induction lsa; intuition; simpl in *.
intuition.
destruct lsb.
simpl in *.
intuition.
inversion H; clear H; subst.
simpl in *.
intuition.
repeat pairInv.
trivial.
pairInv.
eapply in_combine_r in H0.
intuition.
pairInv.
eapply in_combine_r in H.
intuition.
eauto.
Qed.

Theorem In_combine_NoDup_eq_r :
forall (A B : Set)(lsa : list A)(lsb : list B) a b1 b2,
NoDup lsa ->
In (a, b1) (combine lsa lsb) ->
In (a, b2) (combine lsa lsb) ->
b1 = b2.