What is the meaning of "in particular" in this proof?
Do you know "a fortiori"?
It's the "a maiore ad minus" argument, concluding from a general to a more special ("particular") case. https://en.m.wikipedia.org/wiki/Argumentum_a_fortiori
As in:
"All cats are mammals. In particular, all black cats are mammals."
A red shirt is a 'particular' or 'specific* kind of shirt.
So, I could say:
"If I don't wear a shirt, then in particular I don't wear a red shirt"
This is just like the:
"If there is no proof, then in particular there is no short proof"