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 add_SNo : set set set term + = add_SNo infix + 2281 2280 const minus_SNo : set set term - = minus_SNo const int : set const ordsucc : set set lemma !x:set.!y:set.SNo x -> - x + y iIn int -> ordinal y -> SNo y -> - x + ordsucc y iIn int const nat_p : set prop var x:set var y:set hyp SNo x hyp nat_p y hyp - x + y iIn int claim ordinal y -> - x + ordsucc y iIn int