A Renormalizable 4-Dimensional Tensor Field Theory (vol 1, pg 69, 2013)

This note fills a gap in the article (Ben Geloun and Rivasseau, Commun Math Phys 318:69-109, 2013). We provide the proof of Eq. (82) of Lemma 5 in Ben Geloun and Rivasseau (Commun Math Phys 318:69-109, 2013) and thereby complete its power-counting analysis with a more precise next-to-leading-order estimate.