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We consider non-perturbative effects in theories with extra dimensions andthe deconstructed versions of these theories. We establish the rules forinstanton calculations in 5D theories on the circle, and use them for anexplicit one-instanton calculation in a supersymmetric gauge theory. Theresults are then compared to the known exact Seiberg-Witten type solution forthis theory, confirming the validity both of the exact results and of the rulesfor instanton calculus for extra dimensions introduced here. Next we considerthe non-perturbative results from the perspective of deconstructed extradimensions. We show that the non-perturbative results of the deconstructedtheory do indeed reproduce the known results for the continuum extradimensional theory, thus providing the first non-perturbative evidence in favorof deconstruction. This way deconstruction also allows us to make exactpredictions in higher dimensional theories which agree with earlier results,and helps to clarify the interpretation of 5D instantons.Comment: 32 pages, LaTeX, 1 figure included. Reference added, small typos  corrected. Version to appear in Phys. Rev.

Exact results in 5D from instantons and deconstruction