apply Nat.dvd_add
case hdvd.h₁
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₀ : faithful₀ n round
hfaithful₁ : faithful₁ n round
hfa : trunc n a = a
hfb : trunc n b = b
hba : 2 * b ≤ a
lt_round : a - b < round (a - b)
ulp_dvd : ulp n b ∣ ulp n (a - b)
hba' : b ≤ a
ulp_sub_le : ulp n (a - b) - (a - b) % ulp n (a - b) ≤ b
⊢ ulp n b ∣ trunc n (a - b) + ulp n (a - b)
case hdvd.h₁.h₁
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₀ : faithful₀ n round
hfaithful₁ : faithful₁ n round
hfa : trunc n a = a
hfb : trunc n b = b
hba : 2 * b ≤ a
lt_round : a - b < round (a - b)
ulp_dvd : ulp n b ∣ ulp n (a - b)
hba' : b ≤ a
ulp_sub_le : ulp n (a - b) - (a - b) % ulp n (a - b) ≤ b
⊢ ulp n b ∣ trunc n (a - b)

case hdvd.h₁.h₂
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₀ : faithful₀ n round
hfaithful₁ : faithful₁ n round
hfa : trunc n a = a
hfb : trunc n b = b
hba : 2 * b ≤ a
lt_round : a - b < round (a - b)
ulp_dvd : ulp n b ∣ ulp n (a - b)
hba' : b ≤ a
ulp_sub_le : ulp n (a - b) - (a - b) % ulp n (a - b) ≤ b
⊢ ulp n b ∣ ulp n (a - b)