const SNo : set prop const minus_SNo : set set term - = minus_SNo axiom SNo_minus_SNo: !x:set.SNo x -> SNo - x const In : set set prop term iIn = In infix iIn 2000 2000 const SNoS_ : set set const SNoLev : set set axiom SNoLev_ind: !p:set prop.(!x:set.SNo x -> (!y:set.y iIn SNoS_ (SNoLev x) -> p y) -> p x) -> !x:set.SNo x -> p x const add_SNo : set set set term + = add_SNo infix + 2281 2280 const Empty : set lemma !x:set.SNo x -> (!y:set.y iIn SNoS_ (SNoLev x) -> - y + y = Empty) -> SNo - x -> - x + x = Empty claim !x:set.SNo x -> - x + x = Empty