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That hypothesis is now universally accepted.But the big idea of Dr Gold's whose proof or disproof is pending is the "deep, hot biosphere".
"I never expected to have a play on Broadway," said Mr. Auburn, whose "Proof" began Off Broadway at the nonprofit Manhattan Theater Club.
We require the following lemma whose proof is immediate.
We will need the following result whose proof is elementary.
Theorem 1, whose proof is quite simple, reads as follows.
We have the following result whose proof is easy.
As for gradient oscillations, we instead have the following result, whose proof is contained in Sect.
This is summarized in the following proposition, whose proof is given in Sect.
We also need the following lemma whose proof can be found in literature (cf. [33]).
We first recall the following proposition whose proof appears in [25].
We obtain the following two lemmas whose proof are found in [4].
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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