const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const ordsucc : set set axiom ordsuccI2: !x:set.x iIn ordsucc x const ordinal : set prop const SNo : set prop const SNoLev : set set const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 axiom ordinal_SNoLev_max_2: !x:set.ordinal x -> !y:set.SNo y -> SNoLev y iIn ordsucc x -> y <= x const SNoS_ : 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) -> x <= SNoLev x -> SNoLev x = x var x:set hyp SNo x hyp !y:set.y iIn SNoS_ (SNoLev x) -> y < x hyp ordinal (SNoLev x) claim SNo (SNoLev x) -> SNoLev x = x