Geodesic
Distributive groupoids are symmetric-by-medial: An elementary proof
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 4, pp. 541-546.

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We present an elementary proof (purely in equational logic) that distributive groupoids are symmetric-by-medial.
Classification : 03B35, 20N02, 68T15
Keywords: distributive groupoids; automated reasoning; Prover9 
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     title = {Distributive groupoids are symmetric-by-medial: {An} elementary proof},
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Stanovský, David. Distributive groupoids are symmetric-by-medial: An elementary proof. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 4, pp. 541-546. http://geodesic.mathdoc.fr/item/CMUC_2008__49_4_a2/