cases (decode e : Option α) <;> simp
α : Type u_1
inst✝ : Encodable α
e i : ℕ
⊢ (encode (decode e)).predO = some i → ∃ a, decode i = some a
case some
α : Type u_1
inst✝ : Encodable α
e i : ℕ
val✝ : α
⊢ encode val✝ = i → ∃ a, decode i = some a