There is an exercise in "Introduction to computer theory" by Daniel IA Cohen (ch. 4, ex. 20) the main part of which goes like:
Explain why we can take any pair of equivalent regular expressions and replace the letter $a$ in both with any regular expression $\mathbf R$ and the letter $b$ with any regular expression $\mathbf S$ and the resulting regular expressions will have the same language.
This book is oriented on a reader unaccostumed to a rigor mathematical language and throughout all the book the author stresses that any kind of a formal notation is of a secondary importance to the ideas that it conveys, thus I think that an informal argument is expected here.
Question 1 What kind of argument should it be? How such a question can be approached?
I find it super difficult to understand because it's not only about a transformation of a particular regular expression, but about the validity of a statement about their generated languages. So I come up with something like "assume we have regular expressions $\mathbf R_1$ and $\mathbf R_2$ which generate the same langauge. A letter $a$ in $\mathbf R_1$ can be met in one of the following subexpressions: $a$, $(a)$, $a \mathbf r$, $a + \mathbf r$, $a^*$..." and it represents a letter $a$ or a string of $a$'s (for $a^*$) in a generated string. And then I just stumble as it seems that I should assume too much to go on: "every string that is generated by $\mathbf R_1$ should also be generated by $\mathbf R_2$ so there should be a part in $\mathbf R_2$ which corresponds to either $a$, or a concatenation of several $a$'s and if we just replace both of this occurences with a regular expression $\mathbf R$ then it will be correspond to one of the words from the language generated by $\mathbf R$ and it will match its said counterpart in $\mathbf R_2$.
Is it an acceptable kind of answer in the informal context and if not, what is the better or an improved version?
Question 2 Where can I find a more strict approach to it?
I can imagine two ways of doing it, first (as the chapter is about finite-state automata) we might prove some kind of correspondence between regular expressions and finite-state automata and the property in question will follow from it. Second, it seems that I have an urge of talking formally in an informal setting, so similar properties should be studied in logic courses in the context of e.g. formal language of Propositional Logic, and I should study a book like Enderton or Mendelson.