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The phrase "system is established" is correct and can be used in written English.
It means that a particular system has been created or put into place. Example: The education system is established in our country, providing access to education for all children. This means that the education system has been set up and is currently functioning in the country.
Exact(59)
In fact, this system is established in its basic form by the fourth week of embryonic life.
"Once an organic system is established, the property becomes self-sustaining," said Beth Fiteni, program coordinator for the Long Island Neighborhood Network.
The simulated test system is established according to Fig. 1.
Two-axis tracking system is established for the PV panel.
First, the target system is established according to system requirements.
A system is established to simulate agravic deployment.
A hierarchical water-cycle health evaluation system is established.
The extension model of biological coupling functional system is established.
Firstly, a set of measurement system is established.
First, an experimental linear positioning system is established.
The efficiency bound of the system is established.
More suggestions(16)
system is provided
regulation is established
system is tested
sector is established
system is incorporated
system is stated
governance is established
scheme is established
cost is established
system is developed
mechanism is established
architecture is established
device is established
leadership is established
system is maintained
procedure is established
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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