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 minus_SNo : set set term - = minus_SNo axiom int_minus_SNo: !x:set.x iIn int -> - x iIn int const SNo : set prop axiom SNo_eps_: !x:set.x iIn omega -> SNo (eps_ x) axiom mul_SNo_minus_distrR: !x:set.!y:set.SNo x -> SNo y -> x * - y = - x * y var x:set var y:set var z:set hyp y iIn omega hyp SNo (eps_ y) hyp z iIn int hyp x = eps_ y * z hyp SNo z claim SNo (eps_ y * z) -> ?w:set.w iIn omega & ?u:set.u iIn int & - x = eps_ w * u