have h : b - (a - round (a - b)) = round (a - b) - (a - b) := by
  apply tsub_eq_of_eq_add
  rewrite [tsub_add_eq_add_tsub le_round]
  rewrite [add_tsub_cancel_of_le hca]
  exact Eq.symm $ tsub_tsub_cancel_of_le hba
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
le_round : a - b ≤ round (a - b)
left✝ : trunc n (a - b - round (a - b)) = a - b - round (a - b)
hfr₂ : trunc n (round (a - b) - (a - b)) = round (a - b) - (a - b)
hfe : round (a - round (a - b)) = a - round (a - b)
hca : round (a - b) ≤ a
⊢ round (a - b) - round (b - round (a - round (a - b))) = 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
le_round : a - b ≤ round (a - b)
left✝ : trunc n (a - b - round (a - b)) = a - b - round (a - b)
hfr₂ : trunc n (round (a - b) - (a - b)) = round (a - b) - (a - b)
hfe : round (a - round (a - b)) = a - round (a - b)
hca : round (a - b) ≤ a
h : b - (a - round (a - b)) = round (a - b) - (a - b)
⊢ round (a - b) - round (b - round (a - round (a - b))) = a - b