rewrite [Nat.dvd_mod_iff (ulp_dvd_ulp n hba)]
case hdvd
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_carry : a + b < 2 ^ Nat.size a
round_le : round (a + b) ≤ a + b
size_eq : Nat.size (a + b) = Nat.size a
ulp_eq : ulp n (a + b) = ulp n a
mod_ulp₁ : a % ulp n a = 0
mod_ulp₂ : (a + b) % ulp n a = b % ulp n a
error_eq : a + b - trunc n (a + b) = b % ulp n a
⊢ ulp n b ∣ b % ulp n a
case hdvd
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_carry : a + b < 2 ^ Nat.size a
round_le : round (a + b) ≤ a + b
size_eq : Nat.size (a + b) = Nat.size a
ulp_eq : ulp n (a + b) = ulp n a
mod_ulp₁ : a % ulp n a = 0
mod_ulp₂ : (a + b) % ulp n a = b % ulp n a
error_eq : a + b - trunc n (a + b) = b % ulp n a
⊢ ulp n b ∣ b