The company submits a plan for the table tops, FAA reviews the plan and if they find it acceptable it will be executed. The table tops are a simulation of the operation.
The proving runs are 99% a practical exercise of the table tops. The CPM (Certificate Project Manager) needs to put a check mark in a box to call it complete. During the proving runs FAA will simulate events that might take place during a normal flight.
Example: FAA Inspector gives the Captain a card that states "Number 3 Engine on Fire" The Captain needs to complete the event as per company guide lines, Check list, Emergency, diversion etc. These event can be anything from Engine fires to Hi-Jacking, passenger heart attack etc.
In the end everything is in the CPM hands, as long as he can put a checkmark in the box he is happy.
