induction lsa; intuition; simpl in *.
destruct lsb;
simpl in *.
discriminate.
f_equal.
eapply IHlsa.
omega.
Qed.
Definition numberedMap(A B : Set)(f : nat -> nat -> A -> B)(ls : list A) :=
map (fun p => [i, a] <-2 p; f i (length ls) a) (zip (allNatsLt (length ls)) ls).

Lemma numberedMap_length :
forall (A B : Set)(ls : list A)(f : nat -> nat -> A -> B),
length (numberedMap f ls) = length ls.