A squared pairwise-sum bound at unit positive sum

Proved

WorkbookSource.base_957

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

lean-workbooksource-checked

prove: $2(ab+ac+bc)^2 + \frac{8}{27} \ge ab+ ac+bc +5abc$ given $a,b,c >0$ and $a+b+c=1$

Source: InternLM Lean-Workbook, record lean_workbook_957 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_957 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 1) : 2 * (a * b + a * c + b * c) ^ 2 + 8 / 27 ≥ a * b + a * c + b * c + 5 * a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_957; Apache-2.0

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