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"tangible proof that" is a correct and commonly used phrase in written English.
It is typically used to introduce evidence or confirmation of something that can be physically seen or touched. Example: The fingerprints found at the crime scene were tangible proof that the suspect had been present.
Exact(39)
It gave children tangible proof that their savings were growing.
They offer tangible proof that music is atmosphere -- reverie -- as well as sound.
"There was no tangible proof that Panama is working well or better than expected.
A dividend is tangible proof that the company you have invested in is rewarding you for holding the shares.
To ease my conscience, I search for tangible proof that donor-conceived children are not psychologically harmed by their very conception.
He added that "all Venezuelans should accept the results of the C.N.E.," the electoral body, "unless there is tangible proof that the reports are incorrect".
Similar(20)
His laughter was near-tangible proof that I'd said and done something right in that moment.
Somehow that one small detail stunned me with its tangible, definite proof that she was my child.
Indeed, the book is just the sort of tangible proof of accomplishment that might have vindicated Crane's ambitions in the eyes of his father, C. A. Crane, a hardheaded businessman whose doubts about his son's career were never fully dispelled.
"We have not been given any tangible proof to say that he is definitely a Pakistani.
Mr Abbas badly needs this reprieve, partly to rebuild his all but destroyed police forces.More important, an end to the Israeli incursions, assassinations and house demolitions would give tangible proof to Palestinians that the road map is something more than words on paper.
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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