const SNo : set prop const ordsucc : set set const Empty : set axiom SNo_2: SNo (ordsucc (ordsucc Empty)) const nat_p : set prop const exp_SNo_nat : set set set axiom SNo_exp_SNo_nat: !x:set.SNo x -> !y:set.nat_p y -> SNo (exp_SNo_nat x y) const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set axiom nat_p_omega: !x:set.nat_p x -> x iIn omega const eps_ : set set axiom SNo_eps_: !x:set.x iIn omega -> SNo (eps_ x) const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 axiom mul_SNo_com: !x:set.!y:set.SNo x -> SNo y -> x * y = y * x axiom mul_SNo_eps_power_2: !x:set.nat_p x -> eps_ x * exp_SNo_nat (ordsucc (ordsucc Empty)) x = ordsucc Empty claim !x:set.nat_p x -> exp_SNo_nat (ordsucc (ordsucc Empty)) x * eps_ x = ordsucc Empty