const Sigma : set (set set) set term setprod = \x:set.\y:set.Sigma x \z:set.y const In : set set prop term iIn = In infix iIn 2000 2000 const ordsucc : set set const Empty : set const If_i : prop set set set axiom tuple_2_Sigma: !x:set.!f:set set.!y:set.y iIn x -> !z:set.z iIn f y -> Sigma (ordsucc (ordsucc Empty)) (\w:set.If_i (w = Empty) y z) iIn Sigma x f claim !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