proposition: Lemma monoidal_leftunitorinvnat {C : category} (M : monoidal C) : leftunitorinv_nat luinv_{M}.
proof: Proof. intros x y f. apply (z_iso_inv_on_right _ _ _ (_,,_,,monoidal_leftunitorisolaw M x)). cbn. rewrite assoc. apply (z_iso_inv_on_left _ _ _ _ (_,,_,,monoidal_leftunitorisolaw M y)). apply pathsinv0, monoidal_leftunitornat. 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