A mixed-degree cyclic product inequality

Proved

WorkbookSource.base_29151

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

lean-workbooksource-checked

If a,b,c >0 prove that $bc\left(a^3+a^2+1\right)+ac\left(b^3+b^2+1\right)+ab\left(c^3+c^2+1\right)\geq abc\left(6+ab+bc+ca\right)$

Source: InternLM Lean-Workbook, record lean_workbook_29151 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_29151 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) :  b * c * (a ^ 3 + a ^ 2 + 1) + a * c * (b ^ 3 + b ^ 2 + 1) + a * b * (c ^ 3 + c ^ 2 + 1) ≥ a * b * c * (6 + a * b + b * c + c * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29151; Apache-2.0

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