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
  Lin(A) = V & A c= B implies Lin(B) = V
proof
  assume that
A1: Lin(A) = V and
A2: A c= B;
  V is Subspace of Lin(B) by A1,A2,Th10;
  hence thesis by A1,VECTSP_4:25;
end;
