const ordinal : set prop const SNo_ : set set prop const minus_SNo : set set term - = minus_SNo axiom minus_SNo_SNo_: !x:set.ordinal x -> !y:set.SNo_ x y -> SNo_ x - y const In : set set prop term iIn = In infix iIn 2000 2000 const SNoS_ : set set const SNoLev : set set const SNo : 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 lemma !x:set.!y:set.ordinal x -> SNoLev y iIn x -> ordinal (SNoLev y) -> SNo_ (SNoLev y) y -> SNo_ (SNoLev y) - y -> - y iIn SNoS_ x claim !x:set.ordinal x -> !y:set.y iIn SNoS_ x -> - y iIn SNoS_ x