A cyclic fourth-power reciprocal sum bounds a cubic product sum

Proved

WorkbookSource.base_41666

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

lean-workbooksource-checked

Let $w,x,y,z$ be positive. Prove that

\frac{w^4}{z}+\frac{x^4}{w}+\frac{y^4}{x}+\frac{z^4}{y}\geq wz^2+xw^2+yx^2+zy^2 .

Source: InternLM Lean-Workbook, record lean_workbook_41666 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_41666 (w x y z : ℝ) (hw : 0 < w) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (w^4 / z + x^4 / w + y^4 / x + z^4 / y) ≥ w * z^2 + x * w^2 + y * x^2 + z * y^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_41666; Apache-2.0

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