On the type-definability of the binding group in simple theories

Let T be simple, work in C ^eq over a boundedly closed set. Let p ∈ S(φ)) be internal in a quasi-stably-embedded type-definable set Q (e.g., Q is definable or stably-embedded) and suppose (p, Q) is ACL-embedded in Q (see definitions below). Then Aut(p/Q) with its action on p ^c is type-definable in C ^eq over φ. In particular, if p ∈ S(φ) is internal in a stably-embedded type-definable set Q, and p ^c ∪ Q is stably-embedded, then Aut(p/Q) is type-definable with its action on p ^c.