
theorem Th11:
  for X being non empty Ordinal, x be Element of X, L being
  well-unital non trivial doubleLoopStr, e being Function of X, L
  holds eval(UnitBag x, e) = e.x
proof
  let X be non empty Ordinal, x be Element of X, L be well-unital
  non trivial doubleLoopStr, e be Function of X, L;
  reconsider edx = e.x as Element of L;
  support UnitBag x = {x} by Th8;
  hence eval(UnitBag x, e) = power(L).(e.x, (UnitBag x).x) by POLYNOM2:15
    .= power(L).(e.x, 0+1) by Th9
    .= power(L).(edx, 0) * (edx) by GROUP_1:def 7
    .= 1_L * (edx) by GROUP_1:def 7
    .= e.x;
end;
