The main assumption is that the specification (the proposition you want to prove) is (much) simpler than the proof. This means that the user/customer can read

The main assumption is that the specification (the proposition you want to prove) is (much) simpler than the proof. This means that the user/customer can read the specification, and understand what it means, even if the proof is not comprehensible to them. Of course, the proof must then be machine-checkable. This makes the clarify of specifications into a market-driven problem. What do you do if you have a formally proven contract, but nobody can understand what the spec is? Well, you probably won't be able to sell it, because nobody will trust you. Instead, you try to simplify the specification, so you have something that people will trust. This is very similar to established practice of mathematics, where getting a proof accepted is really a social process, in which you try to convince your fellow mathematicians that the proof is correct.