proposition: Lemma full_sub_precategory_inclusion : full (sub_precategory_inclusion C (full_sub_precategory C')).
proof: Proof. intros a b f. apply hinhpr. unfold hfiber. exists (f,, tt). reflexivity. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Subcategory.Core