{ cases b <;> simp }
case hi.succ.hc
n : ℕ
b : Bool
n✝ : ℕ
hb : succ n✝ = 0 → b = true
ih : size (succ n✝) - 1 = log 2 (succ n✝)
⊢ (bif b then 1 else 0) < 2

case hi.succ
n : ℕ
b : Bool
n✝ : ℕ
hb : succ n✝ = 0 → b = true
ih : size (succ n✝) - 1 = log 2 (succ n✝)
⊢ bit b (succ n✝) ≠ 0
case hi.succ
n : ℕ
b : Bool
n✝ : ℕ
hb : succ n✝ = 0 → b = true
ih : size (succ n✝) - 1 = log 2 (succ n✝)
⊢ bit b (succ n✝) ≠ 0