A product of quadratic symmetric sums at fixed sum two

Proved

WorkbookSource.base_23576

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c \geq 0$ such that $a+b+c=2$ . Prove that $1.(a^2+b^2+c^2)(a^2b^2+b^2c^2+c^2a^2) \leq 2$

Source: InternLM Lean-Workbook, record lean_workbook_23576 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_23576 (a b c : ℝ) (h : a + b + c = 2) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0): (a^2 + b^2 + c^2) * (a^2 * b^2 + b^2 * c^2 + c^2 * a^2) ≤ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23576; Apache-2.0

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