simp [not_lt.mpr this]
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 : M
h : ¬a - √a * √a < √a
this : a - √a * √a - √a ≤ √a
⊢ (if √a < a - √a * √a - √a then (a - √a * √a - √a) * (a - √a * √a - √a) + √a else √a * √a + √a + (a - √a * √a - √a)) =
    a
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 : M
h : ¬a - √a * √a < √a
this : a - √a * √a - √a ≤ √a
⊢ √a * √a + √a + (a - √a * √a - √a) = a