How does the Cauchy-Schwarz inequality imply this?

Let $$(X_i)_{1\leq i \leq n}$$ be a sequence of orthogonal random variables (pairwise independent random variables) and let $$S_i = \sum_{k=1}^{i}{X_k}$$.

in Almost sure convergence by William F. Stout, Page 18, it is said :

Note that $$S_{i}{ }^{2} \leq i \sum_{j=1}^{i} X_{j}^{2}$$ follows from the Cauchy-Schwarz inequality.

I'm a bit confused as to how the CS inequality is used here, the usual inner product is the expectation but I fail to see which inner product is being considered here, any clarifications will be greatly appreciated, thanks.

It's just the vector form of Cauchy-Schwarz applied to vectors $$(1,1,\ldots,1)$$ and $$(x_1,\ldots,x_i)$$. One gets $$(x_1+\cdots+x_i)^2\le(1^2+\cdots+1^2)(x_1^2+\cdots+x_i^2)= i(x_1^2+\cdots+x_i^2).$$