lean_workbook_plus_6789

Proved

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

prove or disprove $a^3+b^3+c^3\geq{a^2+b^2+c^2}$ given $a,b,c>0$ and $abc=1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6789 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a * b * c = 1) : a ^ 3 + b ^ 3 + c ^ 3 ≥ a ^ 2 + b ^ 2 + c ^ 2   :=  by sorry

Source

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

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