const In : set set prop term iIn = In infix iIn 2000 2000 const Sing : set set axiom SingE: !x:set.!y:set.y iIn Sing x -> y = x const Repl : set (set set) set axiom ReplE: !x:set.!f:set set.!y:set.y iIn Repl x f -> ?z:set.z iIn x & y = f z const binunion : set set set axiom binunionE: !x:set.!y:set.!z:set.z iIn binunion x y -> z iIn x | z iIn y const Inj1 : set set const Empty : set axiom Inj1_eq: !x:set.Inj1 x = binunion (Sing Empty) (Repl x Inj1) claim !x:set.!y:set.y iIn Inj1 x -> y = Empty | ?z:set.z iIn x & y = Inj1 z