A quadratic sum with a triple-product correction at fixed sum three

Proved

WorkbookSource.base_7706

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

lean-workbooksource-checked

Given $a, b, c$ positive real numbers such that the sum of all three variables is 3, prove that

\sum_{cyc}(a^2)+\frac{4abc}{3}\ge \frac{13}{3}

Source: InternLM Lean-Workbook, record lean_workbook_7706 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_7706 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a^2 + b^2 + c^2 + (4 * a * b * c) / 3 ≥ 13 / 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7706; Apache-2.0

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