const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y const omega : set const ordsucc : set set axiom omega_ordsucc: !x:set.x iIn omega -> ordsucc x iIn omega axiom ordsuccI2: !x:set.x iIn ordsucc x const ordinal : set prop const SNo : set prop const SNoLev : set set const SNoLt : set set prop term < = SNoLt infix < 2020 2020 axiom ordinal_SNoLev_max: !x:set.ordinal x -> !y:set.SNo y -> SNoLev y iIn x -> y < x var x:set hyp SNo x hyp SNoLev x iIn omega hyp ordinal (SNoLev x) claim ordinal (ordsucc (SNoLev x)) -> ?y:set.y iIn omega & x < y