The Time Taken to do the Associativity of App Proof

The time it took us to explain this proof may leave the impression that the proof is complicated. In a way, it is. But it happens quickly.

The time taken to do this proof is about 1/10 second. The rest of the time (about 2/10 seconds) is spent in pre- and post-processing.

Basically, this proof flashes across your screen before you can read it;
you see the **Q.E.D.** and don't bother to scroll back to read it. You
have more important things to do than read successful proofs.