Definition twosided_disp_nat_trans_laws (τθ : twosided_disp_nat_trans_data) : UU := ∏ (x₁ x₂ : C₁) (y₁ y₂ : C₂) (f : x₁ --> x₂) (g : y₁ --> y₂) (xy₁ : D x₁ y₁) (xy₂ : D x₂ y₂) (fg : xy₁ -->[ f ][ g ] xy₂), #2 FG fg ;;2 τθ _ _ xy₂ = transportb_disp_mor2 (nat_trans_ax τ _ _ f) (nat_trans_ax θ _ _ g) (τθ _ _ xy₁ ;;2 #2 FG' fg).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Total. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor.