Definition predoublecategory_ver_left_unitor_naturality ( C : predoublecategory_sq_hor_ver_unit_assoc_data) : UU := ∏ (a b c d : C) (f: a -h-> b) (g: a -v-> c) (h: b -v-> d) (k: c -h-> d) (α : sqq f g h k), ((ver_sq_identity f) ·sqv α) ·sqh (pr1 (get_ver_left_unitor h)) = boundary_sq_transport (id_hor_right _ @ !(id_hor_left _)) (id_hor_right _ @ !(id_hor_left _)) ((pr1 (get_ver_left_unitor g)) ·sqh α).
Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence.