That theorem is not valid constructively, so no way to make a computer program out of it. I.e., there is no program that given types A, B and injections (f : A

That theorem is not valid constructively, so no way to make a computer program out of it. I.e., there is no program that given types A, B and injections (f : A -> B) and (g : B -> A) produces a bijection A -> B.