Hmm. Maybe this might help:

Here I'm using the mother wavelet function as defined in the wiki. So the only points at which this function is nonzero are in the half-open interval

Now, what if you could show that if either or That would certainly be sufficient to show the zero part of the delta functions, wouldn't it? Because then, under the integral sign, each function would drag the other one down to zero.

What happens when both and What does the integrand do?