An eighth-degree symmetric power sum bound with a mixed correction

Proved

WorkbookSource.base_34838

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

lean-workbooksource-checked

Let $a,b,c \in R^+$ . Prove:

(a^2+b^2+c^2)^4 - a^8-b^8-c^8 \geq 14b^2c^2(b^2c^2+4a^4)

Source: InternLM Lean-Workbook, record lean_workbook_34838 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_34838 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 + c^2)^4 - a^8 - b^8 - c^8 ≥ 14 * b^2 * c^2 * (b^2 * c^2 + 4 * a^4)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_34838; Apache-2.0

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