Prove2Me

A mixed cubic bound for a pairwise sum

Proved
WorkbookSource.plus_11306

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

lean-workbooksource-checked

Let a,b,c>0,a+b+c=1.a,b,c>0,a+b+c=1. Prove that a2(b+c)+b2(c+a)+c2(a+b)+169≥6(ab+bc+ca).a^2(b+c)+b^2(c +a)+c^2(a+b)+\frac{16}{9}\geq 6(ab+bc+ca).

Source: InternLM Lean-Workbook, record lean_workbook_plus_11306 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_11306 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) : a^2 * (b + c) + b^2 * (c + a) + c^2 * (a + b) + 16 / 9 ≥ 6 * (a * b + b * c + c * a)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_11306; Apache-2.0

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