Proposition enriched_rezk_completion_ump_essentially_surjective : essentially_surjective (enriched_precomp E₃ EF). Proof. intros G. refine (hinhpr (enriched_rezk_completion_ump_enriched_functor (pr2 G) ,, _)). use make_z_iso. - simple refine (_ ,, _) ; cbn. + exact (nat_z_iso_inv enriched_rezk_completion_ump_nat_z_iso). + exact (enriched_rezk_completion_ump_comm_inv_enrichment _). - refine (enriched_rezk_completion_ump_comm ,, _). exact (enriched_rezk_completion_ump_comm_enrichment _). - split. + abstract (use subtypePath ; [ intro ; apply isaprop_nat_trans_enrichment | ] ; use nat_trans_eq ; [ apply homset_property | ] ; intro x ; cbn ; apply z_iso_after_z_iso_inv). + abstract (use subtypePath ; [ intro ; apply isaprop_nat_trans_enrichment | ] ; use nat_trans_eq ; [ apply homset_property | ] ; intro x ; cbn ; apply z_iso_inv_after_z_iso). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.FullyFaithful. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.FunctorCategory. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.Precomposition. Require Import UniMath.CategoryTheory.Monoidal.Categories.