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The phrase "a proof of the negative" is correct and usable in written English.
It can be used in contexts discussing logical arguments, scientific hypotheses, or philosophical discussions where one is trying to demonstrate that something is not true.
Example: "In the debate over climate change, some argue that a proof of the negative is necessary to disprove the skeptics' claims."
Alternatives: "evidence against" or "refutation of the claim".
Exact(1)
The proof of Russell's Paradox can then be deprived of its sting: it simply becomes a proof of the negative existential ¬∃x x = {y | y ∉ y}.
Similar(59)
Moreover, as a further proof of the negative regulation exerted by PI3K/AKT on miR-29b expression, inhibition of PI3K by LY294002 increased miR-29b and reduced Sp1 protein levels.
Within such judgements the term t represents a proof of the proposition A. A proof in the latter sense is also called a proof object.
as "x is a proof of the proposition T".
Prior 1956 contains a proof of the Barcan formula.
A proof of the disjunction \ \bA \vee \bB\) is either a proof of \ \bA\) or a proof of \ \bB\) together with the information as to which of \ \bA\) or \ \bB\) it is a proof.
Midwives said the findings were only the latest proof of the "negative implications" of caesareans, and urged women who did not need the procedure for medical reasons, not to take the decision to have one lightly.
Although researchers mainly find proofs of the negative effects of accelerating aging on the economy and on social structures, some demographers call for a calmer evaluation of the consequences of aging (Lloyd-Sherlock et al. 2012; Van Dalen and Henkens 2011; Vaupel and Loichinger 2006).
Obtain a proof of completion of the DMV traffic school.
However, the current work represents a proof-of-concept study.
As a proof of concept, we implemented the above algorithms.
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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