[jonsterling]

Hmm, I think you should aim for sentences to be correct on their own and be arranged such that understanding & precision is built incrementally (in the way you suggest). This is harder, but that's what good writing does---I want my "simplified" parts to be real approximations of the precise parts; we mustn't settle for the simplifications failing to approximate the precise versions.

It may be easy for experts to avoid getting confused by a literally false claim, which is clarified in the next paragraph. But your paper will often be read by people who are not experts in the paper's topic, so some will end up being confused by this.

It's stressful for me to read that kind of paper, since it causes a lot of cognitive dissonance as you read! Maybe it's not like that for everyone, but I prefer to read papers that don't use the approach you appear to suggest.

[kartickv]

I agree with you that simplifications should approximate the precise versions. Mine did approximate them. Note that approximate means "not perfectly agreeing with". But my advisor wanted them to agree perfectly, at which point they are no longer approximations.