theorem Th71:
  for F being non empty SubStr of GPFuncs X st
  id X is Element of F holds
    F is unital & the_unity_wrt the multF of F = id X
proof
  let F be non empty SubStr of GPFuncs X;
  the_unity_wrt op(GPFuncs X) = id X by Th69;
  hence thesis by Th30;
end;
