proposition: Lemma is_binat_trans_inv_from_binatiso {F G : bifunctor_data A B C} {α : binat_trans F G} (isiso: is_binatiso α) : is_binat_trans (inv_from_binatiso isiso).
proof: Proof. split. - intros ? ? ? ?. apply pathsinv0. apply (z_iso_inv_on_right _ _ _ (α a b1 ,, isiso a b1)). rewrite assoc. apply (z_iso_inv_on_left _ _ _ _ (α a b2 ,, isiso a b2)). apply pathsinv0, (pr12 α). - intros ? ? ? ?. apply pathsinv0. apply (z_iso_inv_on_right _ _ _ (α a1 b ,, isiso a1 b)). rewrite assoc. apply (z_iso_inv_on_left _ _ _ _ (α a2 b ,, isiso a2 b)). apply pathsinv0, (pr22 α). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.ProductCategory