Computer scientists routinely prove theories with an infinite number of states. It is actually usually the easiest way to prove things because you don’t have to

Computer scientists routinely prove theories with an infinite number of states. It is actually usually the easiest way to prove things because you don’t have to handle edge cases. A typical theory says: For all x:A, P x In other words, given any x (from an infinite set A) P x is true. Where P is a proposition. You typically prove it using straightforward induction/recursion.