A failed attempt to prove a theorem

I have claimed that I have proved this theorem:

Theorem Let f is a T_1-separable (the same as T_2 for symmetric transitive) compact funcoid and g is an reflexive, symmetric, and transitive endoreloid such that ( \mathsf{FCD}) g = f. Then 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.

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