Paracompact Space is Countably Paracompact

Theorem
Let $T = \left({X, \vartheta}\right)$ be a paracompact space.

Then $T$ is a countably paracompact space.

Proof
From the definition, $T$ is paracompact space iff every open cover of $X$ has an open refinement which is locally finite.

This also applies to all countable open covers.

So every countable open cover of $X$ has an open refinement which is locally finite.

This is precisely the definition for a countably paracompact space.