lean_workbook_plus_75568

Proved

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

Let $a, b, c > 0$ satisfy $a + b + c \ge \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$ . Prove that $a^3 + b^3 + c^3 \ge a + b + c$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_75568 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : a + b + c ≥ 1/a + 1/b + 1/c → a^3 + b^3 + c^3 ≥ a + b + c   :=  by sorry

Source

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

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