The phrase 'the proceedings' is correct and is used in written English.
Generally, it is used in the context of court proceedings or to describe the steps taken in a process, especially when it involves a lot of details. For example, "The proceedings of the trial lasted four days."
Dictionary
the proceedings
noun
Plural of proceeding
Exact(60)
Tania recorded the proceedings.
Gorbachev chaired the proceedings.
The proceedings were undeniably flawed.
Putin supervised the proceedings closely.
The proceedings began that September.
The proceedings are kept secret.
Some live-tweeted the proceedings.
The proceedings occupied an hour.
DealBook followed the proceedings below.
The proceedings were over quickly.
The proceedings had surprising and peculiar moments.
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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