. apply Nat.dvd_sub hba'
  . trans ulp n a
    . exact ulp_dvd_ulp n hba'
    . exact ulp_dvd_of_trunc_eq hfa
  . exact ulp_dvd_of_trunc_eq hfb
case hdvd.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 ∣ a - b
no goals