theorem
  for F being unital non empty SubStr of D*+^ holds
  the_unity_wrt the multF of F = {}
proof
  let F be unital non empty SubStr of D*+^;
  set p = the_unity_wrt op(F);
  reconsider q = p as Element of F qua SubStr of D*+^;
  q^{} = p by FINSEQ_1:34
    .= p[*]p by SETWISEO:15
    .= q^q by Th63;
  hence thesis by FINSEQ_1:33;
end;
