const SNo : set prop const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_Lt3: !x:set.!y:set.!z:set.!w:set.SNo x -> SNo y -> SNo z -> SNo w -> x < z -> y < w -> (x + y) < z + w const eps_ : set set const ordsucc : set set const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const nat_p : set prop var x:set var y:set hyp nat_p x hyp x iIn omega hyp SNo (eps_ (ordsucc x)) hyp y iIn x hyp SNo (eps_ (ordsucc y)) claim eps_ (ordsucc x) < eps_ (ordsucc y) -> (eps_ (ordsucc x) + eps_ (ordsucc x)) < eps_ (ordsucc y) + eps_ (ordsucc y)