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Since, then there exist such that, whenever.
Since, then there exist such that and.
If not, then there exist such that.
If As, then there exist constants (4.15).
Suppose that holds, then there exist,, such that.
If (1.2). where, then there exist and such that (1.3).
(i) If As, then there exist constants (4.15) .
Since, then there exist and such that (4.3).
In fact, let and, then there exist such that and.
for some, then there exist and, such that (2.17).
Suppose that, then there exist and 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