simp only [Option.some.injEq, exists_eq_left', Nat.unpair_pair, of_list_decode_eq_some_cons has,
  of_list_decode_eq_some_cons hbs, Option.map_some', Option.some_bind]
case some.some.cons.cons
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 : σ → α × β → γ
hf : Primrec₂ f
h : Primrec₂ fun x p => some (Primrec.decodeZipWithRec f x p)
F : σ → ℕ → Option (List γ) := fun x n => (decode n).bind fun p => some (List.zipWith (fun a b => f x (a, b)) p.1 p.2)
x : σ
e : ℕ
a : α
as : List α
has : decode e.unpair.1 = some (a :: as)
b : β
bs : List β
hbs : decode e.unpair.2 = some (b :: bs)
this : e.unpair.1.pred.unpair.2.pair e.unpair.2.pred.unpair.2 < e
⊢ ∃ a,
    some (e.unpair.1.pred.unpair.2.pair e.unpair.2.pred.unpair.2) = some a ∧
      (((decode a.unpair.1).bind fun a_1 => Option.map (Prod.mk a_1) (decode a.unpair.2)).bind fun a =>
            some (List.zipWith (fun a b => f x (a, b)) a.1 a.2)).iget =
        List.zipWith (fun a b => f x (a, b)) as bs
no goals