I'm looking for a reference for analogues of the Blakers-Massey triad connectivity theorem (and its higher-order generalization) for ring spectra. That is:


Suppose that $A\to A\_1$ is a $k\_1$-connected map of (associative) ring spectra and $A\to A\_2$ is a $k\_2$-connected map of ring spectra, and that the maps are cofibrations so that the pushout, call it $A\_{12}$, is a homotopy pushout. Then as long as all of the rings are connective the map of spectra 
$$
A\to holim (A\_1\to A\_{12}\leftarrow A\_2)
$$
is $(k\_1+k\_2)$-connected.


Has anyone worked out a detailed proof of this? I would be happy to see this in any reasonable theory of structured ring spectra.


EDIT: I know how a proof should go: Filter the spectrum $A\_{12}$ by "word length" and examine the sequence of subquotients (the "associated graded object"), which are wedges of "tensor products" of the spectra $A\_i/A$ regarded as bimodules over $A$. But I do not want to delve into technicalities if the details are already out there somewhere.



Homotopy excision for structured ring spectra -- reference?
Theorems 1.4–1.11 in Ching and Harper's paper “Higher homotopy excision and Blakers-Massey theorems for structured ring spectra” ([arXiv:1402.4775](http://arxiv.org/abs/1402.4775))
give higher homotopy excision and Blakers-Massey (and their dual versions) for structured ring spectra and more generally, for algebras over operads.


