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The phrase "adherence to these rules" is correct and usable in written English.
You can use it when discussing compliance or following specific guidelines or regulations.
Example: "The success of the project depends on strict adherence to these rules to ensure safety and efficiency."
Alternatives: "compliance with these rules" or "following these rules".
Exact(4)
Adherence to these rules will possibly avert the disciplinary action Armstrong is facing as he attempts to win the Tour de France for an eighth time.
However, this condemnation does not guarantee adherence to these rules, and ignorance about sexuality and sexual risks may adversely influence safe sex practices during Muslim adolescents' first contact with sex.
The community will evolve rules defining which properties should apply to which kinds of entities and will police the articles for adherence to these rules in the same way they do now for other article attributes.
However, it was also acknowledged that local patient needs would dictate more or less stringent adherence to these rules, and that the degree of adherence might change quickly without the opportunity for broad notification.
Similar(51)
Germany's adherence to those rules is not absolute either.
"ATI's request seeks official documents which, if they exist, would inform the public about NASA's and Dr. Hansen's adherence to these ethics rules.
Golf depends upon personal adherence to the rules.
He was against rationalism, against adherence to the rules, against functionalism.
Joan, the woman most damaged by her adherence to the rules, gets there first.
A 2015 Pentagon manual on adherence to the rules of war explicitly requires such notification.
The vital elements are vigilance and strict adherence to the rules.
More suggestions(11)
adherence to these criteria
adherence to these policies
adherence to these arrangements
conformity to these rules
adherence to these terms
adherence to these regulations
adherence to these standard
adherence to these recommendations
adherence to these principles
adhere to these rules
adherence to these guidelines
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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