proposition: Lemma lunitorinv_preserves_leftwhiskering_with_unit {C : category} (M : monoidal C) : luinv^{M}_{I_{ M}} ⊗^{ M}_{r} I_{ M} · α^{ M }_{ I_{ M}, I_{ M}, I_{ M}} = I_{ M} ⊗^{ M}_{l} luinv^{M}_{I_{ M}}.
proof: Proof. set (t := monoidal_triangle_identity_inv_alt M I_{M} I_{M}). use (_ @ ! z_iso_inv_on_left _ _ _ _ (_,, α^{M}_{_,_,_} ,, _) _ (! t)). - apply maponpaths_2. apply maponpaths. apply unitorsinv_coincide_on_unit_alt. - split ; apply (monoidal_associatorisolaw 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