reserve GF for Field,
  V for VectSp of GF,
  W for Subspace of V,
  x, y, y1, y2 for set,
  i, n, m for Nat;

theorem Th10:
  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 ModuleStr of V by STRUCT_0:def 5;
  hence thesis by VECTSP_7:def 3;
end;
