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The phrase "after the first course" is correct and usable in written English.
It can be used to indicate a point in time or sequence following the initial course of a meal or event.
Example: "We will serve dessert after the first course is finished."
Alternatives: "following the first course" or "subsequent to the first course".
Exact(60)
We had to ask for clean plates after the first course.
After the first course, Tom gets up to go to the men's room; one of his friends follows him.
She got a bit restless once the music started, and we had a few tricky moments, but after the first course she fell asleep.
But maybe after the first course I would say: "Sorry, Michel, I have an important phone call to make," and never show up again.
The meal begins with a basket of thick and superb focaccia, and if you don't pace yourself you may find your appetite flagging after the first course.
In the current case, pain and palsy occurred 1 year after the first course of heavy ion radiotherapy.
Lequesne's algo-functional index was significantly improved five and eight months after the first course (by 1.74±2.2, P<0.0001; and by 0.89±2.4, P=0.017; respectively) and five months after the second course (by 1.26±3, P<0.008).
99mTc-HYNIC-annexin V imaging showed tracer uptake in the primary tumour (large white arrow) and the bone metastasis (fine white arrow) as soon as 24 h after the first course of chemotherapy.
After the first course of chemotherapy, diagnostic CTs showed a decrease in the primary lung tumour greatest diameter, which was consistent with an apoptotic tumour response to chemotherapy (lower left and lower right: simple white arrows).
Such factors may contribute to our finding that muscle cramping did not vary statistically across the course segments, although inspection of the data suggests that cramping and near cramping tended to be most common after the first course segment.
The patient progressed locally after the first course of chemotherapy and an additional biopsy was taken.
More suggestions(17)
after the first degree
after the first run
after the first trail
after the first instance
after the first change
after the first tour
after the first golf
after the first point
after the first class
after the first case
after the first preparation
after the first race
after the first leg
after the first interval
after the first fusion
after the first act
after the first pull
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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