The phrase "argument in the case of" is correct and usable in written English.
It can be used when discussing a specific argument or reasoning related to a particular situation or legal case.
Example: "The argument in the case of Smith v. Jones centers around the interpretation of the contract terms."
Alternatives: "argument regarding" or "argument pertaining to".
The administration's legal argument in the case of Mr. Awlaki appeared to have three elements.
There is, by the way, a possible out from this argument in the case of high-skill immigrants.
R. Choate, O. P. Lord & J. W. Perry, for the defendants, submitted a restatement in writing of their argument in the case of Amesbury v. Bowditch Mutual Fire Ins.
[C5.] An assistant district attorney ended a day-and-a-half-long closing argument in the case of the former general counsel of Tyco International, Mark A. Belnick, and urged jurors to convict him.
My 325xi test car -- a sedan with the smaller of two available engines, a 2.5-liter 6 -- made a convincing argument in the case of sport sedan vs. sport utility.
What decides the moral argument in the case of abortion is the wickedness of making other people's deepest and most difficult decisions for them and enforcing your own view by law.
This week the Supreme Court heard oral arguments in the case of McCutcheon v. Federal Election Commission.
Court TV's big story this week followed the closing arguments in the case of Richard Sharpe, described as the "cross-dressing dermatologist" from Massachusetts.
On 2 October, the court heard arguments in the case of Vernon Madison, who was sentenced to death for murdering an Alabama police officer in 1985.
In the fall, the Supreme Court is expected to hear arguments in the case of a North Carolina death row inmate, Ernest P. McCarver, who has an I.Q. of 67.
This Wednesday, the Supreme Court will hear oral arguments in the case of Trump v. Hawaii, about the Administration's latest revised order.
