const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const ordinal : set prop const SNo : set prop axiom ordinal_SNo: !x:set.ordinal x -> SNo x const omega : set const nat_p : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 const minus_SNo : set set term - = minus_SNo const int : set lemma !x:set.x iIn omega -> ordinal x -> SNo x -> !y:set.nat_p y -> - x + y iIn int var x:set hyp x iIn omega hyp nat_p x claim ordinal x -> !y:set.nat_p y -> - x + y iIn int