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

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.