proposition: Lemma extension_conn_map_elim {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)) : ExtensionAlong f P d.
proof: Proof. exists (conn_map_elim f P d). apply conn_map_comp. Defined.
imports: HoTT.Basics HoTT.Types Equiv.BiInv Extensions HProp HFiber NullHomotopy Limits.Pullback PathAny Colimits.Pushout