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"progressively crucial" is a grammatically correct phrase and can be used in written English
It means something is becoming increasingly important or essential over time. You can use it when discussing the importance of something that is gradually becoming more and more crucial. For example: "As technology advances, data privacy becomes progressively crucial in our everyday lives."
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The use of mathematical models to investigate biological systems is becoming progressively crucial to better understand their complex behaviors [ 1].
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Large Eddy Simulation (LES) is progressively becoming a crucial design tool for the next generation of aeronautical combustion chambers.
New paradigms are emerging, such as "Nearly Zero Energy Building" (nZEB), and resource efficiency is progressively becoming a crucial topic in the building sector, implying an appropriate consideration of performance over the whole life cycle.
microRNA are progressively emerging as crucial regulators of gene expression, since they affect the tumorigenesis as oncogenes or oncosuppressors [ 6, 18– 20].
These interactions were determined stage by stage as the HA/Agg/LP layer was progressively constructed; this is crucial to reveal the properties not only of the final layer but also of the intermediate stages, such as the HA layer prior to its complexation with Agg/LP.
A yes to one or two of these questions means you have a touch of what the authors of this provocative book call orthorexia, an obsession with eating "healthfully" that becomes so strong it leads to progressively rigid dieting that eliminates crucial food groups and nutrients.
This thermal budget control issue gets more crucial as the technology node progressively shrinking.
A company's degree of "data ethics awareness" is not only crucial for survival in a market where consumers progressively set the bar, it's also necessary for society as a whole.
The effects of metabolic syndrome in elderly individuals represent a crucial point because elderly populations worldwide are growing progressively, and the prevalence of metabolic syndrome increases with age, always with a higher rate in women than in men (7– 10).
In fact, the comprehension of language is crucial to correctly perform the TT, in which verbal instructions that become progressively more difficult are given, and that imply the understanding of the semantic significance of each word.
An increasing body of data is progressively indicating that the comprehension of the epigenetic landscape, actively integrated with the genetic elements, is crucial to delineate the molecular basis of the inter-individual complexity of ageing process.
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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