reserve GF for add-associative right_zeroed right_complementable Abelian
  associative well-unital distributive non empty doubleLoopStr;
reserve M for Abelian add-associative right_zeroed right_complementable
  vector-distributive scalar-distributive scalar-associative scalar-unital
   non empty ModuleStr over GF;
reserve W,W1,W2,W3 for Subspace of M;
reserve u,u1,u2,v,v1,v2 for Element of M;
reserve X,Y for set, x,y,y1,y2 for object;

theorem
  for M being strict Abelian add-associative right_zeroed
right_complementable vector-distributive scalar-distributive
scalar-associative scalar-unital non empty ModuleStr over GF holds (Omega).M
  + (Omega).M = M by Th11;
