lean_workbook_plus_46860

Proved

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

Let $a,b,c\ge 0$ and $\frac{ab}{1+a+b}+\frac{bc}{1+b+c}+\frac{ca}{1+c+a}=1.$ Prove that

1+a+b+c \ge 4abc

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_46860 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a * b * c ≠ 0) (h : (a * b / (1 + a + b)) + (b * c / (1 + b + c)) + (c * a / (1 + c + a)) = 1) : 1 + a + b + c ≥ 4 * a * b * c   :=  by sorry

Source

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

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