const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const Sep : set (set prop) set const Power : set set var x:set var f:set set var y:set var z:set hyp !w:set.w iIn Power x -> !u:set.u iIn Power x -> Subq w u -> Subq (f w) (f u) hyp Sep x (\w:set.!u:set.u iIn Power x -> Subq (f u) u -> w iIn u) iIn Power x hyp y iIn f (Sep x \w:set.!u:set.u iIn Power x -> Subq (f u) u -> w iIn u) hyp z iIn Power x hyp Subq (f z) z hyp Subq (Sep x \w:set.!u:set.u iIn Power x -> Subq (f u) u -> w iIn u) z claim Subq (f (Sep x \w:set.!u:set.u iIn Power x -> Subq (f u) u -> w iIn u)) (f z) -> y iIn z