fact: Definition disp_iso_total {a b : C} {f g : C⟦a,b⟧} {x : invertible_2cell f g} {aa : D a} {bb : D b} {ff : aa -->[ f ] bb} {gg : aa -->[ g ] bb} (xx : ff ==>[ x ] gg) : UU := ∑ (zz : gg ==>[ x^-1 ] ff), (@vcomp2 (total_bicat D) (a ,, aa) (b ,, bb) (f ,, ff) (g ,, gg) (f ,, ff) (pr1 x ,, xx) (x^-1 ,, zz) = @id2 (total_bicat D) (a ,, aa) (b ,, bb) (f ,, ff)) × (@vcomp2 (total_bicat D) (a ,, aa) (b ,, bb) (g ,, gg) (f ,, ff) (g ,, gg) (x^-1 ,, zz) (pr1 x ,, xx) = @id2 (total_bicat D) (a ,, aa) (b ,, bb) (g ,, gg)).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Bicategories.Core.Bicat UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Invertible_2cells