A finite basis of the set of all monotone partial functions defined over a finite poset

Let X be an arbitrary poset. A partial function f with n variables defined over X is said to be monotone if the following condition is satisfied: if x₁⩽y₁,..., x_m⩽y _n, and both the values f(x₁,..., x_n) and f(y₁,....y_n) are defined, then f(x₁,..., x_n)⩽f(y₁,...,y_n) It is shown that the set of all monotone partial functions has a finite basis