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 const Empty : set axiom add_SNo_0R: !x:set.SNo x -> x + Empty = x axiom add_SNo_minus_SNo_rinv: !x:set.SNo x -> x + - x = Empty axiom add_SNo_assoc: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x + y + z = (x + y) + z const SNoLt : set set prop term < = SNoLt infix < 2020 2020 axiom add_SNo_Lt1_cancel: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> (x + y) < z + y -> x < z claim !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> z < x + - y -> (z + y) < x