remove strings of lowercase characters (with minimum length requirement)

Hi all,
I want to delete all lowercase characters from my file, but only strings of length 7 and more.
For example, how can I go from:

JHGEFigeIGDUIirfyfiyhgfoiyfKJHGuioyrDHG

To:

JHGEFigeIGDUIKJHGuioyrDHG

There should be a trick to add to sed 's/[a-z]//g', but I can't figure it out.
Thanks!

Start with this:

sed 's/[a-z]\{7,\}//g'

{7,} means the character class recurs 7 or more times

awesome! thanks a lot!