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'''Theorem (Edmonds <ref>J. Edmonds,''Submodular functions, matroids, and certain polyhedra'', In: R. Guy, H. Hanani, N. Sauer and J. Schönheim, Editors, Combinatorial Structures and Their Applications, Proceedings Calgary International Conference on Combinatorial Structures and Their Applications, Calgary, Alberta, June 1969, Gordon and Breach, New York (1970), pp. 69–87. [http://dx.doi.org/10.1007/3-540-36478-1_2 DOI link (LNCS version)].</ref>).''' Let <math>M_1=(S,r_1)</math> and <math>M_2=(S,r_2)</math> be two matroids. Then the maximum size of a common independent set of <math>M_1</math> and <math>M_2</math> is <math>\min_{X \subseteq S} (r_1(X)+r_2(S \setminus X)).</math>