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As such, given a proof of correctness for a logical representation, it is difficult to conclude that the "actual" protocol is correct.
Alternatively if one doesn't accept that Zeno has given a proof that motion is illusory as we hopefully do not one then owes an account of what is wrong with his argument: he has given reasons why motion is impossible, and so an adequate response must show why those reasons are not sufficient.
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"That was interesting and promising and gave a proof of concept that these vaccines can be developed.
We give a proof by contradiction.
For completeness, we give a proof.
Here we give a proof for it.
For result (ii), we will give a proof by contradiction.
Now we will give a proof of our main result.
We will give a proof of the following result.
We only give a proof of Theorem 9.
We give a proof of the following for completeness.
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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