const In : set set prop term iIn = In infix iIn 2000 2000 term nIn = \x:set.\y:set.~ x iIn y term Subq = \x:set.\y:set.!z:set.z iIn x -> z iIn y const SNoLev : set set const add_SNo : set set set term + = add_SNo infix + 2281 2280 const minus_SNo : set set term - = minus_SNo const omega : set const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const Empty : set const SNo : set prop const abs_SNo : set set const eps_ : set set var x:set var y:set hyp SNo x hyp !z:set.z iIn omega -> abs_SNo (y + - x) < eps_ z hyp SNo y hyp Empty < x + - y hyp SNoLev (x + - y) iIn omega claim abs_SNo (y + - x) = x + - y -> (x + - y) < eps_ (SNoLev (x + - y))