proposition: Lemma pre_composition_with_ess_surj_and_fully_faithful_is_fully_faithful (p : essentially_surjective H) (Hff : fully_faithful H): fully_faithful (pre_composition_functor A B C H).
proof: Proof. apply pre_composition_with_ess_surj_and_full_is_fully_faithful. - exact p. - apply fully_faithful_implies_full_and_faithful. exact Hff. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering