Proof using.
intros.
induction log; simpl in *; intuition.
- subst. break_exists.
repeat break_match; intuition.
simpl in *.
subst. congruence.
- repeat break_match; in_crush.
Qed.

Theorem In_get_output' :
forall l client id o,
In (ClientResponse client id o) l ->
exists o', get_output' l (client, id) = Some o'.