proposition: Proposition lunitor_h_runitor_h {C : double_cat} (x : C) : lunitor_h (identity_h x) = runitor_h (identity_h x).
proof: Proof. refine (!(square_id_left_v' _) @ _ @ square_id_left_v' _). apply maponpaths. rewrite <- linvunitor_lunitor_h'. rewrite !transportf_square_prewhisker. apply maponpaths. refine (!(square_assoc_v' _ _ _) @ _ @ square_assoc_v' _ _ _). do 2 apply maponpaths. refine (!_). rewrite <- lunitor_square'. rewrite transportf_square_id. apply maponpaths_2. rewrite hcomp_runitor_lunitor. rewrite lunitor_id_id_h. 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