proposition: Lemma unique_adjoint_equivalence_inv {a b : B} : ∏ (f : adjoint_equivalence a b), inv_adjequiv f = inv_adjoint_equivalence (pr1 HB) a b f.
proof: Proof. use (J_2_0 (pr1 HB) (λ a b f, _)). intro x; simpl. unfold inv_adjoint_equivalence. rewrite J_2_0_comp. use subtypePath. { intro. exact (isaprop_left_adjoint_equivalence _ (pr2 HB)). } apply idpath. 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