lean_workbook_plus_15629

Proved

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

Let $xyz = a^3$ \nfrom the condition we have $4\ge a^3+3a^2$ \nThen, $(a-1)(a+2)^2\le 0$ \nSo, $a\le 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15629  (x y z a : ℝ)
  (h₀ : x*y*z = a^3)
  (h₁ : 4 ≥ a^3 + 3*a^2) :
  a ≤ 1   :=  by sorry

Source