Between the important thing, when we deal with a type or a formula A of a system of typing that satisfies the strong normalization S.N., is to build a set of terms that satisfies 'a term in the set corresponding to A is equivalent to say that t is of type A. Unfortunally it is impossible to have this equivalency because of S.N., so the work take another formulation to escape this problem and it becomes 'a term in the set corresponding to A is equivalent to say that t is in relation with t' which is of type A'. many studies having this form where been published for many systems and relations. My work will be around the simply typed system in lambda mu calculus.