lean_workbook_plus_67954

Proved

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

Prove that if $abc=1$ and $a,b,c$ are positive reals, then $a^2+b^2+c^2\le a^3+b^3+c^3$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_67954 (a b c : ℝ) (h : a * b * c = 1) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 + b^2 + c^2 ≤ a^3 + b^3 + c^3   :=  by sorry

Source

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

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