LessEqual will generate and store the transitive closure of P.

A partially ordered set, or poset for short, is a pair (P, <=) where P is a set and <= is a partial order on P. The poset (P, <=) defines a directed graph whose vertices are the elements of P and (a,b) is a directed edge whenever a <= b holds. Conversely, a poset can be defined from a directed graph, assuming that the defined binary relation is anti-symmetric, and transitive, and, either reflexive, or irreflexive.

From now on, we fix a poset (P, <=). Two elements a and b of P are said comparable if either a <= b or  b <= a holds, otherwise a and b are said incomparable.

The partial order  <= is said total whenever any two elements of P are comparable.

The element a of P is strictly less than the element b of P if a <= b and a \342\211\240 b both hold.

The element b  of P covers the element a of P if a  is strictly less than b and for no element c of P, distinct from both a and b, both a <= c and c <= b hold.

The relation b covers a defines a homogeneous binary relation on P which is the transitive reduction of (P, <=). This is also a directed acyclic graph on P often refers as the Hasse diagram of (P, <=).