proposition: Proposition transportf_s_square_pre_whisker_v {C : strict_double_cat} {x₁ x₂ y₁ y₂ z₁ z₂ : C} {v₁ v₁' : x₁ -->v y₁} {w₁ : y₁ --> z₁} {v₂ v₂' : x₂ -->v y₂} {w₂ : y₂ --> z₂} (p : v₁ = v₁') (q : v₂ = v₂') {h₁ : x₁ -->h x₂} {h₂ : y₁ -->h y₂} {k : z₁ -->h z₂} (s₁ : s_square v₁ v₂ h₁ h₂) (s₂ : s_square w₁ w₂ h₂ k) : transportf_s_square p q (idpath _) (idpath _) s₁ ⋆v s₂ = transportf_s_square (maponpaths (λ z, z ·v _) p) (maponpaths (λ z, z ·v _) q) (idpath _) (idpath _) (s₁ ⋆v s₂).
proof: Proof. induction p, q ; cbn. apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Examples.StrictTwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Basics.StrictDoubleCatBasics UniMath.Bicategories.DoubleCategories.Core.CatOfStrictDoubleCats