TITLE: $\kappa$-support iterations of $<\kappa$-strategically closed forcing
QUESTION [5 upvotes]: Let $\kappa$ be an uncountable regular cardinal, and suppose that $\langle \mathbb{P}_\alpha,\dot{\mathbb{Q}}_\alpha:\alpha<\delta\rangle$ is a $\kappa$-support iteration of $<\kappa$-strategically closed notions of forcing, i.e.,
a) $\Vdash_{\mathbb{P}_\alpha}``\dot{\mathbb{Q}}_\alpha\text{ is $<\kappa$-strategically complete''}$, and
b) inverse limits are taken at every limit stage of cofinality $\leq\kappa$, and direct limits elsewhere.
It is well-known (even folklore) that the limit forcing $\mathbb{P}_\delta$ is also $<\kappa$-strategically closed (see, e.g., Proposition 7.9 of Cummings chapter in the Handbook of Set Theory).
Is there a place where a proof of this appears in the literature?
I am asking because I need to use that the obvious strategy has some additional properties, and if I can find an appropriate reference then I can avoid taking a rather technical detour in the middle of another proof.

REPLY [2 votes]: To finish this question off:
Proposition A.1.6 of the paper "Sheva-Sheva-Sheva: Large Creatures" by Roslanowski and Shelah gives the required proof and explicitly points out much of what I was looking for. The rest is obvious from what is there.
The paper appears in Israel Journal of Mathematics 159(2007), 109-174.
It is number 777 in Shelah's numbering of papers (hence the name!)