lean_workbook_plus_73113

Proved

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

Let $a,b,c>0$ such that $a+b+c=3$ . \n\n

ab(a^2+b^2) \leq \frac{(a+b)^4}{8}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_73113 :  ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 ∧ a + b + c = 3 → a * b * (a ^ 2 + b ^ 2) ≤ (a + b) ^ 4 / 8   :=  by sorry

Source