const ordinal : set prop const Empty : set axiom ordinal_Empty: ordinal Empty const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const nat_p : set prop axiom omega_nat_p: !x:set.x iIn omega -> nat_p x axiom nat_p_ordinal: !x:set.nat_p x -> ordinal x const Subq : set set prop axiom Subq_Empty: !x:set.Subq Empty x const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 axiom ordinal_Subq_SNoLe: !x:set.!y:set.ordinal x -> ordinal y -> Subq x y -> x <= y claim !x:set.x iIn omega -> Empty <= x