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

Theorem
Let $T = \struct{X, \tau}$ be a topological space.

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

Proof
This follows immediately from Open Cover with Closed Locally Finite Refinement is Even Cover.