moved lemmas for orderings and lattices on predicates to corresponding theories, retaining declaration order of classical rules; tuned headings; tuned syntax
Prod = FOL +
types "*" 2 (infixl 20)
arities "*" :: (term,term)term
consts fst :: "'a * 'b => 'a"
snd :: "'a * 'b => 'b"
Pair :: "['a,'b] => 'a * 'b" ("(1<_,/_>)")
rules fst "fst(<a,b>) = a"
snd "snd(<a,b>) = b"
end