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 setsum : set set set const ordsucc : set set const Empty : set const Inj1 : set set axiom Inj1_setsum_1L: !x:set.setsum (ordsucc Empty) x = Inj1 x const nat_p : set prop claim (!x:set.nat_p x -> Inj1 x = ordsucc x) -> !x:set.nat_p x -> setsum (ordsucc Empty) x = ordsucc x