A cyclic sixth-degree square bound

Proved

WorkbookSource.problem_51805

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

By AM-GM inequality, $a^6+b^4c^2\geq 2a^3b^2c$ $\rightarrow$ $\sum_{cyc}a^6+\sum_{cyc}a^4b^2\geq 2\sum_{cyc}a^3b^2c$

Source: InternLM Lean-Workbook, record lean_workbook_51805 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_51805 (a b c : ℝ) : a^6 + b^6 + c^6 + a^4 * b^2 + b^4 * c^2 + c^4 * a^2 ≥ 2 * (a^3 * b^2 * c + b^3 * c^2 * a + c^3 * a^2 * b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_51805; Apache-2.0

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