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:
 * $\forall x \in S: i_S \left({x}\right) = x$

is an injection.

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

Proof
Suppose $i_S \left({s_1}\right) = i_S \left({s_2}\right)$.

Thus $i_S$ is an injection by definition.