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

Lemma pt_PhaseTwoRespondedE' d r nd lg pt from h to m b :
let: d' := {| dstate := upd from h (dstate d);
dsoup := (post_msg (dsoup d)
{| content := m; from := from; to := to; active := true |}).1 |} in
coh d ->
from != pt ->
from != cn ->
pt_PhaseTwoResponded d r nd lg b pt ->
pt_PhaseTwoResponded d' r nd lg b pt.