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The phrase "according to proof" is correct and usable in written English.
It can be used when referencing evidence or verification that supports a statement or claim.
Example: "According to proof provided by the researchers, the new drug significantly reduces symptoms."
Alternatives: "based on evidence" or "as demonstrated by proof."
Exact(3)
"A guilty capital murderer was removed from the punishment a jury, according to proof beyond a reasonable doubt, determined he deserved," Mr. Merillat said.
Guillen has now filed a lawsuit against Directi and Skenzo for backing out of its auction purchase of Ad.com, seeking $1.4 million, prejudgment interest, and/or damages according to proof.
The lawsuits are seeking damages according to proof.
Similar(57)
Proof According to the proof of Lemma 2.1, we can easily obtain local asymptotical stability of w ∗ for ODE system (1.2).
According to security proof in [22], the design of the decryption key is secure.
According to the proof of Step 1, we know that (3.39).
According to the proof of Theorem 3.1, there exists, such that implies and implies.
According to the proof given by Chipot et al. [25], we have the following theorem.
According to the proof of Theorem 3.1 we can get that (3.19).
According to the proof of Theorem 6.7, we see that (75) is satisfied.
According to the proof of the second part of Theorem 2.1, this inequality is false.
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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