A surprisingly easy proof of yesterday conjecture

I have found a surprisingly easy proof of this conjecture which I proposed yesterday.

Theorem Let S be a set of binary relations. If for every X, Y \in S we have \mathrm{up} (X \sqcap^{\mathsf{FCD}} Y) \subseteq S then there exists a funcoid f such that S = \mathrm{up}\, f.

The proof (currently available in this PDF file) is based on “Funcoids are filters” chapter of my book.

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