have : √(a * a + (a + b)) = a :=
  sqrt_eq_of_le_of_le (by simp [add_assoc]) (by simp [add_assoc, two_mul, show b ≤ a from by simpa using h])
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
a b : M
h : ¬a < b
⊢ unpair (a * a + a + b) = (a, b)
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
a b : M
h : ¬a < b
this : √(a * a + (a + b)) = a
⊢ unpair (a * a + a + b) = (a, b)