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 SNo : set prop const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 const minus_SNo : set set term - = minus_SNo const int : set lemma !x:set.!y:set.x iIn omega -> SNo x -> y iIn omega -> nat_p y -> ordinal y -> (- x) * - y iIn int var x:set var y:set hyp x iIn omega hyp SNo x hyp y iIn omega claim nat_p y -> (- x) * - y iIn int