Therefore being exposed to 1 Sievert for a second (the real unit behind the sievert is the J/s, which is equivalent to Watts) is the same as being exposed to 1 milisievert for 1000 seconds, or 1 microsievert for 10^6 seconds.
Nope. Sieverts are J/kg. "1 millisievert for 1000 seconds" makes no sense, but "1 millisievert per 1000 seconds" does.
I have a theory that it's impossible to prove anything, but I can't prove it.