  H.Furstenberg and E.Glasner proved that for an arbitrary $k\in\mathbb{N}$,
any piecewise syndetic set of integers contains $k-$term arithmetic progression
and the collection of such progression is itself piecewise syndetic in
$\mathbb{Z}.$ The above result was extended for arbitrary semigroups by V.
Bergelson and N. Hindman, using the algebra of Stone-\v{C}ech compactification
of discrete semigroup. However they provided the abundances for various types
of large sets. In \cite{key-3} V. Bergelson and D. Glasscock introduced the
notion of $\mathcal{CR}-$ set. In this article we prove For any
  $\mathcal{CR}-$set, $A\subseteq\mathbb{N}$ the collection
$\{(a,b):\,\{a,a+b,a+2b,\ldots,a+lb\}\subset A\}$ is $\mathcal{CR}-$set in
$(\mathbb{N\times\mathbb{N}},+).$
