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H.Furstenberg and E.Glasner proved that for an arbitrary $k\in\mathbb{N}$,any piecewise syndetic set of integers contains $k-$term arithmetic progressionand 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 compactificationof discrete semigroup. However they provided the abundances for various typesof large sets. In \cite{key-3} V. Bergelson and D. Glasscock introduced thenotion 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$(\mathbb{N\times\mathbb{N}},+).$

Aboundance of arithmetic progression in $\mathcal{CR}-$set