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In this paper a constructive formalization of quantifier elimination ispresented, based on a classical formalization by Tobias Nipkow. Theformalization is implemented and verified in the programming language/proofassistant Agda. It is shown that, as in the classical case, the ability toeliminate a single existential quantifier may be generalized to full quantifierelimination and consequently a decision procedure. The latter is shown to havestrong properties under a constructive metatheory, such as the generation ofwitnesses and counterexamples. Finally, this is demonstrated on a minimaltheory on the natural numbers.

Formalizing Constructive Quantifier Elimination in Agda