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
  W1 is Subspace of W2 & W1 is Subspace of W3 implies W1 is Subspace of
  W2 /\ W3
proof
  assume
A1: W1 is Subspace of W2 & W1 is Subspace of W3;
  now
    let v;
    assume v in W1;
    then v in W2 & v in W3 by A1,VECTSP_4:8;
    hence v in W2 /\ W3 by Th3;
  end;
  hence thesis by VECTSP_4:28;
end;
