induction lsc; destruct ls; intuition; simpl in *.
omega.
f_equal.
eauto.
Qed.

Theorem map_snd_eq :
forall (C : Set)(lsc : list C)(A B : Set)(ls : list A)(f : A -> B),
(length ls = length lsc) ->
map f ls =
map (fun x => f (snd x)) (combine lsc ls).