Proof using.
unfold candidateEntriesTerm.
intros. break_exists_exists.
repeat find_higher_order_rewrite. intuition.
Qed.

Lemma candidateEntriesTerm_same : forall st st' t,
candidateEntriesTerm t st ->
(forall h, cronies (fst (st' h)) = cronies (fst (st h))) ->
(forall h, currentTerm (snd (st' h)) = currentTerm (snd (st h))) ->
(forall h, type (snd (st' h)) = type (snd (st h))) ->
candidateEntriesTerm t st'.