Q:

Why doesn't Boole return 0?

I'm writing a code to evaluate  if the Cauchy-Riemann conditions are satisfied for a given function. For example, for the function f[z]=Conjugate[E^(z)] it has to evaluate this expression below
Boole[E^x Cos[y] == -E^x Cos[y]]

But it doesn't give a zero output. It just holds unevaluated.
I don't understand why

A:

I think the answer is that in general this expression can either be true or false, depending on values of y. When Cos[y]==0the expression is true.
i.e. Try Boole[Simplify[E^x Cos[y] == -E^x Cos[y], 0 < y < \[Pi]/2]]

