intros a b aL; elim aL; simpl in |- *; auto.
intros H'; case H'; [ intros H'0; rewrite <- H'0 | intros H'0; clear H' ];
auto.
intros a0 l H' H'0; case H'0;
[ intros H'1; rewrite <- H'1; clear H'0 | intros H'1; clear H'0 ];
auto.
case (H' H'1); auto.
Qed.

Theorem addEnd_id1 :
forall (a : poly A0 eqA ltM) (aL : list (poly A0 eqA ltM)),
In a (addEnd a aL).