(2) Any strings from L(G) must be of the form a + a + …. + a.
If the derivation has length 1, then it is of the form E => a, and so s is of the correct form.
Now, assume the truth of the hypothesis for all strings with derivations of length n – 1;
And let E =>* s be a derivation of length n > 1. This derivation must begin with the replacement of E by E + a, and so is of the form E => E + a =>* s' + a = s. Then, s' has a derivation of length n - 1, and so is of the form a + a + … + a. Hence, s itself must have this same form.