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.
Corollary equiv_strings_have_same_reductions:
forall S T:group_str, S ~~ T ->
reduction S = reduction T.