Set of Mappings can be Ordered by Inclusion

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Theorem

Let $S \times T$ be the product of two sets.

Let $\mathcal F$ be a set of mappings on $S \times T$.


Then $\mathcal F$ can be ordered by inclusion.


Proof

By the definition of mapping, a mapping is a specific type of relation.

The result then follows from Set of Relations can be Ordered by Inclusion.

$\blacksquare$