const In : set set prop term iIn = In infix iIn 2000 2000 term In_rec_G_iii = \P:set (set set set set) set set set.\x:set.\g:set set set.!Q:set (set set set) prop.(!y:set.!R:set set set set.(!z:set.z iIn y -> Q z (R z)) -> Q y (P y R)) -> Q x g axiom In_rec_G_iii_c: !P:set (set set set set) set set set.!x:set.!Q:set set set set.(!y:set.y iIn x -> In_rec_G_iii P y (Q y)) -> In_rec_G_iii P x (P x Q) axiom exandE_iiii: !P:(set set set set) prop.!Q:(set set set set) prop.(?R:set set set set.P R & Q R) -> !R:prop.(!P2:set set set set.P P2 -> Q P2 -> R) -> R claim !P:set (set set set set) set set set.!x:set.!g:set set set.In_rec_G_iii P x g -> ?Q:set set set set.(!y:set.y iIn x -> In_rec_G_iii P y (Q y)) & g = P x Q