A mixed reciprocal and product ratio sum is at least three

Proved

WorkbookSource.plus_56684

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

lean-workbooksource-checked

Let $a,b,c>0.$ Prove that $\frac{a}{b}+\frac{2bc}{a+b}+\frac{2b}{c (a+b)}\geq 3$

Source: InternLM Lean-Workbook, record lean_workbook_plus_56684 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_56684 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a / b + 2 * b * c / (a + b) + 2 * b / (c * (a + b)) ≥ 3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_56684; Apache-2.0

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