Proof using.
induction l1; intros; auto.
simpl.
break_let.
destruct a.
find_injection.
rewrite IHl1.
trivial.
Qed.

Lemma collate_neq_update2 :
forall h h' n (f : A -> A -> list B) l ms,
n <> h' ->
collate A_eq_dec h (update2 A_eq_dec f h n ms) l h h' = collate A_eq_dec h f l h h'.