Proof using.
induction xs; intros.
- auto.
- eauto using ZOOOPST_cons_intro, ZOOOPST_head, ZOOOPST_tail.
Qed.

Lemma ZOOOPST_singleton_nil :
forall A B C h,
@zero_or_one_outputs_per_step_trace A B C [(h, inr [])].