simpa using open_leastNumber (P := λ x ↦ x * x ≤ a) ⟨“x | x * x ≤ &a”, by simp, by simp⟩
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
⊢ a < (a + 1) * (a + 1) → ∃ x, x * x ≤ a ∧ a < (x + 1) * (x + 1)
no goals