exact ⟨b / c, by simp, rfl, by rfl⟩
case mp
M : Type u_1
inst✝⁶ : Zero M
inst✝⁵ : One M
inst✝⁴ : Add M
inst✝³ : Mul M
inst✝² : LT M
inst✝¹ : M ⊧ₘ* 𝐏𝐀⁻
inst✝ : M ⊧ₘ* 𝐈open
b c : M
⊢ ∃ x ≤ b, x = b / c ∧ b - c * (b / c) = b - c * x
no goals