Using HSA for previous medical expenses after changing jobs

So here's the situation: I had a job(~4 years) that ended on August 15th and under that employment I had an HDHP and HSA.  After that I had COBRA coverage(with same HSA just not making any contributions) until my next employment came along around October 15.  With my new employer I also have an HDHP with a different HSA and I am enrolled to continue that into next year, though the actual bank holding that HSA will change.  I did not roll over the previous balance of my old HSA because there was like less than $1 in it so I didn't see the need.  Previous to all this, my wife had been using our old HSA to pay for pregnancy/birth expenses from last year.  According to the IRS: "...as long as the IRS-qualified medical expenses were incurred after your HSA was established, you can pay them or reimburse yourself with HSA funds at any time".  My question in this regard is what constitutes 'established'?  My first thought was that the IRS would not care if I have a different HSA provider, particularly if we continued to have an HDHP and used an HSA of some sort across old job/COBRA/new job...but I was not certain on this.  On a side note, we have had an HDHP and HSA of some sort continuously for at least the last 5 years.  Thoughts?