A comparison of two weighted cyclic reciprocal sums

Proved

WorkbookSource.base_9776

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

lean-workbooksource-checked

Prove that : $\frac{1}{7a+b}+\frac{1}{7b+c}+\frac{1}{7c+a}\geq \frac{1}{a+2b+5c}+\frac{1}{b+2c+5a}+\frac{1}{c+2a+5b},\forall a,b,c> 0$

Source: InternLM Lean-Workbook, record lean_workbook_9776 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9776 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (7 * a + b) + 1 / (7 * b + c) + 1 / (7 * c + a)) ≥ (1 / (a + 2 * b + 5 * c) + 1 / (b + 2 * c + 5 * a) + 1 / (c + 2 * a + 5 * b))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9776; Apache-2.0

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