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Lecture Notes in Computer Science
We introduce a deep inference logical system SBVr which extends SBV  with Rename, a self-dual atom-renaming operator. We prove that the cut free subsystem BVr of SBVr exists. We embed the terms of linear λ-calculus with explicit substitutions into formulas of SBVr. Our embedding recalls the one of full λ-calculus into π-calculus. The proof-search inside SBVr and BVr is complete with respect to the evaluation of linear λ-calculus with explicit substitutions. Instead, only soundness ofdoi:10.1007/978-3-642-21691-6_16 fatcat:ehxpjhbmj5fklkfohmehdlbzp4