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"following condition" is a correct and usable phrase in written English.
It is typically used to refer to a specific condition or set of circumstances that will happen after a certain event or action has taken place. Example: "The new policy will only be effective under the following condition: all employees must complete the mandatory training program by the end of the month."
Exact(59)
Introduce the following condition.
Consider the following condition.
Assume the following condition holds.
We introduce the following condition.
Note that satisfies the following condition: (44).
Hence, it leads to the following condition.
Assume that the following condition holds: (3.33).
Assume that and the following condition holds.
If the following condition is satisfied.
Next, we will assume the following condition.
If condition (H1) and the following condition.
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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