A proof of the generalized geometric boundary theorem using filtered spectra

In [Beh12, Lem. A.4.1], Behrens generalized the classical geometric boundary theorem [Rav86, Thm. 2.3.4]. In this article, we will reformulate [Beh12, Lem. A.4.1] to fix a mistake made by Behrens, and prove it using the language of filtered spectra.