const In : set set prop term iIn = In infix iIn 2000 2000 const In_rec_G_ii : (set (set set set) set set) set (set set) prop const In_rec_ii : (set (set set set) set set) set set set axiom In_rec_G_ii_In_rec_ii: !P:set (set set set) set set.(!x:set.!g:set set set.!h:set set set.(!y:set.y iIn x -> g y = h y) -> P x g = P x h) -> !x:set.In_rec_G_ii P x (In_rec_ii P x) axiom In_rec_G_ii_In_rec_ii_d: !P:set (set set set) set set.(!x:set.!g:set set set.!h:set set set.(!y:set.y iIn x -> g y = h y) -> P x g = P x h) -> !x:set.In_rec_G_ii P x (P x (In_rec_ii P)) axiom In_rec_G_ii_f: !P:set (set set set) set set.(!x:set.!g:set set set.!h:set set set.(!y:set.y iIn x -> g y = h y) -> P x g = P x h) -> !x:set.!f:set set.!f2:set set.In_rec_G_ii P x f -> In_rec_G_ii P x f2 -> f = f2 claim !P:set (set set set) set set.(!x:set.!g:set set set.!h:set set set.(!y:set.y iIn x -> g y = h y) -> P x g = P x h) -> !x:set.In_rec_ii P x = P x (In_rec_ii P)