`{Funext} (A : Type) : A <~> (Unit -> A) := (Build_Equiv _ _ (@Unit_ind (fun _ => A)) _). Notation unit_name x := (fun (_ : Unit) => x). Global Instance isequiv_unit_name@{i j} `{Funext} (A : Type@{i}) : @IsEquiv@{i j} _ (Unit -> _) (fun (a:A) => unit_name a). Proof. refine (isequiv_adjointify _ (fun f : Unit -> _ => f tt) _ _). - intros f; apply path_forall@{i i j}; intros x. apply ap@{i i}, path_unit. - intros a; reflexivity. Defined.
Require Import Basics.Overture Basics.Equivalences.