const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y axiom In_irref: !x:set.nIn x x const ordinal : set prop 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 axiom SNoLev_prop: !x:set.SNo x -> ordinal (SNoLev x) & SNo_ (SNoLev x) x claim !x:set.SNo x -> !y:set.y iIn SNoS_ (SNoLev x) -> y != x