Proof using.
induction log; intros.
- simpl. constructor.
- simpl. break_let.
rewrite fst_execute_log'.
rewrite snd_execute_log'.
unfold step_1_star in *.
econstructor.
+ constructor. eauto.
+ auto.
Qed.

(* Specifications: *)
Lemma execute_log_correct :
forall log,
step_1_star init (snd (execute_log log))
(fst (execute_log log)).