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Piechocinska provided proofs for both the classical and quantum cases.
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Whipple provided proof for his model in the form of the shrinking orbit of Encke's Comet.
As stated in the Historical background section, the research of these scientists provided proof for the germ theory of disease and the germ theory of fermentation.
In this case, we carried out a careful histopathological examination of the duodenal specimen, which ultimately provided proof for our diagnosis.
Even Fox News disputed his assertions they'd provided proof for multiple Trump tweets that Barack Obama wiretapped him during the campaign.
In 2010, the CAPRISA 004 trial provided proof for the concept of vaginal microbicides [ 1].
Further studies provided proof for this genotype-phenotype correlation [ 16, 41], although other authors failed to replicate this observation for BRCA1 mutations [ 17, 20].
Approaches aimed at enhancement of the tumor specific response have provided proof for the rationale of immunotherapy in cancer, both in animal models and in humans.
Every distribution needs to provide proofs for the reliability of their packages by themselves.
The sections Appendices 1 to 5 provide proofs for our theorems.
We also provide proofs for robust monotone convergence of the proposed CO-ILC algorithms for a class of uncertainty models.
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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