We then extend our results to variadic decomposability ,
Finally , we give an application to quantifier elimination in integer linear arithmetic
We then extend our results to variadic decomposability , where predicates could admit multiple free variables ( in contrast to monadic decomposability ) .
Finally , we give an application to quantifier elimination in integer linear arithmetic where the variables in a block of quantifiers , if independent , could be eliminated with an exponential ( instead of the standard doubly exponential ) blow - up .