Definition comp_fmonoidal_stronglaws : fmonoidal_stronglaws (fmonoidal_preservestensordata (comp_fmonoidal_lax Fm Gm)) (fmonoidal_preservesunit (comp_fmonoidal_lax Fm Gm)). Proof. split. - intros x y. use make_is_z_isomorphism. + exact (comp_fmonoidal_tensor_inv x y). + exact (comp_fmonoidal_tensor_inv_laws x y). - use make_is_z_isomorphism. + exact comp_fmnoidal_unit_inv. + exact comp_fmonoidal_unit_inv_laws. 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Import BifunctorNotations. Import MonoidalNotations.