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

Lemma pt_PhaseTwoCommitE_consume d e dt lg pt ds from to i m:
let: d' :=   {|
dstate := upd to ds (dstate d);
dsoup := consume_msg (dsoup d) i
|} in
coh d ->
pt != from ->
pt != to ->
find i (dsoup d) =
Some {| content := m; from := from; to := to; active := true |} ->
pt_PhaseTwoCommit d e dt lg pt ->
pt_PhaseTwoCommit d' e dt lg pt.