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 rp_step_external d (C : coh d) this (Hthis : this \in nodes cn pts others) tag from m i :
~~ internal_msg tag from this ->
find i (dsoup d) =
Some {| content := {| tag := tag; tms_cont := m |};
from := from;
to := this;
active := true |} ->
rp_step Hnin tag from m C Hthis = loc this d.