A proarrow equipment on a virtual double category or virtual equipment for short is a virtual double category equipped with the same kind of structure that makes an ordinary double category into a proarrow equipment.
Virtual equipments are the structures that support structures of generalized multicategories.
A virtual equipment is a virtual double category in which all units and all restrictions exist.
This is (CruttwellShulman, def. 7.6).
Section 7 of