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 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 const add_SNo : set set set term + = add_SNo infix + 2281 2280 const minus_SNo : set set term - = minus_SNo const int : set lemma !x:set.!y:set.x iIn omega -> y iIn omega -> SNo x -> SNo y -> - x + - y iIn int var x:set var y:set hyp x iIn omega hyp y iIn omega claim SNo x -> - x + - y iIn int