
theorem Th6:
  for n being Ordinal, L being well-unital non trivial
  doubleLoopStr, x being Function of n, L holds eval(EmptyBag n,x) = 1.L
proof
  let n be Ordinal, L be well-unital non trivial doubleLoopStr, x
  be Function of n, L;
  set b = EmptyBag n;
  reconsider s = support b as empty Subset of n;
  consider y being FinSequence of the carrier of L such that
A1: len y = (len SgmX(RelIncl n, support b)) and
A2: eval(b,x) = Product y and
  for i being Element of NAT st 1 <= i & i <= len y holds y/.i = power (L)
.((x * SgmX(RelIncl n, support b))/.i, (b * SgmX(RelIncl n, support b))/.i) by
Def1;
  SgmX(RelIncl n, s) = {} by PRE_POLY:76,82;
  then y = <*>the carrier of L by A1;
  then eval(EmptyBag n,x) = 1_L by A2,GROUP_4:8;
  hence thesis;
end;
