double recursion for join #2151
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Signed-off-by: Ali Caglayan <[email protected]> <!-- ps-id: 9003322c-1a51-44a4-baca-d660f1480537 -->
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Here is a double recursion principle for
Join. It is slightly more general than a typical double recursion principle since we allow for the types in each join to be different. This generalisation makes the overall lemma clearer to state and prove.One place this will be used is in CayleyDickson.v where we define a H-space multiplication operation on
Join (Susp A) (Susp A)for a Cayley-Dickson imaginaroidA. This lemma makes the construction there much clearer.Presumably there ought to be a dependent variant of this, but I haven't yet thought about how to state or prove it.