apply b₁_lo_of_round_lt_of_ulp_le npos hfaithful₀ hfaithful₁ hfa hfb hba round_lt
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₀ : faithful₀ n round
hfaithful₁ : faithful₁ n round
hcorrect₀ : correct₀ n round
hfa : trunc n a = a
hfb : trunc n b = b
hba : b ≤ a
round_lt : round (a - b) < a - b
no_uflow : 2 ^ n ≤ a - b
ulp_eq_ulp : ulp n (a - b) = ulp n a
bpos : b > 0
le_ulp : b ≤ ulp n a
⊢ trunc n (a - b - round (a - b)) = a - b - round (a - b)
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₀ : faithful₀ n round
hfaithful₁ : faithful₁ n round
hcorrect₀ : correct₀ n round
hfa : trunc n a = a
hfb : trunc n b = b
hba : b ≤ a
round_lt : round (a - b) < a - b
no_uflow : 2 ^ n ≤ a - b
ulp_eq_ulp : ulp n (a - b) = ulp n a
bpos : b > 0
le_ulp : b ≤ ulp n a
⊢ ulp n a ≤ 2 * b