Definition hcomp_bicat_is_prebicategory (B : hcomp_bicat) : is_prebicategory (hcomp_bicat_to_prebicategory_data B). Proof. repeat split. - intros b₁ b₂ b₃ b₄ f g h ; cbn in *. use make_is_z_isomorphism. + exact (hb_lassoc f g h). + split ; apply (pr2 B). - intros b₁ b₂ f ; cbn in *. use make_is_z_isomorphism. + exact (hb_linvunit f). + split ; apply (pr2 B). - intros b₁ b₂ f ; cbn in *. use make_is_z_isomorphism. + exact (hb_rinvunit f). + split ; apply (pr2 B). - apply (pr2 B). - apply (pr2 B). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws.