Now the makings of mate are in place for White—but you aren't done. Follow it through to make sure it works. Black can't move his king, but he does have an interposition: Bg7. You reply RxB+ without hesitation. Black’s king moves not to h8 but to f8, which now has been left open. Life just got a little more complicated because you no longer can mate by just drawing your rook back up the g-file. The king still is under lock and key, for your bishop seals off e7; but since you can’t safely play Rg8, your next move will not be a check—and meanwhile Black still has a queen and rook on the board that he will use to derail the mate if he can.

All right, so after Black’s Kf8 you play carefully. Since you want to get your rook onto h8, start with Rxh7. Now Black has his big chance to play a move of his choosing; what will it be? Well, there isn't much. He can get his queen to the g-file with Qg3, but then it just gets taken (and you must take it before completing the mate; otherwise it interposes at g8 and Black escapes the mate by trading his queen for a rook). After you remove Black’s queen he is out of options, and you mate with Rh8 next move. It just works. Realize, though, that if Black’s queen were better positioned for defense he might have spoiled the sequence. That sort of risk is common when a sequence includes a non-forcing move like Rxh7.