A general induction theorem for rearrangements of n-tuples

In this paper, a general induction theorem for rearrangements of n-tuples in Rⁿ is proved, showing that a certain proposition regarding a pair of n-tuples related by the strong spectral order 〈 is true for any integer n ? 2 if and only if it is true for the case n = 2. With this theorem, a whole series of well-known theorems is derived as particular cases, and some new results are also obtained.