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The phrase "are substantially involved" is correct and usable in written English.
It can be used to describe a significant level of participation or engagement in a particular activity or situation.
Example: "The researchers found that the participants who are substantially involved in the study showed greater improvement in their skills."
Alternatives: "are deeply engaged" or "are significantly participating".
Dictionary
are substantially involved
adverb
In a strong substantial manner; considerably.
synonyms
Exact(5)
All authors are substantially involved in the upkeep and maintenance of HGMD.
All other authors treated the patients and are substantially involved in the collection and monitoring of data.
Two post-graduate research students are participating in the study and are substantially involved in data collection.
Specific genomic mutations or post-transcriptional modifications of molecules that are substantially involved in cell-matrix-stimulated and survival-advantaging signalling have to be taken into consideration.
The authors concluded that "the static nature of x-ray structures obscures the quantitative significance of nonbonded interactions between highly mobile residues, and that short-range electrostatic interactions are substantially involved in cyt c binding" [ 42].
Similar(55)
AR was substantially involved in interpreting the results and writing the manuscript.
DJ made substantial contributions to the conception and design of this study and was substantially involved in the acquisition, analysis and interpretation of data.
The union, Mr. Lhota charged in the letter, "was substantially involved" in his appointment.
Ethics rules bar Mr. Pitt from ever participating in any matter in which he had been substantially involved when he was in private practice.
"As an appointed special prosecutor, Don will be an integral member of our team, who will review this case with me and be substantially involved in our decision".
The Department of Justice in Washington is likely to be substantially involved in any decision to indict because the case is so sensitive and high profile".
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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