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 proj1 : set set const setsum : set set set const ordsucc : set set const Empty : set axiom proj1E: !x:set.!y:set.y iIn proj1 x -> setsum (ordsucc Empty) y iIn x axiom pairE1: !x:set.!y:set.!z:set.setsum (ordsucc Empty) z iIn setsum x y -> z iIn y axiom pairI1: !x:set.!y:set.!z:set.z iIn y -> setsum (ordsucc Empty) z iIn setsum x y axiom proj1I: !x:set.!y:set.setsum (ordsucc Empty) y iIn x -> y iIn proj1 x axiom set_ext: !x:set.!y:set.Subq x y -> Subq y x -> x = y claim !x:set.!y:set.proj1 (setsum x y) = y