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

(* Specifications: *)
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).
Theorem In_combine_NoDup_eq_l :
forall (A B : Set)(lsa : list A)(lsb : list B) a1 a2 b,
NoDup lsb ->
In (a1, b) (combine lsa lsb) ->
In (a2, b) (combine lsa lsb) ->
a1 = a2.