Inclusion Mapping is Injection

Theorem
Let $S, T$ be sets such that $S$ is a subset of $T$.

Then the inclusion mapping $i_S: S \to T$ defined as:
 * $\forall x \in S: \map {i_S} x = x$

is an injection.

For this reason the inclusion mapping can be known as the canonical injection of $S$ to $T$.

Proof
Suppose $\map {i_S} {s_1} = \map {i_S} {s_2}$.

Thus $i_S$ is an injection by definition.