proposition: Lemma isaprop_disp_left_adjoint_equivalence_cell_unit_bicat {C : bicat} {D : disp_cat_data C} {a b : C} {aa : (disp_cell_unit_bicat D) a} {bb : (disp_cell_unit_bicat D) b} (f : adjoint_equivalence a b) (ff : aa -->[ f ] bb) : isaprop (bb -->[ left_adjoint_right_adjoint f] aa) -> isaprop (disp_left_adjoint_equivalence f ff).
proof: Proof. intro p. use isaproptotal2. - intro. apply isapropdirprod. + apply isaprop_disp_left_adjoint_axioms_cell_unit_bicat. + apply isaprop_disp_left_equivalence_axioms. - do 4 intro. apply isaprop_disp_left_adjoint_data_cell_unit_bicat, p. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.Initial UniMath.Bicategories.Core.Examples.Final UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.Core.Univalence UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.DispUnivalence