Let L be an MS-algebra with congruence permutable skeleton. We prove that solving a system of congruences (θ1, . . . , θn; x1, . . . , xn) in L can be reduced to solving the restriction of the system to the skeleton of L, plus solving the restrictions of the system to the intervals [x1, x¯¯1], . . . , [xn, x¯¯n].
We reduce the problem on multiplicities of simple subquotients in an $\alpha $-stratified generalized Verma module to the analogous problem for classical Verma modules.