Proposition hcomp_split_globular_r'_idpath {C : double_cat} {x y z : C} {w : x -->v x} {v₁ v₂ : z -->v z} (q₁ : identity_v z = v₁) (q₂ : identity_v z = v₂) (r : identity_v y = identity_v y ·v identity_v y) {h₁ h₂ h₃ : y -->h z} {k₁ k₂ : x -->h y} (s₁ : square (identity_v y) v₁ h₁ h₂) (s₂ : square (identity_v y) v₂ h₂ h₃) (s₃ : square w (identity_v y ·v identity_v y) k₁ k₂) : (s₃ ⋆h transportf_square r (idpath _) s₁) ⋆v (id_v_square _ ⋆h s₂) = transportb_square (id_v_right _) (idpath _) (s₃ ⋆h (s₁ ⋆v s₂)). Proof. refine (_ @ hcomp_split_globular_r' (idpath _) (idpath _) s₁ s₂ s₃ @ _). - apply maponpaths_2. apply maponpaths. use transportf_square_eq. apply idpath. - use transportf_square_eq. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.Variations. Import TransportSquare.