const In : set set prop term iIn = In infix iIn 2000 2000 term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const omega : set const minus_SNo : set set term - = minus_SNo const int : set axiom int_minus_SNo_omega: !x:set.x iIn omega -> - x iIn int const nat_p : set prop axiom omega_nat_p: !x:set.x iIn omega -> nat_p x const ordinal : set prop axiom nat_p_ordinal: !x:set.nat_p x -> ordinal x const SNo : set prop axiom ordinal_SNo: !x:set.ordinal x -> SNo x axiom Subq_omega_int: Subq omega int axiom minus_SNo_invol: !x:set.SNo x -> - - x = x axiom int_SNo_cases: !p:set prop.(!x:set.x iIn omega -> p x) -> (!x:set.x iIn omega -> p - x) -> !x:set.x iIn int -> p x claim !x:set.x iIn int -> - x iIn int