I am working on an induction proof and would like to know whether this product equality is true:
$$\big (\prod_{i=2}^n (\lambda_i-\lambda_1) \prod_{n\ge i > j \ge 1}(\lambda_i - \lambda_j)\big )$$
$$= \prod_{n\ge i > j \ge 1}(\lambda_i - \lambda_j)$$
The last product is what I need to end up with, so if the equality is true, then I have arrived at the answer. It seems ok to me, but I just wanted to be sure, since accounting for the indices is a bit tricky.
Thanks,