const nat_p : set prop const SNo : set prop axiom nat_p_SNo: !x:set.nat_p x -> SNo x 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 lemma !x:set.!y:set.SNo x -> nat_p y -> SNo 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.nat_p y -> !z:set.nat_p z -> exp_SNo_nat x y * exp_SNo_nat x z = exp_SNo_nat x (y + z)