apply Nat.le_antisymm
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
hcorrect₁ : correct₁ n round
hfa : trunc n a = a
no_uflow : 2 ^ n ≤ a + b
no_carry : a + b < 2 ^ Nat.size a
lt_round : a + b < round (a + b)
⊢ Nat.size (a + b) = Nat.size a
case h₁
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
hcorrect₁ : correct₁ n round
hfa : trunc n a = a
no_uflow : 2 ^ n ≤ a + b
no_carry : a + b < 2 ^ Nat.size a
lt_round : a + b < round (a + b)
⊢ Nat.size (a + b) ≤ Nat.size a

case h₂
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
hcorrect₁ : correct₁ n round
hfa : trunc n a = a
no_uflow : 2 ^ n ≤ a + b
no_carry : a + b < 2 ^ Nat.size a
lt_round : a + b < round (a + b)
⊢ Nat.size a ≤ Nat.size (a + b)