A reciprocal sum lower bound with a product correction

Proved

WorkbookSource.plus_80996

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

lean-workbooksource-checked

Let $a,b,c >0$ such that $a+b+c=3.$ Prove that

\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \ge \frac{1}{3}(13-4abc)

Source: InternLM Lean-Workbook, record lean_workbook_plus_80996 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_80996 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : 1 / a + 1 / b + 1 / c ≥ 1 / 3 * (13 - 4 * a * b * c)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_80996; Apache-2.0

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