reserve V for RealLinearSpace,
  W for Subspace of V,
  x, y, y1, y2 for set,
  i, n for Element of NAT,
  v for VECTOR of V,
  KL1, KL2 for Linear_Combination of V,
  X for Subset of V;

theorem Th13:
  for I being Basis of V, v being VECTOR of V holds v in Lin(I)
proof
  let I be Basis of V, v be VECTOR of V;
  v in the RLSStruct of V by STRUCT_0:def 5;
  hence thesis by RLVECT_3:def 3;
end;
