Add Parametric Morphism: reduction with signature
(group_str_equiv) ==> (@eq group_str) as reduction_mor.

(* Specifications: *)
Lemma equivalence_is_equality_on_reduced_strings:
forall S T:group_str, reduced S -> reduced T ->
S ~~ T -> S = T.
Theorem unique_reduction: forall S:group_str,
exists! R:group_str, S ~~ R /\ reduced R.