`{Funext} {A B : Type} (f : A -> B) `{IsConnMap O _ _ f} (P : B -> Type) `{forall b:B, In O (P b)} (d : forall a:A, P (f a)) (e e' : ExtensionAlong f P d) : e = e'. Proof. apply path_extension. refine (extension_conn_map_elim _ _ _). 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.