Proof using.
induction ns0; intros; simpl in *.
- break_if; auto.
find_apply_lem_hyp irreflexive_R.
intuition.
- break_if; auto.
find_higher_order_rewrite.
trivial.
Qed.

Lemma collate_f_eq :
forall (f : A -> A -> list B) g h n n' l,
f n n' = g n n' ->
collate A_eq_dec h f l n n' = collate A_eq_dec h g l n n'.