Premise 4 is trivially true for the same reason premise 3 is: choose K=1, then K>1 is false, and false implies anything.

Suppose I would pick K=2 though. What would happen then?

#3 and #4 say there exists a K for which the interior statement is true.

K=2 doesn't make the interior true for either, so choosing it doesn't tell us whether #3 and #4 are true or false.

However, if we choose K=1 then we prove #3 and #4 are true.

The crime is the attempt to obstruct justice. Having succeeded in doing so is not a requirement.