induction sz <;> cases n <;> cases m <;> simp [addfull]
sz : ℕ
n m : FinInt sz
⊢ addfull n m = addfull m n
case succ.next.next
n✝ : ℕ
a✝³ : Bool
a✝² : FinInt n✝
n_ih✝ : ∀ (n m : FinInt (Nat.add n✝ 0)), addfull n m = addfull m n
a✝¹ : Bool
a✝ : FinInt n✝
⊢ (match addfull a✝² a✝ with
    | next false r => next (a✝³ && a✝¹) (next (a✝³ != a✝¹) r)
    | next true r => next (a✝³ || a✝¹) (next (a✝³ == a✝¹) r)) =
    match addfull a✝ a✝² with
    | next false r => next (a✝¹ && a✝³) (next (a✝¹ != a✝³) r)
    | next true r => next (a✝¹ || a✝³) (next (a✝¹ == a✝³) r)