const SNo : set prop const minus_SNo : set set term - = minus_SNo axiom SNo_minus_SNo: !x:set.SNo x -> SNo - x 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) axiom add_SNo_cancel_L: !x:set.!y:set.!z:set.SNo x -> SNo y -> SNo z -> x + y = x + z -> y = z var x:set var y:set hyp SNo x hyp SNo y hyp SNo - x hyp SNo - y hyp SNo (x + y) claim (x + y) + - (x + y) = (x + y) + - x + - y -> - (x + y) = - x + - y