Prove2Me

A cyclic sum of quadratic squares

Proved
WorkbookSource.problem_34538

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

lean-workbooksource-checked

For real numbers a,b,ca,b,c,

(a2−ab+b2−a+b2)2+(b2−bc+c2−b+c2)2+(c2−ca+a2−c+a2)2≥0.\left(a^2-ab+b^2-\frac{a+b}{2}\right)^2+\left(b^2-bc+c^2-\frac{b+c}{2}\right)^2+\left(c^2-ca+a^2-\frac{c+a}{2}\right)^2\ge0.

Source: InternLM Lean-Workbook, record lean_workbook_34538 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_34538 (a b c : ℝ) : (a^2 - a * b + b^2 - (a + b) / 2)^2 + (b^2 - b * c + c^2 - (b + c) / 2)^2 + (c^2 - c * a + a^2 - (c + a) / 2)^2 ≥ 0  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_34538; Apache-2.0

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