Lemma tensor_eq'_equiv_tensor_eq'' {C : univalent_category} (TC TD : tensor C) : tensor_eq'' TC TD ≃ tensor_eq' TC TD. Proof. apply weq_subtypes_iff. - intro. repeat (apply impred_isaprop ; intro). apply homset_property. - intro. repeat (apply impred_isaprop ; intro). apply homset_property. - intro pob. split. + intros q ? ? ? ? f g. apply transport_f_f_to_transport. exact (q _ _ _ _ f g). + intros q ? ? ? ? f g. apply transport_to_transport_f_f. exact (q _ _ _ _ f g). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories. Import TensorNotation. Import TensorNotation.