theorem Th26:
  r (*) ZeroLC(R) = ZeroLC R
  proof
    per cases;
    suppose r=0;
      hence thesis by Def2;
    end;
    suppose A1: r<>0;
      now let v be Element of R;
        thus(r(*)ZeroLC(R)).v = ZeroLC(R).(r"*v) by A1,Def2
                             .= 0 by RLVECT_2:20
                             .= ZeroLC(R).v by RLVECT_2:20;
      end;
      hence thesis;
    end;
  end;
