The disengagement algorithm or a new generalization of the exclusion algorithm

Let us consider a finite inf semilattice G with a set 1 of internal binary operations 1₁, isotono, satisfying certain conditions of no dispersion, of increasing and of substitution, and so that the greatest lower bound is distributive relatively to 1₁. A finite subset A of G being given, this article gives a method for enumerating the maximal elements of the sub-algebra A¹ generated by A with regard to 1, when A¹ is finite. This method, called disengagement algorithm, allows to examine each element once; it generalizes an algorithm giving the maximal n-rectangles of a part of a product of distributive lattices algorithm which already generalized a conjecture of Tison in Boolean algebra. Two applications are developed.