A weighted cyclic ratio comparison with pairwise denominators

Proved

WorkbookSource.base_54664

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

lean-workbooksource-checked

For the positive real numbers $a,b,c$ prove that $\frac{c+2a}{b} + \frac{a+2b}{c} + \frac{b+2c}{a} \ge \frac{3a+4c-b}{a+b} + \frac{3b+4a-c}{b+c} + \frac{3c+4b-a}{c+a}$

Source: InternLM Lean-Workbook, record lean_workbook_54664 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_54664 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (c + 2 * a) / b + (a + 2 * b) / c + (b + 2 * c) / a ≥ (3 * a + 4 * c - b) / (a + b) + (3 * b + 4 * a - c) / (b + c) + (3 * c + 4 * b - a) / (c + a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_54664; Apache-2.0

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