induction lsa; destruct lsb; intuition; simpl in *; try omega.
intuition.
pairInv.
intuition.
Qed.

Lemma unzip_zip_inv :
forall (A B : Set)(lsa : list A)(lsb : list B),
length lsa = length lsb ->
unzip (zip lsa lsb) = (lsa, lsb).