const nat_p : set prop const ordsucc : set set const Empty : set axiom nat_1: nat_p (ordsucc Empty) const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set axiom nat_p_omega: !x:set.nat_p x -> x iIn omega const add_nat : set set set axiom add_nat_1_1_2: add_nat (ordsucc Empty) (ordsucc Empty) = ordsucc (ordsucc Empty) const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_nat_add_SNo: !x:set.x iIn omega -> !y:set.y iIn omega -> add_nat x y = x + y claim ordsucc Empty + ordsucc Empty = ordsucc (ordsucc Empty)