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 const ap : set set set axiom apI: !x:set.!y:set.!z:set.setsum y z iIn x -> z iIn ap x y axiom apE: !x:set.!y:set.!z:set.z iIn ap x y -> setsum y z iIn x 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.proj0 x = ap x Empty