theorem
  for X0 being non empty SubSpace of X, f0 being Function of X0,X st for
x being Point of X st x in the carrier of X0 holds x = f0.x holds incl X0 = f0
proof
  let X0 be non empty SubSpace of X, f0 be Function of X0,X;
  assume for x being Point of X st x in the carrier of X0 holds x = f0.x;
  then for x be Point of X st x in the carrier of X0 holds (id X).x = f0.x;
  hence thesis by Th53;
end;
