Cardinality of Set Difference

Theorem
Let $S$ and $T$ be sets such that $T$ is finite.

Then:
 * $\card {S \setminus T} = \card S - \card {S \cap T}$

where $\card S$ denotes the cardinality of $S$.

Proof
From Intersection is Subset:
 * $S \cap T \subseteq S$
 * $S \cap T \subseteq T$

From Subset of Finite Set is Finite:
 * $S \cap T$ is finite.

We have: