const In : set set prop term iIn = In infix iIn 2000 2000 const SNo : set prop const SNoLt : set set prop term < = SNoLt infix < 2020 2020 term SNoCutP = \x:set.\y:set.(!z:set.z iIn x -> SNo z) & (!z:set.z iIn y -> SNo z) & !z:set.z iIn x -> !w:set.w iIn y -> z < w const ordsucc : set set axiom ordsuccI2: !x:set.x iIn ordsucc x const ordinal : set prop const SNoLev : set set var p:set prop var x:set hyp !y:set.ordinal y -> !z:set.SNo z -> SNoLev z iIn y -> p z hyp SNo x claim ordinal (ordsucc (SNoLev x)) -> p x