(f : LocalGenerators@{a}) (X : Type@{i}) (P : Localize f X -> Type@{j}) (loc' : forall x, P (loc x)) (islocal' : forall i, ooExtendableAlong_Over@{a a i j k} (f i) (fun _ => Localize@{a i} f X) (fun _ => P) (islocal_localize@{a i k} f X i)) (z : Localize f X) : P z := match z with | loc x => fun _ => loc' x end islocal'.
Require Import HoTT.Basics HoTT.Types. Require Import Extensions. Require Import ReflectiveSubuniverse Accessible. Import IsLocal_Internal.