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The phrase 'the supplement of' is correct and usable in written English.
You can use this phrase to refer to an addition or enhancement of something. For example, "The supplement of extra study materials gave the students greater confidence in their upcoming exam."
Exact(60)
Judith Palmer The supplement of the Dictionary of National Biography for those who died between 2001 and 2004, published this month, is remarkably rich in writers.
"This is the supplement of choice for high school football players, and we have heard that from more than one source," Tygart said.
The supplement of 10 micrograms a day recommended in the UK for pregnant women and the elderly is based on bone health.
The supplement of (NH4 2CO3 at first alkalinized the medium.
In Annex II of the Supplement of the G-BA VerfO (Suppl.
Thus, Theorem 3.1 can be seen as the supplement of the main result of [1].
This figure has been originally published in the supplement of reference [2] and was slightly adapted.
Theorem 3.1 is, in a certain sense, the supplement of Nunokawa's lemma [4].
However, in the current culture system designed for tissue interaction, the supplement of serum is required.
The information about the supplement of various nutrients was collected from the existing literature.
Improvement of reactivity deterioration of reacted oxygen carriers was achieved by the supplement of steam into the fuel reactor.
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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