const famunion : set (set set) set const Repl : set (set set) set const setsum : set set set term Sigma = \x:set.\f:set set.famunion x \y:set.Repl (f y) (setsum y) 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 famunionI: !x:set.!f:set set.!y:set.!z:set.y iIn x -> z iIn f y -> z iIn famunion x f claim !x:set.!f:set set.!y:set.y iIn x -> !z:set.z iIn f y -> setsum y z iIn Sigma x f