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