Proof using.
unfold entries_match, entries_match'.
intros. intuition.
- eapply H; eauto.
- eapply (H e' e); eauto with *.
Qed.
Definition contiguous
(prevLogIndex : logIndex)
(prevLogTerm : term)
(leaderLog entries : list entry) : Prop :=
(prevLogIndex = 0 \/
exists e, findAtIndex leaderLog prevLogIndex = Some e /\
eTerm e = prevLogTerm) /\
(forall e,
In e leaderLog ->
eIndex e > prevLogIndex ->
eIndex e <= maxIndex entries ->
In e entries) /\
forall e e',
eIndex e = eIndex e' ->
eTerm e = eTerm e' ->
In e entries ->
In e' leaderLog ->
e = e'.

Lemma entries_match_refl :
forall l,
entries_match l l.