Prove2Me

lean_workbook_plus_36158

Proved

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

Prove that if a,b,c>0a,b,c>0 then \n

b+ca+c+ab+a+bc≥4(a2+b2+c2)ab+bc+ca+2\frac{b+c}{a}+\frac{c+a}{b}+\frac{a+b}{c}\geq \frac{4(a^2+b^2+c^2)}{ab+bc+ca}+2

\n

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_36158 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b + c) / a + (c + a) / b + (a + b) / c ≥ 4 * (a ^ 2 + b ^ 2 + c ^ 2) / (a * b + b * c + a * c) + 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

View graph