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"established subsequent" is a correct and usable phrase in written English
You can use it to describe something that happened after something else that had already been established. Here is an example sentence: "The mayor established subsequent policies to ensure the safety of the city's residents."
Exact(6)
62. From intelligence sources, the following facts have been established subsequent to 11 September; for intelligence reasons, the names of associates, though known, are not given.
This is because the pigment and cone cell fates are established subsequent to the photoreceptor-cell fates (Ready et al. 1976; Wolff and Ready 1993).
However, present data are clearly inadequate to differentiate if the STI-associated communities precede, are co-transmitted with or are established subsequent to STI.
While the initiating event leading to joint contractures, prolonged immobility, or pathology of the connective tissues can be established, subsequent events and progression towards pathology are neither understood nor well documented.
As reported by some researchers, once AM fungi symbiosis was established, subsequent increase in water level or even permanent flooding did not affect their colonization in the roots [ 1, 41].
Virtually all extant populations in Canada, southeast Alaska, and northern Washington State were established subsequent to the last glaciation which began 70 60 thousand years ago and reached its greatest extent 23 18 thousand years ago (Pielou 1991).
Similar(54)
To uncoat the engulfed virion and to establish subsequent infection cycles as well as to spread infection to neighboring cells, acquisition of virus-cell/cell cell membrane fusion and enhancement of the cell–cell fusion activirus-cell/cell cellential step for successful selection/adaptation of virus to the new host cells.
It has been demonstrated that S. aureus-infected neutrophils transferred from a diseased into a naïve mouse can establish subsequent infection (Gresham et al., 2000).
Paradoxically, these repressed regions can be actively transcribed under some conditions, leading to the suggestion that initial rounds of transcription might be needed to establish subsequent silencing (Steinmetz et al, 2006).
"Whilst the exact cause of death is yet to be established, the subsequent fire investigation identified that an E-cigarette had been charging in the bedroom exploded, caught fire and ignited the oxygen tube of any oxygen concentrator, which may have been in use by the occupier.
Gelasius' doctrine that both sacred and civil power are of divine origin and independent, each in its own sphere, was then the most progressive thinking on the subject; had his formula been established, the subsequent history of the papacy probably would have been different.
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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