(n : nat) {A B : Type} (C : B -> Type) (f : A -> B) `{forall b, Contr (C b)} : ExtendableAlong n f C. Proof. generalize dependent C; simple_induction n n IHn; intros C ?; [ exact tt | split ]. - intros h. exists (fun _ => center _); intros a. apply contr. - intros h k. apply IHn; exact _. 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.