Definition isVAL (r : resource) :=
match r with
| YES _ _ (VAL _) _ => Logic.True
| _ => False
end.

Lemma join_pures_same phi1 phi2 phi3 :
join phi1 phi2 phi3 ->
pures_same phi1 phi2 /\ pures_same phi2 phi3 /\ pures_same phi1 phi3.