I am considering how to choose between em dashes and double commas. The example I am considering is a sentence originally of the form
We will give another proof of a theorem in 'some' book, an assertion 'such' and 'such', using 'this' approach; the approach is 'such' and 'such'.
For me a sentence like this one is quite clear. But somehow a thought suggested that perhaps there are two many nonperiods in a sentence? Readability will be suppressed? Then I realized replacing the two commas with em dashes seem to preserve the same meaning and potentially improve the readability:
We will give another proof of a theorem in 'some' book -- an assertion 'such' and 'such' -- using 'this' approach -- the approach is 'such' and 'such'.
I am not sure. I would like to have a rule of thumb.