(* note we don't say v='(head v);;(Seqtl v): we want freedom in the choice of the proof H *)
intros.
simpl in |- *.
red in |- *.
simpl in |- *.
intro x.
case x.
intro.
case index.
intros; apply Ap_comp; simpl in |- *; auto with algebra arith.
red in |- *; auto with algebra.
intros; apply Ap_comp; simpl in |- *; auto with algebra arith.
red in |- *; auto with algebra.
Qed.
Hint Resolve conseq_hdtl: algebra.

(* Specifications: *)
Lemma hdtl_x_is_x : forall v : seq (S n) A, v =' hdtl v in _.
unfold hdtl in |- *.