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We use a labelled deduction system ( LND$_{ED-}$TRS ) based on the concept ofcomputational paths (sequences of rewrites) as equalities between two terms ofthe same type, which allowed us to carry out in homotopic theory an approachusing the concept of computational paths. From this, we show that thecomputational paths can be used to perform the proofs of the $LND_{EQ}-TRS_{2}$rewriting system.

Computational Paths -- An approach in the $LND_{EQ}-TRS_{2}$ system