Number of Injective Restrictions

Theorem
Let $f: S \to T$ be a mapping.

Let $Q$ be the set of all injective restrictions of $f$.

Then the cardinality of $Q$ is:


 * $\displaystyle \card {\prod_{i \mathop \in I} \prod_{j \mathop \in J_i} \family {\family {\powerset {S / \mathcal R_f} }_i}_j}$

where:
 * $\mathcal P$ denotes power set
 * $S / \mathcal R_f$ denotes quotient set of the induced equivalence of $f$.