const SNo : set prop const add_SNo : set set set term + = add_SNo infix + 2281 2280 axiom add_SNo_com: !x:set.!y:set.SNo x -> SNo y -> x + y = y + x const SNoLt : set set prop term < = SNoLt infix < 2020 2020 const minus_SNo : set set term - = minus_SNo axiom add_SNo_minus_Lt1b: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x < z + y -> (x + - y) < z const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 const Empty : set const abs_SNo : set set var x:set var y:set var z:set hyp SNo x hyp SNo y hyp SNo z hyp y < x + z hyp Empty <= y + - x claim abs_SNo (y + - x) = y + - x -> abs_SNo (y + - x) < z