  The reconstruction theorem, a cornerstone of Martin Hairer's theory of
regularity structures, appears in this article as the unique extension of the
explicitly given reconstruction operator on the set of smooth models due its
inherent Lipschitz properties. This new proof is a direct consequence of
constructions of mollification procedures on spaces of models and modelled
distributions: more precisely, for an abstract model $Z$ of a given regularity
structure, a mollified model is constructed, and additionally, any modelled
distribution $f$ can be approximated by elements of a universal subspace of
modelled distribution spaces. These considerations yield in particular a
non-standard approximation results for rough path theory. All results are
formulated in a generic $(p,q)$ Besov setting.
