Horses/Color/Induction/Exercise

In the following argumentation, we prove by induction that all horses have the same color.

"Let ${}A(n)$ denote the statement, that any ${}n$ horses have the same color. Base case: If only one horse is there, then this has a certain color and the statement is true. For the induction step, suppose that in each collection of ${}n$ horses, they have the same color. Let's now consider a set of ${}n+1$ horses. If we take out one of them, then by induction hypothesis, all the remaining ${}n$ horses have the same color. If we take out another horse, then again the remaining horses have the same color. Therefore, also all ${}n+1$ horses have the same color“. Analyze this argumentation.

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