A comparison between two cyclic quartic sums

Proved

WorkbookSource.base_47874

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

lean-workbooksource-checked

If a, b, c are real number then: $3(a^4+b^4+c^4)+2(b^3a+a^3c+c^3b)\ge 3(a^3b+b^3c+c^3a)$

Source: InternLM Lean-Workbook, record lean_workbook_47874 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_47874 (a b c : ℝ) :
  3 * (a ^ 4 + b ^ 4 + c ^ 4) + 2 * (b ^ 3 * a + a ^ 3 * c + c ^ 3 * b) ≥
  3 * (a ^ 3 * b + b ^ 3 * c + c ^ 3 * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_47874; Apache-2.0

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