Corollary add_events_snd : forall h le h', add_events h le h' -> map snd h' = map snd h ++ le.Corollary add_events_incl : forall h le h', add_events h le h' -> incl h h'.Corollary add_events_newer : forall h le h' t, add_events h le h' -> newer h' t -> newer h t.

(* Specifications: *)
Lemma add_events_in : forall h le h' e, add_events h le h' -> In e le -> exists t, newer h t /\ In (t, e) h'.
Lemma add_events_ordered : forall h le h', add_events h le h' -> ordered_hist h -> ordered_hist h'.
Lemma add_events_NoDup : forall h le h', add_events h le h' -> NoDup (map fst h) -> NoDup (map fst h').
Lemma add_events_in : forall h le h' e, add_events h le h' -> In e le -> exists t, newer h t /\ In (t, e) h'.
Lemma add_events_ordered : forall h le h', add_events h le h' -> ordered_hist h -> ordered_hist h'.
Lemma add_events_NoDup : forall h le h', add_events h le h' -> NoDup (map fst h) -> NoDup (map fst h').