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Unconventional types of induction

In the theory of crystal bases of quantized enveloping algebras due to Kashiwara, he has a so-called "grand-loop" argument, consisting of 14 induction statements. … Each is a conventional induction, on the face of it, but the method of proof interleaves them, so that the $l$th case of one statement also features in the proof of the $l$th case of others. …