reserve S for 1-sorted,
  i for Element of NAT,
  p for FinSequence,
  X for set;

theorem Th40:
  for X being finite set holds singletons(X) is Basis of bspace(X)
proof
  let X be finite set;
  singletons(X) is linearly-independent & Lin(singletons(X)) = bspace(X)
  by Th36,Th39;
  hence thesis by VECTSP_7:def 3;
end;
