Quantifier elimination is the removal of all quantifiers (the universal quantifier for all and existential quantifier exists) from a quantified system. A first-order theory allows quantifier elimination if, for each quantified formula, there exists an equivalent quantifier-free formula. Examples of such theories include the real numbers with +, *, = , and >, and the theory of complex numbers with +, *, and = . Quantifier elimination is implemented in as Resolve[expr]. Unfortunately, the worst-case time-complexity for real quantifier elimination is doubly exponential in the number of quantifier blocks (Weispfenning 1988, Davenport and Heintz 1988, Heintz et al. 1989, Caviness and Johnson 1998).

cylindrical algebraic decomposition | existential quantifier | quantifier | Tarski's theorem | universal quantifier