Interesting tips, but it also depends on the field.
If you're submitting to a control theory journal, you better have some novel theorems with rigorous mathematical proofs in that "rest of the paper" part. That's a little nontrivial.
Sure, but if you can't articulate why those theorems and proofs are important to be pursued, how it's different from all the related works, what your unique contribution is and why that matters, what the previous works lacked or got wrong, what the impact and value of your work is, i.e. why anyone should care at all, then you'll have a hard time getting it accepted. Just because the math checks out and was difficult and took a lot of effort, it doesn't guarantee that the work is worthy of dissemination.
If you're submitting to a control theory journal, you better have some novel theorems with rigorous mathematical proofs in that "rest of the paper" part. That's a little nontrivial.