性质 1.3. (加法消去律)

加法消去律成立,即若 $\alpha +\gamma =\beta +\gamma$,则 $\alpha =\beta$.

证明 记 $\delta =-\gamma$,则

$$\alpha =\alpha +0=\alpha +\left(\gamma +\delta \right)=\left(\alpha +\gamma \right)+\delta =\left(\beta +\gamma \right)+\delta =\beta +\left(\gamma +\delta \right)=\beta +0=\beta .$$