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Hereby we present a direct proof for the sake of completeness, adapting ideas from Kerr and Li in [40, Theorem 3.4, (vi) (Rightarrow ) (v)] to the setting of extended metric spaces (see also [40]).
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This month's edition of Ideas for E.L.L's celebrates the holidays — Christmas, Hanukkah, Kwanzaa, New Year's, even winter break — but, of course, just as you can pick, choose and adapt ideas from previous posts in this series, much of what we suggest below can be taught any time of year.
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What can you borrow or how can you adapt ideas from other places to your needs?
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To prove this, we adapt ideas from [40, Theorem 3.4, (vi) (Rightarrow ) (v)] (see also [40]) in the context of groups and metric spaces to the algebraic setting.
I encourage interested groups especially those at schools, museums, libraries, nature centers, and other institutions to adapt ideas from our organization to fit their own circumstances and to start planning their own Darwin Days for the celebration of Darwin's 200th birthday in 2009.
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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