A cyclic weighted ratio bound at fixed sum three

Proved

WorkbookSource.base_2671

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

lean-workbooksource-checked

Let $a,b,c >0$ such that $a+b+c=3.$ Prove that

\frac{a+3b}{c} + \frac{b+3c}{a} + \frac{c+3a}{b} \ge 6 (3-abc)

Source: InternLM Lean-Workbook, record lean_workbook_2671 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2671 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (a + 3 * b) / c + (b + 3 * c) / a + (c + 3 * a) / b ≥ 6 * (3 - a * b * c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2671; Apache-2.0

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