lean_workbook_plus_17682

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c>0$ and $\frac{1}{(a-1)(b-1)(c-1)}-\frac{4}{(a+1)(b+1)(c+1)}=\frac{1}{16}$ . Prove that

\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq 1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17682 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 1) : (1 / (a - 1) / (b - 1) / (c - 1) - 4 / (a + 1) / (b + 1) / (c + 1) = 1 / 16) → 1 / a + 1 / b + 1 / c ≥ 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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