I am looking for a reader-friendly proof of the following theorem:


let $A$ be a special $\Gamma$-space then $\pi\_0(A(S^0))$ is a commutative monoid (I have proved up to this), if further it is an abelian group then the adjoint map $t: A(S^0) \to \Omega{BA(S^0)}$ for the structure map $s: \Sigma(A(S^0)) \to BA(S^0)$ is a weak homotopy equivalence


Dan Freed in his [notes](https://www.ma.utexas.edu/users/dafr/M392C-2012/Notes/lecture19.pdf) theorem 19.41 points to Segal's [paper](http://web.math.rochester.edu/people/faculty/doug/otherpapers/segal-csss.pdf) as reference but I cannot find a proof there (did I miss it?).



Adjoint map of $\Gamma$-space prespectrum
It is proposition 1.4 in Segal's [*Categories and cohomology theories*](http://www.sciencedirect.com/science/article/pii/0040938374900226) (a paper I love and I strongly encourage everyone interested in homotopy theory to read).


