(n : nat) {A B : Type} (C : B -> Type) (f : A -> B) (h k : forall b, C b) : ExtendableAlong n.+1 f C -> ExtendableAlong n f (fun b => h b = k b). Proof. revert C h k; simple_induction n n IHn; intros C h k ext; [exact tt | split]. - intros p. exact (fst (snd ext h k) p). - intros p q. apply IHn, ext. 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.