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".