Proposition hcomp_split_globular_l_id' {C : double_cat} {x y z : C} {v₁ v₂ v₃ : z -->v z} (p₁ : identity_v y ·v identity_v y = identity_v y) (p₂ : v₁ ·v v₂ = v₃) (q₁ : identity_v z = v₁) (q₂ : identity_v z = v₂) {h₁ h₂ h₃ : y -->h z} {k : x -->h y} (s₁ : square (identity_v y) v₁ h₁ h₂) (s₂ : square (identity_v y) v₂ h₂ h₃) : id_v_square k ⋆h (transportf_square p₁ p₂ (s₁ ⋆v s₂)) = transportf_square (id_v_left _) p₂ (id_v_square k ⋆h s₁ ⋆v id_v_square k ⋆h s₂). Proof. rewrite (hcomp_split_globular_l_id q₁ q₂). rewrite transportf_f_square. rewrite !transportf_hcomp_r. rewrite !transportf_f_square. use transportf_square_eq. apply maponpaths_2. 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.