Let $\mathbb{W} = \{W_i\}_{i \in I} $ be an indexed set containing every subspace of $V$ that includes $A$. Since the intersection of subspaces is a subspace, $\mathbb{W} = \bigcap_{i \in I} W_i$ is a subspace. $A \subseteq \mathbb{W}$ so $L(A) \subseteq \mathbb{W}$. How do I prove $\mathbb{W} \subseteq L(A)$?
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