Prove2Me

A pairwise squared product bound at fixed sum two

Proved
WorkbookSource.base_49608

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

lean-workbooksource-checked

Let a,b,ca,b,c are nonnegative real numbers satisfying a+b+c=2.a+b+c=2. Prove that (a+b)2(a+c)2(b+c)2(a2+b2+c2)≤8.(a+b)^2(a+c)^2(b+c)^2(a^2+b^2+c^2)\leq8.

Source: InternLM Lean-Workbook, record lean_workbook_49608 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_49608 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a + b + c = 2) : (a + b) ^ 2 * (a + c) ^ 2 * (b + c) ^ 2 * (a ^ 2 + b ^ 2 + c ^ 2) ≤ 8  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_49608; Apache-2.0

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