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The phrase "application of proof" is correct and usable in written English.
It can be used in contexts related to legal, mathematical, or scientific discussions where evidence or verification is being applied.
Example: "The application of proof in this case is crucial to establishing the defendant's guilt."
Alternatives: "use of evidence" or "implementation of verification".
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This carries the idea of definitional freedom, which is a cornerstone of logic programming, over to semantics, again widening the realm of application of proof-theoretic semantics.
Furthermore, proof construction is an engineering task and there is a need to support the design and application of proof-search engineering methods.
He was transferred to Adra Prison, in Damascus, where he filed an application for proof of the charges against him.
This can be seen as a first step towards natural language applications of proof-theoretic semantics.
As an application of the proof of Theorem 2.8, one has the following.
Here we extend the application of the proof load design to estimate the parameters of a bivariate Weibull distribution.
It is indeed a matter of time before the application of automated proof assistants becomes an everyday affair in the life of the mathematician; it is the grand challenge of the automated reasoning community to make it happen sooner than later.
The results of the current application of both proof that the resulting time series trajectories are comparable and matching the data available on periodical basis like intended by the design of the methods.
Volvo said it would recall about 2,700 of its 2012 S60 and XC60 models because of possible fuel leaks caused by what amounts to an exuberant application of rust proofing.
In the case of a first application, proof of attendance of at least two of the cited conferences.
NFP is equivalent to a weaker fragment of arithmetic, but does (unlike NFU) prove Infinity: this is the only application of the Specker proof of ¬AC to a provably consistent theory.
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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