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 eps_ : set set const SNoS_ : set set axiom SNo_eps_SNoS_omega: !x:set.x iIn omega -> eps_ x iIn SNoS_ omega const SNo : set prop const nat_p : set prop const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 lemma !x:set.x iIn omega -> SNo (eps_ x) -> eps_ x iIn SNoS_ omega -> !y:set.nat_p y -> eps_ x * y iIn SNoS_ omega var x:set hyp x iIn omega claim SNo (eps_ x) -> !y:set.nat_p y -> eps_ x * y iIn SNoS_ omega