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