Earlier quoted context omitted.
I have trouble parsing your sentence, to be honest. What are you asking? Are you asking how am I sure that/if my specification is correct? Are you asking how do I make sure I have no bugs without a proof? Maybe you are asking something else entirely?
Because the type system is unsound, you could add an error to your implementation and the type system will not catch it. It will happily tell you that everything type checks. How do you use that to prevent errors?
Just rephrase your question as "How will a pervasive system of sanity checks help me prevent errors?", and I hope you agree that it kind of answers itself.