define new constant of_real for class real_algebra_1;
define set Reals as range of_real;
add lemmas about of_real and Reals
Gate2 = FOL +
consts "~&" :: "[o,o] => o" (infixl 35)
"#" :: "[o,o] => o" (infixl 30)
If :: "[o,o,o] => o" ("if _ then _ else _")
rules nand_def "P ~& Q == ~(P & Q)"
xor_def "P # Q == P & ~Q | ~P & Q"
If_def "if P then Q else R == P&Q | ~P&R"
end