Hi!

I have a question regarding Presburger arithmetics in HOL. HOL supports 
decision procedures such as Omega Test and Cooper's algorithm to decide 
about *closed* Presburger formulas. What if I need to do just universal 
quantification of some variables in an open formula? The question is the 
following: how to obtain an open Presburger formula f(y) in HOL if we 
have !x.f(x,y) initially? Is it possible at all? Or, rather, how much 
work and expertise is required to do such things in HOL?

In particular, I am interested in Cooper's algorithm. I have been 
developing a framework for formal verification of parameterized systems 
which works with Presburger formulas and uses Omega Test. However, the 
size of DNFs is a huge problem, therefore I count on Cooper's algorithm 
which does not require input formulas to be in DNF. The only 
implementation of Cooper's algorithm I could found so far is in HOL.

Thanks!
Vlad


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