"An invention should be described in its dynamic state. The dynamic state is understood as a state in which... "
"An invention should be described in its dynamic state. A dynamic state is understood as the state in which... "
In this case, the articles can be used interchangeably.
Your statement sounds rude and confronting to be honest. You could think of pursuing a more considerate approach as follows:
My apologies, but this doesn't look like a syllabus. This is more like your teaching methods in the class. Do you mind sending the correct document again?
However, if you are willing to stick to your approach, I must say, there is no ...
"In such case" and "in such a case" are both possible. I compared their frequencies at Google Ngram Viewer, which showed that both phrases have very similar frequencies. I also included "in such cases", and found that it is more common than either of the other two:
Google Ngram Viewer
This dictionary shows "such" as ...
It depends on which sense of "proof" you want. Going down Merriam-Webster's list
1a: the cogency of evidence that compels acceptance by the mind of a truth or a fact
3: something that induces certainty or establishes validity
5: evidence operating to determine the finding or judgment of a tribunal
These meanings are usually used uncountably, with ...