lean_workbook_plus_17305

Proved

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

Given $a, b, c$ are positive real numbers and $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \leq 1$ . Prove that $\frac{b+c}{a+bc} + \frac{a+c}{b+ac} + \frac{b+a}{c+ab} \geq \frac{12}{a+b+c-1}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_17305 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : 1 / a + 1 / b + 1 / c ≤ 1) :
  (b + c) / (a + b * c) + (a + c) / (b + a * c) + (b + a) / (c + a * b) ≥ 12 / (a + b + c - 1)   :=  by sorry

Source

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

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