lean_workbook_plus_2640

Proved

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

if $a,b,c>0$ , $abc=1$ ,prove $a^3+b^3+c^3 >= ab+bc+ac$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2640 (a b c : ℝ) (ha : 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