then I would expect the other controller to say something like " Roger I'll descend on top with my xxxx, let me know if yours climbs".
Novel bit of phraseology! The Mil may be pedantic - perhaps this illustrates why! 'Let me know if yours climbs' I DON'T BELIEEEVE IT!!!
As an aside, I do find it worrying that a military ATCO will, and has to my knowledge, disregard co-ordination because the phrase "co-ordination agreed" has not been used. I believe that this is one matter that is under investigation following at least one airprox.
'Has to my knowledge' / 'I believe'; no - not good enough. As said earlier, the Mil haven't used that phrase for donkeys' years. Be very careful about quoting hearsay or dimmed memory as fact.