intuition.
unfold numberedMap.
rewrite map_length.
repeat rewrite zip_length.
apply allNatsLt_length.
apply allNatsLt_length.
Qed.

Lemma nth_zip :
forall (A B : Set)(lsa : list A)(lsb : list B) n a b defa defb,
length lsa = length lsb ->
nth n (zip lsa lsb) (defa, defb) = (a, b) ->
nth n lsa defa = a /\ nth n lsb defb = b.