{A : Type} {B : Type} (f : A -> B) (C : B -> Type) : IsEquiv (fun (g : forall b, C b) => g oD f) -> forall g, ExtensionAlong f C g. Proof. intros E g. pose (e := Build_Equiv _ _ _ E). exists (e^-1 g). apply apD10. exact (eisretr e g). 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.