Abstract
A completeness proof for an inequality prover for dense linear orders without endpoints is presented. The prover employs chaining restricted to shielding terms and mandatory variable elimination. The implementation reported in [3] has proved the continuity of the sum of two continuous functions and an extension of the prover has proved similar continuity theorems for product and quotient as well as the Intermediate Value Theorem of real analysis.
Despite this success, the prover was not known to be complete. Previously, in [4] and [10] completeness proofs for similar provers were presented; however, in both proofs critical restrictions were omitted. In [4] elimination of any eligible variable was not mandatory and in [10] chaining on variables was allowed. Nevertheless, these restrictions are crucial to the success of the prover. Here, both restrictions are included.
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Hines, L.M. Completeness of a prover for dense linear orders. J Autom Reasoning 8, 45–75 (1992). https://doi.org/10.1007/BF00263449
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DOI: https://doi.org/10.1007/BF00263449