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.