theorem Th42: :: VECTSP_5:42

for GF being non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr
for M being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF holds
( M is_the_direct_sum_of (0). M, (Omega). M & M is_the_direct_sum_of (Omega). M, (0). M ) by Th9, Th20;