proposition: Proposition l_lwhisker_v_comp_square {B : verity_double_bicat} {x₁ x₂ y₁ y₂ z₁ z₂ : B} {h₁ : x₁ --> x₂} {h₂ : y₁ --> y₂} {h₃ : z₁ --> z₂} {v₁ v₁' : x₁ -|-> y₁} {v₂ : y₁ -|-> z₁} {w₁ : x₂ -|-> y₂} {w₂ : y₂ -|-> z₂} (τ : v₁' =|=> v₁) (s₁ : square_double_bicat h₁ h₂ v₁ w₁) (s₂ : square_double_bicat h₂ h₃ v₂ w₂) : (τ ◃s s₁) ⋆v s₂ = (τ ▹ v₂) ◃s s₁ ⋆v s₂.
proof: Proof. rewrite rwhisker_hcomp. refine (!_). etrans. { use (ver_bicat_hcomp_v_comp_square B τ (id2 v₂) (id2 _) (id2 _) (τ ◃s s₁)). - exact s₂. - rewrite rwhisker_square_id. apply idpath. - rewrite lwhisker_square_id, rwhisker_square_id. apply idpath. } rewrite hcomp_identity. rewrite rwhisker_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