Is there any actual semantic difference between soundness and correctness? Can I use these words interchangeably when talking about formal reasoning, proof, logics, etc.? Otherwise, is there a ...
edit: Interestingly, the authors also state at one point that the choice of introduction rule is determined by the structure of the previous goal and the list of introduction rules; but at another ...
In many mathematics problems you see the phrase "prove that..." or "show that..." something is. What's the difference between these two phrases? Is "showing" something different from "proving" ...