Prove that Funext is downward closed.

To do this, add some simple definitions to types.UniverseLevel.  I
figured I'd mimic Agda, though we probably don't need [lift] or [lower]
or [isequiv_lift] because we get cumulativity.  The proof of functional
extensionality being downward closed with respect to universe levels is
also straightforward, due to cumulativity.  As a demo, I've made the
lemmas in hit.iso take only one instance of Funext.

Hopefully, this will be the end of most of our woes with universe
inconsistencies and Funext.

As Univalence is not, in fact, downward closed, (see
https://groups.google.com/forum/#!topic/homotopytypetheory/3wp32xV7OX0),
this closes #334.

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1m49.49s | categories/Comma/ProjectionFunctors                      | 1m46.39s
0m32.83s | categories/Adjoint/Composition/AssociativityLaw          | 0m33.37s
0m25.64s | categories/Grothendieck/PseudofunctorToCat               | 0m26.36s
0m17.64s | categories/ExponentialLaws/Law4/Functors                 | 0m15.69s
0m16.97s | categories/Adjoint/UnitCounitCoercions                   | 0m17.10s
0m15.83s | categories/FunctorCategory/Dual                          | 0m16.35s
0m15.68s | categories/Comma/InducedFunctors                         | 0m15.77s
0m13.11s | categories/Functor/Pointwise/Properties                  | 0m13.43s
0m12.61s | hit/Flattening                                           | 0m11.97s
0m12.42s | categories/Pseudofunctor/Core                            | 0m12.62s
0m11.97s | categories/Adjoint/Composition/Core                      | 0m12.26s
0m11.37s | categories/Pseudofunctor/FromFunctor                     | 0m10.91s
0m11.09s | categories/Adjoint/Dual                                  | 0m11.36s
0m10.80s | categories/Adjoint/Composition/IdentityLaws              | 0m11.22s
0m08.73s | categories/Yoneda                                        | 0m08.83s
0m08.32s | categories/ExponentialLaws/Law1/Law                      | 0m08.86s
0m07.72s | categories/Functor/Prod/Universal                        | 0m07.70s
0m07.58s | categories/GroupoidCategory/Morphisms                    | 0m07.72s
0m07.36s | categories/UniversalProperties                           | 0m07.88s
0m06.93s | hit/Connectedness                                        | 0m06.68s
0m06.35s | categories/Adjoint/Paths                                 | 0m06.18s
0m06.34s | categories/Comma/Dual                                    | 0m07.26s
0m06.12s | categories/Category/Morphisms                            | 0m06.15s
0m05.91s | categories/Functor/Paths                                 | 0m06.14s
0m05.77s | categories/Adjoint/UnitCounit                            | 0m05.98s
0m05.55s | categories/Functor/Sum                                   | 0m05.73s
0m05.44s | EquivalenceVarieties                                     | 0m05.40s
0m04.69s | categories/ExponentialLaws/Law2/Functors                 | 0m05.14s
0m04.54s | categories/Category/Sigma/OnMorphisms                    | 0m04.73s
0m04.48s | categories/DualFunctor                                   | 0m04.75s
0m03.63s | categories/ProductLaws                                   | 0m03.60s
0m03.47s | types/ObjectClassifier                                   | 0m03.41s
0m03.36s | categories/Functor/Prod/Functorial                       | 0m03.40s
0m03.04s | types/Sigma                                              | 0m03.28s
0m02.84s | categories/Adjoint/UniversalMorphisms                    | 0m02.86s
0m02.66s | categories/FunctorCategory/Functorial                    | 0m02.56s
0m02.61s | categories/Grothendieck/ToSet                            | 0m02.64s
0m02.48s | Equivalences                                             | 0m02.54s
0m02.27s | categories/Functor/Attributes                            | 0m02.16s
0m02.14s | categories/Category/Sum                                  | 0m02.10s
0m02.13s | categories/Category/Sigma/Core                           | 0m02.02s
0m02.00s | categories/Comma/Core                                    | 0m02.03s
0m01.99s | categories/NaturalTransformation/Dual                    | 0m01.82s
0m01.86s | PathGroupoids                                            | 0m01.89s
0m01.80s | categories/NaturalTransformation/Isomorphisms            | 0m01.82s
0m01.78s | categories/HomFunctor                                    | 0m01.79s
0m01.66s | categories/FunctorCategory/Morphisms                     | 0m01.47s
0m01.58s | categories/NaturalTransformation/Paths                   | 0m01.67s
0m01.31s | categories/Category/Sigma/OnObjects                      | 0m01.25s
0m01.27s | types/Prod                                               | 0m01.22s
0m01.26s | categories/NaturalTransformation/Pointwise               | 0m01.28s
0m01.25s | categories/Category/Prod                                 | 0m01.38s
0m01.22s | categories/Limits/Core                                   | 0m01.10s
0m01.14s | categories/NaturalTransformation/Composition/Laws        | 0m01.20s
0m01.07s | categories/Functor/Pointwise                             | 0m01.05s
0m00.98s | categories/ExponentialLaws/Law  N/A                      | 0m00.94s
0m00.98s | categories/ExponentialLaws/Law1/Functors                 | 0m01.04s
0m00.96s | categories/CategoryOfSections/Core                       | 0m00.92s
0m00.95s | hit/epi                                                  | 0m00.96s
0m00.93s | categories/Functor/Prod                                  | 0m00.89s
0m00.92s | hit/Spheres                                              | 0m00.86s
0m00.91s | categories/NaturalTransformation/Prod                    | 0m01.00s
0m00.82s | types/Paths                                              | 0m00.87s
0m00.81s | categories/Functor/Composition/Functorial                | 0m00.82s
0m00.78s | Trunc                                                    | 0m00.74s
0m00.63s | types/Universe                                           | 0m00.60s
0m00.63s | categories/NaturalTransformation/Composition/Core        | 0m00.62s
0m00.62s | categories/NaturalTransformation/Sum                     | 0m00.49s
0m00.60s | categories/InitialTerminalCategory                       | 0m00.68s
0m00.60s | contrib/HoTTBookExercises                                | 0m00.54s
0m00.56s | categories/categories                                    | 0m00.53s
0m00.56s | categories/Functor/Composition/Laws                      | 0m00.46s
0m00.55s | Functorish                                               | 0m00.57s
0m00.55s | hit/quotient                                             | 0m00.48s
0m00.53s | types/Sum                                                | 0m00.54s
0m00.52s | hit/Suspension                                           |   N/A
0m00.52s | categories/Comma/Projection                              | 0m00.59s
0m00.51s | types/Record                                             | 0m00.50s
0m00.50s | hit/Circle                                               | 0m00.49s
0m00.46s | categories/Limits/Functors                               | 0m00.42s
0m00.45s | categories/ExponentialLaws/Law3/Functors                 | 0m00.51s
0m00.45s | HSet                                                     | 0m00.38s
0m00.45s | Fibrations                                               | 0m00.40s
0m00.44s | categories/NaturalTransformation/Identity                | 0m00.38s
0m00.43s | types/Forall                                             | 0m00.44s
0m00.42s | Tactics                                                  | 0m00.45s
0m00.40s | categories/Cat/Core                                      | 0m00.49s
0m00.40s | categories/KanExtensions/Functors                        | 0m00.45s
0m00.38s | HProp                                                    | 0m00.40s
0m00.35s | TruncType                                                | 0m00.36s
0m00.33s | categories/KanExtensions/Core                            | 0m00.32s
0m00.32s | categories/IndiscreteCategory                            | 0m00.29s
0m00.32s | Misc                                                     | 0m00.31s
0m00.32s | categories/Functor/Functor                               | 0m00.36s
0m00.29s | categories/Grothendieck/Grothendieck                     | 0m00.28s
0m00.28s | categories/Functor/Dual                                  | 0m00.31s
0m00.28s | categories/Cat/Morphisms                                 | 0m00.30s
0m00.28s | categories/NaturalTransformation/Composition/Functorial  | 0m00.32s
0m00.27s | hit/minus1Trunc                                          | 0m00.27s
0m00.26s | categories/Functor/Composition/Core                      | 0m00.22s
0m00.25s | categories/Category/Objects                              | 0m00.22s
0m00.25s | types/Arrow                                              | 0m00.26s
0m00.24s | categories/Notations                                     | 0m00.22s
0m00.23s | categories/Grothendieck/ToCat                            | 0m00.21s
0m00.22s | categories/ExponentialLaws/ExponentialLaws               | 0m00.25s
0m00.21s | hit/iso                                                  | 0m00.20s
0m00.21s | categories/Utf8                                          | 0m00.23s
0m00.21s | categories/Adjoint/Adjoint                               | 0m00.22s
0m00.20s | categories/DependentProduct                              | 0m00.17s
0m00.20s | categories/SetCategory/Functors/Functors                 | 0m00.24s
0m00.20s | categories/FunctorCategory/Core                          | 0m00.16s
0m00.19s | categories/Pseudofunctor/Pseudofunctor                   | 0m00.18s
0m00.19s | types/Bool                                               | 0m00.20s
0m00.18s | Conjugation                                              | 0m00.19s
0m00.18s | categories/Adjoint/Utf8                                  | 0m00.16s
0m00.18s | categories/NaturalTransformation/NaturalTransformation   | 0m00.20s
0m00.18s | categories/FunctorCategory/Utf8                          | 0m00.16s
0m00.18s | categories/Comma/Comma                                   | 0m00.20s
0m00.18s | FunextVarieties                                          | 0m00.16s
0m00.18s | categories/Category/Category                             | 0m00.14s
0m00.17s | categories/Limits/Limits                                 | 0m00.12s
0m00.17s | categories/NatCategory                                   | 0m00.18s
0m00.17s | categories/NaturalTransformation/Notations               | 0m00.16s
0m00.16s | categories/Comma/Utf8                                    | 0m00.14s
0m00.16s | contrib/HoTTBook                                         | 0m00.17s
0m00.16s | categories/Functor/Prod/Prod                             | 0m00.18s
0m00.16s | categories/SetCategory/Core                              | 0m00.14s
0m00.16s | categories/FunctorCategory/FunctorCategory               | 0m00.15s
0m00.16s | categories/GroupoidCategory/Core                         | 0m00.19s
0m00.16s | categories/NaturalTransformation/Core                    | 0m00.15s
0m00.16s | categories/Functor/Utf8                                  | 0m00.16s
0m00.16s | categories/Category/Core                                 | 0m00.13s
0m00.15s | categories/Cat/Cat                                       | 0m00.15s
0m00.15s | categories/Category/Dual                                 | 0m00.12s
0m00.15s | categories/Adjoint/Notations                             | 0m00.16s
0m00.15s | categories/Comma/Notations                               | 0m00.18s
0m00.15s | categories/Adjoint/Composition/Composition               | 0m00.12s
0m00.15s | Overture                                                 | 0m00.17s
0m00.15s | categories/Adjoint/Composition/LawsTactic                | 0m00.17s
0m00.14s | categories/Adjoint/Identity                              | 0m00.12s
0m00.14s | hit/unique_choice                                        | 0m00.12s
0m00.14s | categories/Profunctor/Representable                      | 0m00.14s
0m00.14s | categories/NaturalTransformation/Utf8                    | 0m00.12s
0m00.13s | categories/ExponentialLaws/Law3/Law3                     | 0m00.11s
0m00.13s | categories/GroupoidCategory/GroupoidCategory             | 0m00.09s
0m00.13s | categories/Profunctor/Core                               | 0m00.12s
0m00.13s | hit/Interval                                             | 0m00.14s
0m00.13s | HoTT                                                     | 0m00.14s
0m00.13s | categories/Profunctor/Notations                          | 0m00.11s
0m00.13s | coq/Init/Peano                                           | 0m00.10s
0m00.13s | categories/ExponentialLaws/Law1/Law1                     | 0m00.21s
0m00.13s | types/Unit                                               | 0m00.13s
0m00.13s | categories/Functor/Composition/Composition               | 0m00.14s
0m00.13s | categories/Profunctor/Utf8                               | 0m00.14s
0m00.12s | categories/KanExtensions/KanExtensions                   | 0m00.12s
0m00.12s | Contractible                                             | 0m00.12s
0m00.12s | categories/Functor/Notations                             | 0m00.14s
0m00.12s | categories/Category/Univalent                            | 0m00.15s
0m00.12s | categories/Category/Subcategory/Wide                     | 0m00.10s
0m00.12s | types/UniverseLevel                                      |   N/A
0m00.12s | categories/Category/Notations                            | 0m00.09s
0m00.12s | UnivalenceAxiom                                          |   N/A
0m00.12s | categories/FunctorCategory/Notations                     | 0m00.10s
0m00.12s | categories/CategoryOfSections/CategoryOfSections         | 0m00.12s
0m00.11s | Pointed                                                  | 0m00.11s
0m00.11s | categories/Category/Sigma/Sigma                          | 0m00.12s
0m00.10s | categories/Adjoint/Core                                  | 0m00.14s
0m00.10s | categories/ExponentialLaws/Law4/Law4                     | 0m00.10s
0m00.10s | categories/Functor/Core                                  | 0m00.12s
0m00.10s | categories/Profunctor/Profunctor                         | 0m00.10s
0m00.10s | categories/Category/Subcategory/Subcategory              | 0m00.12s
0m00.10s | categories/SetCategory/SetCategory                       | 0m00.11s
0m00.10s | categories/Profunctor/Identity                           | 0m00.14s
0m00.10s | categories/Category/Subcategory/Full                     | 0m00.11s
0m00.10s | categories/Functor/Pointwise/Pointwise                   | 0m00.12s
0m00.10s | hit/Truncations                                          | 0m00.11s
0m00.09s | categories/Category/Utf8                                 | 0m00.12s
0m00.09s | coq/Init/Specif                                          | 0m00.06s
0m00.09s | categories/ExponentialLaws/Law2/Law2                     | 0m00.16s
0m00.08s | categories/DiscreteCategory                              | 0m00.11s
0m00.08s | categories/Functor/Identity                              | 0m00.09s
0m00.08s | categories/Category/Strict                               | 0m00.08s
0m00.08s | coq/Init/Logic_Type                                      | 0m00.06s
0m00.08s | categories/NaturalTransformation/Composition/Composition | 0m00.10s
0m00.08s | types/Empty                                              | 0m00.07s
0m00.06s | FunextAxiom                                              | 0m00.06s
0m00.05s | coq/Init/Datatypes                                       | 0m00.04s
0m00.05s | coq/Program/Tactics                                      | 0m00.06s
0m00.04s | coq/Init/Logic                                           | 0m00.03s
0m00.04s | coq/Init/Prelude                                         | 0m00.04s
0m00.03s | coq/Bool/Bool                                            | 0m00.02s
0m00.03s | coq/Init/Tactics                                         | 0m00.04s
0m00.02s | coq/Init/Notations                                       | 0m00.04s
Simplify types/UniverseLevel.v

We don't actually need the fancy equality type, nor the paths.
Strictly speaking, we don't need [lift] or [lower] or the equivalence,
either.
Merge pull request #339 from JasonGross/funext-downward-closed

Prove that Funext is downward closed.
Oops, wrong button, sorry!