A sixth-degree bound involving three triangle factors

Proved

WorkbookSource.base_11853

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

lean-workbooksource-checked

If $a, b, c \ge 0$ , then $4a^2b^2c^2 \geq (b + c - a)(c + a - b)(a + b - c)(a^3 + b^3 + c^3 + abc)$

Source: InternLM Lean-Workbook, record lean_workbook_11853 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_11853 {a b c : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : 4 * a ^ 2 * b ^ 2 * c ^ 2 ≥ (b + c - a) * (c + a - b) * (a + b - c) * (a ^ 3 + b ^ 3 + c ^ 3 + a * b * c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_11853; Apache-2.0

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