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Make join-assoc level-polymorphic #1204

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ricky136973
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The original join-assoc in Cubical.HITs.Join assumes all types involved are of level 0. This restriction can be relaxed to only require the types being of the same level, not necessarily 0.

@anshwad10
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Why do they have to be the same level? why not generalize it more so that they can all be different levels

@ricky136973 ricky136973 marked this pull request as draft May 18, 2025 00:06
@ricky136973 ricky136973 marked this pull request as ready for review May 20, 2025 04:23
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ricky136973 commented May 20, 2025

The original proof does not type check if I just simply assigning the types with different levels. I renamed it into join-assoc-samelevel and wrote a new join-assoc using the old one that supports different levels.

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anshwad10 commented May 20, 2025

The original proof does not type check if I just simply assigning the types with different levels.

Why would that be? only reason I can think of is that the lemmas it was using (spanEquivToPushoutPath and 3x3-span.3x3-lemma) weren't level-polymorphic enough, but if thats the case why not generalize them too?

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