Proposition lassociator_v_comp_square {w₁ w₂ x₁ x₂ y₁ y₂ z₁ z₂ : B} {hw : w₁ --> w₂} {hx : x₁ --> x₂} {hy : y₁ --> y₂} {hz : z₁ --> z₂} {u₁ : w₁ -|-> x₁} {u₂ : x₁ -|-> y₁} {u₃ : y₁ -|-> z₁} {v₁ : w₂ -|-> x₂} {v₂ : x₂ -|-> y₂} {v₃ : y₂ -|-> z₂} (s₁ : square_double_bicat hw hx u₁ v₁) (s₂ : square_double_bicat hx hy u₂ v₂) (s₃ : square_double_bicat hy hz u₃ v₃) : lassociator u₁ u₂ u₃ ◃s s₁ ⋆v s₂ ⋆v s₃ = lassociator v₁ v₂ v₃ ▹s s₁ ⋆v (s₂ ⋆v s₃). Proof. exact (pr21 (pr1 (pr222 B)) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ s₁ s₂ s₃). 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.