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

Lemma pt_PhaseTwoRespondedE_consume d e dt lg b pt ds i this:
let: d' :=   {|
dstate := upd this ds (dstate d);
dsoup := consume_msg (dsoup d) i
|} in
coh d -> pt \in pts -> pt != this ->
pt_PhaseTwoResponded d e dt lg b pt ->
pt_PhaseTwoResponded d' e dt lg b pt.