Proposition twosided_disp_nat_trans_ax (τθ : twosided_disp_nat_trans) {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). Proof. apply (pr2 τθ). Qed.
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.