Non-standard definition of fiber about cubical HOT 8 CLOSED

I see! This is ok for now I think, but it's probably better to eventually have the same definitions everywhere. We could do this change to internalFiber at same time as we try to change the internal definition of contractible to what we really need in comp for Glue (any partial element can be extended to a total one).

I can fix the rest of the files to use the more standard definition of fiber and then merge the PR.

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NB. What we have currently is fiber f y = Sigma (x:X), y = f x, that is the identity type y = f x instead of the conventional f x = y. I am not saying this is worse of better, but it is certainly better if everybody adopts the same definitions, as these two definitions are not definitionally equal and hence are not interchangeable in existing code.

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The reason for the non-standard definition is that it's the one we picked for the CCHM paper as it makes composition for Glue-types a little simpler as far as I remember (I think we have to invert one path less with this definition...). However I agree that it would be for the best to use the standard definition, but this would require a change to the Glue types in Agda as they take a family of equivalences. I know how to do the change on paper, but I don't know the Agda code base well enough to do it myself.

@Saizan : Can you help us with this?

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@Saizan So you are not suggesting changing the internal representation of fiber? What would you change instead? I tried to figure out where the code related to equivalences are in Agda, but I couldn't find it...

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I'm very much in favor of doing this change now btw! Better do it sooner rather than later so that we don't have to rewrite too much code in the library.

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@mortberg I meant we could do this c90f40a

Then we just have to fix things like contrSingl and other low level proofs of isEquiv

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This has been solved in #7

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