A quartic pairwise bound with a cubic correction

Proved

WorkbookSource.base_6148

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

lean-workbooksource-checked

Let $a,b,c$ to be non negative real numbers satisfying $a+b+c=2$ . $b^2c^2+c^2a^2+a^2b^2+\dfrac{11}{8}abc\le 1$

Source: InternLM Lean-Workbook, record lean_workbook_6148 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_6148 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a + b + c = 2) : b^2 * c^2 + c^2 * a^2 + a^2 * b^2 + (11 / 8) * a * b * c ≤ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6148; Apache-2.0

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