Proof using.
red. unfold ghost_log_correct. intros. simpl in *.
find_apply_hyp_hyp; intuition; eauto.
Qed.

Lemma doLeader_replicaMessage :
forall h st os st' ms m,
doLeader st h = (os, st', ms) ->
In m ms ->
type st = Leader /\
exists h',
m = replicaMessage st' h h'.