lean_workbook_plus_14749

Proved

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

Given real numbers $x,y,z\geq -1$ satisfying $x^3 +y^3 + z^3 \geq x^2 + y^2 + z^2$ , prove that $x^5 + y^5 + z^5 \geq x^2 + y^2 + z^2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14749 (x y z : ℝ) (hx : x ≥ -1) (hy : y ≥ -1) (hz : z ≥ -1) (h : x^3 + y^3 + z^3 ≥ x^2 + y^2 + z^2) : x^5 + y^5 + z^5 ≥ x^2 + y^2 + z^2   :=  by sorry

Source

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

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