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

Lemma PhaseTwo_PCommitted_pt d pt round lg next_data r nd (C : coh d)
(Hpt : pt \in nodes _ _ _) :
pt \in pts ->
getStP Hnin C Hpt = (r, PCommitted nd) ->
PhaseTwo d round next_data lg ->
[/\ pt_state d (round, PCommitted next_data) (rcons lg (true, next_data)) pt,
no_msg_from_to cn pt (dsoup d)
& no_msg_from_to pt cn (dsoup d)].