proposition: Lemma tensor_eq''_equiv_tensor_eqi'' {C : univalent_category} (TC TD : tensor C) : tensor_eqi'' TC TD ≃ tensor_eq'' TC TD.
proof: Proof. use weq_iso. - intro tei. use tpair. + intros x y. exact (! pr1 tei x y). + intros x1 x2 y1 y2 f g. exact (pr2 tei _ _ _ _ f g). - intro te. use tpair. + intros x y. exact (! pr1 te x y). + intros x1 x2 y1 y2 f g. rewrite pathsinv0inv0. rewrite pathsinv0inv0. apply (pr2 te). - intro te. use total2_paths_b. + repeat (apply funextsec ; intro). apply pathsinv0inv0. + repeat (apply funextsec ; intro). apply homset_property. - intro tei. use total2_paths_b. + repeat (apply funextsec ; intro). apply pathsinv0inv0. + repeat (apply funextsec ; intro). apply homset_property. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.Core.Univalence UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories