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I'm currently writing my (math) thesis. Some properties of the objects I'm studying are used often and are relatively elementary. So, I would like to state them once and then avoiding referring to them each time I need as I believe it would disrupt the reading. So, I have the following sentences at some point:

We recall useful properties of A and B. In order to keep a smooth reading, we use these properties in most of the proofs below without explicitly referring to them.

The bold part feels like bad english to me, so I'm wondering what would be a better formulation for it.

closed as primarily opinion-based by Mitch, Jason Bassford, user240918, JEL, Robusto Sep 7 '18 at 1:58

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    A "better" approach might be to change your opinion. Google Books claims thousands of written instances of a smooth reading, and I see nothing wrong with your cited text. But if you really don't like it, just switch to something like for [the sake of] clarity [and simplicity]. – FumbleFingers Sep 4 '18 at 13:36
  • @FumbleFingers Ok, then I'll keep it as is unless something much better appears as an answer. I thought about "for the sake of clarity/simplicity" but, unless the meaning of "clarity" isn't clear to me, I'm not sure this is the intended purpose. Regarding, simplicity, I believe that "for the sake of simplicity" has a different meaning in maths (basically you make more assumptions to have less technical problems). Anyway, thanks for your comment. – Surb Sep 4 '18 at 13:40
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    Have you thought of asking over at some math.SE, where they might have a better handle on what the usual English wording or even conventions are for this? – Mitch Sep 4 '18 at 13:42
  • @Mitch I haven't and this is a good point. If it is ok for this community, I will first leave this post as is and if nothing comes out of it, I'll reask in math.SE. – Surb Sep 4 '18 at 13:44
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    Why bother with the phrase at all? I would simply write "We will use these properties in most of the proofs below without explicitly referring to them." – Derek Sep 4 '18 at 14:22