[phkahler]

>> It's part of the inductive proof process. Assuming that it holds for n you need to show that it implies that it holds for n + 1 as well.

No. That's wrong. They assert it up front (that it is true for any n horses) and then go on to use it in the proof for n+1. The only time it's OK to assert your claim up front is if you're trying to prove it false by contradiction.

For an inductive proof, you must prove that if it holds for one case (n=1 here) it also holds for the next case. The base case is important and is proven (or obviously) true. A set of n is not the base case here, and they assert something about it without proof.

EDIT: Nope, my dumb. The wording is odd, but for induction we show that it is true for n=X (X is the base case and is 1 in this example). the inductive step is to show that being true for n implies being true for n+1 which is what they did here.