Indexed Union Subset
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Theorem
Let $A$, $B_x$ and $C_x$ be classes.
It can be inferred from the context, but the meaning of the subscript on $B_x$ and $C_x$ needs to be explained.
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Then:
- $\displaystyle \forall x \in A: B_x \subseteq C_x \implies \bigcup_{x \mathop \in A} B_x \subseteq \bigcup_{x \mathop \in A} C_x$
In particular: $\bigcup_{x \mathop \in A} B_x$ and $\bigcup_{x \mathop \in A} C_x$.
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Proof
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