split
m n : ℕ
⊢ (m / succ n + if succ n ∣ m + 1 then 1 else 0) ≤ succ (m / succ n)
case inl
m n : ℕ
h✝ : succ n ∣ m + 1
⊢ m / succ n + 1 ≤ succ (m / succ n)

case inr
m n : ℕ
h✝ : ¬succ n ∣ m + 1
⊢ m / succ n + 0 ≤ succ (m / succ n)