moved lemmas for orderings and lattices on predicates to corresponding theories, retaining declaration order of classical rules; tuned headings; tuned syntax
Gate = FOL +
consts nand,xor :: "[o,o] => o"
rules nand_def "nand(P,Q) == ~(P & Q)"
xor_def "xor(P,Q) == P & ~Q | ~P & Q"
end