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_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 const add_SNo : set set set term + = add_SNo infix + 2281 2280 const ordsucc : set set const Empty : set var x:set var y:set hyp - x + y iIn int hyp !z:set.z iIn omega -> - x + y = z -> ordsucc Empty + - x + y iIn int claim (!z:set.z iIn omega -> - x + y = - z -> ordsucc Empty + - x + y iIn int) -> ordsucc Empty + - x + y iIn int