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 p_matches_tag_internal_inv d i t m pt r ps lg :
coh d ->
pt \in pts ->
find i (dsoup d) =
Some {| content := {| tag := t; tms_cont := m |};
from := cn;
to := pt;
active := true |} ->
internal_msg t cn pt ->
pt_state d (r, ps) lg pt ->
Inv d ->
p_matches_tag ps t.