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The phrase "a simpler proof of" is correct and usable in written English
You can use it when discussing mathematical or logical proofs, indicating that the proof being presented is easier to understand or follow than previous ones. Example: "In this paper, we present a simpler proof of the theorem that demonstrates the relationship between the two variables."
Exact(11)
See also [7] for a simpler proof of this result.
In this paper we first present a simpler proof of Theorem 1.2.
In 1903, he gave a simpler proof of the prime number theorem.
Beal is trying to pull off another anatomical feat: coming up with a "simpler" proof of Fermat's last theorem.
We also consider maximal functions over circles in the plane and obtain a simpler proof of Wolff's endpoint result.
We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality.
Similar(49)
We demonstrate our approach with the design of a simple proof-of-concept chip.
"Hello World" is a simple proof-of-concept piece of homebrew already on the Interwebs, so you can try it now.
First, we conduct a simple proof-of-concept validation of the LEMONS approach, by using LEMONS to generate libraries of short, linear proteinogenic peptides.
We have implemented a simple proof-of-concept prototype[43], so the next step will be to implement a large-scale prototype to gauge performance impacts on typical cloud applications.
The present settings have been fixed throughout the paper as a simple proof-of-concept, and also because the scalability of the current implementation of the MFEA is yet to be thoroughly verified for handling larger number of tasks at a time.
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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