To prove: Uber cannot be cheaper than driving your own vehicle.

Proof of negation of the TP using counterexample:

1. Monthly insurance cost for own vehicle = a few hundred dollars = $k. Monthly insurance cost for Uber = $0.

2. Assume an extreme case where you don't travel at all in the entire month. Total cost of transportation for owning a car = $k. Total cost of transportation for Uber-ing everywhere = $0.

3. Assuming that the costs are proportional to the kms you have traveled you get this: http://imgur.com/A61dXx9

The inflection point where Uber is no longer cheaper than driving is (k / (mu - mc)), where mu and mc are the slopes for the lines for Uber and own car, and "k" is the insurance intercept.