A comparison of two symmetric linear reciprocal sums

Proved

WorkbookSource.base_18124

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a, b, c$ are positive numbers. Prove that: $\frac {2}{a + b} + \frac {2}{a + c} + \frac {2}{b + c}\geq\frac {5}{a + b + 3c} + \frac {5}{a + c + 3b} + \frac {5}{b + c + 3a}$

Source: InternLM Lean-Workbook, record lean_workbook_18124 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_18124 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 2 / (a + b) + 2 / (a + c) + 2 / (b + c) ≥ 5 / (a + b + 3 * c) + 5 / (a + c + 3 * b) + 5 / (b + c + 3 * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18124; Apache-2.0

View graph