apply Nat.mul_le_mul_right
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
hfa : trunc n a = a
hfb : trunc n b = b
hba : b ≤ a
no_uflow : 2 ^ n ≤ a + b
carry : 2 ^ Nat.size a ≤ a + b
round_le : round (a + b) ≤ a + b
ulp_add_eq_two_mul_ulp : ulp n (a + b) = 2 * ulp n a
ulp_le : ulp n a ≤ b
h₀ : b % ulp n a = (a + b) % ulp n a
h₁ : ulp n a ∣ ulp n (a + b)
h₂ : a + b - trunc n (a + b) = (a + b) / ulp n a * ulp n a % ulp n (a + b) + b % ulp n a
⊢ 1 * ulp n a ≤ b / ulp n a * ulp n a
case h
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₁ : faithful₁ n round
hfa : trunc n a = a
hfb : trunc n b = b
hba : b ≤ a
no_uflow : 2 ^ n ≤ a + b
carry : 2 ^ Nat.size a ≤ a + b
round_le : round (a + b) ≤ a + b
ulp_add_eq_two_mul_ulp : ulp n (a + b) = 2 * ulp n a
ulp_le : ulp n a ≤ b
h₀ : b % ulp n a = (a + b) % ulp n a
h₁ : ulp n a ∣ ulp n (a + b)
h₂ : a + b - trunc n (a + b) = (a + b) / ulp n a * ulp n a % ulp n (a + b) + b % ulp n a
⊢ 1 ≤ b / ulp n a