simpl in |- *.
unfold subtype_image_equal in |- *.
auto with algebra.
Qed.
Hint Resolve subtype_elt_comp: algebra.

(* Specifications: *)
Lemma in_part_subtype_elt :
forall (A : Setoid) (B : part_set A) (b : B), in_part (subtype_elt b) B.