proposition: Proposition comprehension_functor_mor_factorisation_pr2 {C : comp_cat} {Γ₁ Γ₂ Γ₃ : C} {s₁ : Γ₁ --> Γ₂} {s₂ : Γ₂ --> Γ₃} {A₁ : ty Γ₁} {A₂ : ty Γ₂} {A₃ : ty Γ₃} (t : A₂ -->[ s₂ ] A₃) (Ht : is_cartesian t) (t' : A₁ -->[ s₁ · s₂ ] A₃) : comprehension_functor_mor (comp_cat_comprehension C) (cartesian_factorisation Ht _ t') · π _ = π _ · s₁.
proof: Proof. rewrite comprehension_functor_mor_comm. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.Limits.Pullbacks UniMath.Bicategories.ComprehensionCat.BicatOfCompCat