const ordinal : set prop const omega : set axiom omega_ordinal: ordinal omega const In : set set prop term iIn = In infix iIn 2000 2000 const SNoS_ : set set const minus_SNo : set set term - = minus_SNo axiom minus_SNo_SNoS_omega: !x:set.x iIn SNoS_ omega -> - x iIn SNoS_ omega const SNo : set prop axiom SNo_minus_SNo: !x:set.SNo x -> SNo - x const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_com: !x:set.!y:set.SNo x -> SNo y -> x + y = y + x axiom minus_SNo_invol: !x:set.SNo x -> - - x = x const abs_SNo : set set axiom abs_SNo_dist_swap: !x:set.!y:set.SNo x -> SNo y -> abs_SNo (x + - y) = abs_SNo (y + - x) const SNoLev : set set const SNo_ : set set prop axiom SNoS_E2: !x:set.ordinal x -> !y:set.y iIn SNoS_ x -> !P:prop.(SNoLev y iIn x -> ordinal (SNoLev y) -> SNo y -> SNo_ (SNoLev y) y -> P) -> P const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const eps_ : set set claim !x:set.SNo x -> (!y:set.y iIn SNoS_ omega -> (!z:set.z iIn omega -> abs_SNo (y + - x) < eps_ z) -> y = x) -> !y:set.y iIn SNoS_ omega -> (!z:set.z iIn omega -> abs_SNo (y + - - x) < eps_ z) -> y = - x