Definition E_consume_external d i this tag m from P :=
let: d' := {| dstate := upd this (loc this d) (dstate d);
dsoup := consume_msg (dsoup d) i |} in
coh d ->
find i (dsoup d) =
Some {| content := {| tag := tag; tms_cont := m |};
from := from;
to := this;
active := true |} ->
~~ internal_msg tag from this ->
P d ->
P d'.

Lemma PhaseOne_msg_next_data d (C : coh d) i m pt round next_data lg  :
find i (dsoup d) =
Some {| content := {| tag := prep_req; tms_cont := m |};
from := cn;
to := pt;
active := true |} ->
internal_msg prep_req cn pt ->
PhaseOne d round next_data lg ->
behead m == next_data.