const In : set set prop term iIn = In infix iIn 2000 2000 const omega : set const nat_p : set prop axiom omega_nat_p: !x:set.x iIn omega -> nat_p x const SNo : set prop const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 const exp_SNo_nat : set set set const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom exp_SNo_nat_mul_add: !x:set.SNo x -> !y:set.nat_p y -> !z:set.nat_p z -> exp_SNo_nat x y * exp_SNo_nat x z = exp_SNo_nat x (y + z) claim !x:set.SNo x -> !y:set.y iIn omega -> !z:set.z iIn omega -> exp_SNo_nat x y * exp_SNo_nat x z = exp_SNo_nat x (y + z)