intros.
unfold head in |- *.
apply Ap_comp; auto with algebra.
Qed.
Hint Resolve seq_S_O_contains_single_elt: algebra.

Lemma seq_S_O_head_fixes_everything :
forall (A : Setoid) (v v' : seq 1 A), head v =' head v' in _ -> v =' v' in _.