Writing preliminary results in research papers Suppose we want to put $10$ basic results in the preliminary section of a mathematical researh paper, without proof, but only with reference. It could be done in following way:

Theorem 1: If $G$ is finite group, and $H\leq G$ then $|H|$ divides $|G|$. 
Proof: See [1, Theorem 2].
Theorem 2: A group of prime order is cyclic.
Proof: See [1, Corollary 3].
.....

Instead of writing it in this way, can we cite for proof before starting statement of theorem, like 

Theorem 1: [1, Theorem 2] If $G$ is finite group, and $H\leq G$ then $|H|$ divides $|G|$.
Theorem 2: [1, Corollary 3]. A group of prime order is cyclic.

Of course, it is quite understandable, from second way of expression; but my question is that whether this is appropriate in writing the research papers?
I want to put the basic results in the paper since they make the paper self contained to some extent; but writing in second way saves some space, and makes paper handy, quickly readable in first glance for experts at least. Just citing a result without mentioning its statement in preliminary may make the paper uninteresting to follow easily for young research scholars. 
Suggestions please! Thanks for the patience!
 A: I would usually quote without a proof environment and either a reference at the start of the theorem, or with a small comment above to the effect of "the following is standard, see [1, Theorem 10]", or something like this. (I generally prefer the latter, as starting a theorem with "Theorem 1:[1, Theorem 10]" can take up quite a lot of theorem statement space.
One should only include results of standard results if they are some way instructive or useful for your paper, otherwise they only serve to make the paper unnecessarily long. I would steer clear of including really elementary results, or well-known theorems from the subject area of the paper. However, you may wish to include some basic theorems from a different area. So, for example, a paper on group theory which uses some elementary results from complex analysis may wish to include those results; the audience might not be familiar with standard results of complex analysis. 
My suggestion is that you include a section of your introduction called "standard results" or similar which contains all of these results. Then you can begin the section with the following: "This section contains standard results which will be used throughout and can be found in various textbooks on the subject; see, for example, [1,2,3]."
