Question about Lemma 1 in the paper

[buttercutter]

I have questions on Lemma 1 of the DDIM paper

1. How to derive equation (25) or (7) in the paper ?
2. How to use bishop equation (2.115) for the lemma proof ?

[jaylee2000]

A bit late, but if I understood correctly:
Equation (25) is a choice rather than something to be proved.

By taking equation (25) and the induction argument, we can prove Lemma 1.