proposition: Lemma monoidal_triangle_identity'_inv (x y : C) : luinv_{M} (x ⊗_{M} y) · αinv_{M} I_{M} x y = luinv_{M} x ⊗^{M}_{r} y.
proof: Proof. apply pathsinv0. apply (z_iso_inv_on_left _ _ _ _ ((z_iso_from_associator_iso M _ _ _))). cbn. set (luix := make_z_iso _ _ (monoidal_leftunitorisolaw M x)). set (luixy := functor_on_z_iso (rightwhiskering_functor M y) luix). set (luipxy := make_z_iso _ _ (monoidal_leftunitorisolaw M (x ⊗_{ M} y))). apply pathsinv0. apply (z_iso_inv_on_right _ _ _ luixy). apply (z_iso_inv_on_left _ _ _ _ luipxy). exact (! monoidal_triangleidentity' x y). 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