lean_workbook_plus_6977

Proved

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

Prove that for positive reals a, b, c, the following inequality holds: $\sum\frac{b+c}{a^2+bc}\leq\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6977 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (b + c) / (a ^ 2 + b * c) + (a + c) / (b ^ 2 + a * c) + (a + b) / (c ^ 2 + a * b) ≤ 1 / a + 1 / b + 1 / c   :=  by sorry

Source

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

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