name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
BddLat.hasForgetToBddOrd._proof_1 | Mathlib.Order.Category.BddLat | ∀ (X : BddLat),
BddOrd.ofHom (BddLat.Hom.hom (CategoryTheory.CategoryStruct.id X)).toBoundedOrderHom =
CategoryTheory.CategoryStruct.id (BddOrd.of ↑X.toLat) | false |
AddHom.instAdd.eq_1 | Mathlib.Algebra.Group.Hom.Basic | ∀ {M : Type u_2} {N : Type u_3} [inst : Add M] [inst_1 : AddCommSemigroup N],
AddHom.instAdd = { add := fun f g => { toFun := fun m => f m + g m, map_add' := ⋯ } } | true |
CoalgCat.mk.noConfusion | Mathlib.Algebra.Category.CoalgCat.Basic | {R : Type u} →
{inst : CommRing R} →
{P : Sort u_1} →
{toModuleCat : ModuleCat R} →
{instCoalgebra : Coalgebra R ↑toModuleCat} →
{toModuleCat' : ModuleCat R} →
{instCoalgebra' : Coalgebra R ↑toModuleCat'} →
{ toModuleCat := toModuleCat, instCoalgebra := instCoalge... | false |
Prod.seminormedRing._proof_12 | Mathlib.Analysis.Normed.Ring.Basic | ∀ {α : Type u_1} {β : Type u_2} [inst : SeminormedRing α] [inst_1 : SeminormedRing β] (n : ℕ) (x : α × β),
Semiring.npow (n + 1) x = Semiring.npow n x * x | false |
Nat.div_ne_zero_iff_of_dvd | Init.Data.Nat.Lemmas | ∀ {b a : ℕ}, b ∣ a → (a / b ≠ 0 ↔ a ≠ 0 ∧ b ≠ 0) | true |
Lean.Widget.instEmptyCollectionInteractiveGoals | Lean.Widget.InteractiveGoal | EmptyCollection Lean.Widget.InteractiveGoals | true |
CategoryTheory.Functor.Faithful.div_comp | Mathlib.CategoryTheory.Functor.FullyFaithful | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] (F : CategoryTheory.Functor C E) [F.Faithful]
(G : CategoryTheory.Functor D E) [inst_4 : G.Faithful] (obj : C → D) (h_obj : ∀ (X : C), G... | true |
ModuleCat.Hom._sizeOf_1 | Mathlib.Algebra.Category.ModuleCat.Basic | {R : Type u} → {inst : Ring R} → {M N : ModuleCat R} → [SizeOf R] → M.Hom N → ℕ | false |
PseudoEpimorphismClass.recOn | Mathlib.Topology.Order.Hom.Esakia | {F : Type u_6} →
{α : Type u_7} →
{β : Type u_8} →
[inst : Preorder α] →
[inst_1 : Preorder β] →
[inst_2 : FunLike F α β] →
{motive : PseudoEpimorphismClass F α β → Sort u} →
(t : PseudoEpimorphismClass F α β) →
([toRelHomClass : RelHomClass F (fun... | false |
CategoryTheory.Subgroupoid.obj_surjective_of_im_eq_top | Mathlib.CategoryTheory.Groupoid.Subgroupoid | ∀ {C : Type u} [inst : CategoryTheory.Groupoid C] {D : Type u_1} [inst_1 : CategoryTheory.Groupoid D]
(φ : CategoryTheory.Functor C D) (hφ : Function.Injective φ.obj),
CategoryTheory.Subgroupoid.im φ hφ = ⊤ → Function.Surjective φ.obj | true |
NNRat.coe_pow._simp_1 | Mathlib.Data.NNRat.Defs | ∀ (q : ℚ≥0) (n : ℕ), ↑q ^ n = ↑(q ^ n) | false |
_private.Mathlib.LinearAlgebra.Matrix.ToLin.0.LinearMap.toMatrix_basis_equiv._simp_1_1 | Mathlib.LinearAlgebra.Matrix.ToLin | ∀ {α : Sort u_1} {a b : α}, (a = b) = (b = a) | false |
List.IsChain.backwards_cons_induction | Mathlib.Data.List.Chain | ∀ {α : Type u} {r : α → α → Prop} {a b : α} (p : α → Prop) (l : List α),
List.IsChain r (a :: l) → (a :: l).getLast ⋯ = b → (∀ ⦃x y : α⦄, r x y → p y → p x) → p b → ∀ i ∈ a :: l, p i | true |
NonUnitalAlgHom.Lmul._proof_4 | Mathlib.Analysis.Normed.Operator.Mul | ∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] (R : Type u_2) [inst_1 : NonUnitalSeminormedRing R]
[inst_2 : NormedSpace 𝕜 R], ContinuousConstSMul 𝕜 R | false |
CategoryTheory.Pretopology.trivial._proof_2 | Mathlib.CategoryTheory.Sites.Pretopology | ∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C] ⦃X : C⦄ (S : CategoryTheory.Presieve X)
(Ti : ⦃Y : C⦄ → (f : Y ⟶ X) → S f → CategoryTheory.Presieve Y),
S ∈ {S | ∃ Y f, ∃ (_ : CategoryTheory.IsIso f), S = CategoryTheory.Presieve.singleton f} →
(∀ ⦃Y : C⦄ (f : Y ⟶ X) (H : S f),
Ti f H ∈ {S ... | false |
Module.Relations.solutionFinsupp._proof_1 | Mathlib.Algebra.Module.Presentation.Free | ∀ {A : Type u_1} [inst : Ring A] (relations : Module.Relations A) [IsEmpty relations.R] (r : relations.R),
(Finsupp.linearCombination A fun g => fun₀ | g => 1) (relations.relation r) = 0 | false |
CategoryTheory.Limits.PreservesFiniteLimitsOfIsFilteredCostructuredArrowYonedaAux.flipFunctorToInterchange_inv_app_app | Mathlib.CategoryTheory.Limits.Preserves.Presheaf | ∀ {C : Type u} [inst : CategoryTheory.SmallCategory C] (A : CategoryTheory.Functor Cᵒᵖ (Type u)) {J : Type}
[inst_1 : CategoryTheory.SmallCategory J] (K : CategoryTheory.Functor J Cᵒᵖ)
(X : CategoryTheory.CostructuredArrow CategoryTheory.yoneda A) (X_1 : J)
(a :
((CategoryTheory.Limits.PreservesFiniteLimitsOf... | true |
CategoryTheory.MorphismProperty.epimorphisms.iff._simp_1 | Mathlib.CategoryTheory.MorphismProperty.Basic | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y),
CategoryTheory.MorphismProperty.epimorphisms C f = CategoryTheory.Epi f | false |
OrderRingHom.apply_eq_self | Mathlib.Algebra.Order.Archimedean.Hom | ∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] [Archimedean α] (f : α →+*o α)
(x : α), f x = x | true |
SheafOfModules.evaluationPreservesLimitsOfSize | Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C}
(R : CategoryTheory.Sheaf J RingCat) (X : Cᵒᵖ),
CategoryTheory.Limits.PreservesLimitsOfSize.{v₂, v, max u₁ v, v, max (max (max u u₁) (v + 1)) v₁, max u (v + 1)}
(SheafOfModules.evaluation R X) | true |
RelIso.emptySumLex_apply | Mathlib.Order.RelIso.Basic | ∀ {α : Type u_1} {β : Type u_2} (r : α → α → Prop) (s : β → β → Prop) [inst : IsEmpty α] (a : α ⊕ β),
(RelIso.emptySumLex r s) a = (Equiv.sumEmpty β α) a.swap | true |
ContinuousLinearMap.semiring._proof_15 | Mathlib.Topology.Algebra.Module.LinearMap | ∀ {R₁ : Type u_1} [inst : Semiring R₁] {M₁ : Type u_2} [inst_1 : TopologicalSpace M₁] [inst_2 : AddCommMonoid M₁]
[inst_3 : Module R₁ M₁] (x : M₁ →L[R₁] M₁), Monoid.npow 0 x = 1 | false |
_private.Mathlib.Probability.Moments.Variance.0.ProbabilityTheory.evariance_eq_zero_iff._simp_1_2 | Mathlib.Probability.Moments.Variance | ∀ {G : Type u_3} [inst : AddGroup G] {a b : G}, (a - b = 0) = (a = b) | false |
cfcₙ_smul._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | Lean.Syntax | false |
NonUnitalCommCStarAlgebra.recOn | Mathlib.Analysis.CStarAlgebra.Classes | {A : Type u_1} →
{motive : NonUnitalCommCStarAlgebra A → Sort u} →
(t : NonUnitalCommCStarAlgebra A) →
([toNonUnitalNormedCommRing : NonUnitalNormedCommRing A] →
[toStarRing : StarRing A] →
[toCompleteSpace : CompleteSpace A] →
[toCStarRing : CStarRing A] →
... | false |
IsDedekindDomain.HeightOneSpectrum.adicAbv._proof_1 | Mathlib.RingTheory.DedekindDomain.AdicValuation | ∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] {K : Type u_2} [inst_2 : Field K]
[inst_3 : Algebra R K] [inst_4 : IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R) {b : NNReal}
(hb : 1 < b) (x : K), 0 ≤ ↑(v.adicAbvDef hb x) | false |
Nat.dvd_of_mem_primeFactorsList | Mathlib.Data.Nat.Factors | ∀ {n p : ℕ}, p ∈ n.primeFactorsList → p ∣ n | true |
_private.Mathlib.LinearAlgebra.Finsupp.Span.0.Finsupp.iInf_ker_lapply_le_bot._simp_1_2 | Mathlib.LinearAlgebra.Finsupp.Span | ∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Sort u_4}
(p : ι → Submodule R M) {x : M}, (x ∈ ⨅ i, p i) = ∀ (i : ι), x ∈ p i | false |
Std.LinearPreorderPackage.le_total | Init.Data.Order.PackageFactories | ∀ {α : Type u} [self : Std.LinearPreorderPackage α] (a b : α), a ≤ b ∨ b ≤ a | true |
_private.Mathlib.Algebra.Lie.Semisimple.Basic.0.LieAlgebra.IsSemisimple.isSimple_of_isAtom._simp_1_15 | Mathlib.Algebra.Lie.Semisimple.Basic | ∀ {a b c : Prop}, (a ∧ b → c) = (a → b → c) | false |
_private.Lean.Compiler.LCNF.LiveVars.0.Lean.Compiler.LCNF.State.rec | Lean.Compiler.LCNF.LiveVars | {motive : Lean.Compiler.LCNF.State✝ → Sort u} →
((visitedJps : Lean.FVarIdHashSet) → motive { visitedJps := visitedJps }) →
(t : Lean.Compiler.LCNF.State✝¹) → motive t | false |
Complex.norm_log_one_add_sub_self_le | Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | ∀ {z : ℂ}, ‖z‖ < 1 → ‖Complex.log (1 + z) - z‖ ≤ ‖z‖ ^ 2 * (1 - ‖z‖)⁻¹ / 2 | true |
AddCommute.addUnits_neg_right | Mathlib.Algebra.Group.Commute.Units | ∀ {M : Type u_1} [inst : AddMonoid M] {a : M} {u : AddUnits M}, AddCommute a ↑u → AddCommute a ↑(-u) | true |
_private.Mathlib.Tactic.Linter.UnusedTactic.0.Mathlib.Linter.UnusedTactic.eraseUsedTactics | Mathlib.Tactic.Linter.UnusedTactic | Std.HashSet Lean.SyntaxNodeKind → Lean.Elab.InfoTree → Mathlib.Linter.UnusedTactic.M✝ Unit | true |
Bornology.IsBounded.snd_of_prod | Mathlib.Topology.Bornology.Constructions | ∀ {α : Type u_1} {β : Type u_2} [inst : Bornology α] [inst_1 : Bornology β] {s : Set α} {t : Set β},
Bornology.IsBounded (s ×ˢ t) → s.Nonempty → Bornology.IsBounded t | true |
continuous_sigmaMk | Mathlib.Topology.Constructions | ∀ {ι : Type u_5} {σ : ι → Type u_7} [inst : (i : ι) → TopologicalSpace (σ i)] {i : ι}, Continuous (Sigma.mk i) | true |
PadicInt.toZMod._proof_2 | Mathlib.NumberTheory.Padics.RingHoms | ∀ {p : ℕ} [hp_prime : Fact (Nat.Prime p)] (x : ℤ_[p]) (a b : ℕ),
x - ↑a ∈ Ideal.span {↑p} → x - ↑b ∈ Ideal.span {↑p} → ↑a = ↑b | false |
Lean.Elab.Tactic.evalDone._regBuiltin.Lean.Elab.Tactic.evalDone.declRange_3 | Lean.Elab.Tactic.BuiltinTactic | IO Unit | false |
_private.Mathlib.RingTheory.Algebraic.Defs.0.Algebra.isAlgebraic_iff._simp_1_3 | Mathlib.RingTheory.Algebraic.Defs | ∀ {p : Prop} {q : p → Prop} (h : p), (∀ (h' : p), q h') = q h | false |
_private.Lean.Elab.LetRec.0.Lean.Elab.Term.mkLetRecDeclView | Lean.Elab.LetRec | Lean.Syntax → Lean.Elab.TermElabM Lean.Elab.Term.LetRecView | true |
Vector.swap._auto_3 | Init.Data.Vector.Basic | Lean.Syntax | false |
WithVal.instNumberField | Mathlib.Topology.Algebra.Valued.WithVal | ∀ {R : Type u_1} {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] [inst_1 : Field R] (v : Valuation R Γ₀)
[NumberField R], NumberField (WithVal v) | true |
Topology.IsEmbedding.comp | Mathlib.Topology.Maps.Basic | ∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} {f : X → Y} {g : Y → Z} [inst : TopologicalSpace X]
[inst_1 : TopologicalSpace Y] [inst_2 : TopologicalSpace Z],
Topology.IsEmbedding g → Topology.IsEmbedding f → Topology.IsEmbedding (g ∘ f) | true |
IsOpen.stronglyLocallyContractibleSpace | Mathlib.Topology.Homotopy.LocallyContractible | ∀ {X : Type u_1} [inst : TopologicalSpace X] [StronglyLocallyContractibleSpace X] {U : Set X},
IsOpen U → StronglyLocallyContractibleSpace ↑U | true |
ModuleCat.CoextendScalars.map' | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | {R : Type u₁} →
{S : Type u₂} →
[inst : Ring R] →
[inst_1 : Ring S] →
(f : R →+* S) →
{M M' : ModuleCat R} → (M ⟶ M') → (ModuleCat.CoextendScalars.obj' f M ⟶ ModuleCat.CoextendScalars.obj' f M') | true |
_private.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Enums.0.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.getMatchEqCondForAux | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Enums | Lean.Name → Lean.Elab.Tactic.BVDecide.Frontend.Normalize.MatchKind → Lean.MetaM Lean.Name | true |
Equiv.prodEmbeddingDisjointEquivSigmaEmbeddingRestricted._proof_1 | Mathlib.Logic.Equiv.Embedding | ∀ {α : Type u_3} {β : Type u_1} {γ : Type u_2} (a : α ↪ γ),
(fun b => Disjoint (Set.range ⇑a) (Set.range ⇑b)) = fun f => ∀ (a_1 : β), f a_1 ∈ (Set.range ⇑a)ᶜ | false |
Ordinal.lt_one_iff_zero | Mathlib.SetTheory.Ordinal.Basic | ∀ {a : Ordinal.{u_1}}, a < 1 ↔ a = 0 | true |
_private.Mathlib.Logic.Equiv.Prod.0.Equiv.piEquivPiSubtypeProd._proof_7 | Mathlib.Logic.Equiv.Prod | ∀ {α : Type u_2} (p : α → Prop) (β : α → Type u_1) [inst : DecidablePred p] (f : (i : { x // p x }) → β ↑i)
(g : (i : { x // ¬p x }) → β ↑i),
(fun x => if h : p ↑x then (f, g).1 ⟨↑x, h⟩ else (f, g).2 ⟨↑x, h⟩, fun x =>
if h : p ↑x then (f, g).1 ⟨↑x, h⟩ else (f, g).2 ⟨↑x, h⟩).1 =
(f, g).1 | false |
Eq.trans_ssubset | Mathlib.Order.RelClasses | ∀ {α : Type u} [inst : HasSSubset α] {a b c : α}, a = b → b ⊂ c → a ⊂ c | true |
Std.DTreeMap.isEmpty | Std.Data.DTreeMap.Basic | {α : Type u} → {β : α → Type v} → {cmp : α → α → Ordering} → Std.DTreeMap α β cmp → Bool | true |
Lean.Elab.Tactic.BVDecide.Frontend.M.simplifyTernaryProof | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.Reflect | (Lean.Expr → Lean.Expr) →
Lean.Expr →
Option Lean.Expr →
Lean.Expr → Option Lean.Expr → Lean.Expr → Option Lean.Expr → Option (Lean.Expr × Lean.Expr × Lean.Expr) | true |
CategoryTheory.PreOneHypercover.Hom.ext'_iff | Mathlib.CategoryTheory.Sites.Hypercover.One | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {S : C} {E : CategoryTheory.PreOneHypercover S}
{F : CategoryTheory.PreOneHypercover S} {f g : E.Hom F},
f = g ↔
∃ (hs₀ : f.s₀ = g.s₀) (_ :
∀ (i : E.I₀), f.h₀ i = CategoryTheory.CategoryStruct.comp (g.h₀ i) (CategoryTheory.eqToHom ⋯)) (hs₁ :
∀... | true |
Set.projIcc_of_le_left | Mathlib.Order.Interval.Set.ProjIcc | ∀ {α : Type u_1} [inst : LinearOrder α] {a b : α} (h : a ≤ b) {x : α}, x ≤ a → Set.projIcc a b h x = ⟨a, ⋯⟩ | true |
CategoryTheory.Category.comp_id._autoParam | Mathlib.CategoryTheory.Category.Basic | Lean.Syntax | false |
Std.DHashMap.Internal.Raw₀.getEntry?_eq_getEntry? | Std.Data.DHashMap.Internal.WF | ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] [PartialEquivBEq α] [LawfulHashable α]
{m : Std.DHashMap.Internal.Raw₀ α β},
Std.DHashMap.Internal.Raw.WFImp ↑m →
∀ {a : α}, m.getEntry? a = Std.Internal.List.getEntry? a (Std.DHashMap.Internal.toListModel (↑m).buckets) | true |
Std.Format.bracket | Init.Data.Format.Basic | String → Std.Format → String → Std.Format | true |
Lean.Meta.Grind.Context.cheapCases._default | Lean.Meta.Tactic.Grind.Types | Bool | false |
linearIndependent_fin_cons | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | ∀ {K : Type u_3} {V : Type u} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {x : V} {n : ℕ}
{v : Fin n → V}, LinearIndependent K (Fin.cons x v) ↔ LinearIndependent K v ∧ x ∉ Submodule.span K (Set.range v) | true |
WeierstrassCurve.Projective.PointClass | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | (R : Type r) → [CommRing R] → Type r | true |
eq_zero_or_one_of_sq_eq_self | Mathlib.Algebra.GroupWithZero.Defs | ∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] [IsRightCancelMulZero M₀] {x : M₀}, x ^ 2 = x → x = 0 ∨ x = 1 | true |
IsOpen.add_closure | Mathlib.Topology.Algebra.Group.Pointwise | ∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [IsTopologicalAddGroup G] {s : Set G},
IsOpen s → ∀ (t : Set G), s + closure t = s + t | true |
Set.IsWF.min_add | Mathlib.Data.Finset.MulAntidiagonal | ∀ {α : Type u_1} {s t : Set α} [inst : AddCommMonoid α] [inst_1 : LinearOrder α] [inst_2 : IsOrderedCancelAddMonoid α]
(hs : s.IsWF) (ht : t.IsWF) (hsn : s.Nonempty) (htn : t.Nonempty), ⋯.min ⋯ = hs.min hsn + ht.min htn | true |
Order.not_isSuccLimit_add_one | Mathlib.Algebra.Order.SuccPred | ∀ {α : Type u_1} [inst : PartialOrder α] (a : α) [inst_1 : Add α] [inst_2 : One α] [SuccAddOrder α] [NoMaxOrder α],
¬Order.IsSuccLimit (a + 1) | true |
UInt16.pow | Init.Data.UInt.Basic | UInt16 → ℕ → UInt16 | true |
ModuleCat.smulNatTrans._proof_8 | Mathlib.Algebra.Category.ModuleCat.Basic | ∀ (R : Type u_1) [inst : Ring R] (x x_1 : R),
{ app := fun M => M.smul (x * x_1), naturality := ⋯ } =
{ app := fun M => M.smul x, naturality := ⋯ } * { app := fun M => M.smul x_1, naturality := ⋯ } | false |
Function.Surjective.smulCommClass | Mathlib.Algebra.Group.Action.Defs | ∀ {M : Type u_1} {N : Type u_2} {α : Type u_5} {β : Type u_6} [inst : SMul M α] [inst_1 : SMul N α] [inst_2 : SMul M β]
[inst_3 : SMul N β] [SMulCommClass M N α] {f : α → β},
Function.Surjective f →
(∀ (c : M) (x : α), f (c • x) = c • f x) → (∀ (c : N) (x : α), f (c • x) = c • f x) → SMulCommClass M N β | true |
CompHausLike.LocallyConstant.sigmaIso._proof_3 | Mathlib.Condensed.Discrete.LocallyConstant | ∀ {P : TopCat → Prop} [inst : ∀ (S : CompHausLike P) (p : ↑S.toTop → Prop), CompHausLike.HasProp P (Subtype p)]
{Q : CompHausLike P} {Z : Type (max u_1 u_2)} (r : LocallyConstant (↑Q.toTop) Z),
CompactSpace ((i : Function.Fiber ⇑r) × ↑(CompHausLike.LocallyConstant.fiber r i).toTop) | false |
extChartAt_self_apply | Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | ∀ (𝕜 : Type u_1) {E : Type u_2} {H : Type u_4} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {x y : H},
↑(extChartAt I x) y = ↑I y | true |
CategoryTheory.InjectiveResolution.definition._@.Mathlib.CategoryTheory.Abelian.Injective.Resolution.4211954440._hygCtx._hyg.8 | Mathlib.CategoryTheory.Abelian.Injective.Resolution | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] →
[CategoryTheory.EnoughInjectives C] → (Z : C) → CategoryTheory.InjectiveResolution Z | false |
Lean.Elab.Info.ofChoiceInfo.elim | Lean.Elab.InfoTree.Types | {motive : Lean.Elab.Info → Sort u} →
(t : Lean.Elab.Info) →
t.ctorIdx = 14 → ((i : Lean.Elab.ChoiceInfo) → motive (Lean.Elab.Info.ofChoiceInfo i)) → motive t | false |
one_half_le_sum_primes_ge_one_div | Mathlib.NumberTheory.SumPrimeReciprocals | ∀ (k : ℕ), 1 / 2 ≤ ∑ p ∈ (4 ^ (k.primesBelow.card + 1)).succ.primesBelow \ k.primesBelow, 1 / ↑p | true |
List.isEmpty_eq_false_iff._simp_1 | Init.Data.List.Lemmas | ∀ {α : Type u_1} {l : List α}, (l.isEmpty = false) = (l ≠ []) | false |
_private.Mathlib.Order.Interval.Set.Fin.0.Fin.preimage_rev_Ico._simp_1_2 | Mathlib.Order.Interval.Set.Fin | ∀ {n : ℕ} {i j : Fin n}, (i.rev < j) = (j.rev < i) | false |
Stream'.Seq.update._proof_2 | Mathlib.Data.Seq.Defs | ∀ {α : Type u_1} (s : Stream'.Seq α) (n : ℕ) (f : α → α), Stream'.IsSeq (Function.update (↑s) n (Option.map f (↑s n))) | false |
Complex.continuousWithinAt_log_of_re_neg_of_im_zero | Mathlib.Analysis.SpecialFunctions.Complex.Log | ∀ {z : ℂ}, z.re < 0 → z.im = 0 → ContinuousWithinAt Complex.log {z | 0 ≤ z.im} z | true |
FreeGroup.Red.Step.cons_not | Mathlib.GroupTheory.FreeGroup.Basic | ∀ {α : Type u} {L : List (α × Bool)} {x : α} {b : Bool}, FreeGroup.Red.Step ((x, b) :: (x, !b) :: L) L | true |
_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform.0.SimpleGraph.unreduced_edges_subset._simp_1_4 | Mathlib.Combinatorics.SimpleGraph.Regularity.Uniform | ∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, (¬a ≤ b) = (b < a) | false |
Complementeds.disjoint_coe._simp_1 | Mathlib.Order.Disjoint | ∀ {α : Type u_1} [inst : DistribLattice α] [inst_1 : BoundedOrder α] {a b : Complementeds α},
Disjoint ↑a ↑b = Disjoint a b | false |
_private.Mathlib.Order.CompleteLattice.PiLex.0.Pi.Colex.instInfSetColexForall._proof_1 | Mathlib.Order.CompleteLattice.PiLex | ∀ {ι : Type u_1} [inst : LinearOrder ι] [WellFoundedGT ι], IsWellFounded ιᵒᵈ fun x1 x2 => x1 < x2 | false |
StrictConcaveOn.lt_map_sum | Mathlib.Analysis.Convex.Jensen | ∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_4} {ι : Type u_5} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜]
[IsStrictOrderedRing 𝕜] [inst_3 : AddCommGroup E] [inst_4 : AddCommGroup β] [inst_5 : PartialOrder β]
[IsOrderedAddMonoid β] [inst_7 : Module 𝕜 E] [inst_8 : Module 𝕜 β] [IsStrictOrderedModule 𝕜 β] {s : Set... | true |
Lean.PrettyPrinter.Formatter.pushToken | Lean.PrettyPrinter.Formatter | Lean.SourceInfo → String → Bool → Lean.PrettyPrinter.FormatterM Unit | true |
Lean.Meta.instReduceEvalLiteral_qq | Qq.ForLean.ReduceEval | Lean.Meta.ReduceEval Lean.Literal | true |
BitVec.getLsb'_ofFnBE | Batteries.Data.BitVec.Lemmas | ∀ {n : ℕ} (f : Fin n → Bool) (i : Fin n), (BitVec.ofFnBE f).getLsb i = f i.rev | true |
Set.Icc.mul_le_right | Mathlib.Algebra.Order.Interval.Set.Instances | ∀ {R : Type u_1} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsOrderedRing R] {x y : ↑(Set.Icc 0 1)},
x * y ≤ y | true |
_private.Init.Omega.IntList.0.List.getElem?_map.match_1_1 | Init.Omega.IntList | ∀ {α : Type u_1} (motive : List α → ℕ → Prop) (x : List α) (x_1 : ℕ),
(∀ (x : ℕ), motive [] x) →
(∀ (head : α) (tail : List α), motive (head :: tail) 0) →
(∀ (head : α) (l : List α) (i : ℕ), motive (head :: l) i.succ) → motive x x_1 | false |
StarRingEquiv.trans | Mathlib.Algebra.Star.StarRingHom | {A : Type u_1} →
{B : Type u_2} →
{C : Type u_3} →
[inst : Add A] →
[inst_1 : Add B] →
[inst_2 : Mul A] →
[inst_3 : Mul B] →
[inst_4 : Star A] →
[inst_5 : Star B] →
[inst_6 : Add C] → [inst_7 : Mul C] → [inst_8 : Star C] → (A ≃⋆+*... | true |
_private.Mathlib.LinearAlgebra.BilinearForm.Orthogonal.0.LinearMap.BilinForm.ker_restrict_eq_of_codisjoint._simp_1_2 | Mathlib.LinearAlgebra.BilinearForm.Orthogonal | ∀ {R : Type u_1} {R₂ : Type u_3} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring R₂]
[inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂}
{x : M} {f : M →ₛₗ[σ₁₂] M₂} {p : Submodule R₂ M₂}, (x ∈ Submodule.comap f p) = (f x ∈ p) | false |
IsPRadical.injective_comp | Mathlib.FieldTheory.IsPerfectClosure | ∀ {K : Type u_1} {L : Type u_2} (M : Type u_3) [inst : CommRing K] [inst_1 : CommRing L] [inst_2 : CommRing M]
(i : K →+* L) (p : ℕ) [ExpChar M p] [IsPRadical i p] [IsReduced M], Function.Injective fun f => f.comp i | true |
Algebra.FinitePresentation.mvPolynomial_of_finitePresentation | Mathlib.RingTheory.FinitePresentation | ∀ {R : Type w₁} {A : Type w₂} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.FinitePresentation R A] (ι : Type v) [Finite ι], Algebra.FinitePresentation R (MvPolynomial ι A) | true |
_private.Lean.Meta.Tactic.Grind.Action.0.Lean.Meta.Grind.Action.loop.match_1 | Lean.Meta.Tactic.Grind.Action | (motive : ℕ → Sort u_1) → (n : ℕ) → (Unit → motive 0) → ((n : ℕ) → motive n.succ) → motive n | false |
isAddRegular_unop | Mathlib.Algebra.Regular.Opposite | ∀ {R : Type u_1} [inst : Add R] {a : Rᵃᵒᵖ}, IsAddRegular (AddOpposite.unop a) ↔ IsAddRegular a | true |
Lean.Meta.CheckAssignment.Context.rec | Lean.Meta.ExprDefEq | {motive : Lean.Meta.CheckAssignment.Context → Sort u} →
((mvarId : Lean.MVarId) →
(mvarDecl : Lean.MetavarDecl) →
(fvars : Array Lean.Expr) →
(hasCtxLocals : Bool) →
(rhs : Lean.Expr) →
motive
{ mvarId := mvarId, mvarDecl := mvarDecl, fvars := fvars, h... | false |
Polynomial.add_modByMonic | Mathlib.Algebra.Polynomial.Div | ∀ {R : Type u} [inst : CommRing R] {q : Polynomial R} (p₁ p₂ : Polynomial R), (p₁ + p₂) %ₘ q = p₁ %ₘ q + p₂ %ₘ q | true |
Nat.maxPowDvdDiv.eq_1 | Mathlib.Data.Nat.MaxPowDiv | ∀ (p n : ℕ), p.maxPowDvdDiv n = if H : 1 < p ∧ n ≠ 0 then Nat.maxPowDvdDiv.go n p H else (0, n) | true |
SSet.Subcomplex.PairingCore.pairing._proof_9 | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | ∀ {X : SSet} {A : X.Subcomplex} (h : A.PairingCore), h.I ∩ h.II = ∅ | false |
_private.Init.Data.Nat.Gcd.0.Nat.gcd_pos_iff._simp_1_2 | Init.Data.Nat.Gcd | ∀ {p q : Prop} [d₁ : Decidable p] [d₂ : Decidable q], (¬(p ∧ q)) = (¬p ∨ ¬q) | false |
Function.OfArity.curry_two_eq_curry | Mathlib.Data.Fin.Tuple.Curry | ∀ {α β : Type u} (f : (Fin 2 → α) → β), Function.OfArity.curry f = Function.curry (f ∘ ⇑(finTwoArrowEquiv α).symm) | true |
Turing.TM2.stepAux.eq_1 | Mathlib.Computability.TuringMachine.StackTuringMachine | ∀ {K : Type u_1} {Γ : K → Type u_2} {Λ : Type u_3} {σ : Type u_4} [inst : DecidableEq K] (x : σ)
(x_1 : (k : K) → List (Γ k)) (k : K) (f : σ → Γ k) (q : Turing.TM2.Stmt Γ Λ σ),
Turing.TM2.stepAux (Turing.TM2.Stmt.push k f q) x x_1 = Turing.TM2.stepAux q x (Function.update x_1 k (f x :: x_1 k)) | true |
_private.Lean.Compiler.LCNF.Simp.DiscrM.0.Lean.Compiler.LCNF.Simp.withDiscrCtorImp.updateCtx.match_1 | Lean.Compiler.LCNF.Simp.DiscrM | (motive : Option (List Lean.Level × Array (Lean.Compiler.LCNF.Arg Lean.Compiler.LCNF.Purity.pure)) → Sort u_1) →
(__do_lift : Option (List Lean.Level × Array (Lean.Compiler.LCNF.Arg Lean.Compiler.LCNF.Purity.pure))) →
((us : List Lean.Level) →
(params : Array (Lean.Compiler.LCNF.Arg Lean.Compiler.LCNF.Pur... | false |
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