const In : set set prop term iIn = In infix iIn 2000 2000 const In_rec_G_iii : (set (set set set set) set set set) set (set set set) prop const In_rec_iii : (set (set set set set) set set set) set set set set axiom In_rec_G_iii_In_rec_iii: !P:set (set set set set) set set set.(!x:set.!Q:set set set set.!R:set set set set.(!y:set.y iIn x -> Q y = R y) -> P x Q = P x R) -> !x:set.In_rec_G_iii P x (In_rec_iii P x) axiom In_rec_G_iii_In_rec_iii_d: !P:set (set set set set) set set set.(!x:set.!Q:set set set set.!R:set set set set.(!y:set.y iIn x -> Q y = R y) -> P x Q = P x R) -> !x:set.In_rec_G_iii P x (P x (In_rec_iii P)) axiom In_rec_G_iii_f: !P:set (set set set set) set set set.(!x:set.!Q:set set set set.!R:set set set set.(!y:set.y iIn x -> Q y = R y) -> P x Q = P x R) -> !x:set.!g:set set set.!h:set set set.In_rec_G_iii P x g -> In_rec_G_iii P x h -> g = h claim !P:set (set set set set) set set set.(!x:set.!Q:set set set set.!R:set set set set.(!y:set.y iIn x -> Q y = R y) -> P x Q = P x R) -> !x:set.In_rec_iii P x = P x (In_rec_iii P)