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"thus I" is a correct and usable phrase in written English
It is often used to introduce a statement or conclusion based on the preceding information or an action taken by the speaker. It can also be used to connect a cause and effect relationship. Example: I studied hard for the exam, thus I was able to achieve a high grade.
Exact(56)
Thus (i) holds.
Thus, (i) and (ii) are proved.
Thus, (i) of Theorem 2.5 is satisfied.
Thus I love it.
/ Thus I exist.
Thus I win.
Thus, I cannot justify your decision".
Thus, I offer a recipe for nachos.
Thus I could not place Lynne Tillman.
And thus, I became their target.
Similar(1)
Thus I-lim X k = Y.
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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