simple induction n.
simpl in |- *.
red in |- *.
auto with algebra.
intros.
simpl in |- *.
red in |- *.
simpl in |- *.
intro i.
case i.
auto with algebra.
Qed.
Hint Resolve Map_embed_Seqtl: algebra.

Lemma Seqtl_Map_embed :
forall (E : Setoid) (A : part_set E) (n : Nat) (f : seq n A),
Seqtl (Map_embed f) =' Map_embed (Seqtl f) in seq _ _.