  We give an a priori proof of the known presentations of (that is,
completeness of families of relations for) the principal subspaces of all the
standard A_1^(1)-modules. These presentations had been used by Capparelli,
Lepowsky and Milas for the purpose of obtaining the classical Rogers-Selberg
recursions for the graded dimensions of the principal subspaces. This paper
generalizes our previous paper.
