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_Lt2: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> y < z -> (x + y) < x + z const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 axiom SNoLtLe: !x:set.!y:set.x < y -> x <= y axiom SNoLe_ref: !x:set.x <= x axiom SNoLeE: !x:set.!y:set.SNo x -> SNo y -> x <= y -> x < y | x = y claim !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> y <= z -> (x + y) <= x + z