.Karoubi (CategoryTheory.Functor J C)} (f : P ⟶ Q) (X : J), CategoryTheory.CategoryStruct.comp (P.p.app X) (f.f.app X) = CategoryTheory.CategoryStruct.comp (f.f.app X) (Q.p.app X)
true
trapezoidal_error
Mathlib.MeasureTheory.Integral.IntervalIntegral.TrapezoidalRule
(ℝ → ℝ) → ℕ → ℝ → ℝ → ℝ
true
Batteries.RBNode.WF_iff._simp_1
Batteries.Data.RBMap.WF
∀ {α : Type u_1} {cmp : α → α → Ordering} {t : Batteries.RBNode α}, Batteries.RBNode.WF cmp t = (Batteries.RBNode.Ordered cmp t ∧ ∃ c n, t.Balanced c n)
false
CategoryTheory.Functor.FullyFaithful.isoEquiv._proof_2
Mathlib.CategoryTheory.Functor.FullyFaithful
∀ {C : Type u_3} [inst : CategoryTheory.Category.{u_1, u_3} C] {D : Type u_4} [inst_1 : CategoryTheory.Category.{u_2, u_4} D] {F : CategoryTheory.Functor C D} (hF : F.FullyFaithful) {X Y : C}, Function.LeftInverse hF.preimageIso F.mapIso
false
_private.Mathlib.Topology.ContinuousMap.Ideals.0.ContinuousMap.mem_setOfIdeal._simp_1_2
Mathlib.Topology.ContinuousMap.Ideals
∀ {α : Type u} (s : Set α) (x : α), (x ∈ sᶜ) = (x ∉ s)
false
Lean.Firefox.ThreadWithMaps.mk.injEq
Lean.Util.Profiler
∀ (toThread : Lean.Firefox.Thread) (stringMap : Std.HashMap String ℕ) (funcMap : Std.HashMap ℕ ℕ) (stackMap : Std.HashMap (ℕ × Option ℕ) ℕ) (lastTime : Float) (toThread_1 : Lean.Firefox.Thread) (stringMap_1 : Std.HashMap String ℕ) (funcMap_1 : Std.HashMap ℕ ℕ) (stackMap_1 : Std.HashMap (ℕ × Option ℕ) ℕ) (lastTime_1 : Float), ({ toThread := toThread, stringMap := stringMap, funcMap := funcMap, stackMap := stackMap, lastTime := lastTime } = { toThread := toThread_1, stringMap := stringMap_1, funcMap := funcMap_1, stackMap := stackMap_1, lastTime := lastTime_1 }) = (toThread = toThread_1 ∧ stringMap = stringMap_1 ∧ funcMap = funcMap_1 ∧ stackMap = stackMap_1 ∧ lastTime = lastTime_1)
true
List.zipWith_nil_left
Init.Data.List.Basic
∀ {α : Type u} {β : Type v} {γ : Type w} {l : List β} {f : α → β → γ}, List.zipWith f [] l = []
true
CategoryTheory.EffectiveEpiStruct.mk.sizeOf_spec
Mathlib.CategoryTheory.EffectiveEpi.Basic
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X Y : C} {f : Y ⟶ X} [inst_1 : SizeOf C] (desc : {W : C} → (e : Y ⟶ W) → (∀ {Z : C} (g₁ g₂ : Z ⟶ Y), CategoryTheory.CategoryStruct.comp g₁ f = CategoryTheory.CategoryStruct.comp g₂ f → CategoryTheory.CategoryStruct.comp g₁ e = CategoryTheory.CategoryStruct.comp g₂ e) → (X ⟶ W)) (fac : ∀ {W : C} (e : Y ⟶ W) (h : ∀ {Z : C} (g₁ g₂ : Z ⟶ Y), CategoryTheory.CategoryStruct.comp g₁ f = CategoryTheory.CategoryStruct.comp g₂ f → CategoryTheory.CategoryStruct.comp g₁ e = CategoryTheory.CategoryStruct.comp g₂ e), CategoryTheory.CategoryStruct.comp f (desc e ⋯) = e) (uniq : ∀ {W : C} (e : Y ⟶ W) (h : ∀ {Z : C} (g₁ g₂ : Z ⟶ Y), CategoryTheory.CategoryStruct.comp g₁ f = CategoryTheory.CategoryStruct.comp g₂ f → CategoryTheory.CategoryStruct.comp g₁ e = CategoryTheory.CategoryStruct.comp g₂ e) (m : X ⟶ W), CategoryTheory.CategoryStruct.comp f m = e → m = desc e ⋯), sizeOf { desc := desc, fac := fac, uniq := uniq } = 1
true
Lean.Elab.Tactic.Location.recOn
Lean.Elab.Tactic.Location
{motive : Lean.Elab.Tactic.Location → Sort u} → (t : Lean.Elab.Tactic.Location) → motive Lean.Elab.Tactic.Location.wildcard → ((hypotheses : Array Lean.Syntax) → (type : Bool) → motive (Lean.Elab.Tactic.Location.targets hypotheses type)) → motive t
false
Submodule.quotientEquivPiSpan._proof_6
Mathlib.LinearAlgebra.FreeModule.Finite.Quotient
∀ {R : Type u_1} [inst : CommRing R], RingHomCompTriple (RingHom.id R) (RingHom.id R) (RingHom.id R)
false
zsmul_add
Mathlib.Algebra.Group.Basic
∀ {α : Type u_1} [inst : SubtractionCommMonoid α] (a b : α) (n : ℤ), n • (a + b) = n • a + n • b
true
_private.Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift.0.CochainComplex.HomComplex.Cochain.leftUnshift_leftShift._proof_1_1
Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift
∀ (n' q : ℤ), q - n' + n' = q
false
fderivPolarCoordSymm._proof_9
Mathlib.Analysis.SpecialFunctions.PolarCoord
RingHomInvPair (RingHom.id ℝ) (RingHom.id ℝ)
false
Multiplicative.isIsometricSMul
Mathlib.Topology.MetricSpace.IsometricSMul
∀ {M : Type u_2} {X : Type u_3} [inst : VAdd M X] [inst_1 : PseudoEMetricSpace X] [IsIsometricVAdd M X], IsIsometricSMul (Multiplicative M) X
true
CompactlySupportedContinuousMap.instNonUnitalRingOfIsTopologicalRing._proof_6
Mathlib.Topology.ContinuousMap.CompactlySupported
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [inst_2 : NonUnitalRing β] [inst_3 : IsTopologicalRing β] (f g : CompactlySupportedContinuousMap α β), ⇑(f + g) = ⇑f + ⇑g
false
Lean.Elab.Tactic.Do.ProofMode.dropStateList
Lean.Elab.Tactic.Do.ProofMode.MGoal
Lean.Expr → ℕ → Lean.MetaM Lean.Expr
true
Subfield.relrank_inf_mul_relrank
Mathlib.FieldTheory.Relrank
∀ {E : Type v} [inst : Field E] (A B C : Subfield E), A.relrank (B ⊓ C) * B.relrank C = (A ⊓ B).relrank C
true
Lean.Compiler.LCNF.Decl.instantiateParamsLevelParams
Lean.Compiler.LCNF.Basic
{pu : Lean.Compiler.LCNF.Purity} → Lean.Compiler.LCNF.Decl pu → List Lean.Level → Array (Lean.Compiler.LCNF.Param pu)
true
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Fin.0._regBuiltin.Fin.reduceOfNat.declare_151._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Fin.2903400553._hygCtx._hyg.14
Lean.Meta.Tactic.Simp.BuiltinSimprocs.Fin
IO Unit
false
_private.Mathlib.CategoryTheory.Shift.ShiftedHomOpposite.0.CategoryTheory.ShiftedHom.opEquiv'_add_symm._proof_1_5
Mathlib.CategoryTheory.Shift.ShiftedHomOpposite
∀ (n m a a' a'' : ℤ), n + a = a' → m + a' = a'' → a + n + m = a''
false
Std.Tactic.BVDecide.Frontend.Normalize.BitVec.bif_eq_not_bif'
Std.Tactic.BVDecide.Normalize.Equal
∀ {w : ℕ} (d : Bool) (a b c : BitVec w), ((bif d then a else c) == ~~~bif d then b else c) = bif d then a == ~~~b else c == ~~~c
true
CategoryTheory.Functor.OplaxMonoidal.ofChosenFiniteProducts._proof_4
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C] {D : Type u_2} [inst_2 : CategoryTheory.Category.{u_1, u_2} D] [inst_3 : CategoryTheory.CartesianMonoidalCategory D] (F : CategoryTheory.Functor C D) (x : C), (CategoryTheory.MonoidalCategoryStruct.leftUnitor (F.obj x)).inv = CategoryTheory.CategoryStruct.comp (F.map (CategoryTheory.MonoidalCategoryStruct.leftUnitor x).inv) (CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.prodComparison F (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) x) (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.CartesianMonoidalCategory.terminalComparison F) (F.obj x)))
false
_private.Mathlib.Data.Finset.Insert.0.Finset.pairwise_cons'._proof_1_3
Mathlib.Data.Finset.Insert
∀ {α : Type u_1} {β : Type u_2} {s : Finset α} {a : α}, a ∉ s → ∀ (r : β → β → Prop) (f : α → β), (((↑s).Pairwise fun x y => r (f x) (f y)) ∧ ∀ b ∈ ↑s, ¬a = b → r (f a) (f b) ∧ r (f b) (f a)) ↔ ((↑s).Pairwise fun x y => r (f x) (f y)) ∧ ∀ b ∈ s, r (f a) (f b) ∧ r (f b) (f a)
false
PowerBasis.repr_mul_isIntegral
Mathlib.RingTheory.Adjoin.PowerBasis
∀ {S : Type u_2} [inst : CommRing S] {R : Type u_3} [inst_1 : CommRing R] [inst_2 : Algebra R S] {A : Type u_4} [inst_3 : CommRing A] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [IsScalarTower R S A] {B : PowerBasis S A}, IsIntegral R B.gen → ∀ {x y : A}, (∀ (i : Fin B.dim), IsIntegral R ((B.basis.repr x) i)) → (∀ (i : Fin B.dim), IsIntegral R ((B.basis.repr y) i)) → minpoly S B.gen = Polynomial.map (algebraMap R S) (minpoly R B.gen) → ∀ (i : Fin B.dim), IsIntegral R ((B.basis.repr (x * y)) i)
true
CategoryTheory.ShortComplex.HomologyMapData._sizeOf_inst
Mathlib.Algebra.Homology.ShortComplex.Homology
{C : Type u} → {inst : CategoryTheory.Category.{v, u} C} → {inst_1 : CategoryTheory.Limits.HasZeroMorphisms C} → {S₁ S₂ : CategoryTheory.ShortComplex C} → (φ : S₁ ⟶ S₂) → (h₁ : S₁.HomologyData) → (h₂ : S₂.HomologyData) → [SizeOf C] → SizeOf (CategoryTheory.ShortComplex.HomologyMapData φ h₁ h₂)
false
_private.Mathlib.RingTheory.Norm.Transitivity.0.Algebra.Norm.Transitivity.comp_det_mul_pow._simp_1_2
Mathlib.RingTheory.Norm.Transitivity
∀ (I : Type u_1) (J : Type u_2) (R : Type u_5) [inst : AddCommMonoid R] [inst_1 : Mul R] [inst_2 : Fintype I] [inst_3 : Fintype J] (M : Matrix I I (Matrix J J R)), (Matrix.comp I I J J R) M = (Matrix.compRingEquiv I J R) M
false
Condensed.ulift._proof_1
Mathlib.Condensed.Functors
CategoryTheory.Precoherent CompHaus
false
_private.Lean.Compiler.IR.LLVMBindings.0.LLVM.BasicBlock.mk.noConfusion
Lean.Compiler.IR.LLVMBindings
{Context : Sort u_1} → {ctx : Context} → {P : Sort u} → {ptr ptr' : USize} → { ptr := ptr } = { ptr := ptr' } → (ptr = ptr' → P) → P
false
CategoryTheory.Lax.LaxTrans.naturality_naturality._autoParam
Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax
Lean.Syntax
false
MonoidAlgebra.of._proof_2
Mathlib.Algebra.MonoidAlgebra.Defs
∀ (R : Type u_2) (M : Type u_1) [inst : Semiring R] [inst_1 : MulOneClass M] (x y : M), (MonoidAlgebra.ofMagma R M).toFun (x * y) = (MonoidAlgebra.ofMagma R M).toFun x * (MonoidAlgebra.ofMagma R M).toFun y
false
Int32.reduceLE
Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt
Lean.Meta.Simp.Simproc
true
_private.Mathlib.NumberTheory.MahlerMeasure.0.Polynomial.card_mahlerMeasure._proof_1_6
Mathlib.NumberTheory.MahlerMeasure
∀ (n : ℕ) (B : NNReal), ∀ a ∈ Finset.univ, ¬2 * ⌊↑(n.choose ↑a) * B⌋₊ + 1 = 0
false
ModuleCat.forget₂_reflectsLimitsOfSize
Mathlib.Algebra.Category.ModuleCat.Abelian
∀ {R : Type u} [inst : Ring R], CategoryTheory.Limits.ReflectsLimitsOfSize.{v, v, max v w, max v w, max (max u (v + 1)) (w + 1), max (v + 1) (w + 1)} (CategoryTheory.forget₂ (ModuleCat R) AddCommGrpCat)
true
ProbabilityTheory.condIndep_of_condIndep_of_le_right
Mathlib.Probability.Independence.Conditional
∀ {Ω : Type u_1} {m' m₁ m₂ m₃ mΩ : MeasurableSpace Ω} [inst : StandardBorelSpace Ω] {hm' : m' ≤ mΩ} {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ], ProbabilityTheory.CondIndep m' m₁ m₂ hm' μ → m₃ ≤ m₂ → ProbabilityTheory.CondIndep m' m₁ m₃ hm' μ
true
LieAlgebra.Orthogonal.invertiblePB._proof_1
Mathlib.Algebra.Lie.Classical
∀ (l : Type u_2) (R : Type u_1) [inst : DecidableEq l] [inst_1 : CommRing R] [inst_2 : Fintype l], IsDedekindFiniteMonoid (Matrix (Unit ⊕ l ⊕ l) (Unit ⊕ l ⊕ l) R)
false
Lean.ElabInline.val
Lean.DocString.Extension
Lean.ElabInline → Dynamic
true
AugmentedSimplexCategory.instMonoidalCategory._proof_11
Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal
∀ (X Y : AugmentedSimplexCategory), CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X (CategoryTheory.MonoidalCategoryStruct.tensorUnit AugmentedSimplexCategory) Y).hom (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.CategoryStruct.id X) (CategoryTheory.MonoidalCategoryStruct.leftUnitor Y).hom) = CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.MonoidalCategoryStruct.rightUnitor X).hom (CategoryTheory.CategoryStruct.id Y)
false
Sequential.instCategory._aux_5
Mathlib.Topology.Category.Sequential
{X Y Z : Sequential} → (X ⟶ Y) → (Y ⟶ Z) → (X ⟶ Z)
false
BddLat.ofHom
Mathlib.Order.Category.BddLat
{X Y : Type u} → [inst : Lattice X] → [inst_1 : BoundedOrder X] → [inst_2 : Lattice Y] → [inst_3 : BoundedOrder Y] → BoundedLatticeHom X Y → (BddLat.of X ⟶ BddLat.of Y)
true
_private.Mathlib.Analysis.Calculus.Deriv.Mul.0.derivWithin_fun_const_smul_field._simp_1_1
Mathlib.Analysis.Calculus.Deriv.Mul
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F] [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {x : 𝕜} {s : Set 𝕜}, derivWithin f s x = (fderivWithin 𝕜 f s x) 1
false
Lean.Grind.CommRing.mk._flat_ctor
Init.Grind.Ring.Basic
{α : Type u} → (add mul : α → α → α) → [natCast : NatCast α] → [ofNat : (n : ℕ) → OfNat α n] → [nsmul : SMul ℕ α] → [npow : HPow α ℕ α] → (∀ (a : α), a + 0 = a) → (∀ (a b : α), a + b = b + a) → (∀ (a b c : α), a + b + c = a + (b + c)) → (∀ (a b c : α), a * b * c = a * (b * c)) → (∀ (a : α), a * 1 = a) → autoParam (∀ (a : α), 1 * a = a) Lean.Grind.CommSemiring.one_mul._autoParam → (∀ (a b c : α), a * (b + c) = a * b + a * c) → autoParam (∀ (a b c : α), (a + b) * c = a * c + b * c) Lean.Grind.CommSemiring.right_distrib._autoParam → (∀ (a : α), 0 * a = 0) → autoParam (∀ (a : α), a * 0 = 0) Lean.Grind.CommSemiring.mul_zero._autoParam → (∀ (a : α), a ^ 0 = 1) → (∀ (a : α) (n : ℕ), a ^ (n + 1) = a ^ n * a) → autoParam (∀ (a : ℕ), OfNat.ofNat (a + 1) = OfNat.ofNat a + 1) Lean.Grind.Semiring.ofNat_succ._autoParam → autoParam (∀ (n : ℕ), OfNat.ofNat n = ↑n) Lean.Grind.Semiring.ofNat_eq_natCast._autoParam → autoParam (∀ (n : ℕ) (a : α), n • a = ↑n * a) Lean.Grind.Semiring.nsmul_eq_natCast_mul._autoParam → (neg : α → α) → (sub : α → α → α) → [intCast : IntCast α] → [zsmul : SMul ℤ α] → (∀ (a : α), neg a + a = 0) → (∀ (a b : α), a - b = a + neg b) → (∀ (i : ℤ) (a : α), -i • a = neg (i • a)) → autoParam (∀ (n : ℕ) (a : α), ↑n • a = n • a) Lean.Grind.Ring.zsmul_natCast_eq_nsmul._autoParam → autoParam (∀ (n : ℕ), ↑(OfNat.ofNat n) = OfNat.ofNat n) Lean.Grind.Ring.intCast_ofNat._autoParam → autoParam (∀ (i : ℤ), ↑(-i) = neg ↑i) Lean.Grind.Ring.intCast_neg._autoParam → (∀ (a b : α), a * b = b * a) → Lean.Grind.CommRing α
false
Sigma.Lex.LT
Mathlib.Data.Sigma.Order
{ι : Type u_1} → {α : ι → Type u_2} → [LT ι] → [(i : ι) → LT (α i)] → LT (Σₗ (i : ι), α i)
true
Std.Do.Iter.foldM_mapM
Std.Do.Triple.SpecLemmas
∀ {ps : Std.Do.PostShape} {α β γ δ : Type w} {n : Type w → Type w''} {o : Type w → Type w'''} [inst : Std.Iterator α Id β] [Std.Iterators.Finite α Id] [inst_2 : Monad n] [inst_3 : MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [inst_6 : Monad o] [LawfulMonad o] [inst_8 : Std.Do.WPMonad o ps] [inst_9 : Std.IteratorLoop α Id n] [inst_10 : Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id n] [Std.LawfulIteratorLoop α Id o] [inst_13 : MonadLiftT n o] [LawfulMonadLiftT n o] {f : β → n γ} {g : δ → γ → o δ} {init : δ} {it : Std.Iter β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps}, ⦃P⦄ Std.Iter.foldM (fun d b => do let c ← liftM (f b) g d c) init it ⦃Q⦄ → ⦃P⦄ Std.IterM.foldM g init (Std.Iter.mapM f it) ⦃Q⦄
true
Lean.Lsp.DocumentSymbol.rec
Lean.Data.Lsp.LanguageFeatures
{motive_1 : Lean.Lsp.DocumentSymbol → Sort u} → {motive_2 : Lean.Lsp.DocumentSymbolAux Lean.Lsp.DocumentSymbol → Sort u} → {motive_3 : Option (Array Lean.Lsp.DocumentSymbol) → Sort u} → {motive_4 : Array Lean.Lsp.DocumentSymbol → Sort u} → {motive_5 : List Lean.Lsp.DocumentSymbol → Sort u} → ((sym : Lean.Lsp.DocumentSymbolAux Lean.Lsp.DocumentSymbol) → motive_2 sym → motive_1 (Lean.Lsp.DocumentSymbol.mk sym)) → ((name : String) → (detail? : Option String) → (kind : Lean.Lsp.SymbolKind) → (range selectionRange : Lean.Lsp.Range) → (children? : Option (Array Lean.Lsp.DocumentSymbol)) → motive_3 children? → motive_2 { name := name, detail? := detail?, kind := kind, range := range, selectionRange := selectionRange, children? := children? }) → motive_3 none → ((val : Array Lean.Lsp.DocumentSymbol) → motive_4 val → motive_3 (some val)) → ((toList : List Lean.Lsp.DocumentSymbol) → motive_5 toList → motive_4 { toList := toList }) → motive_5 [] → ((head : Lean.Lsp.DocumentSymbol) → (tail : List Lean.Lsp.DocumentSymbol) → motive_1 head → motive_5 tail → motive_5 (head :: tail)) → (t : Lean.Lsp.DocumentSymbol) → motive_1 t
false
Mathlib.Tactic.Widget.StringDiagram.IdNode.mk.inj
Mathlib.Tactic.Widget.StringDiagram
∀ {vPos hPosSrc hPosTar : ℕ} {id : Mathlib.Tactic.BicategoryLike.Atom₁} {vPos_1 hPosSrc_1 hPosTar_1 : ℕ} {id_1 : Mathlib.Tactic.BicategoryLike.Atom₁}, { vPos := vPos, hPosSrc := hPosSrc, hPosTar := hPosTar, id := id } = { vPos := vPos_1, hPosSrc := hPosSrc_1, hPosTar := hPosTar_1, id := id_1 } → vPos = vPos_1 ∧ hPosSrc = hPosSrc_1 ∧ hPosTar = hPosTar_1 ∧ id = id_1
true
_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'._simp_1_3
Mathlib.Data.List.Sublists
∀ {α : Type u_1} {R : α → α → Prop} {l₁ l₂ : List α}, List.Pairwise R (l₁ ++ l₂) = (List.Pairwise R l₁ ∧ List.Pairwise R l₂ ∧ ∀ a ∈ l₁, ∀ b ∈ l₂, R a b)
false
Std.IterM.step_filterWithPostcondition._proof_4
Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
∀ {α β : Type u_1} {m : Type u_1 → Type u_3} {n : Type u_1 → Type u_2} [inst : Std.Iterator α m β] {it : Std.IterM m β} {f : β → Std.Iterators.PostconditionT n (ULift.{u_1, 0} Bool)} [inst_1 : Monad n] [inst_2 : MonadLiftT m n] (it' : Std.IterM m β), it.IsPlausibleStep (Std.IterStep.skip it') → (Std.IterM.filterWithPostcondition f it).IsPlausibleStep (Std.IterStep.skip (Std.IterM.filterWithPostcondition f it'))
false
Mathlib.Meta.FunProp.FunPropDecl.funArgId
Mathlib.Tactic.FunProp.Decl
Mathlib.Meta.FunProp.FunPropDecl → ℕ
true
WithBot.addMonoidWithOne
Mathlib.Algebra.Order.Monoid.Unbundled.WithTop
{α : Type u} → [AddMonoidWithOne α] → AddMonoidWithOne (WithBot α)
true
Metric.exists_finite_isCover_of_isCompact_closure
Mathlib.Topology.MetricSpace.Cover
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {ε : NNReal} {s : Set X}, ε ≠ 0 → IsCompact (closure s) → ∃ N ⊆ s, N.Finite ∧ Metric.IsCover ε s N
true
Order.succ_eq_zero
Mathlib.Algebra.Order.SuccPred
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : AddZeroClass α] [inst_2 : OrderBot α] [CanonicallyOrderedAdd α] [inst_4 : One α] [NoMaxOrder α] [inst_6 : SuccAddOrder α] {a : WithBot α}, a.succ = 0 ↔ a = ⊥
true
CategoryTheory.MorphismProperty.isomorphisms.iff._simp_1
Mathlib.CategoryTheory.MorphismProperty.Basic
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y), CategoryTheory.MorphismProperty.isomorphisms C f = CategoryTheory.IsIso f
false
Lean.Grind.OrderedAdd.zsmul_nonpos
Init.Grind.Ordered.Module
∀ {M : Type u} [inst : LE M] [inst_1 : Std.IsPreorder M] [inst_2 : Lean.Grind.IntModule M] [Lean.Grind.OrderedAdd M] {k : ℤ} {a : M}, 0 ≤ k → a ≤ 0 → k • a ≤ 0
true
Affine.Simplex.dist_lt_of_mem_interior_of_strictConvexSpace
Mathlib.Analysis.Convex.StrictCombination
∀ {V : Type u_2} {P : Type u_3} [inst : NormedAddCommGroup V] [inst_1 : NormedSpace ℝ V] [StrictConvexSpace ℝ V] [inst_3 : PseudoMetricSpace P] [inst_4 : NormedAddTorsor V P] {n : ℕ} (s : Affine.Simplex ℝ P n) {r : ℝ} {p₀ p : P}, p ∈ s.interior → (∀ (i : Fin (n + 1)), dist (s.points i) p₀ ≤ r) → dist p p₀ < r
true
Lean.Parser.Term.arrow
Lean.Parser.Term
Lean.Parser.TrailingParser
true
Int.sub_fdiv_of_dvd
Init.Data.Int.DivMod.Lemmas
∀ (a : ℤ) {b c : ℤ}, c ∣ b → (a - b).fdiv c = a.fdiv c - b.fdiv c
true
Lean.Elab.DefViewElabHeaderData.mk.noConfusion
Lean.Elab.DefView
{P : Sort u} → {shortDeclName declName : Lean.Name} → {levelNames : List Lean.Name} → {binderIds : Array Lean.Syntax} → {numParams : ℕ} → {type : Lean.Expr} → {shortDeclName' declName' : Lean.Name} → {levelNames' : List Lean.Name} → {binderIds' : Array Lean.Syntax} → {numParams' : ℕ} → {type' : Lean.Expr} → { shortDeclName := shortDeclName, declName := declName, levelNames := levelNames, binderIds := binderIds, numParams := numParams, type := type } = { shortDeclName := shortDeclName', declName := declName', levelNames := levelNames', binderIds := binderIds', numParams := numParams', type := type' } → (shortDeclName = shortDeclName' → declName = declName' → levelNames = levelNames' → binderIds = binderIds' → numParams = numParams' → type = type' → P) → P
false
_private.Mathlib.GroupTheory.Perm.Centralizer.0.Equiv.Perm.Basis.ofPermHom_support._simp_1_2
Mathlib.GroupTheory.Perm.Centralizer
∀ {α : Type u_1} {β : Type u_2} {s : Finset α} {t : α → Finset β} [inst : DecidableEq β] {b : β}, (b ∈ s.biUnion t) = ∃ a ∈ s, b ∈ t a
false
SSet.Truncated.hoFunctor.monoidal._proof_18
Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal
autoParam (∀ (X : SSet), (CategoryTheory.MonoidalCategoryStruct.rightUnitor (SSet.hoFunctor.obj X)).inv = CategoryTheory.CategoryStruct.comp (SSet.hoFunctor.map (CategoryTheory.MonoidalCategoryStruct.rightUnitor X).inv) (CategoryTheory.CategoryStruct.comp (SSet.Truncated.hoFunctor.monoidal._aux_12 X (CategoryTheory.MonoidalCategoryStruct.tensorUnit SSet)) (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (SSet.hoFunctor.obj X) SSet.Truncated.hoFunctor.monoidal._aux_10))) CategoryTheory.Functor.OplaxMonoidal.oplax_right_unitality._autoParam
false
Nat.instNeZeroHPow
Init.Data.Nat.Basic
∀ {n m : ℕ} [NeZero n], NeZero (n ^ m)
true
IsSelfAdjoint.natCast._simp_1
Mathlib.Algebra.Star.SelfAdjoint
∀ {R : Type u_1} [inst : NonAssocSemiring R] [inst_1 : StarRing R] (n : ℕ), IsSelfAdjoint ↑n = True
false
_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.Const.balanced_modify._proof_1_2
Std.Data.DTreeMap.Internal.Operations
∀ {α : Type u_1} {β : Type u_2} [inst : Ord α] {k : α} {f : β → β} (sz : ℕ) (k_1 : α) (v : β) (l r : Std.DTreeMap.Internal.Impl α fun x => β), (Std.DTreeMap.Internal.Impl.inner sz k_1 v l r).Balanced → (Std.DTreeMap.Internal.Impl.Const.modify k f l).Balanced → (Std.DTreeMap.Internal.Impl.Const.modify k f r).Balanced → (match compare k k_1 with | Ordering.lt => Std.DTreeMap.Internal.Impl.inner sz k_1 v (Std.DTreeMap.Internal.Impl.Const.modify k f l) r | Ordering.gt => Std.DTreeMap.Internal.Impl.inner sz k_1 v l (Std.DTreeMap.Internal.Impl.Const.modify k f r) | Ordering.eq => Std.DTreeMap.Internal.Impl.inner sz k (f v) l r).Balanced
false