exact this.of_eq (by simp)
α : Type u_1
α₁ : Type u_2
α₂ : Type u_3
β : Type u_4
γ : Type u_5
σ : Type u_6
τ : Type u_7
inst✝⁶ : Primcodable α
inst✝⁵ : Primcodable α₁
inst✝⁴ : Primcodable α₂
inst✝³ : Primcodable β
inst✝² : Primcodable γ
inst✝¹ : Primcodable σ
inst✝ : Primcodable τ
f : α → ℕ × ℕ → σ
g : α × ℕ × ℕ → List σ → Option σ
hg : Primrec₂ g
H : ∀ (a : α) (n m : ℕ), g (a, n, m) (List.map (fun i => f a i.unpair) (List.range (n.pair m))) = some (f a (n, m))
g' : α × ℕ → List σ → Option σ :=
  fun x =>
    match (motive := α × ℕ → List σ → Option σ) x with
    | (a, n) => g (a, n.unpair)
this✝¹ : Primrec₂ g'
this✝ : Primrec₂ fun a n => f a n.unpair
this : Primrec₂ fun a p => (fun a n => f a n.unpair) a (p.1.pair p.2)
⊢ Primrec₂ f
no goals