Let x {\displaystyle {}x} be given and suppose that y {\displaystyle {}y} and y ′ {\displaystyle {}y'} are elements fulfilling x + y = 0 = x + y ′ {\displaystyle {}x+y=0=x+y'} . Then
which means altogether y = y ′ {\displaystyle {}y=y'} . For the second part see exercise.