Proposition double_cat_are_conjoints_left {C : double_cat} {x y : C} {h : y -->h x} {v : x -->v y} (c : double_cat_are_conjoints h v) : transportf_square (id_v_left _) (id_v_left _) (rinvunitor_h h ⋆v transportf_square (id_v_right _) (id_v_right _) ((counit_double_cat_are_conjoints c ⋆h unit_double_cat_are_conjoints c) ⋆v lunitor_h h)) = id_v_square h. Proof. exact (pr122 c). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Underlying.HorizontalBicategory.