Strip out uses of [Set]/[Type0]

In trunk, rigid polymorphic universes are not lowered to [Set], so
things work out better if we don't use [Set] anywhere.  There's a bug in
HoTT/coq that forces us to manually choose the elimination schemes for
Unit and Empty, but it seems to be fixed in trunk.

After     | File Name                                                          | Before    || Change
-------------------------------------------------------------------------------------------------------
10m14.33s | Total                                                              | 10m20.01s || -0m05.67s
-------------------------------------------------------------------------------------------------------
1m42.24s  | categories/Comma/ProjectionFunctors                                | 1m47.76s  || -0m05.51s
0m41.39s  | categories/Pseudofunctor/RewriteLaws                               | 0m43.04s  || -0m01.64s
0m19.54s  | categories/Comma/InducedFunctors                                   | 0m20.75s  || -0m01.21s
0m18.76s  | categories/Adjoint/Composition/Core                                | 0m17.52s  || +0m01.24s
0m14.88s  | categories/FunctorCategory/Dual                                    | 0m16.45s  || -0m01.56s
0m06.39s  | categories/UniversalProperties                                     | 0m08.15s  || -0m01.76s
0m36.62s  | categories/Adjoint/Composition/AssociativityLaw                    | 0m35.73s  || +0m00.89s
0m26.16s  | categories/Adjoint/HomCoercions                                    | 0m25.92s  || +0m00.23s
0m24.59s  | categories/Grothendieck/PseudofunctorToCat                         | 0m24.74s  || -0m00.14s
0m17.54s  | categories/Adjoint/UnitCounitCoercions                             | 0m17.82s  || -0m00.28s
0m16.66s  | categories/ExponentialLaws/Law4/Functors                           | 0m16.40s  || +0m00.26s
0m12.73s  | categories/Functor/Pointwise/Properties                            | 0m12.62s  || +0m00.11s
0m12.67s  | hit/Flattening                                                     | 0m12.10s  || +0m00.57s
0m12.14s  | categories/Pseudofunctor/FromFunctor                               | 0m12.22s  || -0m00.08s
0m09.96s  | categories/PseudonaturalTransformation/Core                        | 0m09.18s  || +0m00.78s
0m09.92s  | categories/Adjoint/Composition/IdentityLaws                        | 0m09.49s  || +0m00.42s
0m09.28s  | categories/Yoneda                                                  | 0m08.82s  || +0m00.45s
0m09.03s  | categories/Pseudofunctor/Identity                                  | 0m09.04s  || -0m00.00s
0m08.94s  | categories/Adjoint/Dual                                            | 0m08.52s  || +0m00.41s
0m08.36s  | categories/ExponentialLaws/Law1/Law                                | 0m08.22s  || +0m00.13s
0m08.35s  | categories/Functor/Prod/Universal                                  | 0m07.68s  || +0m00.67s
0m07.78s  | categories/GroupoidCategory/Morphisms                              | 0m07.90s  || -0m00.12s
0m06.76s  | categories/Adjoint/Paths                                           | 0m06.97s  || -0m00.20s
0m06.70s  | hit/Connectedness                                                  | 0m07.04s  || -0m00.33s
0m06.53s  | categories/Structure/IdentityPrinciple                             | 0m06.45s  || +0m00.08s
0m06.27s  | categories/Category/Morphisms                                      | 0m06.09s  || +0m00.17s
0m06.27s  | categories/Functor/Paths                                           | 0m05.82s  || +0m00.44s
0m06.22s  | categories/Comma/Dual                                              | 0m06.17s  || +0m00.04s
0m05.88s  | categories/Functor/Sum                                             | 0m05.39s  || +0m00.49s
0m05.35s  | categories/DualFunctor                                             | 0m05.23s  || +0m00.11s
0m05.32s  | EquivalenceVarieties                                               | 0m05.60s  || -0m00.27s
0m04.52s  | categories/Category/Sigma/OnMorphisms                              | 0m04.60s  || -0m00.08s
0m04.41s  | categories/ExponentialLaws/Law2/Functors                           | 0m04.50s  || -0m00.08s
0m03.75s  | categories/ProductLaws                                             | 0m03.74s  || +0m00.00s
0m03.59s  | categories/Structure/Core                                          | 0m03.56s  || +0m00.02s
0m03.31s  | types/ObjectClassifier                                             | 0m03.37s  || -0m00.06s
0m03.30s  | HSet                                                               | 0m03.31s  || -0m00.01s
0m03.24s  | categories/FunctorCategory/Functorial                              | 0m02.98s  || +0m00.26s
0m03.15s  | types/Sigma                                                        | 0m03.02s  || +0m00.12s
0m03.02s  | categories/Functor/Prod/Functorial                                 | 0m02.63s  || +0m00.39s
0m02.80s  | categories/Functor/Composition/Functorial/Attributes               | 0m03.14s  || -0m00.34s
0m02.79s  | HProp                                                              | 0m02.89s  || -0m00.10s
0m02.72s  | categories/Adjoint/UnitCounit                                      | 0m02.65s  || +0m00.07s
0m02.59s  | categories/Adjoint/UniversalMorphisms                              | 0m02.87s  || -0m00.28s
0m02.50s  | Equivalences                                                       | 0m02.57s  || -0m00.06s
0m02.45s  | categories/Grothendieck/ToSet                                      | 0m02.54s  || -0m00.08s
0m02.33s  | categories/Comma/Core                                              | 0m02.46s  || -0m00.12s
0m02.32s  | categories/Functor/Attributes                                      | 0m02.35s  || -0m00.03s
0m02.24s  | categories/Category/Sum                                            | 0m02.25s  || -0m00.00s
0m02.16s  | categories/Category/Sigma/Core                                     | 0m02.17s  || -0m00.00s
0m02.16s  | categories/NaturalTransformation/Isomorphisms                      | 0m02.12s  || +0m00.04s
0m02.03s  | types/Record                                                       | 0m02.00s  || +0m00.02s
0m02.01s  | PathGroupoids                                                      | 0m01.92s  || +0m00.08s
0m01.99s  | categories/HomFunctor                                              | 0m01.64s  || +0m00.35s
0m01.94s  | categories/NaturalTransformation/Dual                              | 0m01.83s  || +0m00.10s
0m01.92s  | categories/Pseudofunctor/Core                                      | 0m01.86s  || +0m00.05s
0m01.71s  | categories/FunctorCategory/Morphisms                               | 0m01.60s  || +0m00.10s
0m01.65s  | categories/NaturalTransformation/Paths                             | 0m01.55s  || +0m00.09s
0m01.40s  | contrib/HoTTBookExercises                                          | 0m00.97s  || +0m00.42s
0m01.35s  | categories/InitialTerminalCategory/Pseudofunctors                  | 0m01.41s  || -0m00.05s
0m01.29s  | types/Prod                                                         | 0m01.32s  || -0m00.03s
0m01.29s  | categories/Limits/Core                                             | 0m01.28s  || +0m00.01s
0m01.28s  | categories/NaturalTransformation/Pointwise                         | 0m01.22s  || +0m00.06s
0m01.26s  | categories/Category/Prod                                           | 0m01.32s  || -0m00.06s
0m01.24s  | categories/Category/Sigma/OnObjects                                | 0m01.32s  || -0m00.08s
0m01.14s  | categories/Functor/Composition/Functorial/Core                     | 0m01.37s  || -0m00.23s
0m01.05s  | categories/CategoryOfSections/Core                                 | 0m01.03s  || +0m00.02s
0m01.00s  | categories/NaturalTransformation/Prod                              | 0m00.88s  || +0m00.12s
0m01.00s  | categories/NaturalTransformation/Composition/Laws                  | 0m00.98s  || +0m00.02s
0m00.98s  | categories/Functor/Pointwise                                       | 0m01.01s  || -0m00.03s
0m00.98s  | categories/ExponentialLaws/Law1/Functors                           | 0m00.96s  || +0m00.02s
0m00.96s  | categories/ExponentialLaws/Law   N/A                               | 0m00.89s  || +0m00.06s
0m00.92s  | categories/SetCategory/Morphisms                                   | 0m00.75s  || +0m00.17s
0m00.92s  | hit/Spheres                                                        | 0m00.97s  || -0m00.04s
0m00.90s  | categories/Functor/Prod                                            | 0m00.95s  || -0m00.04s
0m00.88s  | hit/epi                                                            | 0m00.96s  || -0m00.07s
0m00.81s  | types/Paths                                                        | 0m00.84s  || -0m00.02s
0m00.78s  | contrib/HoTTBook                                                   | 0m00.74s  || +0m00.04s
0m00.70s  | categories/NaturalTransformation/Composition/Core                  | 0m00.73s  || -0m00.03s
0m00.64s  | types/Sum                                                          | 0m00.63s  || +0m00.01s
0m00.64s  | types/Universe                                                     | 0m00.70s  || -0m00.05s
0m00.64s  | categories/categories                                              | 0m00.72s  || -0m00.07s
0m00.63s  | hit/Suspension                                                     | 0m00.63s  || +0m00.00s
0m00.61s  | Functorish                                                         | 0m00.57s  || +0m00.04s
0m00.59s  | Trunc                                                              | 0m00.59s  || +0m00.00s
0m00.58s  | categories/NaturalTransformation/Sum                               | 0m00.53s  || +0m00.04s
0m00.55s  | hit/quotient                                                       | 0m00.52s  || +0m00.03s
0m00.54s  | hit/Circle                                                         | 0m00.54s  || +0m00.00s
0m00.52s  | categories/Comma/Projection                                        | 0m00.49s  || +0m00.03s
0m00.51s  | UnivalenceImpliesFunext                                            | 0m00.64s  || -0m00.13s
0m00.48s  | categories/Functor/Composition/Laws                                | 0m00.56s  || -0m00.08s
0m00.46s  | categories/InitialTerminalCategory/Functors                        | 0m00.46s  || +0m00.00s
0m00.45s  | categories/Cat/Core                                                | 0m00.38s  || +0m00.07s
0m00.45s  | Tactics                                                            | 0m00.43s  || +0m00.02s
0m00.44s  | types/Forall                                                       | 0m00.50s  || -0m00.06s
0m00.40s  | categories/ExponentialLaws/Law3/Functors                           | 0m00.34s  || +0m00.06s
0m00.40s  | categories/NaturalTransformation/Identity                          | 0m00.40s  || +0m00.00s
0m00.40s  | categories/KanExtensions/Functors                                  | 0m00.47s  || -0m00.06s
0m00.38s  | categories/FundamentalPreGroupoidCategory                          | 0m00.36s  || +0m00.02s
0m00.38s  | Fibrations                                                         | 0m00.35s  || +0m00.03s
0m00.37s  | categories/Limits/Functors                                         | 0m00.48s  || -0m00.10s
0m00.36s  | TruncType                                                          | 0m00.35s  || +0m00.01s
0m00.35s  | categories/HomotopyPreCategory                                     | 0m00.36s  || -0m00.01s
0m00.34s  | categories/IndiscreteCategory                                      | 0m00.28s  || +0m00.06s
0m00.34s  | categories/Functor/Functor                                         | 0m00.30s  || +0m00.04s
0m00.30s  | categories/ExponentialLaws/ExponentialLaws                         | 0m00.29s  || +0m00.01s
0m00.30s  | categories/Functor/Dual                                            | 0m00.34s  || -0m00.04s
0m00.30s  | categories/NaturalTransformation/Composition/Functorial            | 0m00.30s  || +0m00.00s
0m00.30s  | categories/KanExtensions/Core                                      | 0m00.24s  || +0m00.06s
0m00.29s  | categories/Category/Objects                                        | 0m00.26s  || +0m00.02s
0m00.29s  | hit/minus1Trunc                                                    | 0m00.33s  || -0m00.04s
0m00.29s  | categories/Cat/Morphisms                                           | 0m00.34s  || -0m00.05s
0m00.28s  | categories/InitialTerminalCategory/NaturalTransformations          | 0m00.28s  || +0m00.00s
0m00.28s  | categories/Utf8                                                    | 0m00.28s  || +0m00.00s
0m00.28s  | types/Arrow                                                        | 0m00.29s  || -0m00.00s
0m00.28s  | categories/Notations                                               | 0m00.25s  || +0m00.03s
0m00.28s  | categories/Adjoint/Adjoint                                         | 0m00.26s  || +0m00.02s
0m00.27s  | categories/Adjoint/Hom                                             | 0m00.25s  || +0m00.02s
0m00.26s  | categories/NaturalTransformation/Core                              | 0m00.30s  || -0m00.03s
0m00.24s  | categories/CategoryOfGroupoids                                     | 0m00.26s  || -0m00.02s
0m00.23s  | categories/SetCategory/Functors/Functors                           | 0m00.22s  || +0m00.01s
0m00.23s  | categories/Grothendieck/Grothendieck                               | 0m00.26s  || -0m00.03s
0m00.22s  | categories/Pseudofunctor/Pseudofunctor                             | 0m00.22s  || +0m00.00s
0m00.21s  | categories/Limits/Limits                                           | 0m00.17s  || +0m00.03s
0m00.21s  | categories/Cat/Cat                                                 | 0m00.19s  || +0m00.01s
0m00.21s  | hit/iso                                                            | 0m00.21s  || +0m00.00s
0m00.21s  | categories/Grothendieck/ToCat                                      | 0m00.19s  || +0m00.01s
0m00.20s  | categories/DependentProduct                                        | 0m00.18s  || +0m00.02s
0m00.20s  | categories/KanExtensions/KanExtensions                             | 0m00.20s  || +0m00.00s
0m00.20s  | categories/Adjoint/Notations                                       | 0m00.16s  || +0m00.04s
0m00.20s  | categories/Adjoint/Composition/Composition                         | 0m00.17s  || +0m00.03s
0m00.20s  | types/Bool                                                         | 0m00.24s  || -0m00.03s
0m00.20s  | categories/InitialTerminalCategory/InitialTerminalCategory         | 0m00.28s  || -0m00.08s
0m00.20s  | categories/FunctorCategory/Core                                    | 0m00.19s  || +0m00.01s
0m00.19s  | Conjugation                                                        | 0m00.22s  || -0m00.03s
0m00.19s  | categories/Functor/Composition/Composition                         | 0m00.21s  || -0m00.01s
0m00.19s  | categories/GroupoidCategory/Core                                   | 0m00.21s  || -0m00.01s
0m00.19s  | FunextVarieties                                                    | 0m00.16s  || +0m00.03s
0m00.19s  | categories/Category/Pi                                             | 0m00.19s  || +0m00.00s
0m00.18s  | categories/NatCategory                                             | 0m00.16s  || +0m00.01s
0m00.18s  | categories/Functor/Utf8                                            | 0m00.19s  || -0m00.01s
0m00.18s  | categories/NaturalTransformation/Notations                         | 0m00.17s  || +0m00.00s
0m00.18s  | categories/Category/Core                                           | 0m00.15s  || +0m00.03s
0m00.18s  | Overture                                                           | 0m00.15s  || +0m00.03s
0m00.17s  | categories/Functor/Prod/Prod                                       | 0m00.22s  || -0m00.04s
0m00.17s  | categories/Comma/Comma                                             | 0m00.20s  || -0m00.03s
0m00.17s  | categories/ExponentialLaws/Law2/Law2                               | 0m00.13s  || +0m00.04s
0m00.16s  | categories/Functor/Composition/Functorial                          | 0m00.17s  || -0m00.01s
0m00.16s  | categories/NaturalTransformation/NaturalTransformation             | 0m00.29s  || -0m00.12s
0m00.16s  | categories/FunctorCategory/Utf8                                    | 0m00.20s  || -0m00.04s
0m00.16s  | categories/FunctorCategory/FunctorCategory                         | 0m00.22s  || -0m00.06s
0m00.16s  | Modality                                                           | 0m00.19s  || -0m00.03s
0m00.16s  | categories/SetCategory/SetCategory                                 | 0m00.18s  || -0m00.01s
0m00.16s  | types/Unit                                                         | 0m00.13s  || +0m00.03s
0m00.16s  | categories/NaturalTransformation/Utf8                              | 0m00.23s  || -0m00.07s
0m00.15s  | categories/Adjoint/Utf8                                            | 0m00.18s  || -0m00.03s
0m00.15s  | categories/SetCategory/Core                                        | 0m00.14s  || +0m00.00s
0m00.15s  | categories/InitialTerminalCategory/Core                            | 0m00.18s  || -0m00.03s
0m00.15s  | categories/Category/Category                                       | 0m00.16s  || -0m00.01s
0m00.15s  | categories/InitialTerminalCategory/Notations                       | 0m00.14s  || +0m00.00s
0m00.14s  | categories/Comma/Utf8                                              | 0m00.19s  || -0m00.04s
0m00.14s  | Contractible                                                       | 0m00.12s  || +0m00.02s
0m00.14s  | Misc                                                               | 0m00.16s  || -0m00.01s
0m00.14s  | categories/Functor/Notations                                       | 0m00.22s  || -0m00.07s
0m00.14s  | categories/PseudonaturalTransformation/PseudonaturalTransformation | 0m00.16s  || -0m00.01s
0m00.14s  | Tests                                                              | 0m00.16s  || -0m00.01s
0m00.14s  | categories/Profunctor/Identity                                     | 0m00.17s  || -0m00.03s
0m00.14s  | categories/ExponentialLaws/Law1/Law1                               | 0m00.15s  || -0m00.00s
0m00.14s  | categories/NaturalTransformation/Composition/Composition           | 0m00.12s  || +0m00.02s
0m00.14s  | hit/Truncations                                                    | 0m00.12s  || +0m00.02s
0m00.14s  | categories/Adjoint/Composition/LawsTactic                          | 0m00.14s  || +0m00.00s
0m00.14s  | categories/Profunctor/Utf8                                         | 0m00.12s  || +0m00.02s
0m00.13s  | categories/Profunctor/Representable                                | 0m00.15s  || -0m00.01s
0m00.13s  | categories/Profunctor/Core                                         | 0m00.11s  || +0m00.02s
0m00.13s  | hit/Interval                                                       | 0m00.15s  || -0m00.01s
0m00.13s  | categories/Category/Dual                                           | 0m00.16s  || -0m00.03s
0m00.13s  | categories/Adjoint/Identity                                        | 0m00.14s  || -0m00.01s
0m00.13s  | categories/Category/Subcategory/Subcategory                        | 0m00.12s  || +0m00.01s
0m00.13s  | hit/TwoSphere                                                      | 0m00.14s  || -0m00.01s
0m00.12s  | categories/ExponentialLaws/Law3/Law3                               | 0m00.19s  || -0m00.07s
0m00.12s  | categories/DiscreteCategory                                        | 0m00.11s  || +0m00.00s
0m00.12s  | HoTT                                                               | 0m00.16s  || -0m00.04s
0m00.12s  | categories/Profunctor/Notations                                    | 0m00.13s  || -0m00.01s
0m00.12s  | categories/Functor/Core                                            | 0m00.11s  || +0m00.00s
0m00.12s  | hit/unique_choice                                                  | 0m00.15s  || -0m00.03s
0m00.12s  | categories/Comma/Notations                                         | 0m00.14s  || -0m00.02s
0m00.12s  | categories/Functor/Composition/Core                                | 0m00.14s  || -0m00.02s
0m00.12s  | categories/Category/Sigma/Sigma                                    | 0m00.11s  || +0m00.00s
0m00.12s  | categories/FunctorCategory/Notations                               | 0m00.10s  || +0m00.01s
0m00.11s  | categories/Adjoint/Core                                            | 0m00.09s  || +0m00.02s
0m00.11s  | categories/Category/Utf8                                           | 0m00.10s  || +0m00.00s
0m00.11s  | coq/Init/Peano                                                     | 0m00.09s  || +0m00.02s
0m00.11s  | categories/Category/Univalent                                      | 0m00.12s  || -0m00.00s
0m00.11s  | categories/Category/Notations                                      | 0m00.13s  || -0m00.02s
0m00.11s  | categories/Functor/Pointwise/Pointwise                             | 0m00.06s  || +0m00.05s
0m00.11s  | categories/Structure/Utf8                                          | 0m00.11s  || +0m00.00s
0m00.11s  | categories/CategoryOfSections/CategoryOfSections                   | 0m00.14s  || -0m00.03s
0m00.10s  | categories/GroupoidCategory/GroupoidCategory                       | 0m00.10s  || +0m00.00s
0m00.10s  | categories/Functor/Identity                                        | 0m00.09s  || +0m00.01s
0m00.10s  | categories/ExponentialLaws/Law4/Law4                               | 0m00.11s  || -0m00.00s
0m00.10s  | categories/Structure/Notations                                     | 0m00.08s  || +0m00.02s
0m00.10s  | types/UniverseLevel                                                | 0m00.09s  || +0m00.01s
0m00.10s  | UnivalenceAxiom                                                    | 0m00.08s  || +0m00.02s
0m00.10s  | categories/Category/Subcategory/Full                               | 0m00.11s  || -0m00.00s
0m00.10s  | types/Empty                                                        | 0m00.06s  || +0m00.04s
0m00.09s  | categories/Structure/Structure                                     | 0m00.10s  || -0m00.01s
0m00.09s  | categories/Profunctor/Profunctor                                   | 0m00.12s  || -0m00.03s
0m00.09s  | FunextAxiom                                                        | 0m00.04s  || +0m00.05s
0m00.08s  | coq/Init/Specif                                                    | 0m00.08s  || +0m00.00s
0m00.08s  | categories/Category/Subcategory/Wide                               | 0m00.10s  || -0m00.02s
0m00.07s  | categories/Category/Strict                                         | 0m00.08s  || -0m00.00s
0m00.07s  | Pointed                                                            | 0m00.08s  || -0m00.00s
0m00.06s  | coq/Init/Logic_Type                                                | 0m00.07s  || -0m00.01s
0m00.06s  | coq/Program/Tactics                                                | 0m00.04s  || +0m00.01s
0m00.05s  | coq/Init/Notations                                                 | 0m00.04s  || +0m00.01s
0m00.05s  | coq/Init/Datatypes                                                 | 0m00.08s  || -0m00.03s
0m00.04s  | coq/Init/Prelude                                                   | 0m00.04s  || +0m00.00s
0m00.03s  | coq/Init/Logic                                                     | 0m00.03s  || +0m00.00s
0m00.03s  | coq/Init/Tactics                                                   | 0m00.03s  || +0m00.00s
0m00.02s  | coq/Bool/Bool                                                      | 0m00.03s  || -0m00.00s
Merge pull request #408 from JasonGross/no-more-set

Strip out uses of [Set]/[Type0]
Work around bug 3424 in trunk

https://coq.inria.fr/bugs/show_bug.cgi?id=3424

Current code gives error:

Toplevel input, characters 7-13:
Error: In environment
A : Type
a : A
b : A
H' : IsHSet A
Unable to unify "Contr_internal (?194 = ?195)" with
 "forall x y : ?14,
  (fix IsTrunc_internal (n : trunc_index) (A : Type) {struct n} :
   Type :=
     match n with
     | minus_two => Contr_internal A
     | trunc_S n' => forall x0 y0 : A, IsTrunc_internal n' (x0 = y0)
     end) minus_two (x = y)".
Work around a universe problem in trunk
Work around bug 3319 in trunk

https://coq.inria.fr/bugs/show_bug.cgi?id=3319

The error with the old code is:

Toplevel input, characters 154-156:
Error:
In environment
X : PreCategory
P : NotionOfStructure X
xa : @sigT (obj X) (@structure X ?25)
yb : @sigT (obj X) (@structure X ?25)
The term "xa" has type "@sigT (obj X) (@structure X ?25)"
while it is expected to have type
 "@sigT (obj X) (fun x : obj X => @structure X P x)".
Work around bug 3425 in trunk

https://coq.inria.fr/bugs/show_bug.cgi?id=3425
Work around bug 3419 in trunk

https://coq.inria.fr/bugs/show_bug.cgi?id=3419

Current error:

Toplevel input, characters 606-612:
Error:
In environment
A : Type
P : A -> Type
u : {x : _ & P x}
v : {x : _ & P x}
pq : {p : u .1 = v .1 & transport P p u .2 = v .2}
p : u .1 = v .1
q : transport P p u .2 = v .2
x : A
y : P x
x' : A
y' : P x'
p1 : ?73 = ?74
q1 : transport ?69 p1 (x; y) .2 = (x'; y') .2
y'0 : ?96 ?73
q2 : transport ?96 idpath y = y'0
The term "idpath" has type "(x; y) = (x; y)"
while it is expected to have type "(x; y) = (?73; ?103)"
(cannot instantiate "?73" because "x" is not in its scope: available
arguments are "A" "P" "u" "v" "pq" "p" "q" "(x; y)"
"(x'; y')").
Work around bug/HO unification change 3420 in trunk

https://coq.inria.fr/bugs/show_bug.cgi?id=3420

Current error:

Toplevel input, characters 414-425:
Error:
In environment
X : Type
A : X -> Type
P : forall x : X, A x -> Type
h : {f : forall x : X, A x & forall x : X, P x (f x)}
The term "eta_sigma ?53" has type "(projT1 ?53; projT2 ?53) = ?53"
while it is expected to have type
 "(fun x : X => projT1 (sigT_corect_uncurried P h x);
  fun x : X => projT2 (sigT_corect_uncurried P h x)) = h".
Work around trunk having dependent goals

Since [instantiate (n := ...)] is deprecated in trunk, we shouldn't use
it.
Fixups to the replacement std. lib for trunk

proof_admitted is used for the [admit] tactic, and we now are required
to declare ML Modules to get the standard tactics.
Work around bug 3422 in trunk

https://coq.inria.fr/bugs/show_bug.cgi?id=3422

Current error:

Unable to unify
 "{|
  object := Functor (F w) (F z);
  morphism := NaturalTransformation (D:=F z);
  compose := composeT (D:=F z);
  trunc_morphism := fun s d : Functor (F w) (F z) =>
                    trunc_natural_transformation s d |}" with
 "{|
  object := Functor (F w) (F z);
  morphism := NaturalTransformation (D:=F z);
  compose := composeT (D:=F z);
  trunc_morphism := fun s d : Functor (F w) (F z) =>
                    trunc_natural_transformation s d |}"