intros.
apply Trans with (Seqtl (hdtl v ++ w)); auto with algebra.
apply Trans with (Seqtl (head v;; Seqtl v ++ w)); auto with algebra.
unfold hdtl in |- *.
apply Seqtl_comp; auto with algebra.
change (Seqtl (head v;; Seqtl v ++ w) =' Seqtl v ++ w in seq (n + m) A)
in |- *.
generalize dependent (Seqtl_cons_inv (head v) (Seqtl v ++ w)).
auto.
Qed.

Lemma concat_Seqtl :
forall (v : seq (S n) A) (w : seq m A), Seqtl v ++ w =' Seqtl (v ++ w) in _.