apply sterbenz
case inl
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 : b ≤ a
hab' : 2 * b ≤ a
⊢ trunc n (a - round (a - b)) = a - round (a - b)
case inl.hfa
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 : b ≤ a
hab' : 2 * b ≤ a
⊢ trunc n a = a

case inl.hfb
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 : b ≤ a
hab' : 2 * b ≤ a
⊢ trunc n (round (a - b)) = round (a - b)

case inl.hba
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 : b ≤ a
hab' : 2 * b ≤ a
⊢ round (a - b) ≤ a

case inl.hab
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 : b ≤ a
hab' : 2 * b ≤ a
⊢ a ≤ 2 * round (a - b)