 that the elevator will be going in the
right direction.  Proof by induction:

N=1.	Trivially true, since both you and the elevator only have one
	floor to go to.

Assume true for N, prove for N+1:
	If you are on any of the first N floors, then it is true by the
	induction hypothesis.  If you are on the N+1st floor, then both you
	and the elevator have only one choice, namely down.  Therefore,
	it is true for all N+1 floors.
QED.
