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The phrase "allow the progression of" is correct and usable in written English.
It can be used when discussing the facilitation or enabling of a process or development to continue.
Example: "The new policies are designed to allow the progression of innovative ideas within the organization."
Alternatives: "facilitate the advancement of" or "enable the development of".
Exact(9)
In a statement on Friday, Netanyahu said: "Out of consideration to President Donald Trump's position, Israel will take necessary steps to minimise the expansion of developed area beyond the footprint of existing settlements in Judea and Samaria [the occupied Palestinian territories] and exhibit considerable restriction, to allow the progression of the peace process.
These specific features may allow the progression of the replicative helicase despite the impossibility to unwind the two parental strands at the psoralen ICL.
This would allow the progression of the type II pathway, but would be insufficient to trigger the type I pathway.
Moreover, models allow the progression of diseases to be systematically followed in a highly controlled manner, both pre- and postnatally, an analysis that is not possible to assess in humans.
Assembly and maturation of podosomes maintain the extending cell margin, but in order to allow the progression of the leading edge, podosomes need to release their attachment to the substratum and disassemble at the back of the cluster.
Therefore, in Smn 2B/− mice the level of full-length Smn protein appears to be sufficient to allow the progression of skeletal muscle development albeit in a delayed manner.
Similar(51)
He added that it "allows the progression of the disease to accelerate so that it presents a greater threat" of related liver disease, cancer and death.
He and his group study how several processes that contribute to the maintenance of immune tolerance are impaired, allowing the progression of the disease.
Misguided cell motility of our immune cells impedes the immune system's ability to scavenge for infections or tumor cells, allowing the progression of such diseases.
Likewise, PTEN promoter methylation has also been reported in HCC, which allows the progression of the PI3K/PTEN/Akt pathway [ 85].
Noninvasive methods permit multiple measurements of heart function, allowing the progression of post-infarction remodeling to be followed and cell-mediated improvements to be identified.
More suggestions(18)
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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