proposition: Proposition cat_with_terminal_cleaving_left_adjoint_equivalence_help : ∏ (C₁ C₂ : bicat_cat_with_terminal_disp_cat) (F : adjoint_equivalence C₁ C₂), is_cartesian_disp_functor (comp_cat_type_functor (pr1 F)).
proof: Proof. use J_2_0. - exact is_univalent_2_0_bicat_cat_with_terminal_disp_cat. - intros C HC₁ HC₂ ; cbn. apply disp_functor_identity_is_cartesian_disp_functor. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Equivalences UniMath.Bicategories.Core.Bicat UniMath.Bicategories.ComprehensionCat.BicatOfCompCat.DispCatTerminal UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.Examples.Sub1Cell