induction l1; intros.
destruct l2; simpl in L. trivial. omega.
destruct l2; simpl in L. omega.
rewrite (IHl1 l2) with (d:=d).
specialize (N O). simpl in N. rewrite N; trivial. omega.
omega.
intros. apply (N (S i)). simpl; omega.
Qed.

Lemma force_lengthn_app1 {A}{d: Inhabitant A}: forall n l1 l2, length l1 =n -> force_lengthn n (l1 ++ l2) d = l1.