proposition: Lemma total_sigma_cell_eq {a b : total_bicat E} {f g : total_bicat E ⟦a,b⟧} (x y : f ==> g) (eq1 : pr1 x = pr1 y) (eq2 : pr2 x = transportb (λ z, pr2 f ==>[z] pr2 g) eq1 (pr2 y)) : x = y.
proof: Proof. induction x as (x, xx). induction y as (y, yy). cbn in *. induction eq1. cbn in *. apply pair_path_in2. exact eq2. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Bicategories.Core.Bicat UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.Core.AdjointUnique UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.DispUnivalence