proposition: Lemma combine_firstn_l : forall (l : list A) (l' : list B), combine l l' = combine l (firstn (length l) l').
proof: Proof. intro l; induction l as [| x l IHl]; intros l'; [reflexivity|]. destruct l' as [| x' l']; [reflexivity|]. simpl. specialize IHl with l'. rewrite <- IHl. reflexivity. Qed.
imports: PeanoNat