intros.
simpl in |- *.
red in |- *.
intro x; case x; intro i; case i.
simpl in |- *.
auto with algebra.
intros.
simpl in |- *.
apply Refl.
Qed.
Hint Resolve Map_embed_cons: algebra.

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