A cubed quadratic sum bounds pairwise cubic products

Proved

WorkbookSource.plus_58854

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

If $x,y,z$ are positive numbers, then ${({x^2} + {y^2} + {z^2})^3} \ge 8({x^3}{y^3} + {y^3}{z^3} + {x^3}{z^3})$

Source: InternLM Lean-Workbook, record lean_workbook_plus_58854 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_58854 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x^2 + y^2 + z^2)^3 ≥ 8 * (x^3 * y^3 + y^3 * z^3 + x^3 * z^3)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_58854; Apache-2.0

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