const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const omega : set const SNo : set prop axiom omega_SNo: !x:set.x iIn omega -> SNo x const nat_p : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 const minus_SNo : set set term - = minus_SNo lemma !x:set.!y:set.y iIn omega -> SNo y -> !z:set.nat_p z -> x iIn y + z -> x iIn y | x + - y iIn z claim !x:set.!y:set.y iIn omega -> !z:set.nat_p z -> x iIn y + z -> x iIn y | x + - y iIn z