Example 6.4.2 contains the following equation:

\mu~R[\![a]\!]\sigma = \mu~(\mu~R[\![a]\!]\sigma)

but this is not correct according to the expression rules. It should be this:

\mu~R[\![a]\!]\sigma = \mu~(\mu~L[\![a]\!]\sigma)

Because R[\![a]\!]\sigma = \mu~L[\![a]\!]\sigma according to Definition 6.3.2.