1 Gate2 = FOL +
2 consts "~&" :: "[o,o] => o" (infixl 35)
3 "#" :: "[o,o] => o" (infixl 30)
4 If :: "[o,o,o] => o" ("if _ then _ else _")
5 rules nand_def "P ~& Q == ~(P & Q)"
6 xor_def "P # Q == P & ~Q | ~P & Q"
7 If_def "if P then Q else R == P&Q | ~P&R"
8 end