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 W1,W2 being strict Subspace of M holds W1 + W2 = W2 iff W1 /\ W2 = W1
proof
  let W1,W2 be strict Subspace of M;
  W1 + W2 = W2 iff W1 is Subspace of W2 by Th8;
  hence thesis by Th16;
end;
