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 term nIn = \x:set.\y:set.~ x iIn y const ordinal : set prop const Empty : set axiom ordinal_Empty: ordinal Empty axiom EmptyE: !x:set.nIn x Empty axiom FalseE: ~ False const SNoS_ : set set const SNoLev : set set const SNo : set prop const SNo_ : set set prop axiom SNoS_E2: !x:set.ordinal x -> !y:set.y iIn SNoS_ x -> !P:prop.(SNoLev y iIn x -> ordinal (SNoLev y) -> SNo y -> SNo_ (SNoLev y) y -> P) -> P const SNoR : set set var x:set hyp x iIn SNoR Empty claim x iIn SNoS_ Empty -> x iIn Empty