apply Nat.mul_le_mul_left
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)
size_eq : Nat.size (a + b) = Nat.size a
ulp_eq : ulp n (a + b) = ulp n a
d : ℕ
hd : ulp n (a + b) = 2 * d
⊢ 2 * d ≤ 2 * b
case h
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)
size_eq : Nat.size (a + b) = Nat.size a
ulp_eq : ulp n (a + b) = ulp n a
d : ℕ
hd : ulp n (a + b) = 2 * d
⊢ d ≤ b