I found this in the Python docs:
continuemay only occur syntactically nested in afororwhileloop, but not nested in a function or class definition orfinallyclause within that loop. It continues with the next cycle of the nearest enclosing loop.
As the continue-instruction is not made for the with-statement: Is there any alternative other than restructuring the code appropriately? 
Example code (the way I want it to be working):
with open("test.txt", "r") as f:
    if someConditionNotMet(f):
        continue  # "exit" with-statement
    # do lots of stuff
Of course I could write the # do lots of stuff-code inside an else-branch, however, this would only make the code less readable, if there are already two or three nested if-else-branches. In a function I could simply use return and in a while- or for-loop the beforementioned continue. Is there an equivalent to continue in a Python's with-statement?
Well, you could also replace the continue by a break in the text above, logically it would be the same in a with-statement as the code inside it is only executed once, anyway... (but the break only works for for- and while-loops, either).
