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I'm writing a text in which I'd like to explain a concept. In order to explain that, I must explain another concept first which is necessary to understand the first one.

After explaining this other concept first, I'd like to say something like "Now that we've clarified this, we can talk about ...". I'm looking for an expression for the first half of this sentence. I know expressions like

"With that out of the way, ..."

or

"Now that we've agreed on this, ..."

or

"Now that we've settled that, ..."

The point I'd like to get across is that now that we have a common understanding of how the first thing works, we can move on and discuss X.

The examples I gave are a little harsh to me, but maybe okay. I'm just wondering if there are more options here.

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Building upon this, the resting state of an electron requires at least one glass of red wine.

https://idioms.thefreedictionary.com/build+upon

If you are concerned about the reader's state of mind, it is often a good idea to work in positive or constructive words. This helps to subconsciously build up their confidence in what you're saying.

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"Now that we're all on the same page (regarding x), ..." is a phrase I would use to indicate that everyone has the same understanding. It does have the connotation that everyone is also in agreement, however.

  • just to comment "now that we are all on the same page" is a phrase that is the butt of jokes in the UK, by people of a certain age I can not comment on youngsters – WendyG Oct 15 '18 at 14:39
  • I think any phrase intended to indicate everyone has the same understanding can be used sarcastically to mean the opposite – xploshun Oct 15 '18 at 16:16
  • it is more taking the piss out of the kind of people who say it. – WendyG Oct 16 '18 at 8:46
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Now we have covered...

Now we have covered the entire training guide, does anyone have anything to say on what we have learnt so far?’

https://onlineteachersuk.com/say-tell-speak-talk/

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Proceeding

(as in proceeding on... or proceeding to...)

Proceeding

verb
* begin or continue a course of action.
* move forward, especially after reaching a certain point.
* do something as a natural or seemingly inevitable next step.

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