Prove2Me

lean_workbook_plus_5484

Proved

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

Let a,b,c>0,ab+c+bc+a≤1.a,b,c>0, \frac{a}{b+c}+\frac{b}{c+a}\leq 1. Prove that

ca+b≥12.\frac{c}{a+b}\geq \frac{1}{2}.
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_5484 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (b + c) + b / (c + a) ≤ 1 → c / (a + b) ≥ 1 / 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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