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 nat_p : set prop const ordinal : set prop axiom nat_p_ordinal: !x:set.nat_p x -> ordinal x const omega : set 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.x iIn omega -> nat_p x -> ordinal x -> !y:set.nat_p y -> - x + y iIn int var x:set hyp x iIn omega claim nat_p x -> !y:set.nat_p y -> - x + y iIn int