A quartic inequality at unit triple product

Proved

WorkbookSource.base_10672

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

lean-workbooksource-checked

Prove that if $abc=1, a,b,c>0$ then $a^{4}+b^{4}+c^{4}+a+b+c\ge 2(a^{2}b^{2}+b^{2}c^{2}+c^{2}a^{2})$

Source: InternLM Lean-Workbook, record lean_workbook_10672 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10672 (a b c : ℝ) (habc : a * b * c = 1) (ha : a > 0) (hb : b > 0) (hc : c > 0) : a ^ 4 + b ^ 4 + c ^ 4 + a + b + c ≥ 2 * (a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10672; Apache-2.0

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