I came across a sentence that began:
Con esto queda demostrado que . . .
My question is, could one also say
Esto demuestra que . . .
If both are correct (which I suspect they are) then which one would native speakers usually use? In English most people would normally just say This demonstrates that . . . as opposed to With this it is demonstrated that . . . Is that also the case with native Spanish speakers, in general?
Both structures are correct, but they do not mean exactly the same thing.
Quedar demostrado works as a form of the passive voice. As you probably know, the so-called periphrastic passive voice in Spanish works very much as in English, using the verb ser plus the participle, so «Es demostrado» means "It is demonstrated" (or "It is shown"). This other structure uses quedar instead of ser (plus participle).
Quedar + participle emphasizes the fact that the patient of the action (the thing being done something to; in the example, the thing being demonstrated) has already been affected by the action and has stayed changed or affected in some way.
In Spanish you do not really say
Con esto es demostrado que...
Although the above is gramatically correct, it is not commonly done. You would say, as in the example:
Con esto queda demostrado que...
which means that (whatever) is or has been "left in a state of being already demonstrated".
Quedar + participle is used in many places where English would use the common passive voice with to be + participle. It's also used where English would use the equivalent verb to remain or to stay, for example:
Note that I have translated Queda demostrado as either "It is demonstrated" or "It has been demonstrated". This is because this structure emphasizes that the process, if there was one, is complete. This is also why I've added "left" or "stood there" where appropriate.
This is from a translator's point of view. My mother tongue is English. That said, I have an analysis about this that might be useful to you.
Emphasis cannot be shown in Spanish using helping verbs as in English. Therefore, in Spanish one resorts to other techniques in keeping with the language.
For example, for "This did demonstrate that [etc.]", you have to add something like "Sí, lo demuestra" or change the sentence around, with the "con esto" at the beginning.
In English, one might say example: This does demonstrate that [another clause], which could be rendered: Con esto queda demostrado que [another clause]. It emphasizes the result of what is being demonstrated.
If, on the other hand, the process is what is being emphasized, the straightforward "Esto demuestra que (another clause), which in English is "This demonstrates that (another clause), would work.
In any event, I would not translate "Con esto queda demonstrado que [x]" as "With this, it is demonstrated that [x]." In some limited cases, and in addition to what I gave above, it might also be translated it as: "That [he was guilty] is demonstrated by this." That also emphasizes the result.
On the surface, these things are somewhat difficult to grasp until one has made one's own ("interiorized") certain patterns in Spanish that would not ordinarily be studied in a normal language course. It would have to be a course on speech stylistics or translation of spoken language (as one sees in interpreting).
If I say "He did it, I tell you, he **did do it.", what might happen in the translation is this:
"Lo hizo, te digo yo que sí lo hizo." And there might even be this: "Lo hizo, te lo digo que sí lo hizo él".
In that example, the "did do it" can become "sí lo hizo".
