proposition: Proposition runitor_id_id_h {C : double_cat} (x : C) : runitor_h (identity_h x ·h identity_h x) = runitor_h (identity_h x) ⋆h id_h_square (identity_v x).
proof: Proof. refine (!(square_id_right_v' _) @ _ @ square_id_right_v' _). apply maponpaths. rewrite <- !runitor_rinvunitor_h'. rewrite !transportf_square_postwhisker. apply maponpaths. refine (square_assoc_v _ _ _ @ _ @ !(square_assoc_v _ _ _)). apply maponpaths. apply maponpaths_2. etrans. { rewrite <- runitor_square'. apply idpath. } rewrite transportf_square_id. 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