const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const ordinal : set prop const SNo : set prop axiom ordinal_SNo: !x:set.ordinal x -> SNo x const SNoS_ : set set const SNoLev : set set const SNoLt : set set prop term < = SNoLt infix < 2020 2020 lemma !x:set.SNo x -> (!y:set.y iIn SNoS_ (SNoLev x) -> y < x) -> ordinal (SNoLev x) -> SNo (SNoLev x) -> SNoLev x = x var x:set hyp SNo x hyp !y:set.y iIn SNoS_ (SNoLev x) -> y < x claim ordinal (SNoLev x) -> SNoLev x = x