A New Proof of Spinks' Theorem

Skew lattices form a class of non-commutative lattices. Spinks' Theorem [Matthew Spinks, On middle distributivity for skew lattices, ] states that for symmetric skew lattices the two distributive identities and are equivalent. Up to now only computer proofs of this theorem have been known. In the present paper the author presents a direct proof of Spinks' Theorem. In addition, a new result is proved showing that the assumption of symmetry can be omitted for cancellative skew lattices.