reserve x,y for object,
  R for Ring,
  V for LeftMod of R,
  L for Linear_Combination of V,
  a for Scalar of R,
  v,u for Vector of V,
  F,G for FinSequence of the carrier of V,
  C for finite Subset of V;
reserve X,Y,Z for set,
  A,B for Subset of V,
  T for finite Subset of V,
  l for Linear_Combination of A,
  f,g for Function of the carrier of V,the carrier of R;

theorem
  for R being non degenerated Ring
  for V being strict LeftMod of R
  for A being Subset of V st A = the carrier of V holds
    Lin(A) = V
proof
  let R be non degenerated Ring;
  let V be strict LeftMod of R;
  let A be Subset of V;
  assume A = the carrier of V; then
  A = the carrier of (Omega).V;
  hence thesis by Th8;
end;
