Imagine how poorly your idea would be communicated if you included definitions or explanations for every word longer than six letters. It would be hard to cut

Imagine how poorly your idea would be communicated if you included definitions or explanations for every word longer than six letters. It would be hard to cut through all the noise to get to the interesting part of your message. By assuming a particular level of background information (in this case, vocabulary), you're able to focus on the interesting and important insights. The same is true in math. You don't leave out random steps; you leave out steps that you expect your audience to have already mastered. You leave out steps where the working-out process doesn't contain anything particularly new or useful. Anything that comes down to "apply a bunch of lower-level math in a tedious way" doesn't belong in your paper. Re-creating it shouldn't be necessary for getting the basic idea. When this is done properly, the result is clear and concise communication.