calc
  b * b + a₁ < b * b + b        := by simpa using h₁
  _          ≤ a₂ * a₂ + a₂     := add_le_add (mul_le_mul (by simpa using h₂) (by simpa using h₂) (by simp) (by simp)) (by simpa using h₂)
  _          ≤ a₂ * a₂ + a₂ + b := by simp
case neg
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
a₁ a₂ : M
h : a₁ < a₂
b : M
h₁ : a₁ < b
h₂ : ¬a₂ < b
⊢ b * b + a₁ < a₂ * a₂ + a₂ + b
no goals