A product comparison for shifted fourth powers

Proved

WorkbookSource.base_10192

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

lean-workbooksource-checked

Let $a,b,c >0$ .Prove that $(a^{4}+1)(b^{4}+1)(c^{4}+1)\geq (a^{3}b+1)(b^{3}c+1)(c^{3}a+1)$

Source: InternLM Lean-Workbook, record lean_workbook_10192 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10192 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^4 + 1) * (b^4 + 1) * (c^4 + 1) ≥ (a^3 * b + 1) * (b^3 * c + 1) * (c^3 * a + 1)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10192; Apache-2.0

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