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