  Constrained Differential Renormalization (CDR) and the constrained version of
Implicit Regularization (IR) are two regularization independent techniques that
do not rely on dimensional continuation of the space-time. These two methods
which have rather distinct basis have been successfully applied to several
calculations which show that they can be trusted as practical, symmetry
invariant frameworks (gauge and supersymmetry included) in perturbative
computations even beyond one-loop order.
  In this paper, we show the equivalence between these two methods at one-loop
order. We show that the configuration space rules of CDR can be mapped into the
momentum space procedures of Implicit Regularization, the major principle
behind this equivalence being the extension of the properties of regular
distributions to the regularized ones.
