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 add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_In_omega: !x:set.x iIn omega -> !y:set.y iIn omega -> x + y iIn omega 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 SNo : set prop axiom minus_add_SNo_distr: !x:set.!y:set.SNo x -> SNo y -> - (x + y) = - x + - y var x:set var y:set hyp x iIn omega hyp y iIn omega hyp SNo x claim SNo y -> - x + - y iIn int