A product of shifted rational expressions is at least nine halves

Proved

WorkbookSource.plus_66573

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

lean-workbooksource-checked

Let $a,b,c>0.$ Prove that $(1+\frac{ab}{c+a})\left(1+\frac{2a}{b(c+a)}+\frac{c}{a}\right)\geq \frac{9}{2}$

Source: InternLM Lean-Workbook, record lean_workbook_plus_66573 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_66573 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 + a * b / (c + a)) * (1 + 2 * a / (b * (c + a)) + c / a) ≥ 9 / 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_66573; Apache-2.0

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