How is "one solution" proven?

Every puzzle is checked by two different methods that share no code: a fast solver counts the solutions and must find exactly one, then an independent second method (an exact-cover search for classic, X, jigsaw, samurai and 16 x 16, a cage-by-cage search for killer, and a separate plain search for thermo and arrow) must agree. A puzzle that fails either check is thrown away and a new one is made.