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I start you off. If $\displaystyle x$ is the greatest lower bound for $\displaystyle B$ then $\displaystyle x\leq b$ for all $\displaystyle b\in B$. But then $\displaystyle x\leq a$ for all $\displaystyle a\in A$ because $\displaystyle A\subseteq B$. This means that $\displaystyle x\leq y$ where $\displaystyle y$ is greatest lower bound for $\displaystyle A$ because $\displaystyle x$ is a lower bound for $\displaystyle A$ and $\displaystyle y$ is the greatest lower bound for $\displaystyle A$.