induction 1; intuition; simpl in *.
destruct a1.
destruct a2.
remember (split ls1) as z.
destruct z.
remember (split ls2) as z.
destruct z.
simpl in *.
subst.
trivial.
Qed.

Theorem unzip_eq_split :
forall (A B : Set)(ls : list (A * B)),
unzip ls = split ls.