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The phrase "a basic proof of" is correct and usable in written English.
It can be used when introducing a simple or fundamental demonstration of a concept, theorem, or statement in mathematics or logic.
Example: "In this section, we will provide a basic proof of the Pythagorean theorem to illustrate its validity."
Alternatives: "a simple demonstration of" or "a fundamental proof of".
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Figure 1 shows an acceptably low level of noise influences in capturing a white background (condition 1), which is a basic proof of the general idea of an increased file size caused by a moving object (condition 2 compared to 1), the influence of texture of the moving circle (condition 3 vs 2 and 5 vs 4) and the influence of the texture of the background (condition 4 vs 2 and 5 vs 3).
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Finally, in Fig. 6, we present on a toy example of preliminary results for the group sparsity and low-rank sparse decomposition approaches to provide a basic proof-of-principle for these extensions.
Additionally, the observation of FRET inside these viral particles provides a basic proof-of-principle that viral particles can be used as nanoscopic test tubes for probing PPIs.
The physical manipulations described here are basic proof-of-principle, providing a foundation for ambient conditions surrounding the experiment, specifically the presence of an electrically neutral, vibration proof environment.
This can be an important issue in early stage drug development wherein costly, time-consuming synthesis of additional compound would be pursued only if dictated by basic proof-of-concept studies in mice, prior to advancing to PICV, Pirital virus [37], or BSL-4 arenaviral hemorrhagic fever guinea pig models [38], [39], [40].
The criteria for a residence permit will include basic proof of employment/self-employment or study status, or self-sufficiency, building on the criteria set out in the EU free movement directive.
In 1970 Marvin Minsky told Life Magazine, "from three to eight years we will have a machine with the general intelligence of an average human being". However, while the basic proof of principle was there, there was still a long way to go before the end goals of natural language processing, abstract thinking, and self-recognition could be achieved.
The company is currently building up its infrastructure to move beyond the basic proof of concept stage and into being a commercially viable consumer facing service.
However, it does provide basic proof of the manufacturing process, the materials and the power-train.
From basic proof of principle, the main challenge to be addressed is the possibility to magnetize a very large volume of Argon, corresponding to 10 kton or more, for future neutrino physics applications.
Buried in the filings themselves, however, is a damning portrait of the excesses of the housing bubble, when borrowers were able to obtain home loans without basic proof of income or creditworthiness, and banks appeared only too happy to mine profits taking the risky loans and assembling them into securities that could be sold to investors.
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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