A pair-product square sum upper bound at fixed sum three

Proved

WorkbookSource.base_44125

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

lean-workbooksource-checked

Let $a, b, c$ be positive real numbers such that $a+b+c=3$ . Prove that $a^2b^2+b^2c^2+c^2a^2 \le a^2+b^2+c^2+\frac{9}{16}$

Source: InternLM Lean-Workbook, record lean_workbook_44125 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_44125 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a^2 * b^2 + b^2 * c^2 + c^2 * a^2 ≤ a^2 + b^2 + c^2 + 9 / 16  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_44125; Apache-2.0

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