(n : nat) {A B} (f : A -> B) (C : Cyl f -> Type) (ext : ExtendableAlong n cyl C) : ExtendableAlong n cyl C. Proof. revert C ext; simple_induction n n IH; intros C ext; [ exact tt | split ]. - intros g. apply cyl_extension. exact (fst ext g). - intros h k; apply IH. exact (snd ext h k). 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.