Hint Resolve add_events_nil.

(* Specifications: *)
Lemma add_events_1 : forall h t e (Ht : newer h t), add_events h [e] (map_upd h t e).
Lemma add_events_trans : forall h le h' le' h'' (H1 : add_events h le h') (H2 : add_events h' le' h''),
add_events h (le ++ le') h''.
Lemma add_events_add : forall h le h', add_events h le h' ->
exists h2, h' = map_add h h2 /\ forall t e, h2 t = Some e -> newer h t /\ In e le.
Corollary add_events_dom : forall h le h' t e, add_events h le h' -> h' t = Some e ->
h t = Some e \/ In e le.
Corollary add_events_incl : forall h le h', add_events h le h' -> map_incl h h'.
Corollary add_events_newer : forall h le h' t, add_events h le h' -> newer h' t -> newer h t.
Lemma add_events_in : forall h le h' e, add_events h le h' -> In e le ->
exists t, newer h t /\ h' t = Some e.