have h₁ : a ≤ b + round (a - b) := by
  trans b + (a - b)
  . rewrite [← add_tsub_assoc_of_le hba']
    exact Nat.le_of_eq $ Eq.symm $ add_tsub_cancel_left _ _
  . apply Nat.add_le_add_left
    exact lt_round.le
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₀ : faithful₀ n round
hfaithful₁ : faithful₁ n round
hfa : trunc n a = a
hba : 2 * b ≤ a
lt_round : a - b < round (a - b)
hba' : b ≤ a
⊢ ulp n (a - b) - (a - b) % ulp n (a - b) ≤ b
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₀ : faithful₀ n round
hfaithful₁ : faithful₁ n round
hfa : trunc n a = a
hba : 2 * b ≤ a
lt_round : a - b < round (a - b)
hba' : b ≤ a
h₁ : a ≤ b + round (a - b)
⊢ ulp n (a - b) - (a - b) % ulp n (a - b) ≤ b