A cyclic fourth-degree inequality under linear substitutions

Proved

WorkbookSource.base_27236

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

lean-workbooksource-checked

$x=2a-b,y=2b-c,z=2c-a$ then $3(x^4+y^4+z^4-x^3y-y^3z-z^3x) \geq x^2(y-z)^2+y^2(z-x)^2+z^2(x-y)^2$

Source: InternLM Lean-Workbook, record lean_workbook_27236 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_27236 {x y z a b c : ℝ} (hx : x = 2 * a - b) (hy : y = 2 * b - c) (hz : z = 2 * c - a) : 3 * (x ^ 4 + y ^ 4 + z ^ 4 - x ^ 3 * y - y ^ 3 * z - z ^ 3 * x) ≥ x ^ 2 * (y - z) ^ 2 + y ^ 2 * (z - x) ^ 2 + z ^ 2 * (x - y) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_27236; Apache-2.0

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