Definition is_predoublecategory_hor (C : predoublecategory_hor_precat_data) : UU := ((∏ (a b : C) (f : a -h-> b), hor_identity a ·h f = f) × (∏ (a b : C) (f : a -h-> b), f ·h hor_identity b = f)) × ((∏ (a b c d : C) (f : a -h-> b) (g : b -h-> c) (h : c -h-> d), f ·h (g ·h h) = (f ·h g) ·h h) × (∏ (a b c d : C) (f : a -h-> b) (g : b -h-> c) (h : c -h-> d), (f ·h g) ·h h = f ·h (g ·h 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.