A refined reciprocal product inequality with a quadratic correction

Proved

WorkbookSource.plus_53138

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

lean-workbooksource-checked

prove that $6(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})(a+b+c)^{3}+3(ab+bc+ca)\geq55(a+b+c)^{2}$ with $a;b;c>0$

Source: InternLM Lean-Workbook, record lean_workbook_plus_53138 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_53138 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :  6 * (1 / a + 1 / b + 1 / c) * (a + b + c) ^ 3 + 3 * (a * b + b * c + c * a) ≥ 55 * (a + b + c) ^ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_53138; Apache-2.0

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