const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const ordinal : set prop const SetAdjoin : set set set const Sing : set set const ordsucc : set set const Empty : set axiom tagged_not_ordinal: !x:set.~ ordinal (SetAdjoin x (Sing (ordsucc Empty))) const Repl : set (set set) set axiom ReplE_impred: !x:set.!f:set set.!y:set.y iIn Repl x f -> !P:prop.(!z:set.z iIn x -> y = f z -> P) -> P claim !x:set.!y:set.ordinal x -> ~ x iIn Repl y \z:set.SetAdjoin z (Sing (ordsucc Empty))