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If, then there exists such that (4.6).
If, then there exists such that and.
If, then there exists a sequence in such that.
Indeed, if, then there exists a such that (3.22).
If, then there exists a nonzero vector such that.
If, then there exists such that for each.
If, then there exists a constant such that (2.10).
If, then there exists a such that the mesure (5.7).
For each, if, then there exists an such that and.
Indeed, if, then there exists a net in such that.
If, then there exists an such that (5.3).
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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