proposition: Lemma isaprop_is_strict_bicat (B : bicat) : isaprop (is_strict_bicat B).
proof: Proof. apply invproofirrelevance. intros x y. induction x as [LSx CSx]. induction y as [LSY CSy]. use pathsdirprod. - do 2 (use funextsec ; intro). apply isapropisaset. - use subtypePath. { exact (isPredicate_is_coh_strictness_structure_from_locally_strict LSx). } use subtypePath. { exact (isPredicate_strictness_structure_laws B). } repeat use pathsdirprod. + repeat (use funextsec ; intro). apply LSx. + repeat (use funextsec ; intro). apply LSx. + repeat (use funextsec ; intro). apply LSx. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.TwoCategories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Categories.HSET.All UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.TransportLaws