Definition double_bicat_id_square_laws (B : ver_bicat_sq_id_comp_whisker) : UU := (∏ (x : B), id_h_square_bicat (id_v x) = id_v_square_bicat (id_h x)) × (∏ (x y z : B) (h : x -|-> y) (k : y -|-> z), id_h_square_bicat h ⋆v id_h_square_bicat k = id_h_square_bicat (h · k)) × (∏ (x y z : B) (v : x --> y) (w : y --> z), id_v_square_bicat v ⋆h id_v_square_bicat w = id_v_square_bicat (v · w)).
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations.