const nat_p : set prop const ordinal : set prop axiom nat_p_ordinal: !x:set.nat_p x -> ordinal 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.nat_p x -> ordinal x -> !y:set.y iIn omega -> add_nat x y = x + y var x:set hyp x iIn omega claim nat_p x -> !y:set.y iIn omega -> add_nat x y = x + y