Preimage of Composite Relation
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Theorem
Let $\RR_1 \subseteq S_1 \times T_1$ and $\RR_2 \subseteq S_2 \times T_2$ be relations.
Let $\RR_2 \circ \RR_1 \subseteq S_1 \times T_2$ be the composition of $\RR_1$ and $\RR_2$.
Then the preimage of $\RR_2 \circ \RR_1$ is given by:
- $\Preimg {\RR_2 \circ \RR_1} = \Preimg {\Img {\RR_1} \cap \Preimg {\RR_2} }$
Proof
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