proposition: Lemma triangle_1_from_2_for_equiv_over_id {C} {D D' : disp_cat C} (A : disp_adjunction_id_data D D') (E : form_equiv_over_id A) : triangle_2_statement_over_id A -> triangle_1_statement_over_id A.
proof: Proof. Abort. End EquivalencesOverId. Proposition isaprop_form_equiv_over_id {C : category} {D₁ D₂ : disp_cat C} (HF : disp_adjunction_id_data D₁ D₂) : isaprop (form_equiv_over_id HF). Proof. use isapropdirprod ; repeat (use impred ; intro) ; apply isaprop_is_z_iso_disp. Qed.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations 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.Fiber