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This condition says that either a Diophantine condition is satisfied or there exists a point of finite type.
From, there exists a point such that.
Hence, by Lemma 2.8, there exists a point such that.
By (H.E), From, there exists a point such that.
Then and there exists a point such that for, (2.39).
By completeness of, there exists a point, such that.
By Lemma 2.8, there exists a point such that.
Otherwise, if, then there exists a point such that.
Otherwise, if, then there exists a point such that (2.6).
Since is subdifferentiable at, there exists a point such that (2.18).
From, there exists a point such that, and we have (3.14).
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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