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Tetali proved that for any $d$-regular simple graph $G$ on $n$ vertices we have $$\\hom(G,H_{\\mathrm{WR}})\\leq \\hom(K_{d+1},H_{\\mathrm{WR}})^{n/(d+1)}.$$ In this paper we give a short proof of this theorem together with the proof of a conjecture of Cohen, Perkins and Tetali. Our main tool is a simple bijection between the Widom-Rowlinson model and the hard-core model on another graph. 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