theorem
  for V being LeftMod of R for A being Subset of V st Lin(A) = V
  holds ex I being Basis of V st I c= A
proof
  let V be LeftMod of R;
  let A be Subset of V;
  assume Lin(A) = V;
  then consider B being Subset of V such that
A1: B c= A and
A2: B is base by Th19;
  reconsider B as Basis of V by A2;
  take B;
  thus thesis by A1;
end;
