const binunion : set set set const Repl : set (set set) set const Inj0 : set set const Inj1 : set set term setsum = \x:set.\y:set.binunion (Repl x Inj0) (Repl y Inj1) const In : set set prop term iIn = In infix iIn 2000 2000 axiom ReplI: !x:set.!f:set set.!y:set.y iIn x -> f y iIn Repl x f axiom binunionI2: !x:set.!y:set.!z:set.z iIn y -> z iIn binunion x y claim !x:set.!y:set.!z:set.z iIn y -> Inj1 z iIn setsum x y