const SNo : set prop const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_Lt1_cancel: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> (x + y) < z + y -> x < z axiom add_SNo_com: !x:set.!y:set.SNo x -> SNo y -> x + y = y + x claim !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> (x + y) < x + z -> y < z