Techniques for simplifying expressions – Mathematica Stack Exchange

I am hoping to get techniques to use when faced with expressions I think may be simplified.
From two symmetrical looks at a problem I ended up with two inequalities. With excess stuff removed and everything is a non-negative integer:

$xledelta(A_s,X_v)+delta(z,X_s)$ and $xledelta(X_s,A_v)+delta(z,A_s)$

$delta(z)=begin{cases}
0 & z=2^{j}\
1 & otherwise
end{cases}$
and $delta(x,y,ldots)=delta(x)delta(y,…)$

It would be nice to just have a single bound for $x$ if it’s not complicated.

So I define delta as:

d(x_) := If(DigitCount(x, 2, 1) == 1, 0, 1)

I want to simplify:

x <= d(Xs)*d(Av) + d(z)*d(As) && x <= d(As)*d(Xv) + d(z)*d(Xs)

or maybe

Min(d(Xs)*d(Av) + d(z)*d(As), d(As)*d(Xv) + d(z)*d(Xs))

What can I use to investigate this?