Structure of the image of (pseudo)-holomorphic discs with totally real boundary condition

In this paper, we prove that the image of a (pseudo)-holomorphic map from t he unit disc with its boundary on a given totally real submanifold is repre sented as a finite union of the images of "simple" discs allowing multiplic ity with boundaries on the same totally real submanifold. This in particula r fills a technical gap in relation to the Fredholm and the intersection th eory of Gromov's (pseudo)holomorphic discs, which has been present in the l iterature on the applications of pseudo-holomorphic discs.