Indexed Union Subset
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This article, or a section of it, needs explaining, namely:
It can be inferred from the context, but the meaning of the subscript on $B_x$ and $C_x$ needs to be explained.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this point in more detail, feel free to use the talk page.
This article needs to be linked to other articles.
In particular: $\bigcup_{x \mathop \in A} B_x$ and $\bigcup_{x \mathop \in A} C_x$.
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This theorem requires a proof..
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
 It has been suggested that this page or section be merged into Set Union Preserves Subsets. (Discuss) |
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.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this point in more detail, feel free to use the talk page.
If you are able to explain it, then when you have done so you can remove this instance of {{Explain}} from the code.
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 $\bigcup_{x \mathop \in A} C_x$.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links.
To discuss this in more detail, feel free to use the talk page.
Once you have done so, you can remove this instance of {{MissingLinks}} from the code.
Proof
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