Proposition hor_bicat_hcomp_h_comp_square {x₁ x₂ x₃ y₁ y₂ y₃ : B} {h₁ h₁' : x₁ --> x₂} {h₂ h₂' : x₂ --> x₃} {k₁ k₁' : y₁ --> y₂} {k₂ k₂' : y₂ --> y₃} {v₁ : x₁ -|-> y₁} {v₂ : x₂ -|-> y₂} {v₃ : x₃ -|-> y₃} (τ₁ : h₁ ==> h₁') (τ₂ : h₂ ==> h₂') (θ₁ : k₁ ==> k₁') (θ₂ : k₂ ==> k₂') (s₁ : square_double_bicat h₁ k₁ v₁ v₂) (s₁' : square_double_bicat h₁' k₁' v₁ v₂) (s₂ : square_double_bicat h₂ k₂ v₂ v₃) (s₂' : square_double_bicat h₂' k₂' v₂ v₃) (p : θ₁ ▿s s₁ = τ₁ ▵s s₁') (q : θ₂ ▿s s₂ = τ₂ ▵s s₂') : (θ₂ ⋆⋆ θ₁) ▿s s₁ ⋆h s₂ = (τ₂ ⋆⋆ τ₁) ▵s s₁' ⋆h s₂'. Proof. exact (pr2 (pr222 (pr1 (pr222 B))) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ p q). 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.