I generalized a theorem in the preprint article “Filters on posets and generalizations” on my Algebraic General Topology site.

The new theorem is formulated as following:

**Theorem** If $latex (\mathfrak{A}; \mathfrak{Z})$ is a join-closed filtrator and $latex \mathfrak{A}$ is a meet-semilattice and $latex \mathfrak{Z}$ is a complete lattice, then $latex \mathrm{Cor}’ (a \cap^{\mathfrak{A}} b) = \mathrm{Cor}’ a \cap^{\mathfrak{Z}} \mathrm{Cor}’ b.$

From this theorem also follow the following formulas about funcoids:

- $latex \mathrm{Compl}(f\cap^{\mathsf{FCD}}g) = \mathrm{Compl}f\cap^{\mathsf{FCD}}\mathrm{Compl}g$.
- $latex \mathrm{CoCompl}(f\cap^{\mathsf{FCD}}g) = \mathrm{CoCompl}f\cap^{\mathsf{FCD}}\mathrm{CoCompl}g$.

The problem, whether meet of any two discrete funcoids is the same on the lattice of all funcoids and on the lattice of discrete funcoids, remains empty.