Lowering Cooldown

No, it's not the "exact same"... This thread is asking if there's any condition in lowering snap cast's cooldown. That other thread didn't really address it; it just said incompatible spells lowered cooldown, not thoroughly explaining the function.

It might not be the same exact question, but it provides you with enough information to simulate the above scenario three times over. And what function is there to explain, exactly? You essentially asked a "yes or no" question.

And if you wish to be so technically correct, this thread does not ask "if there are any conditions"; it asks "is this specific condition a factor", which, again, can be answered through deduction using the information provided in the previously mentioned thread.