theorem
  for V being strict LeftMod of R,A being Subset of V holds
  A = the carrier of V implies Lin(A) = V
  proof
    let V be strict LeftMod of R, A be Subset of V;
    assume A = the carrier of V;
     then for v being Vector of V holds
       v in Lin(A) iff v in (Omega).V by Th65;
    hence thesis by ZMODUL01:46;
  end;
