have h₀ : b % ulp n a = (a + b) % ulp n a := by
  rewrite [← Nat.mod_add_mod]
  rewrite [Nat.mod_eq_zero_of_dvd (ulp_dvd_of_trunc_eq hfa)]
  rw [Nat.zero_add]
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
⊢ trunc n (a + b - round (a + b)) = a + b - round (a + b)
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
⊢ trunc n (a + b - round (a + b)) = a + b - round (a + b)