proposition: Lemma unit_relativelaxcommutator_unit: relativelaxcommutator_unit unit_relativelaxcommutator_data.
proof: Proof. unfold relativelaxcommutator_unit, unit_relativelaxcommutator_data. etrans. 2: { do 2 apply cancel_postcomposition. rewrite unitors_coincide_on_unit. apply pathsinv0, monoidal_rightunitornat. } repeat rewrite assoc'. apply maponpaths. etrans. 2: { apply maponpaths. rewrite <- unitorsinv_coincide_on_unit. apply pathsinv0, monoidal_leftunitorinvnat. } rewrite assoc. etrans. 2: { apply cancel_postcomposition. apply pathsinv0, (pr22 (fmonoidal_preservesunitstrongly U)). } apply pathsinv0, id_left. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Actegories.CoproductsInActegories UniMath.CategoryTheory.Actegories.ProductsInActegories UniMath.CategoryTheory.Actegories.ProductActegory