const ordinal : set prop const SNo : set prop axiom ordinal_SNo: !x:set.ordinal x -> SNo x const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const nat_p : set prop 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 -> SNo x -> !y:set.y iIn omega -> mul_nat x y = x * y var x:set hyp x iIn omega hyp nat_p x claim ordinal x -> !y:set.y iIn omega -> mul_nat x y = x * y