proposition: Proposition isaprop_is_equiv_over_id : isaprop (is_equiv_over_id F).
proof: Proof. use invproofirrelevance. intros HF₁ HF₂. use subtypePath. { intro. apply isaprop_form_equiv_over_id. } use subtypePath. { intro. apply isaprop_form_disp_adjunction_id. } use (path_right_adjoint_over_id_data HD₁ HD₂). - exact (isaprop_is_equiv_over_id_nat_z_iso HF₁ HF₂). - exact (isaprop_is_equiv_over_id_eq_1 HF₁ HF₂). - exact (isaprop_is_equiv_over_id_eq_2 HF₁ HF₂). Qed.
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.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Equivalences UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq