Combine -v option for grep with -A option - grep

Question

I'd like to ask is it possible to combine somehow -v with -A?
I have example file:
abc
1
2
3
ACB
def
abc
1
2
3
ABC
xyz
with -A I can see the parts I want to "cut":
$ grep abc -A 4 grep_v_test.txt
abc
1
2
3
ACB
--
abc
1
2
3
ABC
it there some option to specify something to see only
def
xyz
?
I found this answer - Combining -v flag and -A flag in grep but it is not working for me, I tried
$ sed -e "/abc/{2;2;d}" grep_v_test.txt
sed: -e expression #1, char 8: unknown command: `;'
also
$ sed "/abc/2d" grep_v_test.txt
sed: -e expression #1, char 6: unknown command: `2'
or
$ sed "/abc/+2d" grep_v_test.txt
sed: -e expression #1, char 6: unknown command: `+'
Sed version is:
$ sed --version
GNU sed version 4.2.1
edit1:
Based on comment I experimented a little bit with both solution, but it is not working as I want to
for grep -v -A 1 abc I would expect line abc and 1 to be removed, but the rest will be printed awk 'c&&!--c; /abc/ {c=2}' grep_v_test.txt prints just the line containing 2, which is not what I wanted.
Very similar it is with sed
$ sed -n '/abc/{n;n;p}' grep_v_test.txt
2
2
edit2:
It seems, I'm not able to describe it properly, let me try again.
What grep -A N abc file does is to print N lines after abc. I want to remove what grep -A will show, so in a file
abc
1
2
3
ACB
def
DEF
abc
1
2
3
ABC
xyz
XYZ
I'll just remove the part abc to ABC and I'll print the rest:
abc
1
2
3
ACB
def
DEF
abc
1
2
3
ABC
xyz
XYZ
so 4 lines will remain... The awk solution prints just def and xyz and skips DEF and XYZ...

Answer 1

To skip 5 lines of context starting with the initial matching line is:
$ awk '/abc/{c=5} c&&c--{next} 1' file
def
xyz
See Extract Nth line after matching pattern for other related scripts.
wrt the comments below, here's the difference between this answer and #fedorqui's answer:
$ cat file
now is the Winter
of our discontent
abc
1
2
bar
$ awk '/abc/{c=3} c&&c--{next} 1' file
now is the Winter
of our discontent
bar
$ awk '/abc/ {c=0} c++>2' file
bar
See how the #fedorqui's script unconditionally skips the first 2 lines of the file?

Answer 2

If I understand you properly, you want to print all the lines that occur 4 lines after a given match.
For this you can tweak the solutions in Extract Nth line after matching pattern and say:
$ awk '/abc/ {c=0} c++>4' file
def
DEF
xyz
XYZ