Ah, got there. From □(A≠cross), we get specifically □(A=cross⇒U=10) and thus □□(A=cross⇒U=10). But we have □(A=cross⇒U=10)⇒A=cross directly as a theorem (axiom?) about the behaviour of A, and we can lift this to □□(A=cross⇒U=10)⇒□(A=cross), so □(A=cross) also and thus □⊥.
Ah, got there. From □(A≠cross), we get specifically □(A=cross⇒U=10) and thus □□(A=cross⇒U=10). But we have □(A=cross⇒U=10)⇒A=cross directly as a theorem (axiom?) about the behaviour of A, and we can lift this to □□(A=cross⇒U=10)⇒□(A=cross), so □(A=cross) also and thus □⊥.