(** *SyncStep simulation*)
(** Proof of the step diagram when the step is a synchronization step. TODO: Split the proof in each diagram. *)
Inductive deltaMap_cases (dmap:delta_map) b ofs:=
| DMAPS df p:  dmap ! b = Some df -> df ofs = Some p -> deltaMap_cases dmap b ofs
| DNONE1 df:  dmap ! b = Some df -> df ofs = None -> deltaMap_cases dmap b ofs
| DNONE2:  dmap ! b = None -> deltaMap_cases dmap b ofs.

Lemma permMapsDisjoint2_empty: forall rmap,
permMapsDisjoint2 (empty_map, empty_map) rmap.