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The phrase "additional proof of the" is correct and usable in written English.
You can use it when referring to extra evidence or documentation that supports a claim or argument.
Example: "The researcher provided additional proof of the theory through various experiments and data analysis."
Alternatives: "further evidence of the" or "supplementary proof of the".
Exact(18)
Mr. McCain has portrayed the fight over the gambling ban as additional proof of the need to restrain the influence of money in politics.
The office of Prime Minister Benjamin Netanyahu reported Friday that during a meeting with Representative Mike Rogers, a Michigan Republican who heads the intelligence committee, Mr. Netanyahu said, "Just yesterday, we received additional proof of the fact that Iran is continuing to make accelerated progress toward achieving nuclear weapons while totally ignoring international demands".
For slightly older children who have already mastered their poses but might need additional proof of the importance of peace, "Kali's Song," the story of a boy who isn't meant to kill animals like the rest of his prehistoric tribe, offers a beautiful parable about the healing power of nature.
The analysis of the carbon and 2D correlation spectra were additional proof of the formation of compound 10.
The decrease in BET surface area, pore volume and diameters gives additional proof of the grafting of the fluorescent chromophore onto the surface of the inner channel.
An additional proof of the polymer-related oxygen contribution to the LK1 signal is the absence of this signal in the ODMR spectra of nanocomposites consisting of CdS NPs in the matrix which does not contain oxygen other than unintended impurity (to be published later).
Similar(42)
An additional proof of this fact is the presence of intensity oscillations in the X-ray scattering.
Additional proof of this can be found at the Denver Public Library, which recently had to quarantine and fumigate four areas at its main branch because of the critters.
Although good technical progress has been made in recent years, additional proof-of-principle studies are needed for the regulatory community to become more accepting of the use of toxicogenomics data as part of the regulatory decision-making process.
As an additional proof of concept, the reaction with thioredoxins (Tdx) h1 and h2 yielded two affinity chromatographic supports with different specificity in the capturing of proteins targets in vitro: Tdx h1 captured a transcription factor whereas Tdx h2 interacted with classical antioxidant proteins [ 41].
Thus, our research is an additional proof of concept of the Co-Training algorithm in employing unlabeled data.
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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