Characterization of Paracompactness in T3 Space/Statement 3 implies Statement 4

Theorem
Let $T = \struct{X, \tau}$ be a $T_3$ Space.

If every open cover of $T$ has a closed locally finite refinement then:
 * every open cover of $T$ is even

Proof
Let every open cover of $T$ has a closed locally finite refinement.

It follows that:
 * every open cover of $T$ is even