Proof using.
intros m.
induction ns; intros; simpl in *; [ intuition | idtac ].
break_if; simpl in *.
- break_or_hyp.
* find_injection; auto.
* find_apply_hyp_hyp.
break_and.
auto.
- find_apply_hyp_hyp.
break_and.
auto.
Qed.

Lemma collate_ls_not_in :
forall ns (f : A -> A -> list B) h mg from to,
~ In from ns ->
collate_ls A_eq_dec ns f h mg from to = f from to.