const binunion : set set set const omega : set const Repl : set (set set) set const minus_SNo : set set term - = minus_SNo term int = binunion omega (Repl omega minus_SNo) const In : set set prop term iIn = In infix iIn 2000 2000 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 axiom binunionE: !x:set.!y:set.!z:set.z iIn binunion x y -> z iIn x | z iIn y claim !p:set prop.(!x:set.x iIn omega -> p x) -> (!x:set.x iIn omega -> p - x) -> !x:set.x iIn int -> p x