bendlang/bend ? reverse-engineered prompt

Build me a small Bend 2 demo app that shows how this language is meant to be used in real life.

I want something simple but impressive, like a tiny game or interactive example with a couple of rules that can never be broken, and proof files that make those rules checked automatically. Please set it up so the code runs fast, uses Bend’s parallel style where it makes sense, and includes clear examples of how to define a law and prove it. If you need anything unclear, look up the current Bend docs online and follow the project’s own guide.

Make it feel like a polished example someone could copy and learn from, with a short README style explanation of what it does, how to run it, and how the laws protect it from mistakes. If there’s a good way to include one or two tests or demos, add those too.