lean_workbook_plus_55107

Disproved

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

If $a,b,c$ are positive numbers and $ab+bc+ca=abc$ , prove that $5(a+b+c) \geq 18 +3(ab+bc+ca)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_55107 (a b c : ℝ) (h : a > 0 ∧ b > 0 ∧ c > 0 ∧ a * b * c = a * b + b * c + c * a) : 5 * (a + b + c) ≥ 18 + 3 * (a * b + b * c + c * a)   :=  by sorry

Source

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

View graph