Add Parametric Morphism: (@app alphabet) with signature
  (group_str_equiv) ==> (group_str_equiv) ==> (group_str_equiv) as
  concat_mor.

(* Specifications: *)
Lemma reduction_equiv: forall S:group_str, reduction S ~~ S.
Lemma string_action_takes_concat_to_composition: forall (S1 S2 S3:group_str), group_str_action S1 (group_str_action S2 S3) = group_str_action (S1 ++ S2) S3.
Lemma equiv_strings_have_same_actions: forall (S1 S2 T:group_str), reduced T -> S1 ~~ S2 -> group_str_action S1 T = group_str_action S2 T.