theorem Th2:
  v in W1 or v in W2 implies v in W1 + W2
proof
  assume
A1: v in W1 or v in W2;
  now
    per cases by A1;
    suppose
A2:   v in W1;
      v = v + 0.M & 0.M in W2 by RLVECT_1:4,VECTSP_4:17;
      hence thesis by A2,Th1;
    end;
    suppose
A3:   v in W2;
      v = 0.M + v & 0.M in W1 by RLVECT_1:4,VECTSP_4:17;
      hence thesis by A3,Th1;
    end;
  end;
  hence thesis;
end;
