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

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.