proposition: Lemma isaprop_disp_left_adjoint_equivalence {C : bicat} {D : disp_bicat C} {a b : C} {aa : D a} {bb : D b} {f : a --> b} (Hf : left_adjoint_equivalence f) (ff : aa -->[f] bb) : is_univalent_2_1 C → disp_univalent_2_1 D → isaprop (disp_left_adjoint_equivalence Hf ff).
proof: Proof. intros HUC HUD. revert Hf. apply hlevel_total2. 2: { apply hlevelntosn. apply isaprop_left_adjoint_equivalence. assumption. } eapply isofhlevelweqf. { apply left_adjoint_equivalence_total_disp_weq. } apply isaprop_left_adjoint_equivalence. apply total_is_univalent_2_1; assumption. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.AdjointUnique UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.DispAdjunctions