theorem Th19:
  g + (h+LG) = (g+h) + LG
  proof
    now let s be Element of G;
      thus(g+(h+LG)).s = (h+LG).(s-g) by Def1
                      .= LG.(s-g-h) by Def1
                      .= LG.(s-(g+h)) by RLVECT_1:27
                      .= ((g+h)+LG).s by Def1;
    end;
    hence thesis;
  end;
