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 SNo : set prop axiom SNo_eps_: !x:set.x iIn omega -> SNo (eps_ x) lemma !x:set.!y:set.!z:set.!w:set.!u:set.z iIn omega -> SNo (eps_ z) -> w iIn int -> x = eps_ z * w -> SNo w -> u iIn omega -> SNo (eps_ u) -> (?v:set.v iIn int & y = eps_ u * v) -> diadic_rational_p (x * y) var x:set var y:set var z:set var w:set hyp z iIn omega hyp SNo (eps_ z) hyp w iIn int hyp x = eps_ z * w hyp SNo w claim SNo (eps_ z * w) -> diadic_rational_p y -> diadic_rational_p (x * y)