rcases hk with ⟨c, rfl⟩
case mk
m k : ℕ
hk✝ : k < m + 1
hk : ∃ c, m = k + c
⊢ m - (m + (m + 1 - ↑⟨k, hk✝⟩)) % (m + 1) = ↑⟨k, hk✝⟩
case mk.intro
k c : ℕ
hk : k < k + c + 1
⊢ k + c - (k + c + (k + c + 1 - ↑⟨k, hk⟩)) % (k + c + 1) = ↑⟨k, hk⟩