A space X is called subparacompact if every open cover of X has a \sigma- discrete closed refinement.

A space X is said to be a collectionwise normal if for every discrete collection F_i of closed sets, there is a pairwise disjoint family of open sets U_i such that F_i \subset U_i.

A space X is called paracompact if every open cover of X has a locally finite open refinement.

My question is:
Show that every collectionwise normal subparacompact space is paracompact.

This result is due to McAuley and it is established in " A note on complete collectionwise normality and paracompactness" but when he explained this result, he referred to lemma due to Dowker in " on a theorem of hanner" I tried to get this paper but I fortunately could not. So, please if you know the complete idea of the proof please guide me.
Thaaaaank you in advance