complete lattices – Math Research of Victor Porton

My problem whether weak partitioning and strong partitioning of a complete lattice are the same was solved by counter-example by

Chain-meet-closed sets on complete lattices

Let is a complete lattice. I will call a filter base a nonempty subset of such that . I will

I conjectured certain formula for the complete lattice generated by a strong partitioning of an element of complete lattice. Now

In this post I defined strong partitioning of an element of a complete lattice. For me it was seeming obvious