Proof using.
intuition eauto using ZOOOPST_head, ZOOOPST_tail.
Qed.

Lemma ZOOOPST_cons_intro :
forall A B C x y,
@zero_or_one_outputs_per_step A B C x ->
zero_or_one_outputs_per_step_trace y ->
zero_or_one_outputs_per_step_trace (x :: y).