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

Lemma trace_I_in_import :
forall tr k h i,
In (h, inl (ClientRequest (fst k) (snd k) i)) tr ->
In (I k) (import tr).