A sharp bound for pairwise squares and a triple product

Proved

WorkbookSource.base_4034

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

lean-workbooksource-checked

Given: $a,b,c\geq 0$ and $a+b+c=2$ . Prove that: $a^2b^2+b^2c^2+c^2a^2+abc\leq 1$

Source: InternLM Lean-Workbook, record lean_workbook_4034 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4034 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a + b + c = 2) : a^2 * b^2 + b^2 * c^2 + c^2 * a^2 + a * b * c ≤ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4034; Apache-2.0

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