A normalized pairwise product bounds a cyclic ratio sum

Proved

WorkbookSource.plus_52543

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

lean-workbooksource-checked

If $a,b,c>0$ then: $\frac{17(b+c)(c+a)(a+b)}{8abc}\ge 5+8(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b})$

Source: InternLM Lean-Workbook, record lean_workbook_plus_52543 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_52543 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (17 * (b + c) * (c + a) * (a + b)) / (8 * a * b * c) ≥ 5 + 8 * (a / (b + c) + b / (c + a) + c / (a + b))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_52543; Apache-2.0

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