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"I hope Andy and me can show that".
we can show that (3.29).
Similarly, we can show that (3.31).
Similarly, we can show that Qw0 ≤ w0.
Similarly, one can show that (2.5) holds.
Then one can show that (2.3).
Similarly, we can show that (y_=w_).
Analogously, one can show that (2.43).
Since, we can show that (3.18).
Similarly, we can show that v = w.
Similarly, we can show that (u_=w_).
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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