lean_workbook_plus_56687

Proved

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

Let $a, b$ and $c$ be positive real numbers such that $\frac{a+b}{c} + \frac{b+c}{2a} +\frac{c+a}{b}=\frac{13}{2} .$ Prove that $a \leq b+c$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_56687 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b) / c + (b + c) / (2 * a) + (c + a) / b = 13 / 2 → a ≤ b + c   :=  by sorry

Source

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

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