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Exact(14)
The proof of conclusion (II).
The proof of conclusion (I).
The proof of conclusion (I) is completed.
This completes the proof of conclusion (1).
The proof of conclusion (b) is complete.
This completes the proof of conclusion (a).
Similar(46)
The proofs of conclusions (ii) and(iii) are similar to (i).
While NK constructs an actual proof (of the conclusion from the given assumptions), LK instead constructs a proof that proves the existence of a proof (of the conclusion from the assumptions).
Premature jubilations had already broken out in Britain, France and the US on 7 November, when the French intelligence service somehow took the initiation of negotiations at Compiègne as proof of their conclusion, and sent out a gun-jumping message.
This completes the proof of the conclusion (I).
In this sense, a valid argument provides one with options for belief rather than a proof of its conclusion.
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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