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