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 minus_SNo : set set term - = minus_SNo axiom minus_SNo_invol: !x:set.SNo x -> - - x = x axiom minus_add_SNo_distr: !x:set.!y:set.SNo x -> SNo y -> - (x + y) = - x + - y const abs_SNo : set set axiom abs_SNo_minus: !x:set.SNo x -> abs_SNo - x = abs_SNo x var x:set var y:set hyp SNo x hyp SNo y hyp SNo - x hyp SNo - y claim SNo (y + - x) -> abs_SNo (x + - y) = abs_SNo (y + - x)