lean_workbook_plus_66192

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 $a,b,c$ are positive real numbers such that $abc\geq 1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_66192 (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 + c * a   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph