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 mul_nat : set set set axiom mul_nat_p: !x:set.nat_p x -> !y:set.nat_p y -> nat_p (mul_nat x y) axiom nat_p_omega: !x:set.nat_p x -> x iIn omega const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 axiom mul_nat_mul_SNo: !x:set.x iIn omega -> !y:set.y iIn omega -> mul_nat x y = x * y claim !x:set.x iIn omega -> !y:set.y iIn omega -> x * y iIn omega