lean_workbook_plus_18303

Proved

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

Let $a,b,c>0$ and $a+b+c=a^3+b^3+c^3.$ Prove that\n\n

abc\leq 1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18303 (a b c : ℝ) (h1 : a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b + c = a^3 + b^3 + c^3) : a * b * c ≤ 1   :=  by sorry

Source