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Optimising problem formulation for cylindrical algebraic decomposition
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The Coq system is a Curry–Howard based proof assistant. Therefore, it contains a full functional, strongly typed programming language, which can be used to enhance the system with powerful automation tools through the implementation of reflexive tactics. We present the implementation of a cylindrical algebraic decomposition algorithm within the Coq system, whose certification leads to a proof producing decision procedure for the first-order theory of real numbers.