proposition: Proposition transportf_s_square_post_whisker_v' {C : strict_double_cat} {x₁ x₂ y₁ y₂ z₁ z₂ : C} {v₁ : x₁ -->v y₁} {w₁ w₁' : y₁ --> z₁} {v₂ : x₂ -->v y₂} {w₂ w₂' : y₂ --> z₂} (p₁ : w₁ = w₁') (p₂ : w₂ = w₂') {h₁ h₁' : x₁ -->h x₂} {h₂ h₂' : y₁ -->h y₂} (p₃ : h₂' = h₂) {k k' : z₁ -->h z₂} (p₄ : k = k') (r : h₁ = h₁') (s₁ : s_square v₁ v₂ h₁' h₂) (s₂ : s_square w₁ w₂ h₂' k) : s₁ ⋆v transportf_s_square p₁ p₂ p₃ p₄ s₂ = transportf_s_square (maponpaths (λ z, _ ·v z) p₁) (maponpaths (λ z, _ ·v z) p₂) r p₄ (transportf_s_square (idpath _) (idpath _) (!r) (!p₃) s₁ ⋆v s₂).
proof: Proof. induction p₁, p₂, p₃, p₄, r ; 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