theorem Th19:
  F |^ 1 = F
proof
  set G=GFuncs the carrier of S;
  reconsider F9=F as Element of G by MONOID_0:73;
  Product(1|->F9) = Product<*F9*> by FINSEQ_2:59
    .= F9 by GROUP_4:9;
  hence thesis by Def4;
end;
