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 proj0 : set set const setsum : set set set const Empty : set axiom proj0E: !x:set.!y:set.y iIn proj0 x -> setsum Empty y iIn x axiom pairE0: !x:set.!y:set.!z:set.setsum Empty z iIn setsum x y -> z iIn x axiom pairI0: !x:set.!y:set.!z:set.z iIn x -> setsum Empty z iIn setsum x y axiom proj0I: !x:set.!y:set.setsum Empty y iIn x -> y iIn proj0 x axiom set_ext: !x:set.!y:set.Subq x y -> Subq y x -> x = y claim !x:set.!y:set.proj0 (setsum x y) = x