Trying to compute the "space of Yoneda lemmas".
No substantial progress on Yoneda
Added proof that Streicher + Circle = UIP
Working on the first equivalence theorem.
Generally starting to reorganize things.
Working on the first equivalence theorem
Converted the definition of paths to one that supports rewriting
Building a rewrite database for paths
Introduced rewriting, made terminology consistent.

Since Coq 8.3 allows rewriting with paths, we are going to use it.
This is going to be of great help. We define a rewrite hints database
"paths" and a "hott_simpl" tactic which autorewrites with it.

We also fix terminology:
- consistently use "fibration A", "total P" and "section P"
- consistently prefer "pr1" and "pr2" over "projT1" and "projT2"
Going through files to make them compatible with rewriting.

Since we introduced rewriting and the hott_simpl tactic many
proofs can be shorter. I am plowing through the files and removing
incompatibilities. I also managed to improve some of the more
complicated proofs. FiberedEquivalences.v is still not done.
Making FiberEquivalences compatible with changes
FiberEquivalences now looks a bit better, mostly shorter
Changing minor things, such as inverse notation
Fiber sequences updated
Throwing out Canonical Structure ebcause using it requires extra thought and careful planning
Changed definition of paths so that the codomain is Set instead of Type.

If we specify Type as the codomain of paths, Coq will actually infer that
paths maps into Prop (which is one of the possible Type's...) This is very
bad for HoTT. So it is better to specify that the codomain is Set. I am
not sure what this implies in terms of universes and sizes. It seems
strange that, for example, the identity type of a universe U should map
into Set. Surely, U ~~> U ought to live at the same level as U? Nevertheless,
this seems the best we can do with the current version of Coq.
Commiting current status before changing things
Renamed Functions.v to Prelude.v
An improved treatment of function extensionality.

We optimize proofs in Funext.v to make them conceptually cleaner.
In particular, from the original, rather monolithic proof, we extract
an obvservation about the axiom of choice being an equivalence from
the space of totality of a relation to the space of choice functions
of a relation. It is likely that this can be further improved, i.e.,
the extra condition about contractibility in the proof of ac_equiv
might be better expressed in terms of is_prop.
Working on univalence