lean_workbook_plus_26982

Proved

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

Prove that if $a,b,c$ are positive real numbers, then $\frac{9}{2(a+b+c)}\le \frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{a+b}\le \frac{1}{2}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_26982 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (9 / (2 * (a + b + c))) ≤ (1 / (b + c) + 1 / (c + a) + 1 / (a + b)) ∧ (1 / (b + c) + 1 / (c + a) + 1 / (a + b)) ≤ (1 / 2) * (1 / a + 1 / b + 1 / c)   :=  by sorry

Source

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

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