proposition: Lemma leftwhisker_of_lunitor_with_unit (x : V) : monoidal_unit V ⊗^{V}_{l} lu^{V}_{x} = lu^{V}_{monoidal_unit V ⊗ x}.
proof: Proof. refine (_ @ ! mon_lunitor_triangle_transposed x). use (z_iso_inv_to_left _ _ _ (mon_rassociator _ _ _ ,, mon_lassociator _ _ _ ,, _)). { split ; apply monoidal_associatorisolaw. } refine (monoidal_triangleidentity _ _ _ @ _). apply maponpaths. apply pathsinv0, unitors_coincide_on_unit. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric