I am currently applying for a PhD position in mathematics and during the corresponding interview, I am supposed to give a short 10 minutes talk about my research proposal. In my particular case, my proposal basically aims at generalizing a (very) recently published result from a mathematician of the department I am applying to (who I would like to have as a supervisor). More precisely, my proposal aims at trying to prove the same statement by weakening the requirements, which, however, requires new tools from the beginning.
Since 10 minutes are rather short, I have the following question(s):
As far as I know, a talk given in a PhD interview should usually aim at explaining the things on a rather basic level, so that also non-experts of the field can follow the basic ideas (am I right?). So, since 10 minutes are rather short, I will have to explain some of the basics first. Afterwards, I should probably explain the recent work, since in the end my proposal aims at generalizing this paper. However, all of this is already quite dense, so I won't have to much time to explain my actual proposal, i.e. the steps I have planned to prove the stronger statement.
So, is it fine when most of the presentation is on more basic things, aiming at explaining the basics, the current literature as well as the paper on which my work will be based, or should I shorten this part and work out more the steps I planned in order to achieve my objectives (which is rather hard, as I only have a vague plan, since the precise steps will come when actually working on the project as a PhD student)?
EDIT: This question is not duplicate to PhD interview - short (!) presentation. My question is about a presentation for a proposal, whereas the linked question is about a presentation on an already completed research project. These are two totally different things. In the latter case one can obviously talk about obtained results, which is not possible when presenting a proposal.