Express quantifiers for quantifier elimination

Questions
1

Hi there,

I am trying to express a problem of the form:

ForAll(a, Exists(b, Exists(c, f(a, b, c))))

And then I want to attempt to run quantifier elimination on the expression and see what simplifications are possible. How would I write this in the Wolfram language?

Also, is it possible to constrain the variables before analyzing the quantifiers - e.g. instead of analyzing the ForAll over all values of a, to only consider “forall a between 0 and 10” or something similar?

Thanks!
David

2

Something like this:

ForAll[a, -10 < a < 10,
 Exists[{b, c}, b >= 0 && c >= 0,
  b^2 + c^2 < a + d]]
Reduce[%]