It did get the tyre inflated, on which we found a big slash:
It was a bit unnerving to us since a few months ago, one of our neighbours also discovered flat tyres in the morning. In her case, all four tyres were flat and it was obvious that somebody did that deliberately. We drove to the nearest tyre shop and have the tyre guy check on the slash. His conclusion was that we drove on something sharp on the road. According to the tyre guy, the slash mark would be different if it was deliberately made. That comforted us a little bit.
So, what I expected to be an uneventful morning when I could blog on faye turned out to be spent in the tyre shop.