. exact carry
case a
n x : ℕ
npos : 0 < n
carry : 2 ^ Nat.size x ≤ next n x
⊢ 2 ^ Nat.size x ≤ next n x

case a
n x : ℕ
npos : 0 < n
carry : 2 ^ Nat.size x ≤ next n x
⊢ next n x < 2 ^ Nat.size x + 2 ^ expt n (next n x)
case a
n x : ℕ
npos : 0 < n
carry : 2 ^ Nat.size x ≤ next n x
⊢ next n x < 2 ^ Nat.size x + 2 ^ expt n (next n x)