A lower bound on a sum of three shifted squares

Proved

WorkbookSource.base_11043

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that : $(xy+ 2)^{2}+ (x- 1)^{2}+ (y- 1)^{2}\geqq 4$

Source: InternLM Lean-Workbook, record lean_workbook_11043 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_11043 (x y : ℝ) : (x * y + 2) ^ 2 + (x - 1) ^ 2 + (y - 1) ^ 2 ≥ 4  :=  by sorry

Source