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"hence in this case" is correct and usable in written English.
You can use it to introduce a conclusion or result which has been reached after considering the facts or evidence. For example, "We have examined the data closely and come to the conclusion that the building materials used are insufficient for the stated purpose. Hence in this case, immediate repairs are necessary."
Exact(60)
For binary sequences Manhattan distance coincides with Hamming distance, hence in this case HSC is a special case of MSC.
Hence in this case it disposed of overlapping issues merely by reference a fortiori to its 'approval' of the challenged provisions in the Gospel Army opinion.
Hence in this case.
Hence in this case and.
Hence, In this case, and Thus, (3.33).
Hence, in this case, assumption (e) is applicable.
Hence, in this case, our upper bound is asymptotically tight.
Hence, in this case, the Sandwich theorem does not hold.
Hence, in this case, we have an equilibrium.
Hence in this case we have also β E ≤ 1.
Hence, in this case there can be no other reason than the mere will of God.
More suggestions(17)
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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