proposition: Lemma adjoint_equivalence_total_disp_weq {a b : B} (aa : D a) (bb : D b) : @adjoint_equivalence E (a,,aa) (b,,bb) ≃ ∑ (f : adjoint_equivalence a b), disp_adjoint_equivalence f aa bb.
proof: Proof. unfold adjoint_equivalence, disp_adjoint_equivalence. cbn. eapply weqcomp. { apply weqinvweq. apply weqtotal2asstol. } eapply weqcomp. 2: { apply weqtotal2asstol. } eapply weqfibtototal. intros f. cbn. eapply weqcomp. 2: { apply weqtotal2comm. } eapply weqfibtototal. intros ff. apply left_adjoint_equivalence_total_disp_weq. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Bicategories.Core.Bicat UniMath.CategoryTheory.DisplayedCats.Core UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.AdjointUnique UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.Core.Univalence