Proof using.
intros. unfold deghost in *. simpl.
repeat break_match; subst; simpl.
repeat find_rewrite. reflexivity.
Qed.

Lemma lt_committed_committed :
forall net e e' t h,
log_matching (deghost net) ->
committed net e t ->
eIndex e' <= eIndex e ->
In e (log (snd (nwState net h))) ->
In e' (log (snd (nwState net h))) ->
committed net e' t.