Is he really gone?

My very elderly dog very sadly had to be put to sleep a few days ago. This was carried out at my home by a vet I trust 100% and I was with my dog until the very end, so I witnessed the whole procedure. It was all carried out very gently and peacefully.

However, I have a nagging and worrisome (and obsessive!) doubt in my mind and I hope that you can help me - it may sound foolish, but I can't help but wonder - what if my dog wasn't completely dead?

My dog was sedated first with a small injection which took effect within 5 to 10 mins. I also saw the main injection of barbiturate and saw the vet draw some blood into the syringe before injecting the barbiturate (so proving that she was indeed injecting into a vein in his leg). Within seconds my lovely dog had passed peacefully away. His heartbeat was checked and there was nothing (his breathing may have also been checked, it's hard to remember all of the events). After a few minutes his bladder emptied, and there was also a single exhalation of air, presumably as his lungs collapsed. When we moved him a while later, some fluid came out of his mouth and nose. I looked at his body and there was no sign of breathing.

Now I know this sounds daft, but is there even a remote chance of him coming back to life after all that? I just have this horrible obsessive thought of him not being fully dead and coming back to life in the vets' refrigerator or freezer (the vets took him back to the practice as we wanted him cremated). Surely though none of the aforementioned events would NOT have occurred if he hadn't died (the voiding of the bladder, the finale exhalation of breath, the fluid from the nose and mouth)?

I guess I'm just looking for reassurance here. I daren't ask my vet this or she may think I'm asking if she did her job properly, which is most certainly NOT the case. It's me that's the problem here. The grieving process is causing these crazy, worrisome thoughts to ping around in my brain.

So, as mentioned above, surely none of the aforementioned events would NOT have occurred if he hadn't died (the voiding of the bladder, the final exhalation of breath, the fluid from the nose and mouth)?

I'm sorry if this appears even vaguely ridiculous. Many thanks in anticipation of your answer.

Thank you very much for your fast, kind and informed response, it's really helped to put my mind at rest.