The Institute for the Study of War (former Chief of Staff of the Army’s organization) has weighed in on the Iraqi Government reports of victory in Fallujah. (http://understandingwar.org/backgrounder/fallujah-control-terrain-map-june-17-2016 )
Their take is that the town hall has been captured and rapid advances were made, but lots of areas remain to be cleared on the North side of the main highway through town.
Worse in their analysis, Shi’ite militias, mainly the Badr Brigades, have now entered the city in force. This is likely to lead to an enduring sectarian political problem going forward for Iraq, and for the Mosul Operation.
In the past (Tikrit, for example), the Government has declared victory early, fighting continued for weeks, militias entered after the military (despite prior agreement not to), conducted systematic looting, abuses and destruction; and were left to occupy the area while the regular military moved on toward the next objective.