Lemma bicate_transfs : (∏ a b c d : bicate_id_comp, associator_trans_type a b c d) × (∏ a b : bicate_id_comp, left_unitor_trans_type a b) × (∏ a b : bicate_id_comp, right_unitor_trans_type a b). Proof. repeat split; red; cbn. - exact lassociator_transf. - exact lunitor_transf. - exact runitor_transf. 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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.Bicategories.WkCatEnrichment.prebicategory. Require Import UniMath.Bicategories.WkCatEnrichment.Notations. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations.