Prove2Me

A lower bound for a sum of two squared linear forms

Proved
WorkbookSource.problem_8940

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

lean-workbooksource-checked

Actually, just the first condition 2x+y≥22x+y\ge2 is sufficient: (2x+y)2+(2y−x)2≥4+0⇔x2+y2≥45 (2x+y)^2+(2y-x)^2\ge 4+0 \Leftrightarrow x^2+y^2 \ge \frac45.

Source: InternLM Lean-Workbook, record lean_workbook_8940 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_8940  (x y : ℝ)
  (h₀ : 2 * x + y ≥ 2) :
  (2 * x + y)^2 + (2 * y - x)^2 ≥ 4  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8940; Apache-2.0

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