(n : nat) {A B : Type} (f : A -> B) `{IsConnMap O _ _ f} (P : B -> Type) `{forall b:B, In O (P b)} : ExtendableAlong n f P. Proof. generalize dependent P. simple_induction n n IHn; intros P ?; [ exact tt | split ]. - intros d; apply extension_conn_map_elim; exact _. - intros h k; apply IHn; exact _. Defined.
Require Import HoTT.Basics HoTT.Types. Require Import Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback. Require Import Homotopy.IdentitySystems. Require Import Colimits.Pushout.