const Repl : set (set set) set const setprod : set set set const real : set const SNo_pair : set set set const ap : set set set const Empty : set const ordsucc : set set term complex = Repl (setprod real real) \x:set.SNo_pair (ap x Empty) (ap x (ordsucc Empty)) const In : set set prop term iIn = In infix iIn 2000 2000 const Sigma : set (set set) set const If_i : prop set set set axiom tuple_2_setprod: !x:set.!y:set.!z:set.z iIn x -> !w:set.w iIn y -> Sigma (ordsucc (ordsucc Empty)) (\u:set.If_i (u = Empty) z w) iIn setprod x y axiom ReplI: !x:set.!f:set set.!y:set.y iIn x -> f y iIn Repl x f axiom tuple_2_1_eq: !x:set.!y:set.ap (Sigma (ordsucc (ordsucc Empty)) \z:set.If_i (z = Empty) x y) (ordsucc Empty) = y axiom tuple_2_0_eq: !x:set.!y:set.ap (Sigma (ordsucc (ordsucc Empty)) \z:set.If_i (z = Empty) x y) Empty = x claim !x:set.x iIn real -> !y:set.y iIn real -> SNo_pair x y iIn complex