theorem Th8:
  for b2 be Basis of V ex KL be Linear_Combination of V
  st W = Sum KL & Carrier KL c= b2
  proof
    let b2 be Basis of V;
    W in the ModuleStr of V;
    then W in Lin b2 by VECTSP_7:def 3;
    then consider KL1 being Linear_Combination of b2 such that
    A1: W = Sum KL1 by ZMODUL02:64;
    take KL = KL1;
  thus W = Sum KL by A1;
  thus thesis by VECTSP_6:def 4;
end;
