A cyclic fifth-degree comparison of mixed products

Proved

WorkbookSource.plus_59647

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

lean-workbooksource-checked

Prove that if $a\geq0,$ $b\geq0$ and $c\geq0$ than $a^{5}+b^{5}+c^{5}+abc(ab+ac+bc)\geq a^{4}b+b^{4}c+c^{4}a+abc(a^{2}+b^{2}+c^{2}).$

Source: InternLM Lean-Workbook, record lean_workbook_plus_59647 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_59647 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : a^5 + b^5 + c^5 + a * b * c * (a * b + a * c + b * c) ≥ a^4 * b + b^4 * c + c^4 * a + a * b * c * (a^2 + b^2 + c^2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_59647; Apache-2.0

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