proposition: Proposition local_equivalence_triangle1_inv {x y : B₁} (f : x --> y) : (local_equivalence_counit_inv2cell (#F f))^-1 • ##F ((local_equivalence_unit_inv2cell f)^-1) = id2 (#F f).
proof: Proof. use vcomp_move_R_pM. { is_iso. } rewrite id2_right. refine (!(id2_right _) @ _). use vcomp_move_R_pM. { exact (psfunctor_is_iso F (inv_of_invertible_2cell (local_equivalence_unit_inv2cell f))). } cbn. refine (!_). apply local_equivalence_triangle1. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Properties