Given:   Riders raced over 200 kilometers during first two stages.

Prove:    At least one of the stages were longer than 100 kilometers.

               That is, if , then either .

Indirect Proof:

Let us assume that neither stages are longer than 100 kolometers, that is  .

If  , then  . This is contradiction because we know that during two stages the riders raced over 200 kilometers.

The assumption leads to the contradiction of a known fact. Therefore, the assumption that must be false, which means that at least one of the two stages were longer than 100 kilometers.

The given theorem was proved that at least one of the stages were longer than

100 kilometers.