(***********************************************************)
(* Lemmas about specific sub-predicates *)

Lemma pt_PhaseOneE_consume d e dt lg pt ds i from to m:
let d' :=   {|
dstate := upd to ds (dstate d);
dsoup := consume_msg (dsoup d) i
|} in
coh d -> pt \in pts ->
pt != from ->
pt != to ->
find i (dsoup d) =
Some {| content := m; from := from; to := to; active := true |} ->
pt_PhaseOne d e dt lg pt ->
pt_PhaseOne d' e dt lg pt.