Mathematical Proof, "Let F be a family of dyadic functions"

The proof of his theorem: Let F be a family of dyadic functions on a set X. This document includes two drafts of his theorem. The first being rough with marks in Red and Green on it. And the second having only green lines on it. Possibly a working draft of "A remark on the existence of a denumerable base for a family of dyadic functions." Included in 2011.007-RTH/4. A Remark on the Existence of a Denumerable Base for a Family of Functions. Contained in 2011.007-RTH/6.