An asymmetric weighted reciprocal comparison

Proved

WorkbookSource.base_47025

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

lean-workbooksource-checked

For positive reals $a,b,c$ , show that $\frac{5}{2a+b}+\frac{4}{2b+c}+\frac{3}{2c+a} \ge \frac{12}{3a+2b+c}+\frac{8}{a+3b+2c}+\frac{4}{2a+b+3c}$

Source: InternLM Lean-Workbook, record lean_workbook_47025 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_47025 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (5 / (2 * a + b) + 4 / (2 * b + c) + 3 / (2 * c + a)) ≥ (12 / (3 * a + 2 * b + c) + 8 / (a + 3 * b + 2 * c) + 4 / (2 * a + b + 3 * c))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_47025; Apache-2.0

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