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"The proof for me is really beautiful.
And here's the proof for anyone too young to remember.
"What's the proof for a conspiracy?" he asked.
Another mathematician, Jürgen Moser, provided the proof for another.
This completes the proof for.
The proof for ( MM _2) is similar.
We give the proof for (ii).
We provide the proof for Equation (12).
We give the proof for only.
We give only the proof for AMP.
The proof for edges is similar.
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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