A fourth-power and pairwise-product lower bound

Proved

WorkbookSource.plus_76910

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

lean-workbooksource-checked

Prove that $a^4+b^4+c^4+8(ab+bc+ca) \geq 27$ for real positive numbers $a, b, c$ with $a+b+c=3$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_76910 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_76910 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : a^4 + b^4 + c^4 + 8 * (a * b + b * c + c * a) ≥ 27   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_76910; Apache-2.0

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