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 claim !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)) -> !R:set (set set set) prop.(!y:set.!P2:set set set set.(!z:set.z iIn y -> R z (P2 z)) -> R y (P y P2)) -> R x (P x Q)