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 mul_nat : set set set const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 lemma !x:set.x iIn omega -> nat_p x -> ordinal x -> !y:set.y iIn omega -> mul_nat x y = x * y var x:set hyp x iIn omega claim nat_p x -> !y:set.y iIn omega -> mul_nat x y = x * y