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The phrase "a kind of proof" is correct and usable in written English.
It can be used when discussing a specific type or category of evidence or validation in various contexts, such as mathematics, science, or legal matters.
Example: "In this experiment, we found a kind of proof that supports our hypothesis about the chemical reaction."
Alternatives: "a type of evidence" or "a form of validation".
Exact(21)
The photograph is a kind of proof.
Still's stove is a kind of proof of principle.
"It's a kind of proof of failure if you've reached a lot of people".
The movies allowed Ripley to offer his readers a kind of proof that he couldn't put in a drawing.
The boy sits still and blinks silently, the room around him reflecting in his eyes as a kind of proof of their new transparency.
And those who haven't seem to relish the chance to wave about each of its reports triumphantly, as a kind of proof of humanity's uselessness.
Similar(39)
There's no trace of a positive ID for the guy in the photo, nor is there a confirmation that this was a protest, nor any kind of proof he wasn't, like, picking up his Purple Heart after accidentally dropping it because the ceremony made him so sad.
If "The Seven Ages" is any kind of proof, she's right.
What the study is NOT, however, is any kind of proof of what makes Kenyan runners so good compared to European/Caucasian runners.
That agenda was a characteristically Victorian conflation of science and spirituality, a kind of materialist "proof" of divine design, like natural theology.
These nonconformists are, on the one hand, individual seekers, and on the other a kind of exceptionalist proof that our cherished singularity is also an illusion.
More suggestions(18)
a kind of rationale
a kind of test
a sort of proof
a kind of probation
a kind of indication
a kind of justification
a kind of certification
a kind of verification
a kind of demonstration
a kind of evidence
a kind of probationary
a kind of testing
a kind of testament
a modicum of proof
a level of proof
a scrap of proof
a kind of mouse
a kind of club
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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