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 add_SNo_minus_L2: !x:set.!y:set.SNo x -> SNo y -> - x + x + y = y axiom add_SNo_assoc: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x + y + z = (x + y) + z const SNoLe : set set prop term <= = SNoLe infix <= 2020 2020 const abs_SNo : set set lemma !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo - y -> SNo - z -> x + - z = (x + - y) + y + - z -> abs_SNo (x + - z) <= abs_SNo (x + - y) + abs_SNo (y + - z) var x:set var y:set var z:set hyp SNo x hyp SNo y hyp SNo z hyp SNo - y claim SNo - z -> abs_SNo (x + - z) <= abs_SNo (x + - y) + abs_SNo (y + - z)