lean_workbook_plus_12076

Proved

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

Prove that $a^3+b^3+c^3\geq ab+bc+ac$ given $a,b,c >0$ and $abc>1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12076 (a b c : ℝ) (h : a>0 ∧ b>0 ∧ c>0 ∧ a * b * c > 1) :
  a ^ 3 + b ^ 3 + c ^ 3 ≥ a * b + b * c + a * c   :=  by sorry

Source