fact: Definition twosided_prod_transport_reindex {x₁ x₂ : C₁} {y₁ y₂ : C₂} {xy₁ : D (F x₁) (G y₁)} {xy₂ : D (F x₂) (G y₂)} {f₁ f₂ : x₁ --> x₂} {g₁ g₂ : y₁ --> y₂} (fg : xy₁ -->[ #F f₁ ][ #G g₁ ] xy₂) (p : f₁ = f₂) (q : g₁ = g₂) : transportf (λ z, _ -->[ #F z ][ _ ] _) p (transportf (λ z, _ -->[ _ ][ #G z ] _) q fg) = transportf (λ z, _ -->[ pr1 z ][ dirprod_pr2 z ] _) (pathsdirprod (maponpaths (λ z, #F z) p) (maponpaths (λ z, #G z) q)) fg.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Total