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"are proof that" is correct and usable in written English.
It is used in the context of providing evidence that something is true. For example, "These results are proof that the theory was correct."
Exact(60)
We are proof that every minute matters.
They are proof that God is here.
Differences between retailers are proof that they, too, drive change.
Spira Mirabilis are proof that musical democracy works.
The results are proof that the concept works.
Your Kerberos tickets are proof that you are indeed yourself, and tickets can be stolen.
Devotees say its widespread adoption and track record of success are proof that it works.
The mice in your kitchen are proof that we coexist with nature even inside.
It says that falling prices are proof that competition is vibrant.
They are proof that people do not need a material incentive to save a life.
For critics, such numbers are proof that the publishers are manipulating the market.
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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