A fourth-power ratio sum with symmetric cubic corrections

Proved

WorkbookSource.base_37266

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

lean-workbooksource-checked

Let a,b,c>0 $\frac {{a^4 + b^4 }}{c} + \frac {{a^4 + c^4 }}{b} + \frac {{b^4 + c^4 }}{a} + 2ab(a + b) + 2bc(b + c) + 2ac(a + c) \ge 6(a^3 + b^3 + c^3 )$

Source: InternLM Lean-Workbook, record lean_workbook_37266 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_37266 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^4 + b^4) / c + (a^4 + c^4) / b + (b^4 + c^4) / a + 2 * a * b * (a + b) + 2 * b * c * (b + c) + 2 * a * c * (a + c) ≥ 6 * (a^3 + b^3 + c^3)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_37266; Apache-2.0

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