Prove2Me

A fifth-power consequence of a cubic bound

Proved
WorkbookSource.problem_31792

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

If {x,y,z}⊂[−2,+∞) \{x,y,z\}\subset[ - 2, + \infty) and x3+y3+z3≥x2+y2+z2 x^3 + y^3 + z^3 \geq x^2 + y^2 + z^2 then x5+y5+z5≥x2+y2+z2 x^5 + y^5 + z^5 \geq x^2 + y^2 + z^2 is still true.

Source: InternLM Lean-Workbook, record lean_workbook_31792 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_31792 (x y z : ℝ) (hx : -2 ≤ x) (hy : -2 ≤ y) (hz : -2 ≤ z) (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/blob/main/lean_workbook.json, record lean_workbook_31792; Apache-2.0

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