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We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank at least three.
Watt, C., Brady, T., Athanasiadis, C.: Shellability of Noncrossing Partition Lattices. Proceedings of the American Mathematical Society, Volume 135, (2007), Issue number 4, pages 939--949.