calc
  b * c * (a / b / c) ≤ b * (a / b) := by simp [mul_assoc]; exact mul_le_mul_left (mul_div_le_pos (a / b) hc)
  _                   ≤ a := mul_div_le_pos a hb
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
a b c : M
hb : 0 < b
hc : 0 < c
⊢ b * c * (a / b / c) ≤ a
no goals