induction sz <;> simp [comp, xor, logic1, logic2, minusOne] at *
sz : ℕ
n : FinInt sz
⊢ comp n = xor n minusOne
case zero
n : FinInt Nat.zero
⊢ logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n nil

case succ
n✝ : ℕ
n_ih✝ : ∀ (n : FinInt n✝), logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n minusOne
n : FinInt (Nat.succ n✝)
⊢ logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n (I minusOne)