const bij : set set (set set) prop term equip = \x:set.\y:set.?f:set set.bij x y f const In : set set prop term iIn = In infix iIn 2000 2000 term PNoEq_ = \x:set.\p:set prop.\q:set prop.!y:set.y iIn x -> (p y <-> q y) term nIn = \x:set.\y:set.~ x iIn y term SNoEq_ = \x:set.\y:set.\z:set.PNoEq_ x (\w:set.w iIn y) \w:set.w iIn z const Empty : set const ordsucc : set set axiom In_0_1: Empty iIn ordsucc Empty const SNo : set prop const SNoLev : set set var x:set hyp SNoLev x = Empty hyp SNo x claim x = Empty -> ?y:set.y iIn ordsucc Empty & Empty = x