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"no proof of" is correct and usable in written English.
It is commonly used to indicate a lack of evidence or support for a certain statement or claim. It can also be used to express uncertainty or doubt about something. Example: There is no proof of ghosts, meaning that there is no convincing evidence to support the idea that ghosts exist.
Exact(58)
There's no proof of it.
No proof of creditworthiness.
There is no proof, of course.
It has no proof of that.
He had no proof of his whereabouts.
There's no proof of any problems.
There is no proof of any cause.
"I have no proof of the injury.
I have no proof of the afterlife.
However, he said he had no proof of this.
But there is no proof of this theory, either.
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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