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The phrase "depending on the progress" is correct and usable in written English.
You may use this phrase to describe a situation or action that is contingent upon something else. For example, "We will determine the timeline for our project depending on the progress made in the first phase."
Exact(36)
Accurate measures of kinetic parameters specifically fermentation rates allowed us to show that depending on the progress of fermentation, different QTL are associated with different fermentation rates; one for Rmax, and one for R70.
He said Japan would consider providing humanitarian aid, depending on the progress of the inquiry.
Depending on the progress of the course we may not have a final.
Pentagon officials stressed that the 2008 supplemental request is likely to change depending on the progress of the wars.
That may involve producing full-tilt, depending on the progress of a possible war -- something the cartel has never done before, those analysts said.
If one or all of the players depart their current teams, the Nets could become spenders, depending on the progress of the ownership shift.
Similar(24)
In democratic countries the science of association is the mother science; the progress of all the others depends on the progress of that one".
From this, he concluded that, "In democratic countries, the science of association is the mother science; the progress of all the others depends on the progress of that one".
It is, however, not possible to cast the temperature dependence in a simple Arrhenius equation because the magnitude of the activation energy depends on the progress variable chosen.
"It depends on the progress," Mr. Coyle said.
This will depend on the progress we make in our step-by-step approach.
More suggestions(19)
depending on the country
depending on the instruction
reporting on the progress
depending on the make
depending on the success
depending on the stage
depending on the completion
depending on the work
depending on the achievement
depending on the stages
depending on the evolutionary
depending on the better
depending on the achievements
depending on the cause
depending on the billboard
depending on the type
depending on the journal
depending on the issue
depending on the carrier
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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