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The phrase "subsequent increase" is correct and usable in written English.
One example of using this phrase could be: "Due to the subsequent increase in demand, the company decided to expand its production facilities."
Exact(60)
Loewy won the bet, and claimed the credit for the subsequent increase in Lucky Strike's sales.
A subsequent increase in measles outbreaks has been blamed directly on the MMR scare.
The caspase activation is reflected from the FRET loss and subsequent increase in blue channel fluorescence.
This inhibition leads to a decrease in vasopressin secretion and a subsequent increase in water excretion.
Mutating this residue to alanine causes a subsequent increase in ion-conduction rates as measured by 86Rb flux assays.
Publicity surrounding a suicide has been definitively linked to a subsequent increase in suicide, especially among young people.
Attention is brought to the subsequent increase of current in the antenna.
This leads to a subsequent increase in the natural periods of the structural system.
DMI improved with subsequent increase in the level of Y. schidigera powder in the diets.
Subsequent increase in the Zn fraction up to 0.35 leads to lower hydrogen production.
Non-payment of the licence fee should be decriminalised but must be done alongside new measures to prevent a subsequent increase in evasion and loss of funding.
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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