A fifth-power bound for a triple product

Proved

WorkbookSource.base_10039

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

lean-workbooksource-checked

prove that $(x+y+z)^5-x^5-y^5-z^5\geq 60xyz(xy+yz+zx)$ if $x,y,z$ are positive reals

Source: InternLM Lean-Workbook, record lean_workbook_10039 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10039 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y + z) ^ 5 - x ^ 5 - y ^ 5 - z ^ 5 ≥ 60 * x * y * z * (x * y + y * z + z * x)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10039; Apache-2.0

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