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Case 2. There exist such that and.
From Theorem 3.1, there exist such that.
Claim 2. There exist such that (3.45).
Since, then there exist such that, whenever.
Since, then there exist such that and.
If not, then there exist such that.
If there exist such that and, then there exist, such that and.
By (F), we get, so there exist such that on.
for all, then there exist such that, for and, for.
(H 1) is continuous, and there exist, such that (1.10).
Suppose that holds, then there exist,, such that.
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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