const SNo : set prop const mul_SNo : set set set term * = mul_SNo infix * 2291 2290 const In : set set prop term iIn = In infix iIn 2000 2000 const SNoL : set set const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const add_SNo : set set set term + = add_SNo infix + 2281 2280 const SNoR : set set axiom mul_SNo_prop_1: !x:set.SNo x -> !y:set.SNo y -> !P:prop.(SNo (x * y) -> (!z:set.z iIn SNoL x -> !w:set.w iIn SNoL y -> (z * y + x * w) < x * y + z * w) -> (!z:set.z iIn SNoR x -> !w:set.w iIn SNoR y -> (z * y + x * w) < x * y + z * w) -> (!z:set.z iIn SNoL x -> !w:set.w iIn SNoR y -> (x * y + z * w) < z * y + x * w) -> (!z:set.z iIn SNoR x -> !w:set.w iIn SNoL y -> (x * y + z * w) < z * y + x * w) -> P) -> P claim !x:set.!y:set.SNo x -> SNo y -> SNo (x * y)