Proof using.
induction log; intros; simpl in *; intuition.
repeat break_match; subst; simpl in *; intuition; try congruence; try find_inversion; simpl.
- eexists. eexists. intuition; eauto.
- find_apply_hyp_hyp. break_exists_exists. intuition.
- find_apply_hyp_hyp. break_exists_exists. intuition.
Qed.

Lemma get_output'_In :
forall l k out,
get_output' l k = Some out ->
In (ClientResponse (fst k) (snd k) out) l.