cyl_extension' {A B} (f : A -> B) (C : B -> Type) (g : forall a, C (pr_cyl (cyl a))) (ext : ExtensionAlong f C g) : ExtensionAlong cyl (C o pr_cyl) g. Proof. rapply cyl_extension. exists (ext.1 o pr_cyl). intros x; apply ext.2. Defined.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.PathSplit Homotopy.IdentitySystems. Require Import Cubical.DPath Cubical.DPathSquare. Require Import Colimits.Coeq Colimits.MappingCylinder.