proposition: Lemma homset_conj_inv_after_conj {c : C} {c' : C'} {g : C⟦c, G c'⟧} (d : D c) {d' : D' c'} (beta : FF _ d -->[#F g · ε _] d') : homset_conj_inv _ _ _ (homset_conj _ _ _ beta) = beta.
proof: Proof. unfold homset_conj. rewrite <- homset_conj_inv_after_conj'. unfold homset_conj_inv. rewrite disp_functor_transportf. rewrite mor_disp_transportf_postwhisker. apply maponpaths_2, homset_property. Defined.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories 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.Constructions UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Equivalences