The phrase "automatically the case" is correct and usable in written English.
It can be used to indicate that something is true or valid without needing further proof or explanation.
Example: "In this scenario, it is automatically the case that the results will be consistent across all trials."
Alternatives: "inherently true" or "by default true".
It is not automatically the case that the majority interest will win out.
Why is it automatically the case that England, say, view themselves as a nation whose strength lies in the forwards?
"Is it automatically the case," Mr. Greenspan asked the members of the Federal Open Market Committee, "that when the economy is tightening up that inflation takes hold?" Mr. Greenspan did not venture a firm answer.
"It's not automatically the case that gay couples in hostile states could travel to another state to get married and then have their marriage recognized for federal purposes, even if DOMA is struck down," said Tobias Barrington Wolff, a law professor at the University of Pennsylvania Law School.
However, that's not always automatically the case anymore, and that is a good thing.
That is however not automatically the case here.
For instance, "Maximum battery life mode" can be configured automatically when the residual capacity is under 30%, while "Enhanced quality mode" adopted automatically in the case of available battery capacity is above 80%.
That designation instructs a court clerk to automatically forward the case to a specific judge.
The Met said in a statement that it had not automatically referred the case to the IPCC due to "oversight".
Mr. Bloomberg is trying to circumvent this legal challenge by passing a bill that would permit the use of "hold-open devices" to keep the doors open while allowing them to shut automatically in the case of fire.
The repaired results are also stored automatically in the case base.
