Definition tensor_associator_card : associator tensor_functor_card. Proof. unfold associator, nat_z_iso, is_nat_z_iso. exists tensor_associator_card_nat_trans. induction c as [nm k], nm as [n m]. unfold is_z_isomorphism. use tpair. - simpl. rewrite natplusassoc. exact (monfunstnid _). - abstract(cbv beta; unfold is_inverse_in_precat; split; simpl; unfold tensor_associator_card_nat_trans_data; simpl; induction (natplusassoc n m k); simpl; apply fincard_hom_extensionality; reflexivity; simpl; unfold tensor_associator_card_nat_trans_data; induction (pathsinv0 (natplusassoc n m k)); simpl; induction (natplusassoc n m k); simpl; apply fincard_hom_extensionality; reflexivity). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. 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.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.CategoryTheory.SimplicialSets.