proposition: Lemma path_internal_adjoint_equivalence {C : bicat} {X Y : C} (HC : is_univalent_2_1 C) (A₁ A₂ : adjoint_equivalence X Y) (H : arrow_of_adjunction A₁ = A₂) : A₁ = A₂.
proof: Proof. use total2_paths_f. - exact H. - apply unique_internal_adjoint_equivalence. apply HC. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.TransportLaws UniMath.Bicategories.Core.EquivToAdjequiv