(n : nat) {A B : Type} (C : B -> Type) (f : A -> B) `{IsEquiv _ _ f} : ExtendableAlong n f C. Proof. revert C; simple_induction n n IHn; intros C; [ exact tt | split ]. - intros h. exists (fun b => eisretr f b # h (f^-1 b)); intros a. refine (transport2 C (eisadj f a) _ @ _). refine ((transport_compose C f _ _)^ @ _). exact (apD h (eissect f a)). - intros h k. apply IHn. 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.