Prove that Full + Faithful -> FullyFaithful

After    | File Name                                              | Before
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2m30.17s | Total                                                  | 2m30.49s
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0m19.27s | categories/Functor/Paths                               | 0m19.48s
0m15.30s | hit/Flattening                                         | 0m16.02s
0m09.70s | categories/GroupoidCategory/Morphisms                  | 0m09.56s
0m08.47s | hit/Connectedness                                      | 0m08.51s
0m07.62s | categories/Functor/Prod/Universal                      | 0m07.64s
0m07.43s | categories/Functor/Sum                                 | 0m07.88s
0m06.96s | categories/Category/Morphisms                          | 0m07.07s
0m06.39s | EquivalenceVarieties                                   | 0m06.17s
0m04.80s | categories/Category/Sigma/OnMorphisms                  | 0m05.14s
0m04.29s | types/ObjectClassifier                                 | 0m04.32s
0m03.72s | types/Sigma                                            | 0m03.62s
0m03.24s | Equivalences                                           | 0m03.25s
0m02.60s | categories/Category/Sum                                | 0m02.54s
0m02.54s | categories/Functor/Attributes                          | 0m01.98s
0m02.38s | categories/Category/Sigma/Core                         | 0m02.37s
0m02.33s | PathGroupoids                                          | 0m02.38s
0m02.30s | categories/NaturalTransformation/Dual                  | 0m02.32s
0m02.09s | categories/HomFunctor                                  | 0m01.99s
0m01.92s | categories/FunctorCategory/Morphisms                   | 0m01.88s
0m01.92s | categories/NaturalTransformation/Paths                 | 0m01.90s
0m01.84s | categories/NaturalTransformation/CompositionLaws       | 0m01.88s
0m01.64s | categories/Category/Sigma/OnObjects                    | 0m01.63s
0m01.61s | types/Prod                                             | 0m01.60s
0m01.58s | categories/Category/Prod                               | 0m01.48s
0m01.55s | categories/NaturalTransformation/Composition           | 0m01.56s
0m01.16s | hit/epi                                                | 0m01.10s
0m01.16s | categories/NaturalTransformation/Prod                  | 0m01.10s
0m01.10s | hit/Spheres                                            | 0m01.12s
0m01.06s | categories/Functor/Prod                                | 0m01.02s
0m01.05s | types/Paths                                            | 0m01.04s
0m01.01s | Trunc                                                  | 0m00.99s
0m00.87s | categories/InitialTerminalCategory                     | 0m00.80s
0m00.78s | types/Universe                                         | 0m00.74s
0m00.72s | hit/quotient                                           | 0m00.61s
0m00.67s | types/Sum                                              | 0m00.69s
0m00.66s | Functorish                                             | 0m00.61s
0m00.62s | hit/Circle                                             | 0m00.58s
0m00.58s | categories/NaturalTransformation/Sum                   | 0m00.54s
0m00.56s | hit/Suspension                                         | 0m00.64s
0m00.54s | categories/Functor/CompositionLaws                     | 0m00.49s
0m00.52s | types/Record                                           | 0m00.56s
0m00.48s | HProp                                                  | 0m00.50s
0m00.48s | types/Forall                                           | 0m00.48s
0m00.46s | Fibrations                                             | 0m00.42s
0m00.43s | HSet                                                   | 0m00.48s
0m00.42s | Tactics                                                | 0m00.40s
0m00.42s | TruncType                                              | 0m00.46s
0m00.34s | categories/categories                                  | 0m00.29s
0m00.34s | categories/Functor/Dual                                | 0m00.28s
0m00.34s | categories/NaturalTransformation/Identity              | 0m00.30s
0m00.33s | categories/IndiscreteCategory                          | 0m00.30s
0m00.32s | Misc                                                   | 0m00.29s
0m00.28s | hit/minus1Trunc                                        | 0m00.30s
0m00.28s | types/Arrow                                            | 0m00.29s
0m00.25s | hit/iso                                                | 0m00.22s
0m00.24s | categories/Category/Objects                            | 0m00.26s
0m00.24s | categories/Functor/Functor                             | 0m00.23s
0m00.24s | categories/Functor/Composition                         | 0m00.24s
0m00.23s | Conjugation                                            | 0m00.24s
0m00.22s | categories/NatCategory                                 | 0m00.20s
0m00.21s | categories/Category/Dual                               | 0m00.15s
0m00.21s | hit/unique_choice                                      | 0m00.16s
0m00.21s | categories/FunctorCategory/Core                        | 0m00.20s
0m00.19s | categories/SetCategory/Functors/Functors               | 0m00.23s
0m00.18s | categories/Profunctor/Representable                    | 0m00.14s
0m00.18s | FunextVarieties                                        | 0m00.22s
0m00.17s | categories/Category/Utf8                               | 0m00.12s
0m00.17s | categories/Notations                                   | 0m00.15s
0m00.17s | categories/Category/Category                           | 0m00.18s
0m00.17s | categories/SetCategory/Core                            | 0m00.18s
0m00.17s | categories/Profunctor/Profunctor                       | 0m00.15s
0m00.17s | categories/Utf8                                        | 0m00.16s
0m00.16s | categories/Category/Core                               | 0m00.14s
0m00.15s | categories/NaturalTransformation/Core                  | 0m00.16s
0m00.15s | hit/Interval                                           | 0m00.11s
0m00.14s | categories/GroupoidCategory/Core                       | 0m00.17s
0m00.14s | categories/NaturalTransformation/NaturalTransformation | 0m00.19s
0m00.14s | Contractible                                           | 0m00.14s
0m00.14s | categories/Profunctor/Core                             | 0m00.18s
0m00.14s | types/Bool                                             | 0m00.14s
0m00.14s | UnivalenceAxiom                                        | 0m00.12s
0m00.14s | Overture                                               | 0m00.18s
0m00.14s | categories/FunctorCategory/Notations                   | 0m00.14s
0m00.14s | categories/Category/Univalent                          | 0m00.16s
0m00.13s | categories/NaturalTransformation/Notations             | 0m00.16s
0m00.13s | categories/Profunctor/Identity                         | 0m00.16s
0m00.13s | categories/Category/Notations                          | 0m00.11s
0m00.13s | coq/Init/Peano                                         | 0m00.14s
0m00.12s | categories/DiscreteCategory                            | 0m00.12s
0m00.12s | categories/Functor/Prod/Prod                           | 0m00.12s
0m00.12s | categories/Category/Sigma/Sigma                        | 0m00.11s
0m00.12s | categories/FunctorCategory/FunctorCategory             | 0m00.14s
0m00.12s | categories/Functor/Core                                | 0m00.08s
0m00.12s | categories/NaturalTransformation/Utf8                  | 0m00.11s
0m00.12s | hit/Truncations                                        | 0m00.14s
0m00.12s | categories/Functor/Notations                           | 0m00.09s
0m00.11s | categories/Functor/Utf8                                | 0m00.11s
0m00.11s | types/Unit                                             | 0m00.15s
0m00.10s | HoTT                                                   | 0m00.12s
0m00.10s | categories/GroupoidCategory/GroupoidCategory           | 0m00.09s
0m00.10s | coq/Init/Specif                                        | 0m00.10s
0m00.10s | categories/Profunctor/Notations                        | 0m00.12s
0m00.10s | categories/SetCategory/SetCategory                     | 0m00.10s
0m00.10s | categories/Category/Subcategory/Full                   | 0m00.11s
0m00.09s | categories/Category/Subcategory/Wide                   | 0m00.13s
0m00.09s | categories/FunctorCategory/Utf8                        | 0m00.16s
0m00.09s | types/Empty                                            | 0m00.09s
0m00.09s | categories/Profunctor/Utf8                             | 0m00.13s
0m00.08s | categories/Functor/Identity                            | 0m00.09s
0m00.08s | categories/Category/Strict                             | 0m00.05s
0m00.08s | coq/Program/Tactics                                    | 0m00.07s
0m00.07s | coq/Init/Datatypes                                     | 0m00.07s
0m00.07s | coq/Init/Tactics                                       | 0m00.04s
0m00.07s | FunextAxiom                                            | 0m00.08s
0m00.06s | categories/Category/Subcategory/Subcategory            | 0m00.11s
0m00.06s | coq/Init/Logic_Type                                    | 0m00.08s
0m00.05s | coq/Init/Logic                                         | 0m00.04s
0m00.04s | coq/Init/Prelude                                       | 0m00.05s
0m00.03s | coq/Bool/Bool                                          | 0m00.03s
0m00.02s | coq/Init/Notations                                     | 0m00.04s
Merge pull request #239 from JasonGross/fully-faithful

Prove that Full + Faithful -> FullyFaithful