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Discover Ludwig"we thus have" is correct and usable in written English.
You can use it when you want to suggest that you have something as the result of a previous statement. For example: "We have discussed the issue thoroughly; we thus have a better understanding of the problem."
Exact(59)
We thus have two experiments occurring.
We thus have the beginnings of a mortgage crisis.
We thus have two measures of central processor utilization for which instrumentation must be provided.
We thus have two coupled first-order differential equations from which to calculate m1 and m2.
We thus have no basis for finding a joint intent on this record.
We, thus, have a better algorithm incorporating the advantages of elitism.
We thus have no occasion to consider whether the Lanham Act permitted an award of double petitioner's profits.
We thus have six choices, each from three objects (states), for a total of 3^6 = 729 transition functions.
We thus have the spectre of the fox guarding the hen house, with corrupt officials continuing to benefit from criminal arrangements.
We thus have that.
where We thus have (3.18).
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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