intros.
unfold Map_embed in |- *; simpl in |- *; red in |- *; simpl in |- *.
intuition.
Qed.
Hint Resolve Map_embed_comp: algebra.

Lemma Map_embed_cons :
forall (E : Setoid) (A : part_set E) (a : A) (n : Nat) (f : seq n A),
Map_embed (a;; f) =' subtype_elt a;; Map_embed f in seq _ _.