Prove2Me

A triangle-factor reciprocal bound at fixed sum six

Proved
WorkbookSource.base_8188

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

lean-workbooksource-checked

If a,b,c positive numbers and a+b+c=6 proove that ∑43(3−a)(3−b)(3−c)a2≤7(a2+b2+c2)2\sum 4 \frac{3(3-a)(3-b)(3-c)}{a^2}\leq \frac{7(a^2+b^2+c^2)}{2}

Source: InternLM Lean-Workbook, record lean_workbook_8188 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_8188 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 6) : 4 * (3 * (3 - a) * (3 - b) * (3 - c)) / a ^ 2 + 4 * (3 * (3 - b) * (3 - c) * (3 - a)) / b ^ 2 + 4 * (3 * (3 - c) * (3 - a) * (3 - b)) / c ^ 2 ≤ 7 / 2 * (a ^ 2 + b ^ 2 + c ^ 2)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8188; Apache-2.0

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