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 SNoLt : set set prop term < = SNoLt infix < 2020 2020 axiom SNoLt_irref: !x:set.~ x < x const omega : set const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 const eps_ : set set const SNoS_ : set set const abs_SNo : set set const add_SNo : set set set term + = add_SNo infix + 2281 2280 const minus_SNo : set set term - = minus_SNo const SNo : set prop const Empty : set var x:set hyp Empty < x hyp SNo x hyp !y:set.y iIn SNoS_ omega -> (!z:set.z iIn omega -> abs_SNo (y + - x) < eps_ z) -> y = x hyp ~ ?y:set.y iIn omega & eps_ y <= x claim Empty != x