I was reading this paper by Bousfield on the localization of spectra. On page 5, Lemma 1.13, there's a rather small curious technical detail on wedge sum. We have for a limit ordinal $\lambda,B_{\lambda}=\bigcup_{\sigma<\lambda}B_{\sigma}$ where $0 =B_{0} \subset B_{1} \subset B_{2} \subset \cdots $. It says that there is a cofiber sequence:
$\bigvee_{s < \lambda} B_{s} \stackrel{1-i}\to \bigvee_{s<\lambda}B_{s} \to B_{\lambda}$
where $i$ is the wedge of the inclusions $B_{s} \hookrightarrow B_{s+1}$. How exactly is this a cofiber sequence. I get the rough idea that one is trying to collapse things in the wedge sum to get the union but I'm not sure how a formal proof would work. I hope someone can help me out with this.