proposition: Proposition local_equivalence_triangle2 {x y : B₁} (f : F x --> F y) : local_equivalence_unit_inv2cell (local_equivalence_inv_onecell f) • local_equivalence_inv_twocell (local_equivalence_counit_inv2cell f) = id2 (local_equivalence_inv_onecell f).
proof: Proof. pose (nat_trans_eq_pointwise (internal_triangle2 (HF x y)) f) as p. cbn in p. rewrite !id2_left, !id2_right in p. exact p. 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