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 real : set const complex : set axiom real_complex: Subq real complex const CSNo_Re : set set axiom real_Re_eq: !x:set.x iIn real -> CSNo_Re x = x const Sep : set (set prop) set axiom SepI: !x:set.!p:set prop.!y:set.y iIn x -> p y -> y iIn Sep x p axiom complex_Re_real: !x:set.x iIn complex -> CSNo_Re x iIn real axiom SepE: !x:set.!p:set prop.!y:set.y iIn Sep x p -> y iIn x & p y axiom set_ext: !x:set.!y:set.Subq x y -> Subq y x -> x = y claim real = Sep complex \x:set.CSNo_Re x = x