have hac : a ≤ round (a + b) := Nat.le_trans (Nat.le_add_right _ _) hi
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₀ : faithful₀ n round
hfaithful₁ : faithful₁ n round
hcorrect₁ : correct₁ n round
hfa : trunc n a = a
hfb : trunc n b = b
hba : b ≤ a
hi : a + b ≤ round (a + b)
⊢ round (a + b) - round (round (round (a + b) - a) - b) = a + b
round : ℕ → ℕ
n a b : ℕ
npos : 0 < n
hfaithful₀ : faithful₀ n round
hfaithful₁ : faithful₁ n round
hcorrect₁ : correct₁ n round
hfa : trunc n a = a
hfb : trunc n b = b
hba : b ≤ a
hi : a + b ≤ round (a + b)
hac : a ≤ round (a + b)
⊢ round (a + b) - round (round (round (a + b) - a) - b) = a + b