lean_workbook_plus_80560

Proved

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

With $a;b;c>0$ . Prove: $\sum \dfrac{bc}{a^2+2bc}\le 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_80560 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b * c / (a ^ 2 + 2 * b * c) + a * c / (b ^ 2 + 2 * a * c) + a * b / (c ^ 2 + 2 * a * b) ≤ 1)   :=  by sorry

Source

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

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