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end{aligned}The next proposition follows then from Proposition 4.20.
The next proposition is a direct corollary of Proposition 4.15.
The next proposition shows that being σ-above is propagated by σ, π, and μ: Proposition 4. Let (a, b) be σ-above.
To make the terminology consistent with the next proposition (Tag 05SS), maybe this should be called a "termwise split exact sequence of complexes" ?
The next proposition can be straightforwardly proved.
Similarly, we can prove the next proposition.
The next proposition is a consequence of Corollary 3.
We establish this fact in the next proposition.
We recall one of the results in the next proposition.
The next proposition is extracted from [10], Lemma 4.4.
Which merger is socially preferred is in the next proposition.
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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