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The phrase "adequate proof for" is correct and usable in written English.
It can be used when discussing the sufficiency of evidence or justification for a particular claim or argument.
Example: "The scientist provided adequate proof for her hypothesis, convincing the committee of its validity."
Alternatives: "sufficient evidence for" or "valid justification for".
Exact(2)
Simpson's blood at the scene, the bloody footprints (in Simpson's shoe size) leaving the scene, the blood on his Ford Bronco and on the glove found at his home (a matching pair with a glove found at the scene), plus Simpson's history of violence against Nicole were more than adequate proof for me.
This was regarded as adequate proof for the survival of the implanted nerve tissue.
Similar(58)
We believe this evidence provides adequate proof of principle for the use of DNA vaccines in channel catfish and the effectiveness of the resistance to viral infection they elicit.
However, most previous clinical trials have not demonstrated adequate proof of immunotherapy efficacy for advanced HCC., On the other hand, our clinical trial of glypican-3 GPC3 -derived glypican-3 GPC3 -derivedadvanced HCC demonstrated that the induction of peptide-specific cytotoxic T lymphocytes (CTLs) siglypican-3 GPC3 -derivedith peptide survaccine
A loss of confidence justified or not in the FAA's ability to require adequate proof of airworthiness from Boeing will be a critical hurdle for other regulators, airline customers and for the flying public.
There is no adequate proof of the truth of metaethics.
More recently, Curtis Franks takes up the issue of the second incompleteness theorem for weak arithmetic theories in his 2009, challenging Pudláak's argument that an intensionally adequate proof predicate can be given for Q.
Even if it is true that the restoration of the Republic was unreal, this is not of itself an adequate proof that Augustus meant it to be unreal or was entirely to blame for its unreality.
Despite not being able to give me adequate proof (because of "security purposes"), in GoDaddy's mind this meant I was liable for the $6,579.51 bill.
Judge Sauls has been repeatedly reversed for taking too narrow an approach with admitting evidence and for punishing defendants too harshly by misinterpreting statutes and sustaining convictions without adequate proof.
Last week, the younger Mr. Sirica said that Ms. Adler had not presented adequate proof.
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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