proposition: Lemma identity_fmonoidal_laxlaws {C : category} (M : monoidal C) : fmonoidal_laxlaws (identity_fmonoidal_data M).
proof: Proof. repeat split; red; unfold fmonoidal_preservesunit, fmonoidal_preservestensordata; cbn; intros. - rewrite id_left. apply id_right. - rewrite id_left. apply id_right. - do 2 rewrite id_right. rewrite (bifunctor_rightid M). rewrite (bifunctor_leftid M). rewrite id_right. apply id_left. - rewrite id_right. rewrite (bifunctor_rightid M). apply id_left. - rewrite id_right. rewrite (bifunctor_leftid M). apply id_left. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric