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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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