const SNo : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom SNo_add_SNo: !x:set.!y:set.SNo x -> SNo y -> SNo (x + y) const minus_SNo : set set term - = minus_SNo axiom SNo_minus_SNo: !x:set.SNo x -> SNo - x axiom add_SNo_assoc: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x + y + z = (x + y) + z axiom add_SNo_minus_L2': !x:set.!y:set.SNo x -> SNo y -> x + - x + y = y claim !x:set.!y:set.!z:set.!w:set.SNo x -> SNo y -> SNo z -> SNo w -> (x + y + z) + - z + w = x + y + w