Can you share a license between two devices?

I want to use aseprite at home and at school, is it possible to have aseprite on my laptop and on my computer with one purchase?

You certainly can, per the FAQ.

Can I install Aseprite in 5, 10, or more computers buying just one copy?

If they are your own computers, yes you can. If you are in a company, you need one license for each developer. If you are in an educational institution, you can request a special license for educational purposes.

how do I prove it?

nevermind upon actual purchase I have discovered that it is a steam key