Proposition transportf_hcomp_l {C : double_cat} {x₁ x₂ y₁ y₂ z₁ z₂ : C} {v₁ v₁' : x₁ -->v x₂} {v₂ v₂' : y₁ -->v y₂} {v₃ : z₁ -->v z₂} {h₁ : x₁ -->h y₁} {h₂ : y₁ -->h z₁} {k₁ : x₂ -->h y₂} {k₂ : y₂ -->h z₂} (p : v₁ = v₁') (q : v₂ = v₂') (s₁ : square v₁ v₂ h₁ k₁) (s₂ : square v₂' v₃ h₂ k₂) : transportf_square p q s₁ ⋆h s₂ = transportf_square p (idpath _) (s₁ ⋆h transportf_square (!q) (idpath _) s₂). Proof. induction p, q ; cbn. 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.Core.UnivalentDoubleCats.