Ltac use_entries_match :=
    match goal with
      | [ _ : eIndex ?e1 = eIndex ?e2,
              H : context [entries_match]
                              |- _ ] =>
        first [ solve [eapply H with (e:=e2)(e':=e1); eauto; congruence] |
                solve [eapply H with (e:=e1)(e':=e2); eauto; congruence]]
    end.

Lemma doLeader_appliedEntries : forall sigma h os st' ms, doLeader (sigma h) h = (os, st', ms) -> applied_entries (update name_eq_dec sigma h st') = applied_entries sigma.