const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const SNo : set prop axiom omega_SNo: !x:set.x iIn omega -> SNo x const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const minus_SNo : set set term - = minus_SNo axiom minus_SNo_Lt_contra1: !x:set.!y:set.SNo x -> SNo y -> - x < y -> - y < x const SNoS_ : set set const ordsucc : set set axiom SNoS_ordsucc_omega_bdd_above: !x:set.x iIn SNoS_ (ordsucc omega) -> x < omega -> ?y:set.y iIn omega & x < y var x:set hyp - omega < x hyp SNo x hyp - x iIn SNoS_ (ordsucc omega) claim - x < omega -> ?y:set.y iIn omega & - y < x