const ordinal : set prop const ordsucc : set set const omega : set axiom ordsucc_omega_ordinal: ordinal (ordsucc omega) const In : set set prop term iIn = In infix iIn 2000 2000 const SNoS_ : set set const minus_SNo : set set term - = minus_SNo axiom minus_SNo_SNoS_: !x:set.ordinal x -> !y:set.y iIn SNoS_ x -> - y iIn SNoS_ x 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 SNoLt : set set prop term < = SNoLt infix < 2020 2020 lemma !x:set.x iIn SNoS_ (ordsucc omega) -> - omega < x -> SNo x -> - x iIn SNoS_ (ordsucc omega) -> ?y:set.y iIn omega & - y < x claim !x:set.x iIn SNoS_ (ordsucc omega) -> - omega < x -> ?y:set.y iIn omega & - y < x