proposition: Proposition hcomp_runitor_lunitor {C : double_cat} (x : C) : id_h_square (identity_v x) ⋆h runitor_h (identity_h x) = id_h_square (identity_v x) ⋆h lunitor_h (identity_h x).
proof: Proof. refine (!(square_id_left_v' _) @ _ @ square_id_left_v' _). apply maponpaths. rewrite <- lassociator_rassociator_h'. rewrite !transportf_square_prewhisker. apply maponpaths. refine (!(square_assoc_v' _ _ _) @ _ @ square_assoc_v' _ _ _). do 2 apply maponpaths. rewrite id_h_square_id. refine (_ @ !(double_triangle_alt _ _)). refine (!_). etrans. { apply maponpaths. refine (!_). rewrite <- id_h_square_id. apply runitor_id_id_h. } rewrite runitor_h_triangle. apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.Bicategories.Core.Bicat UniMath.Bicategories.DoubleCategories.Core.DoubleCats UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws UniMath.Bicategories.DoubleCategories.DerivedLaws.Variations