(***********************)
simple induction v. unfold elemlist in |- *. simpl in |- *. trivial with arith.
simple induction i. simpl in |- *. unfold elemlist in |- *. rewrite trunc_O.
rewrite strip_O. simpl in |- *. rewrite trunc_O. trivial with arith.
intros. simpl in |- *. unfold elemlist in |- *.
rewrite strip_cons_S. unfold elemlist in H. rewrite H. trivial with arith.
generalize H1. simpl in |- *. auto with arith.
Qed.

Lemma length_elemlist :
forall (l : list A) (i : nat),
i < length l -> length (elemlist l i) = 1.