What must be proven?

You are responsible for proving that you are incapable of performing any substantial gainful activity, not just that you can't do your past work (which is relevant). Remember, it is not just a question of IF YOU ARE actually performing

substantial gainful activity

, but if you are CAPABLE of performing it. For Social Security, that is any job that you can do on a regular basis and substantial gainful activity currently is defined as earning $860 a month.