induction lsa; intuition; simpl in *.
intuition.
destruct lsb.
simpl in *.
intuition.
inversion H; clear H; subst.
simpl in *.
intuition.
repeat pairInv.
trivial.
pairInv.
eapply in_combine_l in H0.
intuition.
pairInv.
eapply in_combine_l in H.
intuition.
eauto.
Qed.

Theorem zip_eq_nil_l :
forall (A B : Set)(lsa : list A)(lsb : list B),
zip lsa lsb = nil ->
length lsa = length lsb ->
lsa = nil.