A failed attempt to prove a theorem

I have claimed that I have proved this theorem:

Theorem Let $latex f$ is a $latex T_1$-separable (the same as $latex T_2$ for symmetric transitive) compact funcoid and $latex g$ is an reflexive, symmetric, and transitive endoreloid such that $latex ( \mathsf{FCD}) g = f$. Then $latex g = \langle f \times f \rangle \uparrow^{\mathsf{RLD}} \Delta$.

The proof is with errors and omissions however.

Please help me to correct the proof. See also this question.