`{Funext} (A : Type) (X : pType) : (pointify A ->* X) <~> (A -> X). Proof. snrapply equiv_adjointify. 1: exact (fun f => f o inl). { intros f. snrapply Build_pMap. { intros [a|]. 1: exact (f a). exact pt. } reflexivity. } 1: intro x; reflexivity. intros f. cbv. pointed_reduce. rapply equiv_path_pforall. snrapply Build_pHomotopy. 1: by intros [a|[]]. reflexivity. Defined.
Require Import Basics Types. Require Import Homotopy.IdentitySystems. Require Import WildCat. Require Import Truncations.Core. Require Import ReflectiveSubuniverse. Require Import Extensions.