proposition: Proposition r_rwhisker_v_comp_square {B : verity_double_bicat} {x₁ x₂ y₁ y₂ z₁ z₂ : B} {h₁ : x₁ --> x₂} {h₂ : y₁ --> y₂} {h₃ : z₁ --> z₂} {v₁ : x₁ -|-> y₁} {v₂ : y₁ -|-> z₁} {w₁ : x₂ -|-> y₂} {w₂ w₂' : y₂ -|-> z₂} (τ : w₂ =|=> w₂') (s₁ : square_double_bicat h₁ h₂ v₁ w₁) (s₂ : square_double_bicat h₂ h₃ v₂ w₂) : s₁ ⋆v (τ ▹s s₂)= (w₁ ◃ τ) ▹s s₁ ⋆v s₂.
proof: Proof. rewrite lwhisker_hcomp. refine (!_). etrans. { refine (!_). use (ver_bicat_hcomp_v_comp_square B (id2 v₁) (id2 v₂) (id2 w₁) τ). - exact s₁. - exact (τ ▹s s₂). - rewrite lwhisker_square_id, rwhisker_square_id. apply idpath. - rewrite lwhisker_square_id. apply idpath. } rewrite hcomp_identity. rewrite lwhisker_square_id. apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat