  This short note describes and proves a connectedness property which was
introduced in Blocher et al. [2023] in the context of data depth functions for
partial orders. The connectedness property gives a structural insight into
union-free generic sets. These sets, presented in Blocher et al. [2023], are
defined by using a closure operator on the set of all partial orders which
naturally appears within the theory of formal concept analysis. In the language
of formal concept analysis, the property of connectedness can be vividly
proven. However, since within Blocher et al. [2023] we did not discuss formal
concept analysis, we outsourced the proof to this note.
