lean_workbook_plus_12331

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

If $x, y, z > 0$ and $x+y+z=\frac{1}{2xyz}$ then:\n\n $\sqrt{1+x^4+y^4+z^4} \ge xy+yz+zx \ \ ;$ \n\nGreetings!

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12331 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 1 / (2 * x * y * z)) :  Real.sqrt (1 + x^4 + y^4 + z^4) ≥ x * y + y * z + z * x   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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