const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const nat_p : set prop axiom omega_nat_p: !x:set.x iIn omega -> nat_p x const add_nat : set set set axiom add_nat_p: !x:set.nat_p x -> !y:set.nat_p y -> nat_p (add_nat x y) axiom nat_p_omega: !x:set.nat_p x -> x iIn omega 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 !x:set.x iIn omega -> !y:set.y iIn omega -> x + y iIn omega