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

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