One of the important and difficult skills to learn in technical presentation is how to tell the same story at multiple levels of detail, from a single sentence to a multi-hour tutorial or long-form journal paper.
Moreover, any well-organized presentation (written or spoken) should typically present at multiple levels of resolution. As one of my grad school mentors used to say: "Tell them what you're going to tell them, then tell it to them, then tell them what you told them." This is not redundancy, but rather priming the reader to understand how the pieces fit together and summarizing to help them retain it.
In most good papers, I would thus expect to see the "main idea" presented either five or six times, at various levels of resolution:
- As a few words in the title, naming the most important "keyword" ideas.
- As a few sentences in the abstract, identifying a problem, giving an approach, and claiming evidence of progress.
- As one or two paragraphs in the introduction, sketching the key ideas and how the rest of the paper is organized.
- Optionally, as an overview section providing a sketch of the main sections and the grounding of the approach in prior work.
- In full detail in the main sections.
- In a few summarizing sentences in the final section, highlighting the most important things to remember from the main sections.
So how do you write at a "lower resolution"? I recommend thinking about the difference between what you are doing and how you are doing it. For example, the statement of a theorem is a "what" and the proof is a "how". In a lower resolution, however, the "what" can become a how, presented consistently but less formally. For example, that theorem may be one of several things that you prove as the "how" to get to the "what" of collectively proving a key result. One can then continue going to lower and lower resolutions. For example, all the work on proofs may be one "how" that combines with an implementation "how" and an experiment "how" to get to the "what" of demonstrating progress against the problem you are trying to address.
In short: remain consistent in your terminology, but drop as many levels of detail as you need to fit the space available for each telling of the main idea.