const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const int : set const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 const eps_ : set set term diadic_rational_p = \x:set.?y:set.y iIn omega & ?z:set.z iIn int & x = eps_ y * z const nat_p : set prop axiom omega_nat_p: !x:set.x iIn omega -> nat_p x const SNoS_ : set set axiom nonneg_diadic_rational_p_SNoS_omega: !x:set.x iIn omega -> !y:set.nat_p y -> eps_ x * y iIn SNoS_ omega lemma !x:set.!y:set.x iIn omega -> y iIn int -> (!z:set.z iIn omega -> eps_ x * z iIn SNoS_ omega) -> eps_ x * y iIn SNoS_ omega claim !x:set.diadic_rational_p x -> x iIn SNoS_ omega