const ordinal : set prop const omega : set axiom omega_ordinal: ordinal omega const SNo : set prop const SNoLev : set set const minus_SNo : set set term - = minus_SNo axiom minus_SNo_Lev: !x:set.SNo x -> SNoLev - x = SNoLev x axiom SNo_minus_SNo: !x:set.SNo x -> SNo - x const SNo_ : set set prop axiom SNoLev_: !x:set.SNo x -> SNo_ (SNoLev x) x const In : set set prop term iIn = In infix iIn 2000 2000 const SNoS_ : set set axiom SNoS_I: !x:set.ordinal x -> !y:set.!z:set.z iIn x -> SNo_ z y -> y iIn SNoS_ x 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 claim !x:set.x iIn SNoS_ omega -> - x iIn SNoS_ omega