Definition has_predoublecategory_sq_hor_ver_unit_assoc ( C:predoublecategory_sq_hor_ver_data) : UU := (∏ (a b: C) (f: a -v-> b) , sqq_iso_special (ver_identity a ·v f) f) × (∏ (a b: C) (f: a -v-> b) , sqq_iso_special (f ·v ver_identity b) f) × (∏ (a b c d: C) (f : a -v-> b) (g : b -v-> c) (h : c -v-> d), sqq_iso_special (f ·v (g ·v h)) ((f ·v g) ·v h)).
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.