I have proved the following negative result:

**Theorem** is not boolean if is a non-atomic boolean lattice.

The theorem is presented in this file.

denotes the set of pointfree funcoids from a poset to a poset (see my free ebook).

The theorem and its proof were modeled after theorem 3.8 in this article (December 1979) by Zahava Shmuely.

It would be probably interesting to a find a common generalization of my theorem and the original Zahava Shmuely’s one.

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