Where can I find a proof that a $C^*$-algebra is nuclear iff it has completely positive approximation property?

Question

Def1. A $C^*$-algebra is said to be nuclear, if for every $C^*$-algebra $B$, the $C^*$-norm on $A\otimes B$ is unique.

Def2. $A$ $C^*$-algebra is said to have completely positive approximation property, if there exists a net of finite dimensional $C^*$-algebras $F_\lambda$, with contractive completely positive linear maps $\varphi_\lambda:A\to F_\lambda$ and $\psi_\lambda:F_\lambda\to A$, such that

$$ (\psi_\lambda\circ \varphi_\lambda)(a)\to a $$

holds pointwisely.

The only reference I can find is Christopher Lance's On Nuclear $C^*$-Algebra , where he showed type $I$ $C^*$-algebras and their inductive limits have completely positive approximation property. Where can I find a proof for the general case?

Answer 1

An excellent reference with (relatively) detailed proofs is:

Nathanial P. Brown and Narutaka Ozawa. $C^∗$ -algebras and finite-dimensional approximations. Vol. 88. Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2008, pp. xvi+509.

In particular, have a look at theorem 3.8.7.