Proof using.
induction l; intros; simpl in *.
- find_inversion. auto.
- repeat break_let.
rewrite app_ass.
eauto.
Qed.

Lemma execute_log'_trace_nil:
forall l d d' tr' tr'',
execute_log' l d [] = (tr', d') ->
execute_log' l d tr'' = (tr'' ++ tr', d').