How do I know every maze has exactly one way through?

The studio proves it for every maze before it keeps it: every cell can be reached from the start, the maze has no loop that would make a second way (one passage fewer than its cells), and the finish can be reached. In a book with loops, it proves that no loop runs through the way to the finish, so the way is still the only one. Stars to collect must lie on the way through and ghosts off it. A maze that fails is never printed.