intros.
unfold included, inject_subsets in |- *.
simpl in |- *.
intros.
inversion_clear H.
apply in_part_comp_l with (subtype_elt (subtype_elt x0)); auto with algebra.
Qed.
Hint Resolve inject_subsets_of_part_set_included: algebra.

Lemma inject_subsets_full_inv :
forall (A : Setoid) (B : part_set A), Equal (inject_subsets (full B)) B.