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'this proofs that' is correct and usable in written English, particularly in formal or academic contexts
For example: "This proofs that the hypothesis is correct, as evidenced by the experiment results."
Exact(1)
This proofs that (13) is special case of (8) with t n = Tn,targetand Rn,target= J n /Tn,target.
Similar(58)
Is this proof that the almighty Oprah is only human after all?
Was this proof that austerity measures could not only work, but actually be popular?
Is this proof that videophoning is just one of those technologies that is constantly predicted but never arrives?
Isn't this proof that who you are is flawed?
Is this proof that global warming is already making hurricanes worse?
Is this proof that young people are brainwashed to be Democrats?
This complete the proof that.
This completes the proof that (4.19) solves Eq. (4.17).
This is the proof that it works".
"This is proof that she has been doing well; there's no cheating in this, this comes from other people.
More suggestions(4)
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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