proposition: Corollary unitorsinv_coincide_on_unit : luinv_{M} I_{M} = ruinv_{M} I_{M}.
proof: Proof. apply (cancel_z_iso _ _ (lu_{M} I_{M},,(luinv_{M} I_{M},,monoidal_leftunitorisolaw M I_{M}))). cbn. etrans. 2: { rewrite unitors_coincide_on_unit. apply pathsinv0, (monoidal_rightunitorisolaw M I_{M}). } apply (monoidal_leftunitorisolaw M I_{M}). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.Notations UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful UniMath.CategoryTheory.opp_precat