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The phrase "a systematic proof of this" is correct and usable in written English.
It can be used when referring to a structured and methodical demonstration or verification of a statement or theory.
Example: "In order to validate our hypothesis, we need to provide a systematic proof of this claim."
Alternatives: "a methodical demonstration of this" or "a structured verification of this".
Exact(1)
A systematic proof of this statement goes beyond the scope of this paper and is left for further work.
Similar(59)
Holmstrom (1982) offers a systematic proof in terms of the free rider problem which generalises to moral hazard in a multi-agent setting.
So we will not find systematic "proofs" of God's existence in the Zohar or anywhere else.
We give a simple proof of this conjecture.
A quick proof of this concerns ordinals.
Uncharacteristically, Fermat provided a proof of this last result.
The present communication is a proof of this concept.
(For completeness, a proof of this result is also given).
For example, a proof that \(∀ x, P x)\) often starts with "choose an arbitrary \(x\)." See the fa15 notes for a systematic list of proof structures.
We now present a systematic way of doing this.
We provide an alternative self-contained proof of this fact.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com