proposition: Proposition local_equivalence_eq_two_cell {x y : B₁} {f g : x --> y} {τ θ : f ==> g} (p : ##F τ = ##F θ) : τ = θ.
proof: Proof. use (vcomp_rcancel (local_equivalence_unit_inv2cell _)). { apply property_from_invertible_2cell. } rewrite !local_equivalence_unit_natural. do 2 apply maponpaths. 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